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faltersainse [42]
3 years ago
15

(cosxtanx-tanx+2cosx-2)/tanx+2=cosx-1 can someone show me how to prove this?

Mathematics
1 answer:
uysha [10]3 years ago
7 0

Answer:

See detail below.

Step-by-step explanation:

A word of caution before getting to the actual problem: I believe there is an important set of brackets missing in the original post. The expression on the left hand side should be:

(cosxtanx-tanx+2cosx-2)/(tanx+2)

Without the brackets, it is left unclear whether the denominator is just tanx or tanx+2. I recommend to use brackets wherever any doubt could arise.

Now to the actual problem: \we can make the following transformations on the left hand side:

\frac{\cos x \tan x + 2\cos x -2}{\tan x +2}=\frac{\cos x \frac{\sin x}{\cos x}  + 2\cos x -2}{\frac{\sin x +2\sin x}{\cos x} }=\\=\frac{\cos x \sin x - \sin x + 2\cos^2 x - 2\cos x}{\sin x + 2\cos x}=\\=\frac{\cos x \sin x +2\cos^2 x }{\sin x + 2\cos x}-1=\\=\cos x -1

which is shown to be the same as the right hand side, which was to be shown.

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B. You used 13 gallons when you traveled 342 miles. How many miles did you<br> travel per gallon?
svet-max [94.6K]

Answer:

26.307 miles per gallon

Step-by-step explanation:

Divide the miles traveled by the number of gallons used.

In this case, divide 342 by 13 to get the answer of 26.307 miles per gallon.

8 0
2 years ago
Find the area of the circle to the nearest whole number, if necessary!
astra-53 [7]

Answer:

The circle has an area of about 1385 square mm.

Step-by-step explanation:

Let's recall that circles have an area that can be found with the following formula:

A=\pi r^{2}

where r is the radius of the circle.

Now, focus your eyes on the circle. We are shown that the diameter of this circle is 42 mm, but we only want the radius. Since the radius is half the diameter, the radius is 21 mm. Now, we can solve for the area of the circle.

A=\pi (21)^2\\A=441\pi \\A=1385.44236...

So, to the nearest whole number, the area of the circle is 1385 square mm.

5 0
2 years ago
I NEED AN ANSWER PLEASE :(((
Alekssandra [29.7K]

Answer:

80 lemons

Step-by-step explanation:

Let x represent the amount of lemons that were on the tree.

We can use this to set up an equation:

40\%x=32

Note that percentages can also be written as that number over 100.

\frac{40}{100}x=32

Simplify the fraction.

\frac{2}{5}x=32

Multiply both sides by 5

2x=160

Divide both sides by 2

x=80

There were 80 lemons on the tree before he picked the lemons.

6 0
2 years ago
if an exterior angle of a triangle has a measure of 35 degrees, what is the measure of the adjacent interior angle?
Alona [7]

Answer:

145

Step-by-step explanation:

Adjacent interior angle = x

Sum of exterior angle and adjacent interior angle = 180

35 + x = 180

x = 180 - 35

x = 145

3 0
3 years ago
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polet [3.4K]

Answer:

10

Step-by-step explanation:

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2 years ago
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