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butalik [34]
3 years ago
15

If sin theta = 1/3 and tan theta < 0, what is the value of cos theta?

Mathematics
1 answer:
STatiana [176]3 years ago
5 0
If sin Ф=1/3>0 and tan Ф<0; then Ф belongs to the second quadrant and cos Ф will be negative (cos Ф<0).

sin²Ф+cos²Ф=1
(1/3)²+cos²Ф=1
1/9+cos²Ф=1
cos²Ф=1-1/9
cos²Ф=8/9
cos Ф=⁺₋√(8/9)=⁺₋2√2 / 3

We have two possible solutions.
cos Ф=2√2 / 3 This solutions is not possible, because in this case cos Ф has to be negative (cos Ф<0)

cos Ф=(-2√2) / 3 this solutions is right.

answer:B. -2 square root 2 /3    (or    (-2√2) /3  )
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Answer:

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Step-by-step explanation:

7. If lines m and n are congruent, then angles DCF and CFE are congruent. 15x+3=18x-6. Solve for x. --> 15x+9=18x-->3x=9-->x=3

8.If line m is parallel to line n, then the corresponding angles are congruent. So, 20x+1=22x-13 Solve for x. 20x+14=22x-->14=2x-->x=7.

9. The supplementary angle of 110 is 70. Note that all of the inner angles of a triangle are equal to 180. Form an equation using the the values: (4x+8)+(2x+12)+70=180. Simplify; 6x+90=180. Solve for x: 6x+90=180-->6x=90-->x=15.

Hope this helps!

8 0
3 years ago
The land area of a country is about 5.0 million square​ miles, and the population is about 600 million people. What is the avera
podryga [215]

Answer:

120 people/sq. mile

Step-by-step explanation:

Population Density is the concept of how "crowdy" a place is. The more the population density, the more crowded that place is.

The population density is found by dividing the "number of people" by the "land area" (in sq mile or sq km).

Here, it is given there are 600 million people, so

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6 0
4 years ago
3(-8m - 1) + 5 (m + 8)
Vlada [557]

Step-by-step explanation:

3(-8m-1) + 5(m+8) (remove the parentheses)

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7 0
3 years ago
A concrete slab 4 inches deep will be poured for the floor of greenhouse A. How many cubic feet of concretar are needed for the
Mars2501 [29]

This question is incomplete

Complete Question

Consider greenhouse A with floor dimensions w = 16 feet , l = 18 feet.

A concrete slab 4 inches deep will be poured for the floor of greenhouse A. How many cubic feet of concrete are needed for the floor?

Answer:

96 cubic feet

Step-by-step explanation:

The volume of the floor of the green house = Length × Width × Height

We convert the dimensions in feet to inches

1 foot = 12 inches

For width

1 foot = 12 inches

16 feet = x

Cross Multiply

x = 16 × 12 inches

x = 192 inches

For length

1 foot = 12 inches

18 feet = x

Cross Multiply

x = 18 × 12 inches

x = 216 inches

The height or depth = 4 inches deep

Hence,

Volume = 192 inches × 216 inches × 4 inches

= 165888 cubic inches

From cubic inches to cubic feet

1 cubic inches = 0.000578704 cubic foot

165888 cubic inches = x

Cross Multiply

x = 16588 × 0.000578704 cubic foot

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Therefore, 96 cubic feet of concrete is needed for the floor

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3 years ago
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Answer:

the answer is 8

Step-by-step explanation:

8 0
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