Select the correct answer. The sum of the digits of a three-digit number is 13. The tens digit, t, is 1 more than the hundreds digit, h. The units digit, u, is 3 more than the sum of the tens and hundreds digits. Which system of equations can be used to find each digit?
Could someone help me understand? im a but confused
Answers
Using the system of equations we get the values of 3 digit number as:
238
Given:
The sum of the digits of a three-digit number is 13.
The tens digit, t, is 1 more than the hundreds digit, h. The units digit, u, is 3 more than the sum of the tens and hundreds digits.
we are asked to determine each digit of the given number:
we frame the equation as:
tens digit (t) = 1+h
hundreds digit (h) = h
units digit (u) = 3+(t+h)
hence,
h + (1+h) + (3+(t+h)) = 13
open the brackets.
h+1+h+3+(t+h)=13
substitute t value from the above mentioned state.
h+1+h+3+((1+h)+h)=13
h+1+h+3+1+h+h=13
arrange the like terms and add.
4h + 5 = 13
4h = 13-5
4h=8
h = 8/4
h = 2
hence we get the hundreds digit as 2.
now substitute it to get t and u value.
t = 1+h
t = 1+2
t = 3
tens digit = 3
u = 3+(t+h)
u = 3+(3+2)
u = 3+5
u = 8
units digit = 8
Related Questions
a restaurant owner wishes to estimate the proportion of people who eat out at least three a week. if is assumed to be 0.4, find the required sample size to yield 90% confidence interval whose length is below 0.03.
Answers
To find the required sample size for a resturant owner wishes to estimate the proportion of people who eat atleast three a week, we can use the formula for the margin of error of a proportion estimate. Therefore, the required sample size is 663.
Margin of error = z * [tex]\sqrt{(p * (1 - p) / n)}[/tex]
where z is the z-score corresponding to the desired level of confidence (for 90% confidence, z = 1.645), p is the population proportion (0.4 in this case), and n is the sample size.
We want the length of the confidence interval to be below 0.03, so the margin of error should be less than 0.03 / 2 = 0.015.
Substituting the values and solving for n, we get:
[tex]0.015=1.645 * \sqrt{(0.4 * (1 - 0.4) / n)}[/tex]
[tex]n = (1.645 / 0.015)^2 * 0.4 * (1 - 0.4)[/tex]
[tex]n = 661.84[/tex]
Therefore, the required sample size is 662. To be safe, we can round up to the next whole number, so the required sample size is 663.
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Suppose that when a certain lake is stocked with a population P of fish, the annual birth and death rates?and?are inversely proportional to sqrt(P), so that..
dP/dt=k*sqrt(P)
(a) Find P(t) if P(0)=C
(b) If C=102 and after 7 months there are 155 fish in the lake, how many fish will there be after 1.6 years?
Answers
The value of P(t) is [tex]\frac{dP}{dt} = k \cdot \sqrt{P}[/tex] and there will be approximately 220 fish in the lake after 1.6 years.
(a) This is a separable differential equation and can be solved using the separation of variables. We have:
[tex]\frac{dP}{dt}[/tex] = k * [tex]\sqrt{P}[/tex]
[tex]\frac{dP}{\sqrt{P}}[/tex] = k * dt
Integrating on both sides:
2 * [tex]\sqrt{P}[/tex] = k * t + C1
where C1 is a constant of integration. Solving for P, we have:
P(t) = [tex](k * t + C1)^2[/tex] / 4
Using the initial condition P(0) = C, we can solve for C1:
C = [tex](C1)^2[/tex] / 4
C1 = 2 * [tex]\sqrt{C}[/tex]
Therefore, we have:
[tex]\frac{dP}{dt} = k \cdot \sqrt{P}[/tex]
(b) There will be approximately 220 fish in the lake after 1.6 years.
