Which integer is equivalent to 25 3/2

the radius of a sheridan balloon is increasing at a rate of 3 centimeters per minute. how fast is the volume changing when the r

san4es73 [151]

The volume of the balloon is $2352\pi cc/min$

Explanation:

The radius of the balloon is increasing at a rate of 3 cm/min.

To determine the volume of the balloon when the radius is 14 cm, we shall use the formula $V=\frac{4}{3} \pi r^3$

The rate of change of r with respect to time t is given by,

$\frac{d}{d t}(r)=3 \mathrm{cm} / \mathrm{minute}$

Now, we shall determine the $\frac{d}{d t}(V)$

$\begin{aligned}\frac{d}{d t}(V) &=\frac{d}{d t}\left(\frac{4}{3} \pi r^{3}\right) \\&=\frac{4}{3} \pi\left(3 r^{2}\right)\frac{d}{d t}(r) \\&=4 \pi r^{2}\frac{d}{d t}(r)\end{aligned}$

Now, we shall determine the $\frac{d}{d t}(V)$ at $r=14 \mathrm{cm}$ and substituting $\frac{d}{d t}(r)=3 \mathrm{cm} / \mathrm{minute}$ , we get,

$\begin{aligned}\left(\frac{d V}{d t}\right)_{r=14} &=4 \pi r^{2} \frac{d}{d t}(r)\\&=4 \pi(14)^{2} (3)\\&=4 \pi 196 (3)\\&=2352\end{aligned}$

Thus, The volume of the balloon is $2352\pi cc/min$

7 0

3 years ago

#2 and #3 please. I'm lost

Dennis_Churaev [7]

Alternate means it will be across and on the opposite side, there for the alternate interior angle for 2 would be the same number as the function you're solving.
For example: if you're going to find the alternate interior of 17x+9, it will be 17x+9, the angle on the lower right hand side of the top parallel line.

5 0

3 years ago

1. Match the letter of the centre to the lines that define it.

denis-greek [22]

Answer:

A. (Orthocenter) → Altitude

B. (Incenter) → Angle bisector

C. (Centroid) → Median

D. (Circumcenter) → Perpendicular bisector

Step-by-step explanation:

A. The orthocenter is the point of concurrency of the three altitudes of a triangle, therefore, the matching line with the letter A is altitude

B. The incenter is the point of concurrency of the bisectors of three interior angles of a triangle, therefore, the matching line with the letter B is angle bisector

C. The centroid is the point of concurrency of the three medians of the triangle, therefore, the matching line to the letter C is median

D. The circumcenter is the point of concurrency of the three perpendicular bisectors of the three sides of a triangle, therefore, the matching line to the letter D (which corresponds with the circumcenter) is perpendicular bisector.

3 0

3 years ago

If (-1,4) and (3,-2) are end points of diameter of the circle, then the equation of the circle is

Volgvan

Answer:

If you've more doubts you can ask :)

Step-by-step explanation:

If the centre of a circle is (a, b) and radius r, then the equation of the circle is :

$(x - x)^2 + (y-b)^2 = r^2$