Find the solutions to x² = 18.
A. x = +6√3
B. x = +2√3
C. x= 13√6
D. x = ±3-√2

Answer:

- 6x³ - 1

Step-by-step explanation:

Substitute x = g(x) into f(x), that is

(f ￮ g)(x)

= f(x³ )

= - 6(x³) - 1

= - 6x³ - 1

To compute the volume of the solid of revolution S, obtained by revolving the bounded region R enclosed by the curve y = x^2(6 - x) and the x-axis about the z-axis, we can use the method of cylindrical shells. The volume of the solid of revolution S is approximately 2440.98 cubic units. First, let's find the limits of integration for x. The curve y = x^2(6 - x) intersects the x-axis at x = 0 and x = 6.

So, the limits of integration for x will be from 0 to 6. Now, let's consider a vertical strip of thickness dx at a given x-value. The height of this strip will be the distance between the curve y = x^2(6 - x) and the x-axis, which is simply y = x^2(6 - x). To find the circumference of the cylindrical shell at this x-value, we use the formula for circumference, which is 2πr, where r is the distance from the axis of revolution to the curve. In this case, the distance from the z-axis to the curve is x, so the circumference is 2πx.

The volume of this cylindrical shell is the product of its circumference, height, and thickness. Therefore, the volume of the shell is given by dV = 2πx * x^2(6 - x) * dx. To find the total volume of the solid of revolution S, we integrate the expression for dV over the limits of x: V = ∫[0 to 6] 2πx * x^2(6 - x) dx.

Simplifying the integrand, we have: V = 2π ∫[0 to 6] x^3(6 - x) dx.

Evaluating this integral will give us the volume of the solid of revolution S. To evaluate the integral V = 2π ∫[0 to 6] x^3(6 - x) dx, we can expand and simplify the integrand, and then integrate with respect to x.

V = 2π ∫[0 to 6] (6x^3 - x^4) dx

Now, we can integrate term by term:

V = 2π [(6/4)x^4 - (1/5)x^5] evaluated from 0 to 6

V = 2π [(6/4)(6^4) - (1/5)(6^5)] - [(6/4)(0^4) - (1/5)(0^5)]

V = 2π [(3/2)(1296) - (1/5)(7776)]

V = 2π [(1944) - (1555.2)]

V = 2π (388.8)

V ≈ 2π * 388.8

V ≈ 2440.98

Therefore, the volume of the solid of revolution S is approximately 2440.98 cubic units.

Learn more about integration here: https://brainly.com/question/31040425

#SPJ11

Step-by-step explanation:

a) angles that share 1 side and are next to each other

<DBA, <ABE

<ABE, <EBC

b) two angles whose measures add to 180°

<ABE, <EBC

<ABD, <DBC

c) two adjacent angles whose noncommon sides lie on a line

<ABE, <EBC

<ABD, <DBC

Answer:

B) AD=AD

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

If x= -2 then replace X with -2

Therefore it is -2 times -2^2

=4^4

=16

True, it is important to exercise caution when making predictions outside of the experimental region.

When using a least squares regression line, we should not predict a value of y unless the given value of x is within the range of the data used to construct the regression model, which is known as the experimental region.

Extrapolating beyond this region may lead to unreliable predictions as the regression model may not hold true outside of the range of the data. Therefore, it is important to exercise caution when making predictions outside of the experimental region.

Learn more about experimental region

brainly.com/question/4680820

#SPJ11

Answer:

111

Step-by-step explanation:

Answer:

111

Step-by-step explanation:

Answer:

12 Square Units

Step-by-step explanation:

It seems that you are referring to the exponential growth formula which is:

N(t) = N₀ * (1 + r)^t

Where:
N(t) is the number of individuals at time t
N₀ is the initial number of individuals (in this case, 25 alive in 1955)
r is the growth rate
t is the time period (in years)

In this problem, we have:
N₀ = 25 individuals (alive in 1955)
N(t) = 500 individuals (existed in 2013)
t = 2013 - 1955 = 58 years

We need to solve for r. To do that, rearrange the formula:

r = [(N(t) / N₀)^(1/t)] - 1

Plug in the given values:

r = [(500 / 25)^(1/58)] - 1

r ≈ 0.029

So, the answer is (d) 0.029.

