If you do in fact mean [tex]f(1)=f(6)=0[/tex] (as opposed to one of these being the derivative of [tex]f[/tex] at some point), then integrating twice gives
[tex]f''(x) = -\dfrac1{x^2}[/tex]
[tex]f'(x) = \displaystyle -\int \frac{dx}{x^2} = \frac1x + C_1[/tex]
[tex]f(x) = \displaystyle \int \left(\frac1x + C_1\right) \, dx = \ln|x| + C_1x + C_2[/tex]
From the initial conditions, we find
[tex]f(1) = \ln|1| + C_1 + C_2 = 0 \implies C_1 + C_2 = 0[/tex]
[tex]f(6) = \ln|6| + 6C_1 + C_2 = 0 \implies 6C_1 + C_2 = -\ln(6)[/tex]
Eliminating [tex]C_2[/tex], we get
[tex](C_1 + C_2) - (6C_1 + C_2) = 0 - (-\ln(6))[/tex]
[tex]-5C_1 = \ln(6)[/tex]
[tex]C_1 = -\dfrac{\ln(6)}5 = -\ln\left(\sqrt[5]{6}\right) \implies C_2 = \ln\left(\sqrt[5]{6}\right)[/tex]
Then
[tex]\boxed{f(x) = \ln|x| - \ln\left(\sqrt[5]{6}\right)\,x + \ln\left(\sqrt[5]{6}\right)}[/tex]
Sodas cost $1.75 each. Write a direct
proportional equation using (s) for sodas and
(t) for total cost.
Answer:
t = 1.75(s)
Step-by-step explanation:
I gotchu
the width of a large butterfly is about 0.08. What is the width when it is written in scientific notation
Answer: 8 x 10^2
Step-by-step explanation:
scientific notation has to be greater than 1, less than 10
therefore:
0.08 = 8 x 10^2
Use the table values below to select the correct statement.
The true statement is (c) the function f(x) is an exponential function
How to determine the correct statement?From the table, we can see that:
As x increases by 2.y does not increase with the same common differenceThis means that the table represents an exponential function
The rate is then calculated as:
f(n) = f(1) * r^n-1
Using f(3), we have
102 = 17 * r^3-1
This gives
r^2 = 6
Take the square roots
r = 2.45
Hence, the true statement is (c) the function f(x) is an exponential function
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Write your answer as a fraction in simplest form.
-1 3/4 • 2 1/8
WILL GIVE BRAINLIEST
Directions: Factor the following trinomials containing negative numbers. Follow the rules for operations with signed numbers to identify the correct binomial factors.
1. x2 + 6x - 7
2. x2 - 5x + 6
3. x2 - 6x - 7
4. x2 + 5x - 6
5. x2 + x - 12
6. x2 - 2x - 8
7. x2 - 4x - 5
8. x2 + 2x - 3
9. x2 - 16
10. x2 - x - 12
11. x2 -9x + 18
12. x2 -5x - 14
13. x2 - 7x + 10
14. x2 -11x + 24
15. x2 - x - 30
Factorization refers to the process by which the terms that are common in an expression are obtained.
What is factorization?Factorization refers to the process by which the terms that are common in an expression are obtained.
Given the trinomials, the correct binomial factors are;
1) (x−1)(x+7)
2) (x−2)(x−3)
3) (x+1)(x−7)
4) (x−1)(x+6)
5) (x−3)(x+4)
6) (x+2)(x−4)
7) (x+1)(x−5)
8) (x−1)(x+3)
9) (x+4)(x−4)
10) (x+3)(x−4)
11) (x−3)(x−6)
12) (x+2)(x−7)
13) (x−2)(x−5)
14) (x−3)(x−8)
15) (x+5)(x−6)
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Find the value of z.
X
7
Y
3
Z
Z = √[?]
Answer:
z = [tex]\sqrt{30}[/tex]
Step-by-step explanation:
using the Altitude- on- Hypotenuse theorem
(leg of big Δ )² = (part of hypotenuse below it ) × (whole hypotenuse)
z² = 3 × (3 + 7) = 3 × 10 = 30 ( take square root of both sides )
z = [tex]\sqrt{30}[/tex]
help answer this please
Answer:
Step-by-step explanation:
2x + 5y = 8
-5 -5
2x = 8 - 5y
divide both sides by 2
[tex]\frac{2x}{2} = \frac{8-5y}{2}[/tex]
divide by 2 undoes the multiplication by 2
x = [tex]\frac{8- 5y}{2}[/tex]
divide 8 - 5y by 2
x = - [tex]\frac{5}{2}[/tex] y + 4
45.7 kilometers =
meters
Answer:
45.7 kilometers = 45,700 meters
Explanation:
Hi!
