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3 years ago

A circle with a circumference of 51 inches to find the area

1 answer:

4 0

$\textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=51 \end{cases}\implies 51=2\pi r\implies \boxed{\cfrac{51}{2\pi }=r} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad \implies A=\pi \left( \cfrac{51}{2\pi } \right)^2\implies A=\cfrac{51^2}{2^2\pi }\implies A\approx 206.98$

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All of the following proportions are equivalent except

shtirl [24]

All are equal except A/D = C/B

I replaced the values with numbers
a=5 b=10 c=50 d=100

10/5=100/50 so it’s not b/a = d/c
5/10=50/100 so it’s not a/b = c/d
5/50 = 10/100 so it’s not a/c = b/d
5/100 is NOT 50/10 so it’s NOT a/d = c/b

8 0

4 years ago

A writer earns 8% of total sales dollars as a commission. If 2000 copies of his book are sold at $14.95 each, how much commissio

Tasya [4]

Answer:

C $2392

Step-by-step explanation:

4 0

3 years ago

A delivery truck drove 39 miles per hour. it took 3 hours to travel between two towns. what is the distance between the two tow

lesya692 [45]

I could be wrong but this is what I think.

D=RT
D=39 (3)
D=117

8 0

3 years ago

23) A backyard has a perimeter of 144m.

german

A) 144/4 = 36 metres per side
b) 18*3 = 54
54+54+18+18= 144 metres

dimensions would be 54 by 18

3 0

3 years ago

The radius of a right circular cone is increasing at a rate of 1.5 in/s while its height is decreasing at a rate of 2.1 in/s. At

givi [52]

Answer:

The volume of the cone is changing at a rate of approximately 8670.796 cubic inches per second.

Step-by-step explanation:

Geometrically speaking, the volume of the right circular cone ( $V$ ), in cubic inches, is defined by the following formula:

$V = \frac{1}{3}\cdot \pi \cdot r^{2}\cdot h$ (1)

Where:

$r$ - Radius, in inches.

$h$ - Height, in inches.

Then, we derive an expression for the rate of change of the volume ( $\dot V$ ), in cubic inches per second, by derivatives:

$\dot V = \frac{1}{3}\cdot \pi \cdot (2\cdot r\cdot h \cdot \dot r + r^{2}\cdot \dot h)$ (2)

Where:

$\dot r$ - Rate of change of the radius, in inches per second.

$\dot h$ - Rate of change of the height, in inches per second.

If we know that $r = 120\,in$ , $\dot r = 1.5\,\frac{in}{s}$ , $h = 107\,in$ and $\dot h = -2.1\,\frac{in}{s}$ , then the rate of change of the volume is:

$\dot V \approx 8670.796\,\frac{in^{3}}{s}$

The volume of the cone is changing at a rate of approximately 8670.796 cubic inches per second.

8 0

3 years ago