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3 years ago

Find the range of the function.

1 answer:

5 0

The vertex form of a quadratic function is given by
$f(x)=a (x-h)^{2} +k$ , where (h, k) is the vertex of the equation.
In the given function, (h, k) = (2, 2), also a = 1 which is positive, this means that the parabola is facing up, hence the range is given by y ≥ k.
Therefore, range is y ≥ 2.

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Given the information in the picture, which trigonometric identity can be used to solve for the height of the blue ladder that i

Stells [14]

The trigonometric identity can be used to solve for the height of the blue ladder that is leaning against the building is $\rm sin=\dfrac{o}{h}$ .

We have to determine

Which trigonometric identity can be used to solve for the height of the blue ladder that is leaning against the building?.

<h3>Trigonometric identity</h3>

Trigonometric Identities are the equalities that involve trigonometry functions and hold true for all the values of variables given in the equation.

Trig ratios help us calculate side lengths and interior angles of right triangles:

The trigonometric identity that can be used to solve for the height of the blue ladder is;

$\rm Sin47=\dfrac{50}{H}\\\\H=\dfrac{50}{sin47}\\\\H=68 feet$

Hence, the trigonometric identity can be used to solve for the height of the blue ladder that is leaning against the building is $\rm sin=\dfrac{o}{h}$ .

To know more about trigonometric identity click the link given below.

brainly.com/question/1256744

6 0

3 years ago

12-2x=-2(y-x), solve for x

Romashka [77]

Solve: 12 - 2x = -2(y - x)

Steps:

1. Expand -2(y - x): -2y + 2x

12 - 2x = -2y + 2x

2. Then subtract 12 from both sides

12 - 12 - 2x = -2y + 2x - 12

3. Simplify,

-2x = -2y + 2x - 12

4. Then, subtract 2x from both sides

-2x - 2x = -2y + 2x - 2x - 12

5. Simplify,

-4x = -2y - 12

6. Then, divide both sides by -4

-4x/-4 = -2y/-4 - 12/-4

7. Simplify,

x = 1/2y + 3 <======= <em>Answer</em>

Hope this helped!!!!

8 0

3 years ago

PLEASE HELP ME I WILL CHOOSE BRAINLIEST!!!!

kakasveta [241]

Answer:

Exact height = 8*sqrt(3) mm

Approximate height = 13.856 mm

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Explanation:

If you do a vertical cross section of the cylinder, then the 3D shape will flatten into a rectangle as shown in the diagram below.

After flattening the picture, I've added the points A through F

point A is the center of the sphere and cylinder
points B through E are the corner points where the cylinder touches the sphere
point F is at the same horizontal level as point A, and it's on the edge of the cylinder.

Those point labels will help solve the problem. We're told that the radius of the sphere is 8 mm. So that means segment AD = 8 mm.

Also, we know that FA = 4 mm because this is the radius of the cylinder.

Focus on triangle AFD. We need to find the height x (aka segment FD) of this triangle so we can then double it later to find the height of the cylinder. This in turn will determine the height of the bead.

------------------------------

As the hint suggests, we'll use the pythagorean theorem

a^2 + b^2 = c^2

b = sqrt(c^2 - a^2)

x = sqrt(8^2 - 4^2)

x = sqrt(48)

x = sqrt(16*3)

x = sqrt(16)*sqrt(3)

x = 4*sqrt(3)

This is the distance from D to F

The distance from D to E is twice that value, so DE = 2*(FD) = 2*4*sqrt(3) = 8*sqrt(3) is the exact height of the bead (since it's the exact height of the cylinder).

Side note: 8*sqrt(3) = 13.856 approximately.