Using the values given, we have:
C = 102
t = 7 months = 7/12 years = 0.5833 years
P(7 months) = 155
We can use this information to solve for k:
[tex]155 =[/tex] [tex]\frac{(k * 0.5833 + 2 *\sqrt{102})^2}{4}[/tex]
[tex]k = \frac{(4 * 155 - 4 * 2^2 *\sqrt{102})}{0.5833^2}[/tex]
Now that we have k, we can find P(1.6 years):
[tex]P(t) = \frac{\left( k \cdot t + 2 \cdot \sqrt{C} \right)^2}{4}[/tex]
By solving, the final value of k is approximately = 10.04
Substituting the value of k, we get:
P(1.6 years) = [tex]\frac{\left( 10.04 \cdot 1.6 + 2 \cdot \sqrt{102} \right)^2}{4}[/tex]
By evaluating the expression, we get:
P(1.6 years) = 220.72
So, there will be approximately 220 fish in the lake after 1.6 years.
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in exercises 37 and 38, the graph of a function f(x) is given
Answers
Answer:
Exercise 37:
In this exercise, the question is to find the x-coordinate of the point of inflection of the graph of the function f(x).
The point of inflection of the graph of the function f(x) is at the x-coordinate of 1.
10, 24, 26 right or acute or obtuse or not a
Answers
After adding the given angles 10 + 24 + 26, which comes to 60°, we know that is is an acute angle.
What are acute angles?A protractor can be used to measure acute angles, which are those that are smaller than 90°.
A form of angle known as an obtuse angle is one that is always greater than 90° but less than 180°.
An acute angle is one that is smaller than 90 degrees in length.
The correct angle is larger than this angle (which is equal to 90 degrees).
For instance, acute angles include 30°, 45°, 60°, 75°, 33°, 55°, 85°, etc.
So, we have the angles:
10°, 24° and 26°.
Add all 3 angles as follows:
10 + 24 + 26 = 60°
And we know that all angles smaller than 90° are acute angles.
Therefore, after adding the given angles 10 + 24 + 26, which comes to 60°, we know that is is an acute angle.
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find a quadratic equation in X whose roots are -2 and 3/4
Answers
Answer:
4x² + 5x - 6 = 0
Step-by-step explanation:
Quadratic equation:
[tex]\boxed{x^2-(sum \ of \ roots)x+product \ of \ roots=0}[/tex]
[tex]Sum \ of \ roots = -2 + \dfrac{3}{4}[/tex]
[tex]= \dfrac{-2*4}{1*4}+\dfrac{3}{4}\\\\=\dfrac{-8}{4}+\dfrac{3}{4}\\\\=\dfrac{-5}{4}\\\\[/tex]
[tex]\sf product \ of \ roots =-2 *\dfrac{3}{4}[/tex]
[tex]=\dfrac{-6}{4}[/tex]
Quadratic equation:
[tex]x^2 - \left(\dfrac{-5}{4}\right)x+\left(\dfrac{-6}{4}\right)=0[/tex]
Multiply the entire equation by 4,
4x² - (-5)x + (-6) = 0
4x² + 5x - 6 = 0
One such equation is (x+2)(x-3/4) = 0. Expanding this product, we get x^2 - x/2 + 3/8 = 0
Another equation is x^2 - 4x + 8 = 0 (by Vieta's Formulas)
22 in
98 in
27 in 22 in
What is the
perimeter of this
red polygon?
[?] in
Enter
Answers
Answer:
below
Step-by-step explanation:
2 * 27 + 2*22 + 2*22 + 2 * 98 = 338 in
a thin cylindrical shell of length 200 m and radius 6.00 cm has a uniform surface charge density of (a) what is the total charge on the shell? find the electric field at the following radial distances from the long axis of the cylinder: (b) 2.00 cm, (x) 5.90 cm, (d) 6.10 cm, and (e) 10.0 cm. (use the results of problem 48.
Answers
The total charge on the shell is 678.24 nC, The electric field at the following radial distances from the long axis of the cylinder is (b) 1.524 x 10¹⁶ N/C, (c) 1.75 x 10¹⁵ N/C, (d) 1.63 x 10¹⁵ N/C, and (e) 6.097 x 10¹⁴ N/C.