Learn more about it here:

brainly.com/question/31643371

#SPJ11

After factorising the given expression we have the factors:

a) = 3(x + 4m)

b) = 6h(h + 3a)

Expanding brackets in reverse is a process known as factorising. Fully factorising an expression entails putting it in brackets by eliminating the factors with the highest common denominator.

The easiest method of factoring is:

Factorisation:

a) 3x+12m

= 3(x + 4m)

b) 6h²+18ah​

6h(h + 3a)

Thus, After factorising the given expression we have the factors:

a) = 3(x + 4m)

b) = 6h(h + 3a)

Learn more about factorising

https://brainly.com/question/20293447

#SPJ1

Answer:

C

Step-by-step explanation:

Answer:

I believe that the correct answer is C?

Step-by-step explanation:

Answer:

E

Step-by-step explanation:

Answer: I don't know

Step-by-step explanation:

Mark me as brainiest

Answer:

it's help me ttoo

Step-by-step explanation:

i need help with mathh please im going to fail

The Rule for the dilation is (x, y) → (2x, 2y).

The rule that best represents the dilation applied to Triangle E to create Triangle F is:

(x, y) → (2x, 2y)

This rule shows that the dilation is centered at the origin and has a scale factor of 2, which means that all the coordinates of Triangle E are multiplied by 2 to obtain the corresponding coordinates of Triangle F.

Learn more about Dilation here:

https://brainly.com/question/13176891

#SPJ1

Answer:

x < -3

Step-by-step explanation:

Step 1: Subtract 6 from both sides.

Step 2: Divide both sides by 4.

Therefore, the answer is x < -3.

The interest the customer would pay is $318.78.

Interest can be described as the cost of borrowing. It is the amount of money a borrower has to pay to the lender.

Interest = amount borrowed x interest rate

Daily interest = $2,530.16 x 0.42%

$2,530.16 x 0.0042 = 10.63

Monthly interest = 10.63 x 30 = $318.80

To learn more about interest, please check: https://brainly.com/question/25811386

To prove the identity sinh(2x) = 2 sinh(x) cosh(x), we can use the definitions of sinh(x) and cosh(x) and apply trigonometric identities for exponential functions.

We start with the left-hand side of the identity, sinh(2x). Using the definition of the hyperbolic sine function, sinh(x) = (e^x - e^(-x))/2, we can substitute 2x for x in this expression, giving us sinh(2x) = (e^(2x) - e^(-2x))/2.

Next, we focus on the right-hand side of the identity, 2 sinh(x) cosh(x). Again using the definitions of sinh(x) and cosh(x), we have 2 sinh(x) cosh(x) = 2((e^x - e^(-x))/2)((e^x + e^(-x))/2).

Expanding this expression, we get 2 sinh(x) cosh(x) = (e^x - e^(-x))(e^x + e^(-x))/2.

By simplifying the right-hand side, we have (e^x * e^x - e^x * e^(-x) - e^(-x) * e^x + e^(-x) * e^(-x))/2.

This simplifies further to (e^(2x) - 1 + e^(-2x))/2, which is equal to the expression we derived for the left-hand side.

Hence, we have proved the identity sinh(2x) = 2 sinh(x) cosh(x) by showing that the left-hand side is equal to the right-hand side through the manipulation of the exponential functions.

Learn more about Trignometric Identities here: brainly.com/question/24377281

SPJ11

Answer:

D. –5.2 + (–6.4) = –11.6

Step-by-step explanation:

First, you can eliminate A and C because 5.2 is positive. Since the red arrow is pointing left, it indicates that the number (-5.2) is negative.