Okay, so basically, in one kilometer, there are 1000 meters.
Using this problem, all you have to do is multiply 45.7 by 1000, which is 45,700.
Whatever value is used for kilometers (ex. 2), just multiply by 1000, and you’ll get the value as meters (ex. 2 x 1000 = 2000 meters).
Hope this helps!
To convert kilometers to meters, multiply the kilometer value by 1000 meters which is equal to 1 km.
Convert 45.7 kilometers to meters:
Knowing that 1000 m = 1 km.[tex]\boldsymbol{\sf{Therefore \ \ \longmapsto \ \ 45.7\not{km}*\left(\dfrac{1000 \ m}{1\not{km}}\right)=45700 \ m }}[/tex]
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Using the given definition and [tex]\Delta x=\frac{0-(-2)}n=\frac2n[/tex], we have
[tex]\displaystyle \int_{-2}^0 (7x^2+7x) \,dx = \lim_{n\to\infty} \sum_{i=1}^n \left(7\left(-2+\frac{2i}n\right)^2 + 7\left(-2+\frac{2i}n\right)\right) \frac2n \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac2n \sum_{i=1}^n \left(14 - \frac{42i}n + \frac{28i^2}{n^2}\right)[/tex]
Recall the well-known power sum formulas,
[tex]\displaystyle \sum_{i=1}^n 1 = \underbrace{1 + 1 + 1 + \cdots + 1}_{n\,\rm times} = n[/tex]
[tex]\displaystyle \sum_{i=1}^n i = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]
[tex]\displaystyle \sum_{i=1}^n i^2 = 1 + 4 + 9 + \cdots + n^2 = \frac{n(n+1)(2n+1)}6[/tex]
Reducing our sum leads to
[tex]\displaystyle \int_{-2}^0 (7x^2+7x) \,dx = \lim_{n\to\infty} \frac2n \left(\frac{7n}3 - 7 + \frac{14}{3n}\right) = \lim_{n\to\infty} \left(\frac{14}3 - \frac{14}n + \frac{28}{3n^2}\right)[/tex]
As [tex]n[/tex] goes to ∞, the rational terms containing [tex]n[/tex] will converge to 0, and the definite integral converges to
[tex]\displaystyle \int_{-2}^0 (7x^2+7x) \,dx = \boxed{\frac{14}3}[/tex]
Alok started a business investing Rs 90, 000. After three
months Prabir joined him with capital of Rs 1,20000
If at the end of 2 years, the total profit made
by them was
Rs 96,000 what will the difference
between Alok and Prabir's share in it?
The difference between Alok and Prabir share exists 8000.
What will the difference between Alok and Prabir share?Given: Invested by Alok = Rs 90, 000
Invested by Prabir = Rs 1,20000
The time period of Alok = 3 months
The time period of Prabir = 2 years
They earn a profit = Rs 96,000.
Profit exists directly proportional to the product of the amount invested and the time period of investment.
8000 = 90000 [tex]*[/tex] 24/120000 [tex]*[/tex] 21
= 5/7
5x + 7x = 96000
x = 8000
first = 40000
second = 48000
so the difference exists at 8000.
The difference between Alok and Prabir share exists 8000.
Therefore, the correct answer is 8000.
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Write the ratio of 4 roses to 24 flowers
Answer:
4:24 or also 1:6
Step-by-step explanation:
What's the Value of X in 1/2 + X = 5/6
Answer:
x = 1/3
Step-by-step explanation:
1/2 + X = 5/6
collecting the like terms
X = 5/6 - 1/2
making one fraction on the left side by taking the common denominator
X = (5 - 3)/6
X = 2/6
devide the numerator and denominator by 2, you get
X = 1/3
A yo-yo is moving up and down a string so that its velocity at time t is given by v(t) = 3cos(t) for time t ≥ 0. The initial position of the yo-yo at time t = 0 is x = 3.
Part A: Find the average value of v(t) on the interval open bracket 0 comma pi over 2 close bracket. (10 points)
Part B: What is the displacement of the yo-yo from time t = 0 to time t = π? (10 points)
Part C: Find the total distance the yo-yo travels from time t = 0 to time t = π. (10 points)
Part A - The average value of v(t) over the interval (0, π/2) is 6/π
Part B - The displacement of the yo-yo from time t = 0 to time t = π is 0 m
Part C - The total distance the yo-yo travels from time t = 0 to time t = π is 6 m.
