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Katyanochek1 [597]
4 years ago
8

Which integer is equivalent to 25 3/2

Mathematics
1 answer:
inna [77]4 years ago
5 0
|25| 3/2
I’m pretty sure ^^
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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 <em>A</em> is <em>altitude</em>

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 <em>B</em> is <em>angle bisector</em>

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

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 <em>D</em> (which corresponds with the circumcenter) is <em>perpendicular bisector.</em>

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

<em><u>First we will find the centre, (a , b): </u></em>

<em><u /></em>a = \frac{3+(-1)}{2} = \frac{2}{2} = 1\\\\b = \frac{-2 + 4}{2} = \frac{2}{2} = 1<em><u /></em>

<em><u>Find radius:</u></em>

Radius, r = \frac{Diameter}{2}

Diameter is the distance between (-1, 4) and (3, -2)

diameter = \sqrt{(x_2 - x_1)^2 +(y_2-y_1)^2} \\\\

             = \sqrt{(3-(-1)^2 + (-2-4)^2} \\\\=\sqrt{16 + 36}\\\\=\sqrt{52}\\\\=\sqrt{4 \times 13}\\\\=2\sqrt{13}    \ units

Therefore , r = \frac{2 \times \sqrt{13} }{2} = \sqrt{13}  \ units

<em><u>Equation of the circle is :  </u></em>

                                 (x - 1)^2 +(y-1)^2 = 13<em><u></u></em>

4 0
3 years ago
In a study to support drug discovery for patients with lung cancer, patients were divided into 3 groups based on the severity of
katrin [286]

Answer:

It is an example of an observational study.

Step-by-step explanation:

4 0
4 years ago
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