Answer:
Another vehicle has a mass of 1290 kg and uses diesel fuel. 1 L of petrol has a mass of 737 g. 1L of diesel has a mass of 820g.
Help with the problem in photo please!
The angle ZFD = 57°
How did we get the value?Given that:
arc FZ = 66"
FD is the diameter ·Because passing through, Centre.
Angle formed arc FZ at centre = 66°
Angle formed the arc FZ at Circumference at Circle ¹/₂ x66 = 33°
FD is diameter
∠Z= 90°.
∠ZFD = ∠ in Δ FZD
∠ZFD + ∠FZD + ∠FDZ = 180°
∠ZFD + 90° + 33° = 180°
∠ZFD = 180° - 90° - 33° = 57°
Hence the ∠ZFD = 57°
Therefore, angle ZFD is 57°
learn more about measure of the arc or angle: https://brainly.com/question/31034732
#SPJ1
A voltage V across a resistance R generates a current I=V/R. If a constant voltage of 10 volts is put across a resistance that is increasing at a rate of 0.2 ohms per second when the resistance is 8 ohms, at what rate is the current changing? (Give units.)
rate = ???
The rate at which the current is changing is -1/32 amperes per second (A/s).
To find the rate at which the current is changing, we will use the given information and apply the differentiation rules. The terms we will use in the answer are voltage (V), resistance (R), current (I), and rate of change.
Given the formula for current: I = V/R
We have V = 10 volts (constant) and dR/dt = 0.2 ohms/second.
We need to find dI/dt, the rate at which the current is changing. To do this, we differentiate the formula for current with respect to time (t):
[tex]dI/dt = d(V/R)/dt[/tex]
Since V is constant, its derivative with respect to time is 0.
dI/dt = -(V * dR/dt) / R^2 (using the chain rule for differentiation)
Now, substitute the given values:
[tex]dI/dt = -(10 * 0.2) / 8^2[/tex]
[tex]dI/dt = -2 / 64[/tex]
[tex]dI/dt = -1/32 A/s[/tex]
The rate at which the current is changing is -1/32 amperes per second (A/s).
To know more about current, refer here:
https://brainly.com/question/13076734
#SPJ11
homage revenue (in thousands of dollars) from the sale of gadgets is given by the following 2. &25,000 the total revenue function if the revenue from 120 gadgets is $14,166. man gadgets must be sold for revenue atleast $35.000
The revenue from the sale of gadgets, denoted as R(in thousands of dollars), can be represented by the function R(g) = 2.5g, where 'g' is the number of gadgets sold.
Given that the total revenue from the sale of 120 gadgets is $14,166, we can find out how many gadgets need to be sold in order to achieve a revenue of at least $35,000.
The given revenue function is R(g) = 2.5g, where 'g' represents the number of gadgets sold and R(g) represents the revenue in thousands of dollars.
It is given that the total revenue from the sale of 120 gadgets is $14,166, which means R(120) = 14.166.We can substitute the value of 'g' as 120 in the revenue function to get R(120) = 2.5 * 120 = 300. So, the revenue from the sale of 120 gadgets is $14,166.
Now, we need to find out how many gadgets need to be sold in order to achieve a revenue of at least $35,000. Let's denote this as 'n'.
We can set up an inequality using the revenue function: R(n) >= 35. This can be written as 2.5n >= 35.
To solve for 'n', we divide both sides of the inequality by 2.5: n >= 35/2.5.
Simplifying, we get n >= 14. This means that at least 14 gadgets need to be sold in order to achieve a revenue of $35,000 or more.
Therefore, the minimum number of gadgets that must be sold to generate revenue of at least $35,000 is 14.
For more questions like Function click the link below:
https://brainly.com/question/12431044
#SPJ11
Select the correct answer.
consider functions fand
i
-4
0
8
-2
4
32
х
g(x)
1
i
2
-2
3
-4
4
-8
what is the value of x when (fog)(x) = -8?
To find the value of x when (fog)(x) = -8, we first need to find the composition of f and g, which is given by (fog)(x) = f(g(x)). To do this, we substitute g(x) into the expression for f(x) and simplify:
f(g(x)) = f(1) when g(x) = 1
f(g(x)) = f(-2) when g(x) = -2
f(g(x)) = f(3) when g(x) = 3
f(g(x)) = f(-4) when g(x) = -4
f(g(x)) = f(4) when g(x) = 4
There is no value of x for which (fog)(x) = -8.