Part A: Find the average value of v(t) on the interval (0, π/2)The average value of a function f(t) over the interval (a,b) is
[tex]f(t)_{avg} = \frac{1}{b - a} \int\limits^b_a {f(t)} \, dx[/tex]
So, since velocity at time t is given by v(t) = 3cos(t) for time t ≥ 0. Its average value over the interval (0, π/2) is given by
[tex]v(t)_{avg} = \frac{1}{\frac{\pi }{2} - 0} \int\limits^{\frac{\pi }{2} }_0 {v(t)} \, dt[/tex]
Since v(t) = 3cost, we have
[tex]v(t)_{avg} = \frac{1}{\frac{\pi }{2} - 0} \int\limits^{\frac{\pi }{2} }_0 {3cos(t)} \, dt\\= \frac{3}{\frac{\pi }{2}} \int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt\\= \frac{6}{{\pi}} [{sin(t)}]^{\frac{\pi }{2} }_{0} \\= \frac{6}{{\pi}} [{sin(\frac{\pi }{2})} - sin0]\\ = \frac{6}{{\pi}} [1 - 0]\\ = \frac{6}{{\pi}} [1]\\ = \frac{6}{{\pi}}[/tex]
So, the average value of v(t) over the interval (0, π/2) is 6/π
Part B: What is the displacement of the yo-yo from time t = 0 to time t = π?To find the displacement of the yo-yo, we need to find its position.
So, its position x = ∫v(t)dt
= ∫3cos(t)dt
= 3∫cos(t)dt
= 3sint + C
Given that at t = 0, x = 3. so
x = 3sint + C
3 = 3sin0 + C
3 = 0 + C
C = 3
So, x(t) = 3sint + 3
So, its displacement from time t = 0 to time t = π is
Δx = x(π) - x(0)
= 3sinπ + 3 - (3sin0 + 3)
= 3 × 0 + 3 - 0 - 3
= 0 + 3 - 3
= 0 + 0
= 0 m
So, the displacement of the yo-yo from time t = 0 to time t = π is 0 m
Part C: Find the total distance the yo-yo travels from time t = 0 to time t = π. (10 points)The total distance the yo-yo travels from time t = 0 to time t = π is given by
[tex]x(t) = \int\limits^{\pi}_0 {v(t)} \, dt\\= \int\limits^{\pi }_0 {3cos(t)} \, dt\\= 3 \int\limits^{\pi }_0 {cos(t)} \, dt\\ = 3 \int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt + 3\int\limits^{\pi }_{\frac{\pi }{2}} {cos(t)} \, dt\\= 3 \times 2\int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt\\= 6 [{sin(t)}]^{\frac{\pi }{2} }_{0} \\= 6[{sin\frac{\pi }{2} - sin0]\\\\= 6[1 - 0]\\= 6(1)\\= 6[/tex]
So, the total distance the yo-yo travels from time t = 0 to time t = π is 6 m.
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Madison finished 4/5 of her homework before dinner. What percent of Maddison’s homework is left to finish?
Answer:
1/5 of it
Step-by-step explanation:
5/5 represents all of her homework
5/5-4/5= 1/5
4/5 represents the homework she did before dinner
1/5 represents the homework left to do
What is the sum of ∞Σn=1 2(1/5)^n-1? s=1/5 s=2/5 s=5/3 s=5/2
The sum of the sum notation ∞Σn=1 2(1/5)^n-1 is S= 5/2
How to determine the sum of the notation?The sum notation is given as:
∞Σn=1 2(1/5)^n-1
The above notation is a geometric sequence with the following parameters
Initial value, a = 2Common ratio, r = 1/5The sum is then calculated as
S = a/(1 - r)
The equation becomes
S = 2/(1 - 1/5)
Evaluate the difference
S = 2/(4/5)
Express the equation as products
S = 2 * 5/4
Solve the expression
S= 5/2
Hence, the sum of the sum notation ∞Σn=1 2(1/5)^n-1 is S= 5/2
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Answer:
S = 5/2
Thank me later
Using two six-sided number cubes, each labeled with the numbers 1 through 6, event A is rolling a sum less than 6. Which of the following shows the sample space of event A?
