Can someone please help me with the following question.

1) The weight of an object above Earth can be modeled by a function of the form w(h)=(r/r+h)^2*"w , where r is the radius of Earth
0"
(approximately 3950 miles)," h" is the distance above Earth's surface, and
"w is the weight of the object on the surface of the Earth.
0"

a) At what height will a 150-pound object weigh 50 pounds?
I used the following:"w = 150 w(h)= 50 r=3950
0"
So I plugged these values into the equation given:
50=(3950/3950 + h)^2*150
and my answer was h= 7900
b) How high would a crow carrying a whelk haveto fly for the whelk's weight to change by 0.1%?

To solve part b) of the question, we need to find the height at which the weight of the whelk changes by 0.1%.

Let's call the weight of the whelk on the surface of the Earth W, and the weight at a height h W'. We are given that the weight of the whelk changes by 0.1%, which means the weight at a height h is 99.9% of the weight on the surface.

Therefore, we can set up the equation as follows:
W' = 0.999 * W

Now let's substitute the values we know into the equation. We are given that the weight of the crow carrying the whelk is 150 pounds, so W = 150. We need to find the height h at which the weight changes by 0.1%, so W' = 0.001 * 150.

Now we can plug these values into the equation and solve for h:
0.001 * 150 = (3950 / (3950 + h))^2 * 150

Simplifying the equation gives us:
0.15 = (3950 / (3950 + h))^2

To remove the square, we can take the square root of both sides of the equation:
√0.15 = 3950 / (3950 + h)

Now we can solve for h by isolating the variable. Multiply both sides by (3950 + h):
√0.15 * (3950 + h) = 3950
√0.15 * 3950 + √0.15 * h = 3950

Subtract √0.15 * 3950 from both sides:
√0.15 * h = 3950 - √0.15 * 3950

Finally, isolate h by dividing both sides by √0.15:
h = (3950 - √0.15 * 3950) / √0.15

Using a calculator, we can find the numerical value of h.

To solve part b) of the problem, we need to find the height at which the whelk's weight changes by 0.1%.

Let's start by setting up the equation using the given formula:

w = (r / (r + h))^2 * w

Where:
w = initial weight of the whelk
r = radius of Earth (approximately 3950 miles)
h = height above Earth's surface

Since we want to find the height at which the weight changes by 0.1%, we can express this as a percentage change:

(Change in weight / Initial weight) = 0.1% = 0.001

Let's call the change in weight Δw:

w - w' = Δw = 0.001 * w

We can now substitute these values into the equation:

0.001 * w = ((r / (r + h))^2 * w) - w

Simplifying the equation, we have:

0.001 * w = (r / (r + h))^2 * w - w

Now, let's solve for h:

0.001 * w + w = (r / (r + h))^2 * w

0.001 * w + w = (r^2 / (r + h)^2) * w

0.001 + 1 = r^2 / (r + h)^2

1.001 = r^2 / (r + h)^2

Now, cross multiply:

r^2 = 1.001 * (r + h)^2

Taking the square root of both sides:

sqrt(r^2) = sqrt(1.001 * (r + h)^2)

r = sqrt(1.001) * (r + h)

Now, let's solve for h:

r - sqrt(1.001) * r = sqrt(1.001) * h

h = (r - sqrt(1.001) * r) / sqrt(1.001)

Substituting the value of r (approximately 3950 miles), we can calculate the height at which the whelk's weight changes by 0.1%:

h = (3950 - sqrt(1.001) * 3950) / sqrt(1.001)

Therefore, the crow carrying the whelk would have to fly at a height of h miles for the whelk's weight to change by 0.1%.