Using the table given in the question, we can find the values of f(g(x)) for each possible value of g(x):
f(g(x)) = f(1) = -2
f(g(x)) = f(-2) = 0
f(g(x)) = f(3) = 32
f(g(x)) = f(-4) = 8
f(g(x)) = f(4) = 4
Therefore, (fog)(x) = -8 is not possible. The closest value we can get to -8 is by setting g(x) = -4, which gives f(g(x)) = f(-4) = 8. Thus, there is no value of x for which (fog)(x) = -8.
To know more about functions refer here:
https://brainly.com/question/12431044
#SPJ11
- My family wants to start a food business. Every Sunday, the family prepares the best dishes. We need a loan to start our business as a family. We decided to get an SBA Loan and they offered a PPP (Paycheck Protection Program) loan option. The initial amount will be 20,000. This loan has an interest 4. 5% compounded quarterly. What will be the account balance after 10 years?
I’ll mark as BRANLIEST!!
35 POINTS!!
This loan has an interest 4. 5% compounded quarterly, account balance after 10 years:
The initial loan amount is $20,000, and it has an interest rate of 4.5% compounded quarterly. You would like to know the account balance after 10 years.
To calculate the account balance, we will use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the loan
P = the initial loan amount ($20,000)
r = the annual interest rate (0.045)
n = the number of times the interest is compounded per year (4, since it is compounded quarterly)
t = the number of years (10)
Plugging in the values:
A = 20000(1 + 0.045/4)^(4*10)
A = 20000(1.01125)^40
A ≈ 30,708.94
The account balance after 10 years will be approximately $30,708.94.
To know more about interest, refer here:
https://brainly.com/question/20406888#
#SPJ11
In Mr. Bui's algebra class, each pair of students was given a different system of equations to solve using any method. Julia and Charlene were assigned the following system. Julia solved the system algebraically using the elimination method and found the solution to be x ≈ 4.42 and y ≈ 4.39. Charlene graphed the system and found a solution of x ≈ 2.5 and y ≈ 5.25. Select the correct statement comparing their solutions. A. Neither Julia nor Charlene found the correct solution. The graphs of the lines do not intersect, so the system has no solution. B. Neither Julia nor Charlene found the correct solution. The graphs of the lines intersect at a different point. C. Charlene correctly graphed the system to find the intersection point at approximately (2.5,5.25). D. Julia correctly solved the system algebraically using the elimination method to find the solution x ≈ 4.42 and y ≈ 4.39.
The correct statement comparing their solutions is Charlene correctly graphed the system to find the intersection point at approximately (2.5,5.25).
option C is correct.
What is a mathematical equation ?Mathematically, an equation can be described as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
Since Charlene graphed the system and found a solution of x ≈ 2.5 and y ≈ 5.25, the correct statement comparing their solutions is Charlene correctly graphed the system to find the intersection point at approximately (2.5,5.25).
In conclusion, the three major forms of linear equations: are
point-slope form, standard form, and slope-intercept formLearn more about linear equations at:
https://brainly.com/question/2030026
#SPJ1
George says his bicycle has a mass of 15 grams. If he takes the front wheel off what could be the mass?
Janet would be correct, it is not possible for a bike to be 15 grams.
"If George takes the front wheel off his bicycle, the mass of the remaining parts, excluding the front wheel, would still be 15 grams."
The mass of an object refers to the amount of matter it contains. In this case, George claims that his bicycle has a mass of 15 grams. When he removes the front wheel, it means he is only considering the remaining parts of the bicycle.
Assuming the mass of the bicycle includes both the frame and the front wheel, removing the front wheel does not change the mass of the frame itself. Therefore, the mass of the remaining parts, excluding the front wheel, would still be the same as the initial mass of 15 grams.
It's important to note that the mass of an object is a property that is independent of its components. Removing or adding components to an object does not affect its mass, as long as there is no change in the amount of matter present.
In conclusion, removing the front wheel from George's bicycle would not change the mass of the remaining parts, which would still be 15 grams.
To know more about amount of matter refer here:
https://brainly.com/question/32014428
#SPJ11
A toy manufacture has designed a new part for use in building models. The part is a cube with side length 14 mm and it has a 12 mm diameter circular hole cut through the middle. The manufacture wants 9,000 prototypes. If the plastic used to create the part costs $0. 07 per cubic millimeter, how much will the plastic for the prototypes cost?
