The equation for the volume of a cylinder is v=πr²h the positive value of r, in terms of h and V, is

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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

Please help!! (please don’t reply if you’re just going to say “ don’t know “ etc please and thank you)

Nastasia [14]

Answer:

a = -1 , b = 4 , c = 3 , d = 1

Step-by-step explanation:

The general rules of exponent:

$1) \ a^m * a^n = a^{m+n}\\2) \ a^m / a^n = a^{m-n}\\3) (-1)^m = 1 \ (if \ m \ is \ +) and \ = \ -1 \ (if \ m \ is \ -)$

===================================================

Given:

$(-xy)^3 (xz) =ax^by^cz^d$

The right hand side = (-xy)³ (xz) = (-1)³ x³ y³ x z = (-1) x⁴ y³ z

Comparing the right hand side with the left hand side

∴ a = -1

∴ b = 4

∴ c = 3

∴ d = 1

8 0

3 years ago

An airplane flying into a headwind travels the 1890-mile flying distance between two cities in 3 hours. On the return flight, th

aksik [14]

Answer:

Velocity (against wind) = 1,890 / 3 = 630 mph

Velocity (with the wind) = 1,890 / 2.5 = 756 mph

Plane speed (still air) = 630 + wind speed

Plane speed (still air) = 756 - wind speed

Adding both equations equals

2 * Plane speed (still air) = 1,386

Plane Speed = 693 mph

Source: https://www.1728.org/veloccal.htm

Step-by-step explanation:

4 0

3 years ago

Alicia is solving the equation 2.3 x minus 1.6 = 8.8 minus 2.9 x. Which equations represent possible ways to begin solving for x

bija089 [108]

Answer:

what are the options

Step-by-step explanation:

8 0

3 years ago

How do you graph lines using intercepts Ex. 3y= 1/2x-2 (How would you graph that?)

scZoUnD [109]

Read this article https://weteachscience.org/mentoring/resources/lesson-plans/algebra-1-%E2%80%93-how-to-graph-a-linea...

6 0

3 years ago