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navik [9.2K]
4 years ago
5

A scientist measures the angle x and the distance y between the Earth and the Sun. Using complete sentences, explain how the sci

entist can use only these two measurements to calculate the distance between the Sun and the shooting star.

Mathematics
1 answer:
Artyom0805 [142]4 years ago
5 0

The scientist can use only the angle x and the distance y to calculate the distance between the Earth and the Sun using the cosine function.

cos x = BC / y

Solving for BC

BC = y cos x

BC is the distance between the Earth and the Sun :D

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If y varies inversely as x, and y = 58 when x = 9, find y when x = 261.
Umnica [9.8K]

Answer:

2

Step-by-step explanation:

y=k/x

58=k/9

k=58×9

k=522

y=522/x

when x=261

y=522/261

y=2

4 0
3 years ago
Convert the following sum into a product. cosx + cos3x + cos5x + cos7x
kvv77 [185]

Answer:

4\cos x\cos (4x)\cos (2x)

Step-by-step explanation:

Given: cosx + cos3x + cos5x + cos7x

To convert: the given sum into product

Solution:

Use formula: \cos A+\cos B=2\cos \left ( \frac{A+B}{2} \right )\cos \left ( \frac{A-B}{2} \right )

cosx + cos3x + cos5x + cos7x=2\cos \left ( \frac{x+3x}{2} \right )\cos \left ( \frac{x-3x}{2} \right )+2\cos \left ( \frac{5x+7x}{2} \right )\cos \left ( \frac{5x-7x}{2} \right )\\=2\cos (2x)\cos (-x)+2\cos (6x)\cos (-x)\\=2\cos (2x)\cos (x)+2\cos (6x)\cos (x)\\=2\cos x\left [ \cos (2x)+\cos (6x) \right ]

cosx + cos3x + cos5x + cos7x=2\cos \left ( \frac{x+3x}{2} \right )\cos \left ( \frac{x-3x}{2} \right )+2\cos \left ( \frac{5x+7x}{2} \right )\cos \left ( \frac{5x-7x}{2} \right )\\=2\cos x\left [ \cos (2x)+\cos (6x) \right ]\\=2\cos x\left [2 \cos \left ( \frac{2x+6x}{2} \right )\cos \left ( \frac{2x-6x}{2} \right ) \right ]\\=2\cos x\left [ 2\cos (4x) \cos (-2x) \right ]\\=4\cos x\cos (4x)\cos (2x)

4 0
3 years ago
Given the trinomial 2x*2 + 4x − 2, what is the value of the discriminant? a. 0 b. 10 c. 32 d. 36
Komok [63]
2x^{2}+4x-2 \\  \\ \Delta=b^{2}-4ac \\  \\ \Delta=4^{2}-4*2*(-2)=16+16=32

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<em>"Associate with people who are likely to improve you."</em>
7 0
3 years ago
Read 2 more answers
The shape of the top surface of a table is a trapezium. Find its area if its parallel
AleksandrR [38]

Step-by-step explanation:

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4 0
3 years ago
Find the slope of the graph and the unit rate
Lilit [14]

Answer:

<u>For the 1st graph</u>

Slope     = \frac{6}{10}

Unit rate =0.6 mi/h

               

<u>For the 2nd graph</u>

Slope     = \frac{9}{4}

Unit rate =2.25 mi/h=


Step-by-step explanation:

<u>For the 1st graph</u>

Slope is given as \frac{Rise}{Run}

Rise = (6-0) = 6

Run = (10-0) = 10

Therefore,

Slope     = \frac{6}{10}

Unit rate = \frac{6}{10}

               =0.6 mi/h

<u>For the 2nd graph</u>

Rise = (9-0) = 6

Run = (4-0) = 10

Therefore,

Slope     = \frac{9}{4}

Unit rate = \frac{9}{4}

               =2.25 mi/h


7 0
3 years ago
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