{(1, 1), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3)}
{(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1)}
{(1, 1), (1, 2), (1, 3), (1, 5), (2, 1), (2, 2), (2, 3), (3, 1), (3, 3), (4, 1)}
{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (3, 3), (4, 1), (4, 2)}
the sample space is:
{ (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (3, 1), (4, 1), (2, 2), (2, 3), (3, 2)}
Which of the following shows the sample space of event A?Event A is rolling a sum less than 6.
Let's define the possible elements in this experiment as:
(outcome of dice 1, outcome of dice 2)
The outcomes where the sum is less than 6 are:
dice 1 dice 2 sum
1 1 2
1 2 3
1 3 4
1 4 5
2 1 3
3 1 4
4 1 5
2 2 4
3 2 5
2 3 5
So there are 10 outcomes, then the sample space is:
{ (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (3, 1), (4, 1), (2, 2), (2, 3), (3, 2)}
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Answer:
B) {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1)}
Step-by-step explanation:
If the question said less than 6 meaning you have to find all possible solution that are 5 or lower.
However, if the problem said equal or less than 6 then you have to find all possible solution that are 6 or lower.
B option is only option that don't have sum of 6. Therefore, option B is correct.
13
Company A has 800 employees, and it decides to grant each of the employees 50 share options as
part of its new rewards plan. The options are exercisable over 5 years and subject to a 3-year
service condition. The fair value of each option at the grant date is $16. The company estimates
that 80% of its employees will meet the service condition required for receiving the options.
Calculate the total share-based payment expense for Company A assuming that 80% of the
employees actually meet the service condition.
$512,000
$853,333
$341,333
$170,667
Option A. The total share expense that the company would share would be given as 512,000
What is meant by share expense?These are the necessary expenses that are needed for the smooth functioning of a particular business that are not within the confinement of the O and M agreement. It has to do with shared facilities.
How to solve for the share expenseThe total number of the employees that are knwon to satistfy condition are given as
800 * 0.8
= 640
The options that are estmated that would be exercised
This is given as the employees * share option
= 640×50
=32000.
The total shae for the company would be gotten as
= 32000× $16
This gives us $512,000.
Hence it can be concluded that the total share of the company if they have 80 percent meeting the condition is $512000.
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add the two equations, 0.75x+1.5y=40 and −1.5x−1.5y=−60 , to find the value of x .
The value of x in the equation is 26.7
How to solve an equation?0.75x + 1.5y = 40
−1.5x − 1.5y = −60
add both equation to eliminate y .
Therefore,
−1.5x + 0.75x = -0.75x
1.5y + (- 1.5y) = 0
40 + (-60) = -20
Hence,
-0.75x = - 20
divide both sides by -0.75
-0.75x / -0/75 = - 20 / -0.75
x = - 20 / -0.75
x = 26.6666666667
x = 26.7
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Stopyra Incorporated makes a single product—a cooling coil used in commercial refrigerators. The company has a standard cost system in which it applies overhead to this product based on the standard labor-hours allowed for the actual output of the period. Data concerning the most recent year appear below:
Budgeted variable manufacturing overhead $ 28,200
Budgeted fixed manufacturing overhead $ 89,280
Budgeted hours 12,000 labor-hours
Actual production (a) 16,000 units
Standard hours per unit (b) 0.60 labor-hours
Standard hours allowed for the actual production (a) × (b) 9,600 labor-hours
Actual variable manufacturing overhead $ 26,967
Actual fixed manufacturing overhead $ 74,280
Actual hours 8,900 labor-hours
The variable overhead rate variance is:
$6,528 U
$6,528 F
$6,052 U
$6,052 F
The variable overhead rate variance is: c. $6,052 U.
Variable overhead rate varianceFirst step is to calculate variable component of the predetermined overhead rate using this formula
Variable component of the predetermined overhead rate= Budgeted variable manufacturing overhead/Budgeted hours
Let plug in the formula
Variable component of the predetermined overhead rate=$ 28,200/12,000 labor-hours
Variable component of the predetermined overhead rate=$2.35 per labor-hour
Second step is to calculate variable overhead rate variance using this formula
Variable overhead rate variance=(AH×AR)-(AH×SR)
Let plug in the formula
Variable overhead rate variance= $ 26,967- ( 8,900 labor-hours×$2.35 per labor-hour)
Variable overhead rate variance= $ 26,967- $20,915
Variable overhead rate variance= $6,052 U (Unfavorable)
Therefore the variable overhead rate variance is: c. $6,052 U.