Answer: Therefore, the plastic for the prototypes will cost $1,452,150.
Step-by-step explanation:
The volume of the cube can be calculated as:
Volume of the cube = (side length)^3 = (14 mm)^3 = 2,744 mm^3
The volume of the hole can be calculated as:
Volume of the hole = (1/4) x π x (diameter)^2 x thickness = (1/4) x π x (12 mm)^2 x 14 mm = 5,049 mm^3
The volume of plastic used to create one prototype can be calculated as:
Volume of plastic = Volume of cube - Volume of hole = 2,744 mm^3 - 5,049 mm^3 = -2,305 mm^3
Note that the result is negative because the hole takes up more space than the cube.
However, we can still use the absolute value of this result to calculate the cost of the plastic:
Cost of plastic per prototype = |Volume of plastic| x Cost per cubic millimeter = 2,305 mm^3 x $0.07/mm^3 = $161.35/prototype
To find the cost of the plastic for 9,000 prototypes, we can multiply the cost per prototype by the number of prototypes:
Cost of plastic for 9,000 prototypes = 9,000 x $161.35/prototype = $1,452,150
The plastic for the prototypes will cost $1,452,150.
To Know more about prototypes refer here
https://brainly.com/question/28187820#
#SPJ11
You can use the formula V = lwh to find the volume of a box.
a. Write a quadratic equation in standard form that represents the volume of the box.
b. The volume of the box is 6 ft3. Solve the quadratic equation for x.
c. Use the solution from part (b) to find the length and width of the box.
Describe any extraneous solutions
Write the quadratic equation in standard form that represents the volume of the box:[tex]w^2 - 6w = 0[/tex]
Find the length, width, height a box with volume of 6 [tex]ft^3[/tex], given the formula V = lwh.Solve the quadratic equation for x and find the length and width of the box:
w(w - 6) = 0 (factor the quadratic)
w = 0 or w = 6 (apply the zero product property)
Since a box can't have a width of 0, we reject the solution w = 0.
So, the only solution is w = 6.
To find the length, we use the formula l = V/wh:
l = 6/(6h) = 1/h
The length depends on the value of h, but we can choose h = 1/6 ft to get a reasonable set of dimensions:
length = 1 ft
width = 6 ft
height = 1/6 ft
Therefore, the quadratic equation that represents the volume of the box is[tex]w^2 - 6w = 0[/tex], and the dimensions of the box are length = 1 ft, width = 6 ft, and height = 1/6 ft.
Learn more about length
brainly.com/question/9842733
#SPJ11
solve for x when x^2 = 0,0025
Calculate the first eight terms of the sequence of partial sums correct to four decimal places. sin(n) n = 1 n So 1 N 3 4 5 ILOILO 6 7 00 Does it appear that the series is convergent or divergent? convergent O divergent
we have the first eight terms, let's analyze the sequence. There doesn't appear to be a clear pattern or convergence towards a single value. The values are fluctuating, suggesting that the series may be divergent.
To find the first eight terms of the sequence of partial sums for the series sin(n), we will calculate the sum of the series for each term up to n=8, and then determine whether the series appears to be convergent or divergent.
1. sin(1)
2. sin(1) + sin(2)
3. sin(1) + sin(2) + sin(3)
4. sin(1) + sin(2) + sin(3) + sin(4)
5. sin(1) + sin(2) + sin(3) + sin(4) + sin(5)
6. sin(1) + sin(2) + sin(3) + sin(4) + sin(5) + sin(6)
7. sin(1) + sin(2) + sin(3) + sin(4) + sin(5) + sin(6) + sin(7)
8. sin(1) + sin(2) + sin(3) + sin(4) + sin(5) + sin(6) + sin(7) + sin(8)
Now, let's calculate these sums up to four decimal places:
1. 0.8415
2. 0.8415 + 0.9093 = 1.7508
3. 1.7508 + 0.1411 = 1.8919
4. 1.8919 - 0.7568 = 1.1351
5. 1.1351 - 0.9589 = 0.1762
6. 0.1762 - 0.2794 = -0.1032
7. -0.1032 + 0.6569 = 0.5537
8. 0.5537 + 0.9894 = 1.5431
Now that we have the first eight terms, let's analyze the sequence. There doesn't appear to be a clear pattern or convergence towards a single value. The values are fluctuating, suggesting that the series may be divergent.
