Simplify the expression (x^1/6)^3

Solve for x. Round your answer to the nearest tenth. 9.2 X 16.5

Contact [7]

Answer:

152

Step-by-step explanation:

6 0

3 years ago

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alisha [4.7K]

Answer:

$d=3\sqrt{2}\ units$

Step-by-step explanation:

The complete question is

Line L contains points (3, 5) and (7, 9). Points P has coordinates (2, 10). Find the distance from P to L

step 1

Find the equation of the line L contains points (3,5) and (7,9)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the given values

$m=\frac{9-5}{7-3}$

$m=\frac{4}{4}=1$

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=1\\point\ (3,5)$

substitute

$y-5=(1)(x-3)$

isolate the variable y

$y=x-3+5$

$y=x+2$ -----> equation A

step 2

Find the equation of the perpendicular line to the given line L that passes through the point P

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal

so

The slope of the given line L is $m=1$

The slope of the line perpendicular to the given line L is

$m=-1$

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=-1\\point\ (2,10)$

substitute

$y-10=-(x-2)$

isolate the variable y

$y=-x+2+10$

$y=-x+12$ ----> equation B

step 3

Find the intersection point equation A and equation B

$y=x+2$ -----> equation A

$y=-x+12$ ----> equation B

solve the system by graphing

The intersection point is (5.7)

see the attached figure

step 4

we know that

The distance from point P to the the line L is equal to the distance between the point P and point (5,7)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

(2,10) and (5,7)

substitute

$d=\sqrt{(7-10)^{2}+(5-2)^{2}}$

$d=\sqrt{(-3)^{2}+(3)^{2}}$

$d=\sqrt{18}\ units$

simplify

$d=3\sqrt{2}\ units$

see the attached figure to better understand the problem

6 0

3 years ago

Find Tan Θ given sin Θ = √3/2 and cos Θ = 1/2 a √3 b 3 c 2 d 4

densk [106]

We know:

$\tan\Theta=\dfrac{\sin\Theta}{\cos\Theta}$

We have:

$\sin\Theta=\dfrac{\sqrt3}{2},\ \cos\Theta=\dfrac{1}{2}$

Substitute:

$\tan\Theta=\dfrac{\frac{\sqrt3}{2}}{\frac{1}{2}}=\dfrac{\sqrt3}{2}:\dfrac{1}{2}=\dfrac{\sqrt3}{2}\cdot\dfrac{2}{1}=\sqrt3$

Answer: a. √3

4 0

3 years ago

Read 2 more answers

What is meant by the term financial planning?

Naily [24]

Answer:

a Long-term goals are reached over an extended period of time, so your current income does not affect

them.

Step-by-step explanation:

Financial planning refers to long term goals that are planned and reached over an extended period of time to keep one solvent in cases of emergency without having a direct effect on current income.

Solvency simply means having more assets than liabilities to be able to stay afloat of one's debts.

8 0

3 years ago

Anyone know how to solve this? Pease show how you got the answer:)

Alekssandra [29.7K]

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5 0

3 years ago