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3 years ago

the lateral area of a cylinder is 325 pi in2 the radius is 13 in find the following Volume. surface area

1 answer:

5 0

Volume: 2112.5π
Surface Area: 663π

First, let's find the height of the cylinder. Using the formula for lateral surface area, 2*π*r*h:

2*π*13*h = 325π
(divide π by both sides)
26h = 325
h = 12.5 in.

Next, let's solve the surface area of the cylinder using the formula π*r²*h.

π * 13² * 12.5 = π * 169 * 12.5 = 2112.5π.

Next, let's solve the surface area using the formula 2πrh + 2πr².

(2 * π * 13 * 12.5) + (2 * π * 13²) = 325π + 338π = 663π.

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LA plane is trying to travel 250 miles at a bearing of 20° E of S, however, it ends 230 miles away from the

Semmy [17]

Answer:

The wind pushed the plane $65.01$ miles in the direction of $45.56 ^{\circ}$ East of North with respect to the destination point.

Step-by-step explanation:

Let origin, O, br the starting point and point D be the destination at 250 miles at a bearing of 20° E of S, but due to wind let D' be the actual position of the plane at 230 miles away from the starting point in the direction of 35° E of South as shown in the figure.

So, we have |OD|=250 miles and |OD'|=230 miles.

Vector $\overrightarrow{DD'}$ is the displacement vector of the plane pushed by the wind.

From figure, the magnitude of the required displacement vector is

$|DD'|=\sqrt{|AB|^2+|PQ|^2}\;\cdots(i)$

and the direction is $\alpha$ east of north as shown in the figure,

$\tan \alpha=\frac{|PQ|}{|AB|}\;\cdots(ii)$

From the figure,

$|AB|=|OA-OB|$

$\Rightarrow |AB|=|OD\cos 20 ^{\circ}-OD'\cos 35 ^{\circ}|$

$\Rightarrow |AB|=|250\cos 20 ^{\circ}-230\cos 35 ^{\circ}|$

$\Rightarrow |AB|=45.52$ miles

Again, $|PQ|=|OP-OQ|$

$\Rightarrow |PQ|=|OD\sin 20 ^{\circ}-OD'\sin 35 ^{\circ}|$

$\Rightarrow |PQ|=|250\sin 20 ^{\circ}-230\sin 35 ^{\circ}|$

$\Rightarrow |PQ|=46.42$ miles

Now, from equations (i) and (ii), we have

$|DD'|=\sqrt{|45.52|^2+|46.42|^2}=65.01$ miles, and

$\tan \alpha=\frac{|46.42|}{|45.52|}$

$\alpha=\tan^{-1}\left(\frac{|46.42|}{|45.52|}\right)=45.56 ^{\circ}$

Hence, the wind pushed the plane $65.01$ miles in the direction of $45.56 ^{\circ}$ E astof North with respect to the destination point.

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2 years ago

What is the value of c?<br><br> Enter your answer in the box.

Leya [2.2K]

C^2 = 10^2 + 24^2
c^2 = 100 + 576
c^2 = 676
c = 26

8 0

2 years ago

Negative 12 - negative 50

seraphim [82]

Answer:

Step-by-step explanation:

if you're asking what (-12)-(-50) is the answer is 38 simple method to remember is KCF or KFC same thing just worded differently but it means keep change flip! hope that helped have a great day!!

5 0

2 years ago

Convert 6 x 10 to the power of 5 into standard form

WINSTONCH [101]

First let's write it out with just numbers

6× $10^{5}$

Now solve!

Solve exponent first

10^5 = 100,000

Now multiply

6 x 100,000 = 600,000

600,000 is your answer

6 0

3 years ago

Please help I would reall6 appreciate it

madreJ [45]

Help with what? Have a question or a picture to show?

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3 years ago