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3 years ago

Use the drop-down menus to complete the statements to match the information shown by the graph.

Mathematics

1 answer:

Lostsunrise [7]3 years ago

7 0

The right answer is 1/2

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Write each expression as an algebraic (nontrigonometric) expression in u, u > 0.

max2010maxim [7]

Answer:

$\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0$

Step-by-step explanation:

We want to write the trignometric expression:

$\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)\text{ where } u>0$

As an algebraic equation.

First, we can focus on the inner expression. Let θ equal the expression:

$\displaystyle \theta=\sec^{-1}\left(\frac{u}{10}\right)$

Take the secant of both sides:

$\displaystyle \sec(\theta)=\frac{u}{10}$

Since secant is the ratio of the hypotenuse side to the adjacent side, this means that the opposite side is:

$\displaystyle o=\sqrt{u^2-10^2}=\sqrt{u^2-100}$

By substitutition:

$\displaystyle= \sin(2\theta)$

Using an double-angle identity:

$=2\sin(\theta)\cos(\theta)$

We know that the opposite side is √(u² -100), the adjacent side is 10, and the hypotenuse is u. Therefore:

$\displaystyle =2\left(\frac{\sqrt{u^2-100}}{u}\right)\left(\frac{10}{u}\right)$

Simplify. Therefore:

$\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0$

4 0

3 years ago

The actual length of the rectangle below is 41 cm. Using the scale drawing below, find the actual width.

Margaret [11]

Okay, so your scale rectangle has a length of l = 8.2 cm. The actual triangle has a length of L = 41 cm. What is the scale factor? You find out by dividing the scale rectangle l from the actual rectangle L.

41 cm / 8.2 cm = 5

The scale factor is 5. That means the actual rectangle is exactly 5 times bigger than the scale rectangle. Now finding the width is easy! If the width of the scale rectangle is 2.1 cm and the scale factor is 5, you just multiply them together!

2.1 cmx 5 = 10.5 cm

The width of the actual rectangle is 10.5 cm! Hope that helps!

7 0

3 years ago

Read 2 more answers

Can someone please help and answer this problem

OLEGan [10]

Answer:

Use Desmos Graphing Calculator if you have more problems like this

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3 years ago

The lower the average monthly temperature, the higher the monthly heating bill.