Find the inverse of the function g(x)=(x-4)^2+11

Mathematics

1 answer:

dusya [7]3 years ago

4 0

Answer:

y= $\sqrt{x-11} - 4$

Step-by-step explanation:

switch the x and y and solve for y.

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A searchlight is shaped like a parabola. If the light source is located 3 feet from the base along the axis of symmetry and the

Elis [28]

9514 1404 393

Answer:

8√3 ≈ 13.86 ft

Step-by-step explanation:

The light source is usually placed at the focus, so the focus-vertex distance is p=3 ft. The equation for the parabola with its vertex at the origin is ...

y = 1/(4p)x^2

y = 1/12x^2

The opening for some y-value extends ±x from the axis of symmetry, so is a total of 2x in width.

For y=4, the corresponding value of x is ...

4 = 1/12x^2

48 = x^2

√48 = x = 4√3

Then the width of the searchlight opening is ...

2(4√3 ft) = 8√3 ft ≈ 13.86 ft

5 0

3 years ago

The diagram shows a hexagon-shaped tile used for flooring. Each hexagon tile has an area of 18/3 in 2 Find x.

mylen [45]

Answer:

x = 12

Step-by-step explanation:

The hexagonal tile given here is made up of 6 triangles with equal bases and heights.

So, area of hexagonal tile will be equal to 6 times the area of one triangle.

Therefore,

$18 \sqrt{3} = 6 \times \frac{1}{2} \times 2 {( \sqrt{3)} }^{ \frac{x}{12} } . {( \sqrt{3)} }^{ \frac{x}{6} } \\ \\ 18 \sqrt{3} = 6 {( \sqrt{3)} }^{ \frac{x}{12} } . {( \sqrt{3)} }^{ \frac{2x}{12} } \\ \\ \frac{18 \sqrt{3} }{6} = {( \sqrt{3)} }^{ \frac{x}{12} + \frac{2x}{12} } \\ \\ 3 \sqrt{3} = {( \sqrt{3)} }^{ \frac{3x}{12} } \\ \\ 3. {3}^{ \frac{1}{2} } = {3}^{ \frac{3x}{24} } \\ \\ {3}^{1 + \frac{1}{2} } = {3}^{ \frac{x}{8} } \\ \\ {3}^{ \frac{3}{2} } = {3}^{ \frac{x}{8} } \\ (bases \: are \: equal \: so \: exponents \: \\ will \: also \: be \: equal) \\ \implies \frac{3}{2} = \frac{x}{8} \\ \\ x = \frac{3 \times 8}{2} \\ \\ x = 3 \times 4 \\ \\ x = 12$