(a) The total charge of the shell can be found by multiplying the surface charge density by the surface area of the cylinder:
Q = σ × 2π × r × L
where
σ = 9.00 nC/m² (surface charge density)
r = 0.06 m (radius)
L = 200 m (length)
Q = 9.00 nC/m² × 2 × π × 0.06 m × 200 m
Q = 678.24 nC
(b) To find the electric field at a radial distance of 2cm from the long axis of the cylinder, we use the formula:
E = k × Q / r²
where
k = 8.99 x 10⁹ Nm^2/C² (Coulomb's constant)
Q = 678.24 nC (total charge)
r = 0.02 m (radial distance)
E = 8.99 x 10⁹ Nm^2/C² × 678.24 nC/(0.02 m)²
E = 1.524 x 10¹⁶ N/C
(c) To find the electric field at a radial distance of 5.9cm from the long axis of the cylinder, we use the formula:
E = k × Q / r²
where
k = 8.99 x 10⁹ Nm²/C² (Coulomb's constant)
Q = 678.24 nC (total charge)
r = 0.059 m (radial distance)
E = 8.99 x 10⁹ Nm²/C² × 678.24 nC/(0.059 m)²
E = 1.75 x 10¹⁵ N/C
(d) To find the electric field at a radial distance of 6.1cm from the long axis of the cylinder, we use the formula:
E = k × Q / r⁷
where
k = 8.99 x 10⁹ Nm²/C² (Coulomb's constant)
Q = 678.24 nC (total charge)
r = 0.061 m (radial distance)
E = 8.99 x 10⁹ Nm²/C² × 678.24 nC / (0.061 m)²
E = 1.63 x 10¹⁵ N/C
(e) To find the electric field at a radial distance of 10cm from the long axis of the cylinder, we use the formula:
E = k × Q / r²
where
k = 8.99 x 10⁹ Nm²/C² (Coulomb's constant)
Q = 678.24 nC (total charge)
r = 0.10 m (radial distance)
E = 8.99 x 10⁹ Nm²/C² × 678.24 nC / (0.10 m)²
E = 6.097 x 10¹⁴ N/C
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how is "If a polygon has four congruenet
angles, then it is a rectangle. The converse is not always true." not always true? I thought a sqaure can be a rectangle
Answers
If a polygon has four congruent angles then it can be a square and rectangle. Therefore the converse is not always true because square also have this property
What are the properties of a rectangle?The 4 basic property of a rectangle are;
1. A rectangle is a quadrilateral.
2. The opposite sides are parallel and equal to each other.
3. Each interior angle is equal to 90 degrees.
The sum of all the interior angles is equal to 360 degrees.
4.The diagonals bisect each other.
Both the diagonals have the same length.
Some of these properties are also for square. The difference between a square and a rectangle is that the sides of are all equal but only the opposite sides of a rectangle are equal. Both angles in square and rectangle are congruent, they are all 90°.
Therefore the converse of the statement "If a polygon has four congruenet
angles, then it is a rectangle." is not always true because both rectangle and square as these properties
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Does the function have a minimum or maximum value?
Answers
Solve the system of equations below by graphing both equations with a pencil and paper. What is the solution? 4x + 5y = 22 2x + 3y = 12
Answers
The value of x is 3 and value of y is 2 in 4x + 5y = 22 and 2x + 3y = 12
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given system of equations are 4x + 5y = 22 and 2x + 3y = 12
Multiply equation 2 with 2
4x+6y=24
Subtract the above equation from equation 1
4x + 5y -4x-6y= 22-24
-y=-2
y=2
Now plug in y value in equation 2x + 3y = 12
2x+6=12
2x=6
Divide both sides by 2
x=3
Hence, the value of x is 3 and value of y is 2 in 4x + 5y = 22 and 2x + 3y = 12
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Find a linear function h, given h(4)= -14 and h(-4)= 26. Then find h(9).
Answers
The linear function h is given by h(x) = -2x + 20. To find this, we need to solve a system of two equations and two unknowns, x and b.
What is the linear function?A linear function is a mathematical equation that describes a straight line. It is defined by an equation of the form y = mx + b, where x and y are variables, and m and b are constants that determine the slope and y-intercept of the line, respectively. Linear functions are used to describe relationships between two variables, such as in graphing, statistical analysis, and economics. Linear functions can also be used to model complex systems, such as the stock market or the behavior of other physical systems.
