All categories

3 years ago

The radius of a sphere-shaped balloon increases at a rate of 2 centimeters (cm) per second. If the surface area of

Mathematics

1 answer:

djverab [1.8K]3 years ago

5 0

Answer:

7 seconds

Step-by-step explanation:

The radius of a sphere-shaped balloon increases at a rate of 2 centimeters (cm) per second.

surface area of the completely inflated balloon is 784 cm²

SA=4r²

784= 4r²

784/4= r²

196 = r²

14cm = r

Yhe radius of the complete inflated balloon is 14cm

If the ball inflate at the rate of 2 cm per seconds

Then it took 14/2 = 7 seconds to inflate fully

You might be interested in

8a+6ab+5b,-6a-ab-8b and - 4a+2ab+3b<br><br>Pls answer this question

suter [353]

Answer:

4 a+8 ab+8b

Step-by-step explanation:

8 a-4 a+6ab+2ab+5 b+3 b

4 a+8 ab+8b

6 0

3 years ago

A small rocket is fired from a launch pad 10 m above the ground with an initial velocity left angle 250 comma 450 comma 500 righ

jonny [76]

Let $\vec r(t),\vec v(t),\vec a(t)$ denote the rocket's position, velocity, and acceleration vectors at time $t$ .

We're given its initial position

$\vec r(0)=\langle0,0,10\rangle\,\mathrm m$

and velocity

$\vec v(0)=\langle250,450,500\rangle\dfrac{\rm m}{\rm s}$

Immediately after launch, the rocket is subject to gravity, so its acceleration is

$\vec a(t)=\langle0,2.5,-g\rangle\dfrac{\rm m}{\mathrm s^2}$

where $g=9.8\frac{\rm m}{\mathrm s^2}$ .

a. We can obtain the velocity and position vectors by respectively integrating the acceleration and velocity functions. By the fundamental theorem of calculus,

$\vec v(t)=\left(\vec v(0)+\displaystyle\int_0^t\vec a(u)\,\mathrm du\right)\dfrac{\rm m}{\rm s}$

$\vec v(t)=\left(\langle250,450,500\rangle+\langle0,2.5u,-gu\rangle\bigg|_0^t\right)\dfrac{\rm m}{\rm s}$

(the integral of 0 is a constant, but it ultimately doesn't matter in this case)

$\boxed{\vec v(t)=\langle250,450+2.5t,500-gt\rangle\dfrac{\rm m}{\rm s}}$

and

$\vec r(t)=\left(\vec r(0)+\displaystyle\int_0^t\vec v(u)\,\mathrm du\right)\,\rm m$

$\vec r(t)=\left(\langle0,0,10\rangle+\left\langle250u,450u+1.25u^2,500u-\dfrac g2u^2\right\rangle\bigg|_0^t\right)\,\rm m$

$\boxed{\vec r(t)=\left\langle250t,450t+1.25t^2,10+500t-\dfrac g2t^2\right\rangle\,\rm m}$

b. The rocket stays in the air for as long as it takes until $z=0$ , where $z$ is the $z$ -component of the position vector.

$10+500t-\dfrac g2t^2=0\implies t\approx102\,\rm s$

The range of the rocket is the distance between the rocket's final position and the origin (0, 0, 0):

$\boxed{\|\vec r(102\,\mathrm s)\|\approx64,233\,\rm m}$

c. The rocket reaches its maximum height when its vertical velocity (the $z$ -component) is 0, at which point we have

$-\left(500\dfrac{\rm m}{\rm s}\right)^2=-2g(z_{\rm max}-10\,\mathrm m)$

$\implies\boxed{z_{\rm max}=125,010\,\rm m}$

7 0

3 years ago

Which points are on the graph of the function rule f(x) = 10 – 4x?

kondor19780726 [428]

(–2, 18), (0, 10), (2, 2)

8 0

3 years ago

Read 2 more answers

Corey spent 20% of his savings on a printer at Louie's ElectronisHow much did Corey have in his savings account before he bought

Crank

(printer cost) = 0.20 * (savings)
(printer cost)/0.20 = (savings)

savings = 5*(printer cost)

Whatever the cost of the printer was (information not supplied here), Corey's savings was 5 times that amount.

5 0

3 years ago

Suppose you just received a job offer with a starting salary of $37,000 per year and a guaranteed raise of $1500 per year. How m

Taya2010 [7]

Based on the given description above, here is how we are going to solve it.
Let n be the number of years. So the equation will be like this.
37000n + 1500n = 1025000
Now let us solve for n.
38500n = 1025000 <<<divide by sides by 38500 and the result is
n=26.62
Therefore, it will take 26 years and 6 months before you made a total salary of 1,025,000 dollars. Hope that this answer helps.

8 0

2 years ago

Read 2 more answers