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3 years ago

I need help please I don’t understand

Mathematics

1 answer:

Leya [2.2K]3 years ago

3 0

Answer:

Step-by-step explanation:

180 = ∠BAC + 52 +62

66 = ∠BAC

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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 <em>x</em> = 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 <em>x</em> = 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

In the diagram, a circle centered at the origin, a right triangle, and the Pythagorean theorem are used to derive the equation o

ehidna [41]

Answer:

(x – h)2 + (y – k)2 = r2

Step-by-step explanation:

If the center of the circle were moved from the origin to the point (h, k) and point P at (x, y) remains on the edge of the circle the equation of the new circle

(x – h)2 + (y – k)2 = r2

5 0

3 years ago

Read 2 more answers

Sarah weighed three containers of sand for a science project. The first container weighed 19.28 grams, The second container weig

Pepsi [2]

1.72 grams it the amount the 3 container weighed more than the first and second combined

5 0

4 years ago

find the other endpoint of the line segment with the given endpoint and mid point Endpoint: (2, 5), midpoint: (5, 1)

vekshin1

Answer:

the other end point is (5,3)

Step-by-step explanation:

3 0

3 years ago

The area of circular garden is 615.44 feet2. What is the circumference of the garden? (Use 3.14 for .)

ella [17]

Answer:

B.)

87.92 feet

Step-by-step explanation:

Given:

Area of the circular garden $= 615.44 ft^2$

$\pi =3.14$

Finding the radius of the circle.

Area of the circle= $\pi r^2$

$615.44=\pi *r^2$

$r^2=\frac{615.44}{\pi } \\\\r^2=\frac{615.44}{3.14} \\r^2=196\\r=14 ft.$

Circumference of the garden:

$=2\pi r\\=2*3.14*14\\=87.92ft.$

3 0

4 years ago