The linear function h is given by h(x) = -2x + 20. To find this, we need to solve a system of two equations and two unknowns, x and b. The two equations are:
h(4) = -14
h(-4) = 26
We can solve for x and b by subtracting the two equations from each other:
h(4) - h(-4) = -14 - 26
-2(4 + (-4)) = -40
-2(0) = -40
Now we can solve for b by substituting 4 into the equation and solving for b:
h(4) = -2(4) + b
-14 = -8 + b
b = 6
Therefore, the linear function h is given by h(x) = -2x + 6.
To find h(9), we can substitute 9 into the equation and solve for h(9):
h(9) = -2(9) + 6
h(9) = -18 + 6
h(9) = -12
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Which notation describes this transformation?
OA. (x,y)= (-y, x)
OB. (x,y) = (x + 9,y - 2)
OC.
(x, y) = (x - 9,y + 2)
OD.
(x, y) = (-x, y)
Answers
The correct matching is given below.
A. (x, y)= (-y, x) represents the reflection.
B. (x, y) = (x + 9,y - 2) represents the translation.
C. (x, y) = (x - 9,y + 2) represents the translation.
D. (x, y) = (-x, y) represents the reflection.
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
The translation does not change the shape and size of the geometry. But changes the location.
The reflection does not change the shape and size of the geometry. But flipped the image.
A. (x, y) = (-y, x), this represents the reflection over the line y = -x.
B. (x, y) = (x + 9,y - 2), this represents the translation.
C. (x, y) = (x - 9,y + 2), this represents the translation.
D. (x, y) = (-x, y), this represents the reflection over the y-axis.
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Answer: (x' , y') = (x - 9, y + 2)
Step-by-step explanation:
I took the test
Suppose a function g is continuous at a=2
Select the appropriate response in each dropdown below.
lim g(x)
x→2 +
lim g(x) x→2 -
lim g(x)
x→2 and lim g(x) x→2 -
Answers
The appropriate response in each dropdown are
lim g(x)x→+2: Truelim g(x) x→-2: Falselim g(x)x→2 and lim g(x) x→-2: FalseHow to determine the appropriate responseFrom the question, we have the following parameters that can be used in our computation:
Function = g(x)
Also, we have:
The function g is continuous at a=2
This means that the limit at x approaches +2 is to infinity
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The maximum acceleration attained on the interval [0,3] by the particle whose velocity is given by: v(t) = t3 – 3t2 + 12t + 4 is .... a. 21 b. 40 c. 14 d. 9 e. 12
Answers
The maximum acceleration attained on the interval [0,3] by the particle whose velocity is given by: v(t) = t3 – 3t2 + 12t + 4 is 21
The correct answer is an option (a)
The velocity function is given by,
v(t) = t³ – 3t² + 12t + 4
We differentiate above function to get the acceleration function which will be
a(t) = v'(t)
a(t) = 3t² - 6t + 12 + 0
a(t) = 3t² - 6t + 12
Consider the interval [0,3]
We find the value of acccleration function at the end of the intervals.
For t = 0,
a(0) = 3(0)² - 6(0) + 12
a(0) = 0 - 0 + 12
a(0) = 12
And for t = 3,
a(3) = 3(3)² - 6(3) + 12
a(3) = 27 - 18 + 12
a(3) = 21
This means, the function a(t) is increasing and the maximum value of function a(t) would be at t = 3.
Therefore, the maximum acceleration attained on the interval [0,3] is 21
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Use this table to find all the missing expense values. Expenses Budget Percent of Budget Utilities 7% Labor 30% Supplies 25% Rent 35% Advertising 3% TOTAL $4,500 100%
Answers
Answer:
Utilities: $315 (7% of $4500)
Labor: $1350 (30% of $4500)
Supplies: $1125 (25% of $4500)
Rent: $1575 (35% of $4500)
Advertising: $135 (3% of $4500)
Statins are used to keep cholesterol in check and are a top-selling drug in the U.S.
The equation:
S 1.7x 5.5
gives the amount of sales (S) of statin in billions of dollars x years after 1998. According to this equation, how much will/did people in the U.S. spend on statins in the year 2005?
Answers
Answer:
Below
Step-by-step explanation:
2005 is 7 years after 1998 x= 7
S = 1.7 (7) x 5.5 = 65.45 (billion)
Please help me with this question.
