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zloy xaker [14]
3 years ago
9

Three trigonometric functions for a given angle are shown below. sin theta = -77/85, cos theta=36/85 tan theta=77/36 What are th

e coordinates of point (x, y) on the terminal ray of angle theta assuming that the values above were not simplified?
A) (-77,-36)
B)(-77,36)
C) (-36,77)
D) (36, -77)

Mathematics
2 answers:
Marizza181 [45]3 years ago
7 0

Answer:

The correct option is D.

Step-by-step explanation:

It is given that

\sin \theta =\frac{-77}{85}

\cos \theta =\frac{36}{85}

The angle of terminal ray is θ, it means the angle between x-axis and terminal ray is θ.

\sin \theta =\frac{perpendicular}{hypotenuse}

\cos \theta =\frac{base}{hypotenuse}

Therefore the length of perpendicular is 77 and the base of the triangle is 36.

Since sinθ is negative and cosθ is positive, it means point must be lies on fourth quadrant because in fourth quadrant cosine in positive but sine is negative.

The point of terminal ray is (base, perpendicular) and the sign are used according to the quadrant.

Therefore the point of terminal ray is (36,-77) because in fourth quadrant x is positive but y is negative. Option D is correct.

USPshnik [31]3 years ago
4 0

Answer:

D) (36, -77)

Step-by-step explanation:

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3 years ago
B) Alex invests $2000 in an account that has a 6% annual rate of growth. To the nearest year, when
wlad13 [49]

Answer:

part 1) 10 years

part 2) 10 years

Step-by-step explanation:

<u><em>The correct question is:</em></u>

Part 1) Alex invests $2000 in an account that has a 6% annual rate of growth compounded annually. To  the nearest year, when will the investment be worth $3600?

Part 2) Alex invests $2000 in an account that has a 6% annual rate of growth compounded continuously. To  the nearest year, when will the investment be worth $3600?

Part 1) we know that    

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

P=\$2,000\\A=\$3,600\\ r=6\%=6/100=0.06\\n=1  

substitute in the formula above

3,600=2,000(1+\frac{0.06}{1})^{t}  

1.8=(1.06)^{t}  

Apply log both sides

log(1.8)=log[(1.06)^{t}]  

Applying property of exponents

log(1.8)=(t)log(1.06)  

t=log(1.8)/log(1.06)  

t=10.09\ years

Round to the nearest year

t=10\ years

Part 2) we know that

The formula to calculate continuously compounded interest is equal to

A=P(e)^{rt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

P=\$2,000\\A=\$3,600\\ r=6\%=6/100=0.06  

substitute in the formula above

3,600=2,000(e)^{0.06t}  

1.8=[e]^{0.06t}  

Apply ln both sides

ln(1.8)=ln[e]^{0.06t}  

ln(1.8)=(0.06t)ln[e]  

t=ln(1.8)/0.06  

t=9.80\ years

Round to the nearest year

t=10\ years

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A shipment of 20 similar laptop computers to a retail outlet contains 3 that are defective. If a school makes a random purchase
otez555 [7]

Answer:

Step-by-step explanation:

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Defective laptops, n = 3

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Case 1:

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Probability to choose 2 laptops which are non defective

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Case 2:

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Probability to chose 1 defective and one non defective laptop

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Case 3:

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choosing of 2 laptops out of 20 = 20 C 2 = 190

Probability of choosing two defective laptops = 3 / 190 = 0.0158

P'' =

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