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I am Lyosha [343]
2 years ago
14

Given sin theta=1/3 and 0 < theta< π/2; find tan 2 theta.

Mathematics
1 answer:
mote1985 [20]2 years ago
6 0

Answer:

tan2θ = 4√2/7

Step-by-step explanation:

Given sin theta=1/3 and 0 < theta< π/+

Required

tan 2 theta

tan2 theta = 2tanθ/1-tan²θ

Get tan θ

sinθ = opp/hyp

adj = √3²-1²²

adj = √9-1

adj = √8

tanθ = opp/adj = 1/2√2

tan2 theta = 2(1/2√2/1-(1/2√2)²

tan2θ = 1/√2/1-1/8

tan2θ = 1/√2/7/8

tan2θ =  8/7√2

Rationalize

tan2θ = 8√2/14

tan2θ = 4√2/7

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Exponent Practice:<br> x^2/3=64
docker41 [41]
X^2/3 = 64
x^{2} =64^{3}
x = 64^{3/2}

it is easier to first find square root of 64 and than power it to 3
square root of 64 is 8 which means our equation now looks like:
x = 8^3
now the answer is after powering 8 to 3:
x = 512

6 0
3 years ago
Find the midpoint of the segment with the following endpoints.<br> (4,2) and (7,6)
Tema [17]

Answer:

The answer is

<h2>( \frac{11}{2} \: , \: 4)</h2>

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

M = (  \frac{x1 + x2}{2} , \:  \frac{y1 + y2}{2} )

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(4,2) and (7,6)

The midpoint is

M = ( \frac{4 + 7}{2}   \: , \:  \frac{2 + 6}{2} ) \\  = ( \frac{11}{2} \: , \:  \frac{8}{2} )

We have the final answer as

( \frac{11}{2} \: , \: 4)

Hope this helps you

4 0
3 years ago
Evaluate the definite integral. π/18 cos(9x) sin(sin(9x)) dx 0
alexandr402 [8]
Ur answer in attachment hope it helps you

3 0
3 years ago
Find the equation of the line that goes through (-8,11) and is perpendicular to x= - 15. Write the equation in the form x = a, y
galben [10]

Answer:

y=11

Step-by-step explanation:

Hi there!

We want to find the equation of the line that passes through the point (-8, 11) and is perpendicular to x=-15

If a line is perpendicular to another line, it means that the slopes of those lines are negative and reciprocal; in other words, the product of the slopes is equal to -1

The line x=-15 has an undefined slope, which we can represent as 1/0, which is also undefined.

To find the slope of the line perpendicular to x=-15, we can use this equation (m is the slope):

m_1*m_2=-1

m_1 in this instance would be 1/0, so we can substitute it into the equation:

\frac{1}{0} *m_2=-1

Multiply both sides by 0

m_2=0

So the slope of the new line is 0

We can substitute it into the equation y=mx+b, where m is the slope and b is the y intercept:

y=0x+b

Now we need to find b:

Since the equation passes through the point (-8,11), we can use its values to solve for b.

Substitute -8 as x and 11 as y:

11=0(-8)+b

Multiply

11=0+b, or 11=b

So substitute into the equation:

y=0x+11

We can also write the equation as y=11

Hope this helps!

5 0
3 years ago
Jose travels 130 miles in 150 minutes. Home many miles does Jose travel in 1 hour?
Solnce55 [7]

51.60 miles per hour

7 0
3 years ago
Read 2 more answers
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