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What are the first five terms in the recursive sequence defined by the following? (only one is correct)
a1= 1
a2=1
an= an-2+an-1
a) {1,1,2,3,5}
b) {1,1,0,-1,-1}
c) {2,3,5,8,13}
d) {1,-1,2,-3,5}
Answer:
d 1-12-3-5 is the answer
Help me with this equation, please. (Image Attached)
So, the equation is sin(x + y)/sin(x - y) = (1 + cotxstany)/(1 + cotxtany)
The question has to to with trigonometric identities?
What are trigonometric identities?Trigonometric identities are equations that show the relationship between the trigonometric ratios.
How to solve the equation?Given the equation sin(x + y)/sin(x - y)
Using the trigonometric identities.
sin(x + y) = sinxcosy + cosxsiny andsin(x - y) = sinxcosy - cosxsinySo, sin(x + y)/sin(x - y) = (sinxcosy + cosxsiny)/(sinxcosy + cosxsiny)
Dividing the rnumerator and denominator of ight hand side by sinx, we have
sin(x + y)/sin(x - y) = (sinxcosy + cosxsiny)/sinx/(sinxcosy + cosxsiny)/sinx
sin(x + y)/sin(x - y) = (sinxcosy/sinx + cosxsiny/sinx)/(sinxcosy/sinx + cosxsiny/sinx)
= (cosy + cotxsiny)/(cosy + cotxsiny) (since cosx/sinx = cotx)
Dividing the numerator and denominator of the right hand side by cosy, we have
= (cosy + cotxsiny)/cosy/(cosy + cotxsiny)/cosy
= (cosy/cosy + cotxsiny/cosy)/(cosy/cosy + cotxsiny/cosy)
= (1 + cotxstany)/(1 + cotxtany) [since siny/cosy = tany]
So, sin(x + y)/sin(x - y) = (1 + cotxstany)/(1 + cotxtany)
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What are the potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2?
The potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2 are ±(1, 1/2, 1/3, 1/6, 2, 2/3)
How to determine the potential zeros of the function f(x)?The function is given as:
f(x)=6x^4+ 2x^3 - 4x^2 +2
For a function P(x) such that
P(x) = ax^n +...... + b
The rational roots of the function p(x) are
Rational roots = ± Possible factors of b/Possible factors of a
In the function f(x), we have:
a = 6
b = 2
The factors of 6 and 2 are
a = 1, 2, 3 and 6
b = 1 and 2
So, we have:
Rational roots = ±(1, 2)/(1, 2, 3, 6)
Split the expression
Rational roots = ±1/(1, 2, 3, 6)/ and ±2/(1, 2, 3, 6)
Evaluate the quotient
Rational roots = ±(1, 1/2, 1/3, 1/6, 2, 1, 2/3, 1/3)
Remove the repetition
Rational roots = ±(1, 1/2, 1/3, 1/6, 2, 2/3)
Hence, the potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2 are ±(1, 1/2, 1/3, 1/6, 2, 2/3)
The complete parameters are:
The function is given as:
f(x) = 3x^3 + 2x^2 + 3x + 6
The potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2 are ±(1, 1/2, 1/3, 1/6, 2, 2/3)
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pleaseee helpp
which of the following enequalities would produce the region indicated on the graph below
Answer: C
Step-by-step explanation:
The line [tex]y=x+2[/tex] is shaded below and is solid.
This eliminates all the options except for C.
Fill in the P(X=x) values to give a legitimate probability distribution for the discrete random variable , whose possible values are 0, 1, 3, 4, and 5.
For a probability distribution to be represented, it is needed that P(X = 0) + P(X = 1) = 0.44. Hence one possible example is:
P(X = 0) = 0.40.P(X = 1) = 0.04.What is needed for a discrete random variable to represent a probability distribution?The sum of all the probabilities must be of 1, hence:
P(X = 0) + P(X = 1) + P(X = 3) + P(X = 4) + P(X = 5) = 1.
Then, considering the table:
P(X = 0) + P(X = 1) + 0.15 + 0.17 + 0.24 = 1
P(X = 0) + P(X = 1) + 0.56 = 1
P(X = 0) + P(X = 1) = 0.44.
Hence one possible example is:
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Find the mean and standard deviation for the set of data. {25,16,28,6,30,7,26,20,22}
Answer: 8.7 the mean is 20
Step-by-step explanation:
The quadratic functions shown are written in factored form. The roots of a quadratic function will make the factors equal to 0.
