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3 years ago

An angle measures 28°. what is the measures of its complement?

Mathematics

1 answer:

Sidana [21]3 years ago

8 0

Complementary angles add up to 90 so 90-28=the complement angle

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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

3 less than the product of 5 and x?

amm1812

Answer:

5x - 3

The product of 5 and x, minus 3

4 0

3 years ago

The question is in the screenshot. ( I really need help in this one)

Yuki888 [10]

Answer:

V=A*L

V=72*6

V=432 in cube

5 0

3 years ago

You buy a game for $40 , and the sales tax is $2 2 . What percent of the game price are you paying in sales tax?

Len [333]

.05 percent taxes if you spend 40 and 2 dollar worth of taxes

8 0

3 years ago

Expand<br> (2x - 3)4 <br><br> Can you help me expand this by using the binomial theorem?

saw5 [17]

The value of expanding (2x -3)^4 is 16x^4 + 96x^3 +216x^2 -216x + 81

<h3>How to expand the expression?</h3>

The expression is given as:

(2x -3)^4

Using the binomial expansion, we have:

$(2x -3)^4 = ^4C_0 * (2x)^4 * (-3)^0 +^4C_1 * (2x)^3 * (-3)^1 + ^4C_2 * (2x)^2 * (-3)^2 + ^4C_3 * (2x)^1 * (-3)^3 + ^4C_4 * (2x)^0 * (-3)^4$

Evaluate the combination factors.

So, we have:

$(2x -3)^4 = 1 * (2x)^4 * (-3)^0 + 4 * (2x)^3 * (-3)^1 + 6 * (2x)^2 * (-3)^2 + 4 * (2x)^1 * (-3)^3 + 1 * (2x)^0 * (-3)^4$

Evaluate the exponents and the products

$(2x -3)^4 = 16x^4 + 96x^3 +216x^2 -216x + 81$

Hence, the value of expanding (2x -3)^4 is 16x^4 + 96x^3 +216x^2 -216x + 81

Read more about binomial expansions at:

brainly.com/question/13602562

#SPJ1

8 0

2 years ago