Answers
Given matrix [tex]\left[\begin{array}{cccc}1&7&3&-4\\0&1&-1&3\\0&0&0&2\\0&0&1&1\end{array}\right][/tex], so the solution set is empty.
Correct option: c
What is matrix?Mathematicians analyze matrices as a subject of study in a field called matrix theory. It started out as a branch of linear algebra but quickly expanded to cover topics in graph theory, algebra, combinatorics, and statistics. When it's necessary to summarise an infinite or limited collection of objects grouped in rows and columns, matrices are utilised. The initial set of a matrix's attributes are those of its constituent entities. Solving linear equations is made easier by it. Matrices are incredibly priceless items that are used in a variety of contexts. In addition to mathematical applications, matrices are employed in a wide range of scientific disciplines.
Given that,
[tex]\left[\begin{array}{cccc}1&7&3&-4\\0&1&-1&3\\0&0&0&2\\0&0&1&1\end{array}\right][/tex]
now exchange R₄ ↔ R₃
[tex]\left[\begin{array}{cccc}1&7&3&-4\\0&1&-1&3\\0&0&1&1\\0&0&0&2\end{array}\right][/tex]
Therefore, rank of main matrix = 3
rank of Augmented matrix = 4
So, rank of main matrix < rank of Augmented matrix
Thus, there is no solution.
Also we can say, the solution set is empty.
correct option: c
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Arithmetic operations provide meaningful results for variables that a. use any scale of measurement except nominal. b. have non-negative values. c. are quantitative. d. appear as non-numerical values.
Answers
Arithmetic operations provide meaningful results for variables that c. are quantitative.
What is Arithmetic operations?For all real numbers, the four fundamental arithmetic operations in mathematics are: Finding the sum in addition ('+') Subtraction (Difference-finding; "-" Multiplication (Identifying the result; "" Finding the quotient in division (")
The commutative laws of addition and multiplication, such as a + b = b + a and ab = ba, the associative laws of addition and multiplication, such as a + (b + c) = (a + b) + c and a(bc) = (ab)c, as well as the distributive law, which links addition and...
Therefore, option C is correct.
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the manager of a furniture factory that operates a morning and evening shift seven days a week wants to forecast the number of chairs its factory workers will produce on a given day and shift. the production manager gathers chair production data from the factory and lists whether the production day was a weekday or a weekend (i.e., saturday or sunday), and whether the shift was in the morning or evening.
Answers
This type of data can be analyzed using a two-way analysis of variance (ANOVA) to determine the effect of both the day of the week (weekday or weekend) and the shift (morning or evening) on chair production. The manager can use this information to make predictions about future production based on the day of the week and shift.
The manager can start by creating a table to show the average number of chairs produced on each day of the week and shift. Then, a two-way ANOVA can be performed to determine if there is a significant difference in the mean number of chairs produced between weekdays and weekends, and between morning and evening shifts.
If the results of the ANOVA show that there is a significant effect of the day of the week and/or the shift on chair production, the manager can use this information to make more accurate predictions about future chair production. For example, if the results show that chair production is higher on weekdays compared to weekends, the manager can make predictions based on this information and allocate resources accordingly.
It is important to note that other factors such as the availability of materials, number of workers, and machine downtime can also impact chair production and should be considered when making predictions.
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John restaurant on 150 Main Street has 120 tables, but 30 percent of these tables are reserved. Therefore how many tables are available.
Answers
Answer:
84 tables are available
Step-by-step explanation:
30% = 30 ÷ 100
120 x (30 ÷ 100) = 36
36 tables are reserved hence
120-36 = 84
84 tables are available
Select the equivalent expression that uses the Greatest common Factor (GCF) of each term in the expression.
Answers
The equivalent expression that uses the Greatest common Factor (GCF) of each term in the expression are 16 (2x+1 ), 32 ( x + 0.5 ) ,16 ( 2x+1 ) and 16 (2x+1)
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants.
