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3 years ago

Find the volume of the hemisphere in the figure. Use the volume formula and 3.14 for π .

Mathematics

1 answer:

sergejj [24]3 years ago

5 0

Formula for a sphere is V = (4 ⁄ 3) π r^3

The picture shown showed the diameter.

Half of a diameter is the radius.

The radius is 2.95 yd.

Let’s plug in the values into the formula.

V = (4/3) 3.14 (2.95)^3

V = 107.48

NOW THATS THE ANSWER FOR A WHOLE SPHERE BUT YOURE LOOKING FOR THE HEMISPHERE.

So let’s divide that in half:

107.48/2 = 53.74

Your answer is B.) 53.74 yd

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HELP PLZZ Select the correct answer.

stira [4]

Answer:

none

Step-by-step explanation:

There is not a given angle side angle or a side angle side (no two angles and no two sides) so no to the first two.

HL includes two given side, which one must be the hypotenuse, and a right angle so no to that one.

6 0

2 years ago

Solve y ' ' + 4 y = 0 , y ( 0 ) = 2 , y ' ( 0 ) = 2 The resulting oscillation will have Amplitude: Period: If your solution is A

Vlad [161]

Answer:

$y(x)=sin(2x)+2cos(2x)$

Step-by-step explanation:

$y''+4y=0$

This is a homogeneous linear equation. So, assume a solution will be proportional to:

$e^{\lambda x} \\\\for\hspace{3}some\hspace{3}constant\hspace{3}\lambda$

Now, substitute $y(x)=e^{\lambda x}$ into the differential equation:

$\frac{d^2}{dx^2} (e^{\lambda x} ) +4e^{\lambda x} =0$

Using the characteristic equation:

$\lambda ^2 e^{\lambda x} + 4e^{\lambda x} =0$

Factor out $e^{\lambda x}$

$e^{\lambda x}(\lambda ^2 +4) =0$

Where:

$e^{\lambda x} \neq 0\\\\for\hspace{3}any\hspace{3}\lambda$

Therefore the zeros must come from the polynomial:

$\lambda^2+4 =0$

Solving for $\lambda$ :

$\lambda =\pm2i$

These roots give the next solutions:

$y_1(x)=c_1 e^{2ix} \\\\and\\\\y_2(x)=c_2 e^{-2ix}$

Where $c_1$ and $c_2$ are arbitrary constants. Now, the general solution is the sum of the previous solutions:

$y(x)=c_1 e^{2ix} +c_2 e^{-2ix}$

Using Euler's identity:

$e^{\alpha +i\beta} =e^{\alpha} cos(\beta)+ie^{\alpha} sin(\beta)$

$y(x)=c_1 (cos(2x)+isin(2x))+c_2(cos(2x)-isin(2x))\\\\Regroup\\\\y(x)=(c_1+c_2)cos(2x) +i(c_1-c_2)sin(2x)\\$

Redefine:

$i(c_1-c_2)=c_1\\\\c_1+c_2=c_2$

Since these are arbitrary constants

$y(x)=c_1sin(2x)+c_2cos(2x)$

Now, let's find its derivative in order to find $c_1$ and $c_2$

$y'(x)=2c_1 cos(2x)-2c_2sin(2x)$

Evaluating $y(0)=2$ :

$y(0)=2=c_1sin(0)+c_2cos(0)\\\\2=c_2$

Evaluating $y'(0)=2$ :

$y'(0)=2=2c_1cos(0)-2c_2sin(0)\\\\2=2c_1\\\\c_1=1$

Finally, the solution is given by:

$y(x)=sin(2x)+2cos(2x)$

5 0

3 years ago

What is the value of x?<br> 33<br> 65<br> C=?

loris [4]

Answer:

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Two ropes, AD and BD, are tied to a peg on the ground at point D. The other ends of the ropes are tied to points A and B on a fl

Arlecino [84]

Answer:

A. 3.66 feet

Step-by-step explanation:

Using trigonometry, we know that ...

BC = DC·tan(30°)

AC = DC·tan(45°)

AB = AC -BC = DC(tan(45°) -tan(30°))

AB = 5√3·(1 -√3/3) = 5(√3 -1)

AB ≈ 3.66 . . . feet

8 0

3 years ago

Kenny bought a new car stereo that cost $220, but he had a coupon for a 14% discount. How much did Kenny pay for the car stereo.

jok3333 [9.3K]

Answer:

189,2$

Step-by-step explanation:

220*0,86=189,2

14% = 14/100 = 0,14

1-0,14 = 0,86

price* factor between 0 and 1, 0 -> item is free, 1 -> full price

7 0

2 years ago

Read 2 more answers