Drag each function to show whether it has roots at x=−2 and x=3, roots at x=2 and x=−3, or neither.
The following classification of quadratic equations is presented below:
x = - 2 and x = 3: h(x) = (x + 2) · (x - 3), k(x) = - 3 · (x + 2) · (x - 3). x = 2 and x = - 3: g(x) = 8 · (x + 3) · (x - 2), m(x) = (x + 3) · (x - 2). Neither: j(x) = (x - 2) · (x - 3)How to classify quadratic equations in terms of its roots
In this problem we have quadratic equations in factored form, whose form is presented below:
y = a · (x - r₁) · (x - r₂) (1)
Where r₁ and r₂ are the roots of the equation and a is the leading coefficient. A value of x is a root if and only if y is zero. Besides, we must located all the quadratic equations according to their roots.
x = - 2 and x = 3
h(x) = (x + 2) · (x - 3)
k(x) = - 3 · (x + 2) · (x - 3)
x = 2 and x = - 3
g(x) = 8 · (x + 3) · (x - 2)
m(x) = (x + 3) · (x - 2)
Neither
f(x) = 3 · (x - 1) · (x + 2)
j(x) = (x - 2) · (x - 3)
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Which expression represents seven less than the product of thirteen times a number, and two squared?
(13x + 22) · 7
7(13x · 22)
7 + 13x + 22
7 + 13x · 22
(13x · 22) − 7
Seven less than the product of thirteen times a number, and two squared is as follows;
(13x × 2²) - 7
How to represent an expression?The expression says seven less than the product of thirteen times a number, and two squared.
Let
the number = x
Hence, the product of thirteen times a number, and two squared is as follows:
13(x)(2²)
Therefore, seven less than the product of thirteen times a number, and two squared is as follows;
(13x × 2²) - 7
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Divide the following polynomial using synthetic division, then place the answer in the proper location on the grid. Write answer in descending powers of x. (x3 + 6x2 + 3x + 1 ) ÷ (x - 2)
When we divide [tex]x^{3} +6x^{2} +3x+1[/tex] by (x-2) we will get the quotient be [tex]x^{2} +8x+19[/tex] and remainder be 39.
Given two expressions be [tex]x^{3} +6x^{2} +3x+1[/tex] and (x-2).
We are required to divide the first expression by second expression.
Division means distributing parts of something. The number which is being divided is known as quotient.Divisor is a number which divides the number.
Expressions refers to the combination of numbers, fractions, coefficients, determinants, indeterminants. It expresses some relationship or show equation of line.
We know that relationship between quotient, divisor, divident and remainder is as under:
Dividend=Divisor*Quotient+Remainder
[tex]x^{3} +6x^{2} +3x+1[/tex]=(x-2)*([tex]x^{2} +8x+19[/tex])+39
Quotient=[tex]x^{2} +8x+19[/tex]
Remainder=39
Hence when we divide [tex]x^{3} +6x^{2} +3x+1[/tex] by (x-2) we will get the quotient be [tex]x^{2} +8x+19[/tex] and remainder be 39.
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What is the best estimated volume of the figure?
can anyone solve this for me with a detailed explanation step by steps and reasoning so i can grasp concepts
The answer is 756 m³.
The formula to find volume is : length × width × height
To estimate, round each dimension to the nearest whole number.
⇒ 12.3 ≅ 12
⇒ 7.2 ≅ 7
⇒ 8.6 ≅ 9
Volume = 12 × 7 × 9
Volume = 84 × 9
Volume = 756 m³
Answer:
The ans to this question is 756 which is Option (B)
Step-by-step explanation:
Estimate volume = rounding every digit
= 12.3 = 12
= 7.2 = 7
= 8.6 = 9
= 12x7x9 = 756
I need help solving this problem!
Answer: A
Step-by-step explanation:
The domain is the range of possible x that doesn't make y impossible to find, in this case, all real numbers work
The range is the range of possible y that doesn't make x impossible to find in the inverse function, in this case, all real numbers work
The answer is A.
As any number can be replaced in place of x for the function y, the domain of the function is All Real Numbers. Since any number can be inputted, the result will also vary accordingly. Hence, the range of the function is All Real Numbers.
This is true for the listed function :
[tex]\boxed {y = \sqrt[3]{x-2} - 5}[/tex]