Then, you look at the second arrow, the green one. It is pointing left, so it would be -6.4.

I hope this helps :)

Answer:

64 square units

Step-by-step explanation:

All you have to do is multiply 8 by 8 to get 64.

Step-by-step explanation:

the graph is not showing

Answer:

Step-by-step explanation:

Where we have "x" must replace for the number shown on table

We have for "x" tha numbers: 0; 1; 2; 3; 4 and 5

Equation:

1.y = x+4

y = x + 4

For x = 0

y = x + 4

y = 0 + 4

y = 4

For x = 1

y = x + 4

y = 1 + 4

y = 5

For x = 2

y = x + 4

y = 2 + 4

y = 6

For x = 3

y = x + 4

y = 3 + 4

y = 7

For x = 4

y = x + 4

y = 4 + 4

y = 8

For x = 5

y = x + 4

y = 5 + 4

y = 9

So:

x     y

0    4

1     5

2    6

3    7

4    8

5    9

I hope help you.

Taring a kitchen scale before weighing an ingredient is essential to obtain accurate measurements by removing the weight of the container, streamlining the process, and ensuring precise and reliable results in culinary preparations.

Taring a kitchen scale before weighing an ingredient is necessary to accurately measure the weight of the ingredient without including the weight of the container or vessel in which it is placed. Taring essentially resets the scale to zero, accounting for the weight of the container so that only the weight of the ingredient being added is measured.

By taring the scale, you eliminate the need to manually subtract the weight of the container from the final measurement. This allows for more precise and efficient measurements in recipes or other culinary applications.

Taring is particularly important when working with small or precise quantities of ingredients, where even a slight variation in weight can significantly impact the final outcome of a dish. It ensures that the weight of the container does not contribute to the measurement, providing accurate and reliable results.

Additionally, taring simplifies the weighing process by eliminating the need to calculate or estimate the weight of the container separately. It saves time and reduces the chances of errors in measurements, promoting consistency and precision in cooking and baking.

Learn more about baking at: brainly.com/question/20692796

#SPJ11

Answer:

this is impossible

Step-by-step explanation:

Answer: x<1 or x>5

Step-by-step explanation:

|-x+3|>2

-x+3>2

-x+3-3>2-3

-x>-1

x<1

-x+3<-2

-x+3-3<-2-3

-x<-5

x>5

x<1 or x>5

Which of the following pairs of numbers has a least common multiple of 48 ?

A. 3 and 12

C. 4 and 9

D. 6 and 8

-KeonLee

I hope it help

#Carry on learning

To plot this probability on the number line, locate the point that represents the value 0.71.

To calculate the probability that a student likes pizza and has a job, we need to find the intersection of the two events.

To find the probability, we divide the number of students who like pizza and have a job by the total number of students.

Probability

= Number of students who like pizza and have a job / Total number of students

= 12 / (12 + 5)

= 12 / 17

= 0.71

To plot this probability on the number line, locate the point that represents the value 0.71 which is as follow:

-1    0    1

|     |     |

|     |---- |-----|

      0.7  0.71

Learn more about Probability here:

https://brainly.com/question/32004014

#SPJ1

Answer:

Step-by-step explanation:

\(13x^2-16x=x^2-x\\\\13x^2-16x-x^2+x=0\\\\12x^2-15x=0\\{\qquad}^{\div3}\qquad\quad^{\div3}\\4x^2-5x=0\quad\implies\quad a=4\,,\ b=-5\,,\ c=0\\\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-5)\pm\sqrt{(-5)^2-4\cdot4\cdot0}}{2\cdot4}=\dfrac{5\pm\sqrt{25}}8\\\\\\x_1=\dfrac{5+5}8=\dfrac54\,,\qquad x_2=\dfrac{5-5}8=0\)

Answer:

Step-by-step explanation: