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2 years ago

Determine the equation of the graph shown y = a(x - h)^2 + k

Mathematics

1 answer:

LUCKY_DIMON [66]2 years ago

4 0

Answer:

$y=-(x+1)^2+4$

Step-by-step explanation:

we know that

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

Is the equation of a vertical parabola written in vertex form

where

(h,k) is the vertex

a is the leading coefficient

In this problem we have

The vertex is the point (-1,4)

$(h,k)=(-1,4)$

substitute

$y=a(x+1)^2+4$

Find the value of a

we have the ordered pair (0,3)

substitute the value of x and the value of y in the quadratic equation and solve for a

$3=a(0+1)^2+4$

$3=a+4\\a=3-4\\a=-1$

therefore

$y=-(x+1)^2+4$

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Can one of y’all help me with this pls

Dafna11 [192]

Answer:

d. 42

Step-by-step explanation:

PEDMAS

We do brackets first, so:

4 + 4 = 8

Then multiplication,

5 x 8 = 40

Then addition

40 + 2 = 42

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2 years ago

Read 2 more answers

Hi! how do i find surface area of a cylinder? for some reason i can’t get the right answer

asambeis [7]

$SA=2\pi r^2+2\pi rh$

Use the formula above to find the surface area of a cylinder.

For the given cylinder the given data is the height (6mi) and diameter (16mi), use the diameter to find the radius:

$\begin{gathered} r=\frac{d}{2} \\ \\ r=\frac{16mi}{2}=8mi \end{gathered}$

Surface area:

$\begin{gathered} SA=2\pi(8mi)\placeholder{⬚}^2+2\pi(8mi)(6mi) \\ SA=128\pi mi^2+96\pi mi^2 \\ SA=224\pi mi^2 \end{gathered}$ Then, the surface area of the given cylinder is: 224π square miles

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4 months ago

What is 45.908 divided by 300.6?

raketka [301]

45.908 / 300.6 = 0.152721224
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3 years ago

The length of the diagonal of a wooden cube is 24 cm. The cube is cut into the cylinder of the

jek_recluse [69]

The biggest possible volume of the cylinder will be $2089.497\hspace{1mm}\text{cm}^3$ .

<h3>What will be the diameter and height of the cylinder obtained from a cube and what are the formulas for the diagonal of a cube and the volume of a cylinder?</h3>

If a cylinder with the biggest possible volume is cut inside the cube, the height of the cylinder and the diameter of the cylinder will be equal to the side length of the cube.
For example, consider the following figure in which the cylinder is cut inside of the cube and since the side length of the cube is $x$ , the diameter and the height of the cylinder are also $x$
If the side length of a cube is $x$ unit, then its diagonal will be $x\sqrt{3}$ unit.
The formula for the volume of a cylinder is $V=\pi r^2h$ , where $r$ is the radius and $h$ is the height of the cylinder. If $d$ is the diameter, then $r=\frac{d}{2}$ .

Now, given that the diagonal of the cube is $24$ cm. So, if the side length of the cube is $x$ cm, then we must have

$x\sqrt{3}=24\\\Longrightarrow x=\frac{24}{\sqrt{3}}\\\Longrightarrow x=8\sqrt{3}$

Thus, the side length of the cube is $8\sqrt{3}$ cm.

So, the height of the cylinder with maximum volume will be $h=8\sqrt{3}$ cm and the diameter will be $d=8\sqrt{3}$ cm i.e. the radius will be $r=\frac{d}{2}=\frac{8\sqrt{3}}{2}=4\sqrt{3}$ cm.