Find the angle between the given vectors to the nearest tenth of a degree.

If r = 8 units and h = 10 units, what is the volume of the cylinder shown above? use 3.14 for pi,

Basile [38]

I hope this helps you

Volume =pi.r^2.h

Volume =3,14.8^2.10

Volume =31,4.64

Volume =200,96

8 0

2 years ago

Y=-1/3x^2-4x-5 in vertex form

grigory [225]

Answer:

$Y=-\frac{1}{3}(x+6)^2+7$ [Vertex form]

Step-by-step explanation:

Given function:

$Y=-\frac{1}{3}x^2-4x-5$

We need to find the vertex form which is.,

$y=a(x-h)^2+k$

where $(h,k)$ represents the co-ordinates of vertex.

We apply completing square method to do so.

We have

$Y=-\frac{1}{3}x^2-4x-5$

First of all we make sure that the leading co-efficient is =1.

In order to make the leading co-efficient is =1, we multiply each term with -3.

$-3\times Y=-3\times\frac{1}{3}x^2-(-3)\times4x-(-3)\times 5$

$-3Y=x^2+12x+15$

Isolating $x^2$ and $x$ terms on one side.

Subtracting both sides by 15.

$-3Y-15=x^2+12x-15-15$

$-3Y-15=x^2+12x$

In order to make the right side a perfect square trinomial, we will take half of the co-efficient of $x$ term, square it and add it both sides side.

square of half of the co-efficient of $x$ term = $(\frac{1}{2}\times 12)^2=(6)^2=36$

Adding 36 to both sides.

$-3Y-15+36=x^2+12x+36$

$-3Y+21=x^2+12x+36$

Since $x^2+12x+36$ is a perfect square of $(x+6)$ , so, we can write as:

$-3Y+21=(x+6)^2$

Subtracting 21 to both sides:

$-3Y+21-21=(x+6)^2-21$

$-3Y=(x+6)^2-21$

Dividing both sides by -3.

$\frac{-3Y}{-3}=\frac{(x+6)^2}{-3}-\frac{21}{-3}$

$Y=-\frac{1}{3}(x+6)^2+7$ [Vertex form]

8 0

3 years ago

Which ordered pair represents the y-intercept of the graph of the equation y = -3x - 9?

Mnenie [13.5K]

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Equation
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y = -3x - 9

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Option 1
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If I substitute x = -9, I should get y = 0

When x = -9
y = -3 (-9) - 9
= 18 (I did not get 0, wrong)

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Option 2
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If I substitute x = -3, I should get y = 0
y = -3(-3) - 9
y = 9 - 9
y = 0 (Yes, I got 0, correct)

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Option 3
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If I substitute x = 0, I should get y = -3
y = -3 (0) - 9
y = 0 - 9
y = -9 (I did not get -3, wrong)

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Option 4
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If I substitute x = 0, I should get y = -9
y = -3 (0) - 9
y = 0 - 9
y = -9 (Yes, I got -9, correct)

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Answer: (-3, 0) and (0, 9) are ordered pairs of the equation (Answer B, D)
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7 0

3 years ago

What is the solution to the following system?

notsponge [240]

Answer:

the answer is c (2,1,0)

Step-by-step explanation:

4 0

3 years ago

What is the value of x in the equation x – y = 30, when y = 15?

slamgirl [31]

Since −y does not contain the variable to solve for, move it to the right side of the equation by adding y to both sides.x=y+30

5 0

3 years ago