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kiruha [24]
2 years ago
13

Find the EXACT value of sin(A−B) if cos A = 3/5 where A is in Quadrant IV and cos B = 12/13 where B is in Quadrant IV. Assume al

l angles are measured from standard position. sin(A−B) =
Mathematics
1 answer:
MissTica2 years ago
4 0

\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha - \beta)=sin(\alpha)cos(\beta)- cos(\alpha)sin(\beta)

well, for both angles A and B we're on the IV Quadrant, meaning, the sine is negative, the cosine is positive, likewise, the opposite side is negative and the adjacent side for the angle is positive.

\bf cos(A)=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\qquad \qquad \stackrel{\textit{getting the opposite side}}{b=\pm\sqrt{5^2-3^2}}\implies b = \pm 4 \\\\\\ \stackrel{IV~Quadrant}{b = -4}\qquad \qquad sin(A)=\cfrac{\stackrel{opposite}{-4}}{\underset{hypotenuse}{5}} \\\\[-0.35em] ~\dotfill\\\\ cos(B)=\cfrac{\stackrel{adjacent}{12}}{\underset{hypotenuse}{13}}\qquad \qquad \stackrel{\textit{getting the opposite side}}{b=\pm\sqrt{13^2-12^2}}\implies b = \pm 5

\bf \stackrel{IV~Quadrant}{b = -5}\qquad \qquad sin(B)=\cfrac{\stackrel{opposite}{-5}}{\underset{hypotenuse}{13}} \\\\[-0.35em] ~\dotfill\\\\ sin(A-B)=\cfrac{-4}{5}\cdot \cfrac{12}{13}-\left( \cfrac{3}{5}\cdot \cfrac{-5}{13} \right)\implies sin(A-B)=\cfrac{-48}{65} - \left( \cfrac{-15}{65} \right) \\\\\\ sin(A-B)=\cfrac{-48}{65} + \cfrac{15}{65}\implies sin(A-B)=\cfrac{-33}{65}

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2 years ago
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pshichka [43]

Answer:

b. 58%

Step-by-step explanation:

Calculate the area of the entire rectangle using the formula A = lw.

The lowercase "L" is for length.

"w" is for width.

The lighter square is 10 units long by 5 inches wide.

A = lw

A = (10 in)(5 in)   Multiply

A = 50 in²

Calculate the area for the shaded rectangle, 7 inches by 3 inches.

A = lw

A = (7 in)(3 in)    Multiply

A = 21 in²

Calculate the area for the non-shaded region by subtracting the shaded area from the total area.

50 in² - 21 in² = 29 in²

The chance that a point in the large rectangle will NOT be in the shaded region is 29/50.

Convert this fraction to decimal form by using a calculator. Divide the top number by the bottom number.

29/50 = 0.58

0.58 is in decimal form. To convert it to a percentage, multiply the number by 100.

0.58 = 58%

Therefore the probability that a point chosen inside the large rectangle is not in the shaded region is 58%.

5 0
3 years ago
Bob and Doug are both 100-meter sprinters. Bob's sprint time is normally distributed with a mean of 10.00 seconds and Doug's spr
alexdok [17]

Answer:

The standard deviation (σ) = 0.05

Step-by-step explanation:

The question is to find the standard deviation.

STEEP 1: FIND THE MEAN

(10+9.9) ÷ 2 = 9.95

STEP 2: SQUARE THE DIFFERENCE BETWEEN SPRINT TIME AND MEAN

10-9.95= 0.05

0.05^2 = 0.0025

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From the standard deviation, the percentage probability of the higher value to occurs is

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And Bob has 5%

3 0
2 years ago
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anastassius [24]

Answer:

The result is 150 + 1.5d

Step-by-step explanation:

We want to translate the wordings into algebraic expression.

Firstly, we increase 120 by d%

d% = d/100

So increasing 120 by d % means;

120 + (d/100 * 120)

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Then increase this by 25%

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= 120 + 30 + 1.2d + 0.3d

= 150 + 1.5d

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3 years ago
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AlekseyPX

The steps needed to solve the given equation is required.

Adding the opposite value of the constant to both sides.

Divide both sides by the coefficient of the variable.

The solution to the equation is  

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This is done by adding the opposite value of the constant to both sides.

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Now, we divide both sides by the coefficient of the variable.

The solution to the equation is

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