Given expressions,
2 ( 16x+ 8 )
= 2 * 8 ( 2x+ 1 )
= 16 ( 2x+1 )
16 (2x+1 )
= 16 * 2 ( x + 1/2 )
=32 ( x + 0.5 )
4(8x+4)
= 4 * 4 ( 2x+ 1 )
= 16 ( 2x+1 )
8 (4x+2)
= 8 * 2 ( 2x+1 )
= 16 (2x+1)
Therefore, The equivalent expression that uses the Greatest common Factor (GCF) of each term in the expression are 16 (2x+1 ), 32 ( x + 0.5 ) ,16 ( 2x+1 ) and 16 (2x+1)
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Please help will reward
Answers
The factor g(x) grows over the interval from 14 to 16 is approximately 1.41
How to Determine the Factor a Function Grows over an Interval?To determine the factor by which g(x) grows over the interval from 14 to 16, we need to find the ratio of the values of g(x) at x = 16 and x = 14, then take its exponential.
Let's evaluate g(x) at x=14 and x=16:
g(14) = 4^14 - 4 = 16384
g(16) = 4^16 - 4 = 65536
The factor by which g(x) grows over the interval from 14 to 16 is:
(g(16) / g(14))^(1/(16-14)) = (65536 / 16384)^(1/2) = 2^(1/2) = 1.41
So, g(x) grows by a factor of approximately 1.41 over the interval from 14 to 16.
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A real estate office manages an apartment complex with 40 units. When the rent is $780 per month, all 40 units are occupied. However, when the rent is $852, the average number of occupied units drops to 36. Assume that the relationship between the monthly rent p and the demand x is linear. (Note: the term demand refers to the number of occupied units.)
(a) Write a linear equation giving the demand x in terms of the rent p.
Answers
Answer:
The linear equation giving the demand x in terms of the rent p can be written as x = 40 - 0.042p, where x is the number of occupied units and p is the monthly rent.
Select the correct answer.
Which investment data is best modeled by an exponential function?
A.
The chart shows the Growth of dollars 1,000 in years on the x-axis and on the y-axis is the account balance. The account balance was 1000 dollars on year 1 and with a linear growth reached 2900 dollars at the end of 18 years.
B.
The chart shows the Growth of dollars 1,000 in years on the x-axis and on the y-axis is the account balance. The account balance was 1000 dollars in year 1. It reached 4000 dollars after 11 years and at the end of 18 years, it falls to 1000 dollars.
C.
The chart shows the Growth of dollars 1,000 in years on the x-axis and on the y-axis is the account balance. The account balance was 1000 dollars on year 1 and at the end of 18 years, it was 58,000 dollars.
D.
The chart shows the Growth of dollars 1,000 in years on the x-axis and on the y-axis is the account balance. The account balance remained stable at 1000 dollars for 15 years, and then increased to 1400 dollars after 18 years.
E.
The graph depicts the Growth of dollar 1,000 with the x-axis representing time in years and the y-axis representing account balance. The account balance was 1000 dollars in the first year. It reached the peak of 1800 dollars in year 14.
Answers
Answer:
Letter (C)
Step-by-step explanation:
The chart shows the Growth of dollars 1,000 in years on the x-axis and on the y-axis is the account balance. The account balance was 1000 dollars on year 1 and at the end of 18 years, it was 58,000 dollars. This type of data is best modeled by an exponential function because it shows a continuous increase in the account balance over time.
This circle is centered at the point (3,2), and the length of its radius is 5. What is the equation of the circle
Answers
Answer:
C
Step-by-step explanation:
The standard form of a circle is
(x-a)^2 + (y-b)^2 = r^2
Where (a, b) is the centre and r is the radius
Kim bought 3 cubic feet of cypress
mulch. She paid $2.80 for each cubic
foot. Collin bought 2 cubic feet of
hardwood mulch. He paid $3.20 for
each cubic foot. Who spent more
money on mulch? How do you know?
Answers
To find out, you can multiply the number of cubic feet of mulch by the price per cubic foot.
For Kim: 3 cubic feet x $2.80/cubic foot = $8.40
For Collin: 2 cubic feet x $3.20/cubic foot = $6.40
As $8.40 > $6.40, Kim spent more money on mulch.
assuming each branch of the log functions is analytic, use the chain rule to give another proof that each such function has derivative 1/z. 2
Answers
The derivative of the logarithm function y = ln |e^z| with respect to z is equal to 1/z, assuming each branch of the logarithm function is analytic.
