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3 years ago

14

Lily had 95 inches of yarn. After cutting 4 pieces that were each the same length, she had 15 inches of yarn left.

2 answers:

DanielleElmas [232]3 years ago

7 0

Answer:

20 inches

Step-by-step explanation:

Step 1: Subtract the total from what was left

$95 - 15 = 80$

Step 2: Divide the result into the 4 pieces

$80 \div 4$

$=\frac{80}{4}$

$= 20$

Each of the four pieces Lily cut was 20 inches.

Anika [276]3 years ago

6 0

Each was 10 inches because she had 95 and 95-15=40 divided by 4 = 10

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3 years ago

Stuart pays back two student loans over a 4-yr period. One loan charges the equivalent of 3% simple interest and the other charg

Ugo [173]

Answer:

The first loan L1 = $20,000

This is the loan with 3% simple interest

The second loan L2 = $4,000

This is the loan with 5.5% simple interest

Step-by-step explanation:

L1 + L2 = $24,000 ...(1)

4(3% of L1) + 4(5.5% of L2) = $3,280 ...(2)

Where the first term in equation (2) represents the total interest paid on loan 1 after 4 years

The second term represents total interest accruing to loan 2 after 4 years

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Substitute this value for L1 in equation (2)

288,000 + 10L2 = 328,000

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3 years ago

What is the mean for the numbers 94,26,76,46,77,66,31, and 88?

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3 years ago

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Given tan theta =9, use trigonometric identities to find the exact value of each of the following:_______

Ludmilka [50]

Answer:

$(a)\ \sec^2(\theta) = 82$

$(b)\ \cot(\theta) = \frac{1}{9}$

$(c)\ \cot(\frac{\pi}{2} - \theta) = 9$

$(d)\ \csc^2(\theta) = \frac{82}{81}$

Step-by-step explanation:

Given

$\tan(\theta) = 9$

Required

Solve (a) to (d)

Using tan formula, we have:

$\tan(\theta) = \frac{Opposite}{Adjacent}$

This gives:

$\frac{Opposite}{Adjacent} = 9$

Rewrite as:

$\frac{Opposite}{Adjacent} = \frac{9}{1}$

Using a unit ratio;

$Opposite = 9; Adjacent = 1$

Using Pythagoras theorem, we have:

$Hypotenuse^2 = Opposite^2 + Adjacent^2$

$Hypotenuse^2 = 9^2 + 1^2$

$Hypotenuse^2 = 81 + 1$

$Hypotenuse^2 = 82$

Take square roots of both sides

$Hypotenuse =\sqrt{82}$

So, we have:

$Opposite = 9; Adjacent = 1$

$Hypotenuse =\sqrt{82}$

Solving (a):

$\sec^2(\theta)$

This is calculated as:

$\sec^2(\theta) = (\sec(\theta))^2$

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

Where:

$\cos(\theta) = \frac{Adjacent}{Hypotenuse}$

$\cos(\theta) = \frac{1}{\sqrt{82}}$

So:

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

$\sec^2(\theta) = (\frac{1}{\frac{1}{\sqrt{82}}})^2$

$\sec^2(\theta) = (\sqrt{82})^2$

$\sec^2(\theta) = 82$

Solving (b):

$\cot(\theta)$

This is calculated as:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

Where:

$\tan(\theta) = 9$ ---- given

So:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

$\cot(\theta) = \frac{1}{9}$

Solving (c):

$\cot(\frac{\pi}{2} - \theta)$

In trigonometry:

$\cot(\frac{\pi}{2} - \theta) = \tan(\theta)$

Hence:

$\cot(\frac{\pi}{2} - \theta) = 9$

Solving (d):

$\csc^2(\theta)$

This is calculated as:

$\csc^2(\theta) = (\csc(\theta))^2$

$\csc^2(\theta) = (\frac{1}{\sin(\theta)})^2$

Where:

$\sin(\theta) = \frac{Opposite}{Hypotenuse}$

$\sin(\theta) = \frac{9}{\sqrt{82}}$

So:

$\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2$

$\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2$

$\csc^2(\theta) = \frac{82}{81}$

4 0

3 years ago