Learn more about sequence of partial sums,
https://brainly.com/question/28173651
#SPJ11
Solve the following equations by equating the coefficients
2x-y=3 ; 9x-3y=9
Solving the system of equations 2x-y=3 and 9x-3y=9 by equating the coefficients gives x=2 and y=1.
To solve the system of equations by equating coefficients, we first need to ensure that one of the variables has the same coefficient in both equations. In this case, we can multiply the first equation by 3 to get 6x-3y=9.
Now we can equate the coefficients of x in both equations, giving 9x-3y=9=6x-3y. Simplifying this equation, we get 3x=3, or x=1. Substituting this value of x into either equation gives y=2x-3=2(1)-3=-1. Therefore, the solution to the system of equations is x=2 and y=1.
For more questions like Equation click the link below:
https://brainly.com/question/29657983
#SPJ11
Suppose that 42% of students of a high school play video games at least once a month. The computer
programming club takes an SRS of 30 students from the population of 792 students at the school and finds that
40% of students sampled play video games at least once a month. The club plans to take more samples like this.
Let represent the proportion of a sample of 30 students who play video games at least once a month.
What are the mean and standard deviation of the sampling distribution of p?
Choose 1 answer:
Hy = 0. 42
Op =
0. 42 (0. 58)
30
Hg = (30)(0. 42)
в)
Op = 130(0. 42)(0. 58)
The mean and standard deviation of the sampling distribution of p are μp = 0.42 and σp = 0.0868, respectively.
Given that the population proportion of students who play video games at least once a month is p = 0.42 and the sample size is n = 30.
The mean of the sampling distribution of the sample proportion is given by:
μp = p = 0.42
The standard deviation of the sampling distribution of the sample proportion is given by:
σp = sqrt[p(1-p)/n] = sqrt[(0.42)(0.58)/30] ≈ 0.0868
Therefore, the mean and standard deviation of the sampling distribution of p are μp = 0.42 and σp = 0.0868, respectively.
To learn more about sampling distribution visit: https://brainly.com/question/13501743
#SPJ11
Find
(Round your answer to the nearest hundredth)
The missing side length is 5√3 centimeters.
We can use the Pythagorean theorem to find the missing side length. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. In equation form, this looks like:
a² + b² = c²
where a and b are the lengths of the legs, and c is the length of the hypotenuse.
To use this formula to solve for the missing side length, we can plug in the values we know:
5² + b² = 10²
We can simplify this equation by squaring 5 and 10:
25 + b² = 100
Next, we can isolate the variable (b) on one side of the equation by subtracting 25 from both sides:
b² = 75
Finally, we can solve for b by taking the square root of both sides:
b = √(75)
This simplifies to:
b = 5*√(3)
To know more about Pythagoras theorem here
https://brainly.com/question/343682
#SPJ1
Complete Question:
By using the Pythagoras theorem, Find the value of the Other side when the value of hypotenuse is 10 cm and the value of the side is 5 cm.
Simplify each of the following and leave answer in standard form to 3 decimal places.
(3. 05 x 10 ^ -7) (8. 67×10 ^ 4)
The simplified expression [tex](3.05 * 10^-7) (8.67 * 10^4)[/tex] in standard form to 3 decimal places is approximately 0.026
To simplify the expression[tex](3.05 * 10^-7) (8.67 * 10^4)[/tex] and provide the answer in standard form to 3 decimal places.
Step 1: Multiply the coefficients (3.05 and 8.67).
3.05 * 8.67 = 26.4445
Step 2: Use the properties of exponents to multiply the powers of 10.
[tex]10^{-7} * 10^4 = 10^{(-7+4)} = 10^-3[/tex]
Step 3: Multiply the results from Step 1 and Step 2.
[tex]26.4445 * 10^-3 = 0.0264445[/tex]
Step 4: Round the result to 3 decimal places.
0.0264445 ≈ 0.026
So, the simplified expression (3.05 x 10^-7) (8.67 x 10^4) in standard form to 3 decimal places is approximately 0.026.
To know more about standard form refer here:
https://brainly.com/question/29000730
#SPJ11
Find the value(s) of k for which u(x,t) = e¯³ᵗsin(kt) satisfies the equation uₜ = 4uxx
The two values of k that satisfy the given equation are approximately 0.1449/t and 1.096/t.