The Chain Rule formula computes the derivative of the combination of two or more functions.
For composite functions, the chain rule in differentiation is defined. If f and g are functions, the chain rule expresses the derivative of their combination.
d/dx [f(g(x))] = f'(g(x)) g'(x)
The chain rule states that if y = f(u) and u = g(x), then the derivative of y with respect to x is given by:
dy/dx = df/du * du/dx
Let f(z) = ln |z| and let g(z) = e^z.
Then, for the composition y = f(g(z)),
we have:
u = g(z) = e^z
f(u) = ln |e^z| = ln |u|
du/dz = e^z
df/du = 1/u = 1/e^z
Now, we can use the chain rule to find the derivative of y with respect to z:
dy/dz = df/du * du/dz
= (1/e^z) * e^z
= 1/z
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A vertical dam on a large lake is 30 ft tall and 60 ft wide, and the water level is 5 ft below the top of the dam. In the middle of the dam at the very bottom is a gate in the shape of an equilateral triangle 8 ft on a side as shown in the figure below.
(Assume a density of water = 62.4 lb/ft3.)
25 ft8 ft
Find the hydrostatic force (in lb) on the gate. (Round your answer to the nearest integer.)
Answers
Rounded to the nearest integer, this is 140165 lb.
We need to find the volume of water that will be pressing against the gate.The height of the water above the gate is 25 ft - 5 ft = 20 ft.
The width of the water perpendicular to the gate is half the width of the dam, or 60 ft / 2 = 30 ft.
The area of the equilateral triangle is (8 ft)^2 * √(3) / 4 = 8 * 8 * √(3) / 4 = 16 * √(3) ft^2.
The volume of the water pressing against the gate is the product of the height, width, and area:
20 ft * 30 ft * 16 * √(3) ft^2 = 2400 ft^3 * √(3).
Finally, the hydrostatic force is the product of the volume, the density of water, and g (acceleration due to gravity):
2400 ft^3 * √(3) * 62.4 lb/ft^3 * 9.8 m/s^2 = approximately 140164.96lb
Therefore, Rounded to the nearest integer is 140165 lb.
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Please help me with this question.
Answers
When revolved over the {x} axis will occupy more volume as compared to when revolved over the {y} axis.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that one bag of pebbles covers 5 ft² and costs $8.99.
Refer to the image attached. The reflection over the {x} axis will occupy more volume as compared to the reflection over the {y} axis. The figure generated in both the cases would be a cuboidal prism structure.
Therefore, when revolved over the {x} axis will occupy more volume as compared to when revolved over the {y} axis.
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The mapping F and G are defined on R, the set of real numbers by F(x)=x^2+3 and G(x)=x-2. Find: a) (G composition of F)(x), b) (F composition of G)(x), c) is the composition of F and y commutative. Using Brainly.in app.
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Real numbers include both rational and irrational numbers. All rational and irrational numbers, such as the integers (-2, 0, 1), fractions (1/2, 2.5), and the number 3, are considered real numbers.
What is meant by real numbers?Real numbers include both rational and irrational numbers. All rational and irrational numbers, such as the integers (-2, 0, 1), fractions (1/2, 2.5), and the number 3, are considered real numbers.Real numbers can be used to represent continuous one-dimensional mathematical quantities like temperature, time, or distance.Continuous in this context suggests that values may vary by arbitrary little amounts. An infinite decimal expansion can nearly always represent any real number. Real numbers can be divided into 5 categories: natural/counting, integer, whole, rational and irrational. a common sort of number, such as 1, 15.82, 0.1, 3/4, etc. Real Numbers can be whole, fractional, decimal, positive, negative, large, or small.Given f(x)=|x|, g(x)=[x]
[tex]& \text { fog }(x)=|[x]| \\[/tex]
[tex]- \\2[/tex][tex]\end{array}\right]=-1+} \\[/tex]
Simplifying,
[tex]{gof}(\mathrm{x})=[|\mathrm{x}|] \\[/tex]
[tex]{fog}\left(-\frac{}{\mathbb{R}}\right)={ }_{\mid}-{ }_{\mathbb{R}}\right]_{\mid}=|-1|=1 \\[/tex]
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