Three married couples attend a football game. In how many ways can they be seated in six seats in a row if all the men are seated together and all the women are seated together?6!
20
120
72

Answers

Answer 1
Answer: 6 bc there is only 6 people and 1 row
Answer 2
Answer: 6 bc thier is one row and six people


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What are the possible values of x in 6x^2 + 432 = 0

Literal equation
R=R1+R2 for R2

Answers

so
R=R1+R2
subtract R1 from both sides
R-R1=R2

A paint can has a radius of 4 inches and a height of 15 inches. What is the volume of the paint can? Round to the nearesttenth. Use 3.14 fors
cubic inches
Mark this and retun
JE
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Answers

Answer:

3.14 * 4^2 *15 = 753.6

Step-by-step explanation:

pi * r^2 * height

1. Use the figure below to answer the questions. Give the coordinates for the original points and the points after the given transformation is performed on the original coordinate.

Answers

Answer:

G'(-4, -3)

G'(3, 4)

G'(-8, 6)

Step-by-step explanation:

Coordinates of the original point G on the graph → (-4, 3)

When the point G is reflected over the x-axis,

Rule to be followed fro the reflection,

(x, y) → (x, -y)

By this rule image of the point G will be,

G(-4, 3) → G'(-4, -3)

Rule for the rotation by 90° clockwise,

(x, y) → (y, -x)

G(-4, 3) → G'(3, 4)

Rule for the translation of 4 units left and 3 units up,

(x, y) → [(x - 4), (y + 3)]

G(-4, 3) → [(-4 - 4), (3 + 3)]

            → (-8, 6)

How many solutions are there to the equation 12x 6=5x

Answers

I'm pretty sure the answer would be 1, since it does look linear

Please help


(x) = x2. What is g(x)?

Answers

The answer is A-g(x)=-x^2-4

For what values of r does the function y = erx satisfy the differential equation y'' + 5y' + 6y = 0?

Answers

Answer:

\huge\boxed{r=-2,-3}

Step-by-step explanation:

To solve for the values of r where the differentialequationy'' + 5y' + 6y = 0 is satisfied by the function y=e^(rx), we first need to find the first and second derivatives of y with respect to x, treating r as a constant.

\left[\frac{}{}y\frac{}{}\right]'=\left[\frac{}{}e^(rx)\frac{}{}\right]'

↓ applying the chain rule to the right side:   \displaystyle \left[\frac{}{}f(x)^a\frac{}{}\right]' = a \cdot f(x)^((a\, -\, 1)) \cdot f'(x) where f(x) = e^x and a = r

y'=r\cdot e^((rx \,-\, 1)) \cdot e^x

↓ simplifying using the exponentbaseproduct rule:   x^a \cdot x^b = x^((a \, +\, b))

y' = re^(\left[(rx \,-\, 1)\, +\, 1\right])

\boxed{y' = re^(rx)} \ \ \leftarrow \ \ \text{first derivative}

─────────────────────────────────

↓ taking the derivative of y with respect to x

y'' = \left[\frac{}{} re^(rx)\frac{}{}\right]'

takingout the constant (r) on the right side

y'' = r\left[\frac{}{} e^(rx)\frac{}{}\right]'

↓ simplifying by substituting in the first derivative

y'' = r \cdot y'

y'' = r \cdot re^(rx)

\boxed{y'' = r^2e^(rx)} \ \ \leftarrow \ \ \text{second derivative}

Now, we can plug these derivative expressions into the differential equation and solvefor r.

y'' + 5y' + 6y = 0

pluggingin the derivativeexpressions (think of y as the zeroth derivative of itself)

r^2e^(rx) + 5(re^(rx)) + 6(e^(rx)) = 0

factoringoute^(rx) from the left side

e^(rx)(r^2 + 5r + 6) = 0

factoring the second-degree polynomial factor

e^(rx)(r + 2)(r + 3) = 0

splitting into 3 equations using the zero product property: \text{If } ABC = 0,\text{ then } A=0\text{ or }B=0\text{ or }C=0.

First Equation

e^(rx)=0

↓ taking the natural log of both sides

rx = \ln(0)

\implies \text{un}\text{de}\text{fi}\text{ne}\text{d}

Second Equation

r+2=0

subtracting 2 from both sides

\huge\boxed{r=-2}

Third Equation

r+3=0

subtracting 3 from both sides

\huge\boxed{r=-3}