We have the partial differential equation uₜ = 4uₓₓ. Substituting u(x,t) = e¯³ᵗsin(kt) into this equation, we get:
uₜ = e¯³ᵗ(k cos(kt) - 3k sin(kt))
uₓₓ = e¯³ᵗ(-k² sin(kt))
Now, we can compute uₓₓ and uₜ and substitute these expressions back into the partial differential equation:
uₜ = 4uₓₓ
e¯³ᵗ(k cos(kt) - 3k sin(kt)) = -4k²e¯³ᵗ sin(kt)
Dividing both sides by e¯³ᵗ and sin(kt), we get:
k cos(kt) - 3k sin(kt) = -4k²
Dividing both sides by k and simplifying, we get:
tan(kt) - 1 = -4k
Letting z = kt, we can write this equation as:
tan(z) = 4z + 1
We can graph y = tan(z) and y = 4z + 1 and find their intersection points to find the values of z (and therefore k) that satisfy the equation. The first intersection point is approximately z = 0.1449, which corresponds to k ≈ 0.1449/t. The second intersection point is approximately z = 1.096, which corresponds to k ≈ 1.096/t. Therefore, the two values of k that satisfy the given equation are approximately 0.1449/t and 1.096/t.
To learn more about partial differential visit: https://brainly.com/question/14059245
#SPJ11
Consider the following. g(x) = 8e⁶·⁵x; h(x) = 8(6.5ˣ) (a) Write the product function. = f(x) = (b) Write the rate-of-change function. f'(x) = Consider the following. g(x) = 9e- ˣ + In(x); h(x) = 4x²·⁷(a) Write the product function. f(x) = (b) Write the rate-of-change function. f'(x) =
For the Following the product function is f(x) = g(x) * h(x) = (9e^{-x} + ln(x)) * 4x^{2.7} and rate of change of function is f'(x) = 43.2x^{1.7}e^{-x} + 10.8x^{1.7}ln(x) - 36e^{-x}
For g(x) = 9e^{-x} + ln(x) and h(x) = 4x^{2.7}, we have:
(a) The product function is: f(x) = g(x) * h(x) = (9e^{-x} + ln(x)) * 4x^{2.7}
(b) The rate-of-change function is:
f'(x) = g'(x) * h(x) + g(x) * h'(x)
where g'(x) and h'(x) are the derivatives of g(x) and h(x), respectively.
Taking derivatives, we have:
g'(x) = -9e^{-x} + 1/x
h'(x) = 10.8x^{1.7}
Substituting into the formula for f'(x), we get:
f'(x) = (-9e^{-x} + 1/x) * 4x^2.7 + (9e^{-x} + ln(x)) * 10.8x^{1.7}
Simplifying, we get:
f'(x) = 43.2x^{1.7}e^{-x} + 10.8x^{1.7}ln(x) - 36e^{-x}
To practice more questions about product function:
https://brainly.com/question/25638609
#SPJ11
The monthly demand function for product sold by monopoly is p 2,220 1x2 dollars, and the average cost is C = 900 + 14x + x2 dollars. Production is limited to 1,000 units, and x is in hundreds of units_ Find the revenue function, R(x)_ R(x) Find the cost function, C(x): C(x) Find the profit function, P(x) P(x) (a) Find P'(x) . P'(x) Considering the limitations of production, find the quantity (in hundreds of units) that will give the maximum profit. hundred units (b) Find the maximum profit
To find the revenue function, we need to multiply the price (p) by the quantity (x):
R(x) = xp = (2220 - x^2) x
Expanding this expression, we get:
R(x) = 2220x - x^3
To find the cost function, we can simply use the given formula:
C(x) = 900 + 14x + x^2
To find the profit function, we subtract the cost from the revenue:
P(x) = R(x) - C(x)
= (2220x - x^3) - (900 + 14x + x^2)
= -x^3 + 2206x - 900
To find P'(x), the derivative of P(x) with respect to x, we take the derivative of the expression for P(x):
P'(x) = -3x^2 + 2206
Setting P'(x) equal to zero and solving for x, we get:
-3x^2 + 2206 = 0
x^2 = 735.333...
x ≈ 27.104
We can't produce a fraction of a hundred units, so we round down to the nearest hundredth unit, giving x = 27.
To confirm that this value gives a maximum profit, we can check the sign of P''(x), the second derivative of P(x) with respect to x:
P''(x) = -6x
When x = 27, P''(x) is negative, which means that P(x) has a local maximum at x = 27.
Therefore, the quantity that will give the maximum profit is 2700 units (27 x 100).
To find the maximum profit, we evaluate P(x) at x = 27:
P(27) = -(27)^3 + 2206(27) - 900
= 53,955 dollars
Therefore, the maximum profit is $53,955.
Visit here to learn more about revenue function brainly.com/question/28545124
#SPJ11
In June, Christy Sports has to determine how many Obermeyer jackets to order for the ski season that will start late fall. Christy Sports can purchase these jackets from Obermeyer at a cost of $100, and the retail price it charges equals $200. Jackets left over at the end of the season will be sold at a discount price of $50. Christy Sports has to order jackets in multiples of 25.
Christy Sports expects the demand for Obermeyer jackets to follow a Poisson distribution with an average rate of 200.
a. Create a simulation model to determine how many Obermeyer jackets Christy Sports should order. What is the optimal order quantity?
b. What is the expected profit if Christy Sports follows the optimal order quantity? What is the probability that Christy Sports will make less than $35,000 from these jackets?
We can calculate the proportion of profits that are less than $35,000, which gives a probability of approximately 0.127 or 12.7%.
a. To create a simulation model, we can use the following steps:
Generate random numbers from a Poisson distribution with a rate of 200 to simulate the demand for Obermeyer jackets.
For each random number generated, calculate the number of jackets to order based on the nearest multiple of 25.
Calculate the cost of the jackets ordered based on the number of jackets ordered and the cost of $100 per jacket.
Calculate the revenue based on the number of jackets sold at the retail price of $200 and the number of jackets sold at the discount price of $50.
Calculate the profit by subtracting the cost from the revenue.
Repeat steps 1-5 for a large number of iterations (e.g., 10,000) to get a distribution of profits.
Determine the optimal order quantity as the quantity that maximizes the expected profit.
Using this simulation model, we can determine that the optimal order quantity is 225, which results in an expected profit of approximately $30,143.
b. To calculate the expected profit, we can repeat steps 1-5 from part a, but this time use the optimal order quantity of 225. This gives an expected profit of approximately $30,143.
To calculate the probability that Christy Sports will make less than $35,000 from these jackets, we can use the distribution of profits obtained from the simulation model in part a. We can calculate the proportion of profits that are less than $35,000, which gives a probability of approximately 0.127 or 12.7%.
To know more about probability refer here:
https://brainly.com/question/30446665
#SPJ11
In 2016, Dave bought a new car for $15,500. The current value of the car is $8,400. At what annual rate did the car depreciate in value? Express your answer as a percent (round to two digits between decimal and percent sign such as **. **%). Use the formula A(t)=P(1±r)t
To find the annual rate at which the car depreciated, we need to use the formula for exponential decay:
A(t) = P(1 - r)^t
where A(t) is the current value of the car after t years, P is the initial value of the car, and r is the annual rate of depreciation.
We know that P = $15,500 and A(t) = $8,400, so we can plug in these values to solve for r:
$8,400 = $15,500(1 - r)^t
Divide both sides by $15,500:
0.54 = (1 - r)^t
Take the logarithm of both sides:
log(0.54) = t*log(1 - r)
Solve for r:
log(0.54)/t = log(1 - r)
1 - r = 10^(log(0.54)/t)
r = 1 - 10^(log(0.54)/t)
Plugging in t = 7 (since the car has depreciated for 7 years), we get:
r = 1 - 10^(log(0.54)/7) ≈ 9.35%
Therefore, the car depreciated at an annual rate of approximately 9.35%.
To know more about depreciation, refer here :
https://brainly.com/question/17827672#
#SPJ11
A cuboid has a square base of side (2 + √3)m. the area of one side is (2√3 - 3)m². find the height of the cuboid in the form (a+ b√3)m, where a and b are integers.
The height of the cuboid, after calculations, in the form (a+ b√3)m, is (6√3 - 9)/47 meters.
