PLEASE HELP! I NEED A WRITTEN RESPONSE. WILL GIVE BRAINLIEST

How do you find the surface area of a sphere? What should the label be?

melamori03 [73]

Surface area = 4 pi r^2

where

pi : 3.14 a constant

r : raduis

surface area is the change of volume with respect to raduis

volume = 4/3 pi r^3

dvolume/dr = 4 pi r^2

you can prove the identity with double integration in spherical coordinates or volumes of revolutions and polar coordinates

7 0

4 years ago

A 10 foot ladder is leaning against a wall. Call x the distance from the top of the ladder to the ground, and call y the distanc

liq [111]

$-5.3\:\text{ft/s}$

Step-by-step explanation:

We start by applying the Pythagorean theorem to the ladder, with its length L as the hypotenuse:

$L^2 = 100\:\text{ft}^2 = x^2 + y^2$

where x is the vertical distance from the top of the ladder to the ground and y is the horizontal distance from the bottom of the ladder to the wall. Taking the derivative of the above expression with respect to time, we get

$0 = 2x\dfrac{dx}{dt} + 2y\dfrac{dy}{dt}$

Solving for dx/dt, we get

$\dfrac{dx}{dt} = -\left(\dfrac{y}{x}\right)\dfrac{dy}{dt} = -\left(\dfrac{\sqrt{L^2 - x^2}}{x}\right)\dfrac{dy}{dt}$

We know that

$\dfrac{dy}{dt} = 4\:\text{ft/s}$

when x = 6 ft. So the rate at which the top of the ladder is going down is

$\dfrac{dx}{dt} = -\left(\dfrac{\sqrt{100\:\text{ft}^2 - (6\:\text{ft})^2}}{6\:\text{ft}}\right)(4\:\text{ft/s})$

$\:\:\:\:\:\:\:= -5.3\:\text{ft/s}$

The negative sign means that the distance x is decreasing as y is increasing.

5 0

3 years ago

What is the answer to this problem

Gre4nikov [31]

Baxter ate 1/12, so now the box is 3/4 - 9/12 full. So, (1/12) + (9/12) = 10/12.

10/12 of full box was there before Baxter ate.

8 0

4 years ago

The difference between the observed value of the dependent variable and the value predicted using the estimated regression equat

Elenna [48]

Answer:

For this case we define the dependent variable as Y and the independent variable X. We assume that we have n observations and that means the following pairs:

$(x_1, y_1) ,....,(x_n,y_n)$

For this case we assume that we want to find a linear regression model given by:

$\hat y = \hat m x +\hat b$

Where:

$\hat m$ represent the estimated slope for the model

$\hat b$ represent the estimated intercept for the model

And for any estimation of the dependent variable $\hat y_i , i=1,...,n$ is given by this model.

The difference between the observed value of the dependnet variable and the value predicted using the estimated regression equation is known as residual, and the residual is given by this formula:

$e_i = y_i -\hat y_i , i=1,...,n$

So the best option for this case is:

d. residual

Step-by-step explanation:

For this case we define the dependent variable as Y and the independent variable X. We assume that we have n observations and that means the following pairs:

$(x_1, y_1) ,....,(x_n,y_n)$

For this case we assume that we want to find a linear regression model given by:

$\hat y = \hat m x +\hat b$

Where:

$\hat m$ represent the estimated slope for the model

$\hat b$ represent the estimated intercept for the model

And for any estimation of the dependent variable $\hat y_i , i=1,...,n$ is given by this model.

The difference between the observed value of the dependnet variable and the value predicted using the estimated regression equation is known as residual, and the residual is given by this formula:

$e_i = y_i -\hat y_i , i=1,...,n$

So the best option for this case is:

d. residual

7 0

3 years ago

1.N% of 40 is 10. Solve for N. Just put the number.

Serhud [2]

Step-by-step explanation:

N% of 40=10

N/100×40=10

N=10×100/40=25

2.

60%of homework=45min

1%of homework=45/60=3/4min

100%of homework =3/4 ×100=75 min

7 0

3 years ago