A spherical balloon is inflating with helium at a rate of 6464piπ StartFraction ft cubed Over min EndFraction ft3 min. How fast is the balloon's radius increasing at the instant the radius is 22 ft? How fast is the surface area increasing?

Answers

Answer 1

Answer:

Answer:

the surface area will increase 16 feet per minute

Step-by-step explanation:

Allow me to revise your question for a better understanding.

A spherical balloon is inflating with helium at a rate of 64π Start Fraction ft cubed Over min End Fraction ft3 min. How fast is the balloon's radius increasing at the instant the radius is 2 ft? How fast is the surface area increasing?

My answer:

Given that:

$(dV)/(dt) = 64\pi \frac{\text{ ft}^3}{\text{min}}$ (1)

As we know that, the volume of a spherical balloon can be calculated by using the following formula:

$V = (4)/(3)\pi r^3$ where r is the radius

Substitute V into (1), we have:

$(dV)/(dt) = (d)/(dt)((4)/(3)\pi r^3)\n\n(dV)/(dt) =4\pi r^2(dr)/(dt)$

In this situation, the instant radius is: 2f

So we have:

$64\pi = 4\pi (2)^2(dr)/(dt)\n\n\Rightarrow (dr)/(dt) = 4$

The radius of the balloon is increasing at a rate of 4 feet per minute

The the surface area has the formula as:

SA1 = 4π $r^(2)$

If the radius of the balloon is increasing at a rate of 4 feet per minute, so the

the surface area will increase 16 feet per minute because:

SA2 : 4π $(4r)^(2)$ = 16 (4π $r^(2)$ ) = 16 SA1

Hope it will find you well.

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What are five ways to determine if a quadrilateral is a parallelogram?

Answers

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Find the function h(x) = f(x) - g(x) if f(x) = 3x and g(x) = 32x - 3x.

Answers

f(x)-g(x)
(3x)-(32x-3x)
3x-32x+3x
-26x
h(x)=-26x

Answer:

$h(x) =-26x$

Step-by-step explanation:

Given : $f(x) = 3x$ and $g(x) = 32x - 3x$

To find : $h(x) = f(x) - g(x)$

Solution : Value of $f(x) = 3x$ and $g(x) = 32x - 3x$

$h(x) = f(x) - g(x)$

Put value of f(x) and g(x)

$h(x) =3x-(32x - 3x)$

$h(x) =3x-32x+3x$

$h(x) =6x-32x$

$h(x) =-26x$

Help me please again

Answers

The answer is C.
x=2
y=-30
(2;-30)

Tomas learned that the product of the polynomials (a + b)(a2 – ab + b2) was a special pattern that would result in a sum of cubes, a3 + b3. His teacher put four products on the board and asked the class to identify which product would result in a sum of cubes if a = 2x and b = 1.Which product should Tomas choose?

(2x + 1)(2x2 + 2x – 1)
(2x + 1)(4x3 + 2x – 1)
(2x + 1)(4x2 – 2x + 1)
(2x + 1)(2x2 – 2x + 1)

Answers

This is a simple substitution problem. Clearly the answer here is (2x + 1)(4x2 – 2x + 1). We just have to replace a with 2x and b with 1. The tricky part here is the first term in the second group of terms. 2x is to be squared. Common mistake here is raising the x with 2 and not including the coefficient.

The product that Tomas should choose given that the pattern resulted in a sum of cube is (2x + 1)(4x² – 2x + 1)

Data obtained from the question

Polynomial => (a + b)(a² – ab + b²)
a = 2x
b = 1
Product =?

How to determine the product

(a + b)(a² – ab + b²)

But

a = 2x

b = 1

Substituting the value of a and b, we have

(a + b)(a² – ab + b²)

(2x + 1)[(2x)² – (2x × 1) + 1²]

(2x + 1)(4x² – 2x + 1)

Thus, the product that Tomas should choose is (2x + 1)(4x² – 2x + 1)

Learn more about polynomial:

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Shana sells
t-shirts. It costs Shana $6.50 to buy
each t-shirt. She also pays $150 each
month to rent equipment to add print to the t-shirts.

Shana sells each
t-shirt for $12.

Write an
inequality that can be used to determine the number of t-shirts (T) Shana must
sell each month in order to make a profit for the month.

Answers

12t - (6.50t + 150) > 0 => 5.50t > 150 => t > 150/5.50 => t > 27.27 => t>= 28 t- shirts;

if a one time contribution of $2400 is deposited into an anually compounding account with a 2.9% interest rate, how much will be in the account after 2 years?