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FrozenT [24]
3 years ago
14

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
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