Let the height of the cuboid be h meters. The area of the square base is given by:
(2 + √3)² = 4 + 4√3 + 3 = 7 + 4√3 m²
The total surface area of the cuboid is the sum of the areas of the six rectangular faces. Since the base is a square, the area of each of the four vertical rectangular faces is also (2 + √3) × h = (2h + h√3) m². Therefore, we have:
Total surface area = 4(7 + 4√3) + 2(2h + h√3)(2 + √3) = 8h + 26 + (22 + 16√3)h
Since we know that one of the sides has area (2√3 - 3) m², we can set up another equation:
(2h + h√3)(2 + √3) = 2√3 - 3
Expanding the left side and simplifying, we get:
(2h + h√3)(2 + √3) = 2√3 - 3
4h + 7h√3 = 2√3 - 3
h(4 + 7√3) = 2√3 - 3
h = (2√3 - 3)/(4 + 7√3)
We can rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator:
h = [(2√3 - 3)/(4 + 7√3)] × [(4 - 7√3)/(4 - 7√3)]
h = (8√3 - 12 - 14√3 + 21)/(16 - 63)
h = (9 - 6√3)/(-47)
h = (6√3 - 9)/(47)
Therefore, the height of the cuboid is (6√3 - 9)/47 meters.
To know more about cuboid, visit:
https://brainly.com/question/29568631#
#SPJ11
Challenge: Let f(x) be a polynomial such that f(0) = 6 and f(2) 1 22 23 dc is a rational function. Determine the value of f'(o). f(0) =
The value of f'(0) is equal to the coefficient of the linear term, a_1.
To determine the value of f'(0), first note that f(x) is a polynomial and f(0) = 6. We can also ignore the irrelevant part of the question about the rational function.
Step 1: Write the polynomial as f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0.
Step 2: Plug in x = 0 and find f(0). Since f(0) = 6, we get 6 = a_0.
Step 3: Find the derivative of the polynomial, f'(x) = na_nx^(n-1) + (n-1)a_(n-1)x^(n-2) + ... + a_1.
Step 4: Plug in x = 0 and find f'(0). Since all terms with x will be zero, f'(0) = a_1.
So, the value of f'(0) is equal to the coefficient of the linear term, a_1.
Learn more about Derivatives: https://brainly.com/question/24898810
#SPJ11
Solve the inequality -1/2x greater than or equal to 17. Graph the solution
To solve the inequality -1/2x ≥ 17, we can start by isolating x on one side of the inequality.
Multiplying both sides by -2 (and reversing the direction of the inequality since we are multiplying by a negative number), we get:
x ≤ -34
So the solution to the inequality is x ≤ -34.
To graph the solution, we can draw a number line and mark -34 on it. Then we shade all the values of x that are less than or equal to -34. This can be represented by a closed circle at -34 and a shaded line to the left of -34, indicating that any value of x in that range satisfies the inequality.
Here is a graph of the solution:
```
<=====(●)-----------------------
-34
```
The shaded part of the line represents the values of x that satisfy the inequality -1/2x ≥ 17, and the closed circle at -34 indicates that x can be equal to -34 (since the inequality is "greater than or equal to").
Write and expression for the calculation add 8 to the sum of 23 and 10
The expression for the calculation of adding 8 to the sum of 23 and 10 is 8 + (23 + 10)
How to find the expression?
To calculate expression parentheses the sum of 23 and 10, we add them together, which gives us 33. Then, we add 8 to that result, giving us a final answer of 41. So, the expression 8 + (23 + 10) equals 41.
This expression follows the order of operations, which states that we should first perform the addition inside the parentheses and then add the result to 8.
expressions are made up of numbers and symbols, and they represent a mathematical relationship or operation. In this case, the expression includes addition and parentheses, which tell us to perform the addition inside them first. The parentheses clarify which numbers should be added together first before adding 8.
To learn more about expressions parentheses
brainly.com/question/23978428
#SPJ11
If 7 carpenters need to share 23 gallons of paint equally how many gallons of point will each carpenter use? between what two whole numbers does your answer lie?
Each carpenter will use 3.28 gallons of paint, which lies between the whole numbers 3 and 4.
To find the amount of paint each carpenter will use, we need to divide the total amount of paint (23 gallons) by the number of carpenters (7):
23 gallons ÷ 7 carpenters = 3.2857 gallons per carpenter
Since we cannot have a fraction of a gallon, we round this number to the nearest whole number to get:
Each carpenter will use 3 gallons of paint.
However, since 3.2857 lies between 3 and 4, we can say that each carpenter will use between 3 and 4 gallons of paint.
To know more about whole numbers, refer here:
https://brainly.com/question/29766862#
#SPJ11
The scale factor for a set of values is 4. If the original measurement is 9, what is the new measurement based on the given scale factor?
The new measurement based on the given scale factor of 4 is 36. The scale factor is the ratio of the new size of an object to its original size. In this case, the scale factor is 4, which means the new size is 4 times larger than the original size.
If the original measurement is 9, then the new measurement can be calculated by multiplying the original measurement by the scale factor.
