Six rectangles each with a common base width of 2

Find the equation of the line tangent to the graph of

garik1379 [7]

Answer:

$\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}$

Step-by-step explanation:

We want to find the equation of the line tangent to the graph of:

$\displaystyle y=\sin^{-1}\big(\frac{x}{5}\big)\text{ at } x=\frac{5}{2}$

So, we will find the derivative of our equation first. Applying the chain rule, we acquire that:

$\displaystyle y^\prime=\frac{1}{\sqrt{1-(\frac{x}{5})^2}}\cdot\frac{1}{5}$

Simplify:

$\displaystyle y^\prime=\frac{1}{5\sqrt{1-\frac{x^2}{25}}}$

We can factor out the denominator within the square root:

$\displaystyle y^\prime =\frac{1}{5\sqrt{\frac{1}{25}\big(25-x^2)}}$

Simplify:

$\displaystyle y^\prime=\frac{1}{\sqrt{25-x^2}}$

So, we can find the slope of the tangent line at x = 5/2. By substitution:

$\displaystyle y^\prime=\frac{1}{\sqrt{25-(5/2)^2}}$

Evaluate:

$\displaystyle y^\prime=\frac{1}{\sqrt{75/4}}=\frac{1}{\frac{5\sqrt{3}}{2}}=\frac{2\sqrt{3}}{15}$

We will also need the point at x = 5/2. Using our original equation, we acquire that:

$\displaystyle y=\sin^{-1}(\frac{1}{2})=\frac{\pi}{6}$

So, a point is (5/2, π/6).

Finally, by using the point-slope form, we can write:

$\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}(x-\frac{5}{2})$

Distribute:

$\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}x+\frac{-\sqrt{3}}{3}$

Isolate. Hence, our equation is:

$\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}$

7 0

3 years ago

Brad bought a piece of industrial real estate for $192,345. The value of the real estate appreciated a constant rate per year. T

Zanzabum

Answer:

D. f(t) = 192,345(1.04)^t

Step-by-step explanation:

I took the test and it was right.

Also that is the original price and when you look at exponential functions, the starting point or original price is always first the then rate of increase. The table just shows how it increased in year 1 and 2.

Hope this helps. :)

4 0

3 years ago

Simplify the following expression:

Setler [38]

Answer:

-7 + 8 m + 4 n thus A. is your Answer

Step-by-step explanation:

Expand the following:

-(-8 m - 4 n + 7)

-(7 - 8 m - 4 n) = -7 - -8 m - -4 n:

-7 - -8 m - -4 n

-(-8) = 8:

-7 + 8 m - -4 n

-(-4) = 4:

Answer: -7 + 8 m + 4 n

5 0

4 years ago

A line passes through the point (0,1) and has a positive slope. Which of these points could that line NOT pass through?

Maksim231197 [3]

Answer:

(-3, 1)

(5,-2)

Step-by-step explanation:

8 0

4 years ago

Math!!! help!!! will give brainliest to correct answer

My name is Ann [436]

x=8

Step-by-step explanation:

move the +2 to the right side so it can be subtracted by the 5 to get 3. after that you square both sides of the equation to get rid of the square root symbol. then move the -7 to the right side and add it with 9. then you'll have 2x=16. then divide both sides by 2 to get x by its self and you are left with x =8

5 0

3 years ago