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ale4655 [162]
3 years ago
6

If Acot theta + Bcot theta =4 and

Mathematics
1 answer:
geniusboy [140]3 years ago
7 0

Answer is: B

Step-by-step explanation: correct answer is B

b  

2

−a  

2

 

Given, acotθ+bcscθ=p

           bcotθ+acscθ=q

⇒p  

2

−q  

2

=(p−q)(p+q)

                   =[acotθ+bcscθ−bcotθ−acscθ][acotθ+bcscθ+bcotθ+acscθ]

                   =[cotθ(a−b)−cscθ(a−b)][cotθ(a+b)+cscθ(a+b)]

                   =(a−b)(cotθ−cscθ)(a+b)(cotθ+cscθ)

                   =(a  

2

−b  

2

)(cot  

2

θ−csc  

2

θ)

                   =(−1)(a  

2

−b  

2

)[∵csc  

2

θ−cot  

2

θ=1]

                   =(b  

2

−a  

2

)

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Given the triangle below, what is m<br> A. 46.2<br> B. 41.40<br> C. 48.4<br> D. 38.6°
Brrunno [24]

Answer:

B 41.4

Step-by-step explanation:

complete Pythagoras for general triangles :

c² = a² + b² - 2ab×cos(C)

with "c" being the side opposite of the angle C.

=>

8² = 10² + 12² - 2×10×12×cos(C)

64 = 244 - 240×cos(C)

240×cos(C) = 244 - 64 = 180

cos(C) = 180/240 = 18/24 = 3/4 = 0.75

C = 41.40962211... ≈ 41.4

5 0
3 years ago
A pole that is 3.1 m tall casts a shadow that is 1.18 m long.At the same time , a nearby tower casts a shadow that is 35.75 m lo
Georgia [21]

Answer:

94 m

Step-by-step explanation:

Write a proportion:

3.1 / 1.18 = x / 35.75

Cross multiply and solve:

1.18x = 3.1 × 35.75

1.18x = 110.825

x ≈ 94

Rounded to the nearest meter, the height of the tower is approximately 94 meters.

7 0
3 years ago
What is the absolute value equation for this graph?
Delvig [45]

Answer:

y = |x-3| -1

Step-by-step explanation:

The parent function has been shifted right 3 units and down 1 unit. That is f(x)=|x| has been moved to ...

y = f(x -3) -1

y = |x -3| -1 . . . . matches the last choice

6 0
3 years ago
elaine opened a saving account with a deposit of 1000. The interest on her account is compounded each year at a rate of 2%. Elai
vivado [14]

Answer:

$1,061

Step-by-step explanation:

2% of 1000 is 20.

If 2% is compounded yearly, then

year one- $1,020

year two- $1,040.40

year three- $1,061.21

Rounded to the nearest whole dollar, Elaine would have $1,061 in her savings account after three years.

5 0
3 years ago
Read 2 more answers
A teacher claims that the proportion of students expected to pass an exam is greater than 80%. To test this claim, the teacher a
erica [24]

Answer:

z=-1.591

Step-by-step explanation:

Null Hypotheses,

H_0 : p=0.8\\H_a: p>0.80

So we use z-test for one population proportion (right-tailed test)

According to this informaton, we defined that

\alpha=0.05

z_c=1.64 (critical value)

So our Rejection region is R={z:z>1.64}

z=\frac{\bar{p}-p_0}{\sqrt{p_0(1-p_0)/n}} = \frac{0.755-0.8}{\sqrt{0.8(1-0.8)/200}}=-1.591

Not rejection.

6 0
3 years ago
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