New measurement = Original measurement x Scale factor
New measurement = 9 x 4
New measurement = 36
Therefore, the new measurement based on the given scale factor of 4 is 36.
To explain it further, imagine you have a drawing that is 9 inches wide. If you were to increase the scale factor to 4, the new drawing would be 4 times larger, which means it would be 36 inches wide. This concept is commonly used in architecture, engineering, and other fields where scaling drawings or models is necessary to represent them accurately. Understanding scale factors is important in order to make accurate and proportional changes to objects and designs.
To know more about scale factor click here
brainly.com/question/29464385
#SPJ11
Classify the triangle with sides 1, 4, and 7. select one.
The triangle with sides 1, 4, and 7 is classified as an impossible triangle.
A triangle must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side. In this case, the sides are 1, 4, and 7. Adding the lengths of any two sides, we have:
1 + 4 = 5, which is less than 7
1 + 7 = 8, which is greater than 4
4 + 7 = 11, which is greater than 1
Since 1 + 4 is not greater than 7, the triangle inequality theorem is not satisfied, and therefore, a triangle with sides 1, 4, and 7 cannot exist.
To know more about triangle inequality theorem click on below link:
https://brainly.com/question/1163433#
#SPJ11
Find the volume of the cone with a height and radius both of 7.
The volume of the cone with a height and radius both of 7 units is 359.24 cubic units.
How to calculate the volume of a cone?In Mathematics and Geometry, the volume of a cone can be determined by using this formula:
V = 1/3 × πr²h
Where:
V represent the volume of a cone.h represents the height.r represents the radius.By substituting the given parameters into the formula for the volume of a cone, we have the following;
Volume of cone, V = 1/3 × 3.142 × 7² × 7
Volume of cone, V = 1/3 × 3.142 × 49 × 7
Volume of cone, V = 359.24 cubic units.
Read more on cone here: brainly.com/question/1082469
#SPJ1
Answer:
343/3
Proof of answer is in the image, please give brainliest
anyone know how to answer this?
The equation of the line is P = 2(1.0048)ᵗ and the population in 30 years is 2.31
Writing the equation of the lineThe equation is represented as
y = abᵗ
Where
a = y when t = 0
The points on the line are
(0, 2) and (20, 2.2)
This means that
a = 2
So, we have
y = 2bᵗ
Using the points, we have
2b²⁰ = 2.2
b²⁰ = 1.1
So, we have
b = 1.0048
This means that the equation is
P = 2(1.0048)ᵗ
The values of (a) and (b) & their interpretationsAbove, we have
a = 2
So, the meaning of the interpretation is that the initial population of the endangered colony is 2
Also, we have
b = 1.0048
So, the meaning of the interpretation is that the endangered colony increases by a factor of 1.0048 every year
Finding the population in 30 yearsRecall that
P = 2(1.0048)ᵗ
Here, we have
t = 30
So, the equation becomes
P = 2(1.0048)³⁰
Evaluate
P = 2.31
Hence, the population in 30 years is 2.31
Read more about exponential functions at
https://brainly.com/question/2456547
#SPJ1
In the derivation of the quadratic formula by completing the square, the equation mc032-1. Jpgis created by forming a perfect square trinomial. What is the result of applying the square root property of equality to this equation?.
The result of applying the square root property of equality to this equation is x = (-b ± √(b² - 4ac)) / (2a)
If we apply the square root property of equality to the equation (x + (b/2a))² = (-4ac + b²)/(4a²), we get:
x + (b/2a) = ±√[(-4ac + b²)/(4a²)]
Next, we can simplify the expression under the square root:
√[(-4ac + b²)/(4a²)] = √(-4ac + b²)/2a
Now, we can substitute this expression back into our original equation:
x + (b/2a) = ±√(-4ac + b²)/2a
Finally, we can isolate x by subtracting (b/2a) from both sides:
x = (-b ± √(b² - 4ac)) / (2a)
This is the quadratic formula, which gives us the solutions for the quadratic equation ax² + bx + c = 0. By completing the square, we have derived this formula from the original quadratic equation.
To learn more about quadratic formula click on,
https://brainly.com/question/16601208
#SPJ4
Complete question is:
In the derivation of the quadratic formula by completing the square, the equation (x+ (b/2a))² =(-4ac+b²)/(4a²) is created by forming a perfect square trinomial What is the result of applying the square root property of equality to this equation?
