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vampirchik [111]
3 years ago
8

Hey Can somone please help meeee

Mathematics
1 answer:
Elina [12.6K]3 years ago
3 0

Answer:

7/6 or 1.16 repeating

Step-by-step explanation:

7/8//3/4

7/8 x 4/3

7 x 4/ 8 x 3

7 / 2 x 3=

7/6 or 1.16 repeating

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Consider the function h(x) =x2 – 12x + 58.
alekssr [168]

Answer:

The correct option is;

x ≥ 6; h⁻¹(x) = 6 +√(x - 22)

Step-by-step explanation:

Given the function, h(x) = x² - 12·x + 58

We can write, for simplification;

y = x² - 12·x + 58

Therefore;

When we put x as y to find the inverse in terms of x, we get;

x = y² - 12·y + 58

Which gives;

x - x = y² - 12·y + 58 - x

0 = y² - 12·y + (58 - x)

Solving the above equation with the quadratic formula, we get;

0 = y² - 12·y + (58 - x)

x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}

a = 1, b = -12, c = 58 - x

Therefore;

x = \dfrac{-(-12)\pm \sqrt{(-12)^{2}-4\times (1)\times (58 - x)}}{2\times (1)}= \dfrac{12\pm \sqrt{144-232 + 4 \times x)}}{2}

x =  \dfrac{12\pm \sqrt{4 \times x - 88}}{2} =  \dfrac{12\pm \sqrt{4 \times (x - 22)}}{2}  = \dfrac{12\pm 2 \times \sqrt{ (x - 22)}}{2}

x = \dfrac{12\pm 2 \times \sqrt{ (x - 22)}}{2} = {6 \pm  \sqrt{ (x - 22)}}

We note that for the function, h(x) = x² - 12·x + 58, has no real roots and the real minimum value of y is at x = 6, where y = 22 by differentiation as follows;

At minimum, h'(x) = 0 = 2·x - 12

x = 12/2 = 6

Therefore;

h(6) = 6² - 12×6 + 58 = 22

Which gives the coordinate of the minimum point as (6, 22) whereby the minimum value of y = 22 which gives √(x - 22) is always increasing

Therefore, for x ≥ 6, y or h⁻¹(x) = 6 +√(x - 22)  and not 6 -√(x - 22) because 6 -√(x - 22) is less than 6

The correct option is  x ≥ 6; h⁻¹(x) = 6 +√(x - 22).

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Answer is 3.67 centimeters
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2, 4, 6, 8, 10, 12


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X = ? y = ? 16 45 degrees
mezya [45]

Let's put more details in the figure to better understand the problem:

Let's first recall the three main trigonometric functions:

\text{ Sine }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Hypotenuse}}\text{ Cosine }\theta\text{ = }\frac{\text{ Adjacent Side}}{\text{ Hypotenuse}}\text{ Tangent }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Adjacent Side}}

For x, we will be using the Cosine Function:

\text{ Cosine }\theta\text{ = }\frac{\text{ Adjacent Side}}{\text{ Hypotenuse}}Cosine(45^{\circ})\text{ = }\frac{\text{ x}}{\text{ 1}6}(16)Cosine(45^{\circ})\text{ =  x}(16)(\frac{1}{\sqrt[]{2}})\text{ = x}\text{ }\frac{16}{\sqrt[]{2}}\text{ x }\frac{\sqrt[]{2}}{\sqrt[]{2}}\text{ = }\frac{16\sqrt[]{2}}{2}\text{ 8}\sqrt[]{2}\text{ = x}

Therefore, x = 8√2.

For y, we will be using the Sine Function.

\text{  Sine }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Hypotenuse}}\text{ Sine }(45^{\circ})\text{ = }\frac{\text{ y}}{\text{ 1}6}\text{ (16)Sine }(45^{\circ})\text{ =  y}\text{ (16)(}\frac{1}{\sqrt[]{2}})\text{ = y}\text{ }\frac{16}{\sqrt[]{2}}\text{ x }\frac{\sqrt[]{2}}{\sqrt[]{2}}\text{ = }\frac{16\sqrt[]{2}}{2}\text{ 8}\sqrt[]{2}\text{ = y}

Therefore, y = 8√2.

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1 year ago
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