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Mathematics

1 answer:

Verizon [17]2 years ago

8 0

Answer:

$f^{-1}(x)=x^2+1$

Step-by-step explanation:

The inverse of a function is when the x and y are swapped. So the first step is to write f(x) as y and then swap the x and y

Original Equation:

$f(x)=\sqrt{x-1}\\$

write f(x) as y (since that's what it represents)

$y=\sqrt{x-1}$

Swap x and y

$x=\sqrt{y-1}$

Square both sides

$x^2=y-1$

Add 1 to both sides

$x^2+1=y$

So this gives you the equation:

$f^{-1}(x)=x^2+1$

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How to solve number 4

s2008m [1.1K]

Find the first semicircle area
Area semicircle can be determined by dividing the full area of circle by 2.
The first semicircle radius is 5 cm
semicircle area = 1/2 circle area
semicircle area = 1/2 × π × r²
semicircle area = 1/2 × 3.14 × 5²
semicircle area = 1/2 × 3.14 × 25
semicircle area = 39.25 cm²

Find the second semicircle area
Because the dimension of the second semicircle is congruent to the first semicircle, they have similar area measurement, 39.25 cm².

Find the quarter circle area
The area of quarter circle can be determined by dividing the full area of a circle by 4.
q circle = 1/4 × area of circle
q circle = 1/4 × π × r²
q circle = 1/4 × 3.14 × 10²
q circle = 1/4 × 314
q circle = 78.5 cm²

To find the entire area, add the area above together
area = first semicircle + second semicircle + q circle
area = 39.25 + 39.25 + 78.5
area = 157

The area of shaded region is 157 cm²

4 0

4 years ago

20 POINTS. Given cos θ=4/5, find cot(θ).

nydimaria [60]

$\displaystyle\\\cos\theta=\frac{4}{5}\\\\ \sin\theta=\sqrt{1-\cos^2\theta}=\sqrt{1-\left(\frac{4}{5}\right)^2} =\sqrt{1-\frac{16}{25}} =\sqrt{\frac{9}{25}} =\frac{3}{5}~~\text{(If } \theta \in \text{quadrant 1)}}\\\\\\ \cot(\theta)=\frac{\cos\theta}{\sin\theta}=\frac{~~\dfrac{4}{5}~~}{\dfrac{3}{5}}=\frac{4}{5}\times\frac{5}{3}=\frac{4}{3}\\\\\\\boxed{\cot(\theta)=\frac{4}{3}}$