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3 years ago

100 points !!!!!

Mathematics

1 answer:

olasank [31]3 years ago

5 0

Answer:

Step-by-step explanation:

it matches what i think

branliet plzz

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Let T be the plane-2x-2y+z =-13. Find the shortest distance d from the point Po=(-5,-5,-3) to T, and the point Q in T that is cl

GaryK [48]

Answer:

d=10u

Q(5/3,5/3,-19/3)

Step-by-step explanation:

The shortest distance between the plane and Po is also the distance between Po and Q. To find that distance and the point Q you need the perpendicular line x to the plane that intersects Po, this line will have the direction of the normal of the plane $n=(-2,-2,1)$ , then r will have the next parametric equations:

$x=-5-2\lambda\\y=-5-2\lambda\\z=-3+\lambda$

To find Q, the intersection between r and the plane T, substitute the parametric equations of r in T

$-2x-2y+z =-13\\-2(-5-2\lambda)-2(-5-2\lambda)+(-3+\lambda) =-13\\10+4\lambda+10+4\lambda-3+\lambda=-13\\9\lambda+17=-13\\9\lambda=-13-17\\\lambda=-30/9=-10/3$

Substitute the value of $\lambda$ in the parametric equations:

$x=-5-2(-10/3)=-5+20/3=5/3\\y=-5-2(-10/3)=5/3\\z=-3+(-10/3)=-19/3\\$

Those values are the coordinates of Q

Q(5/3,5/3,-19/3)

The distance from Po to the plane

$d=\left| {\to} \atop {PoQ}} \right|=\sqrt{(\frac{5}{3}-(-5))^2+(\frac{5}{3}-(-5))^2+(\frac{-19}{3}-(-3))^2} \\d=\sqrt{(\frac{5}{3}+5))^2+(\frac{5}{3}+5)^2+(\frac{-19}{3}+3)^2} \\d=\sqrt{(\frac{20}{3})^2+(\frac{20}{3})^2+(\frac{-10}{3})^2}\\d=\sqrt{\frac{400}{9}+\frac{400}{9}+\frac{100}{9}}\\d=\sqrt{\frac{900}{9}}=\sqrt{100}\\d=10u$

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3 years ago

80 points! pls help! Recall that the equation for horizontal distance h in feet of a projectile with initial velocity v0 and ini

dem82 [27]

Answer:

a) 0.6435 radians

b) 80.1 feet/sec

Step-by-step explanation:

a) 75 = (50²/16)sin(theta)cos(theta)

sin(theta)cos(theta) = 0.48

2sin(theta)cos(theta) = 0.96

sin(2theta) = 0.96

2theta = 1.287002218

Theta = 0.6435011088 radians

b) 200 = (v²/16)sin(0.75)cos(0.75)

6416.072347 = v²

v = 80.10038918 feet/sec

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3 years ago

Match each three dimensional figure to its volume based on the given dimensions.

Gre4nikov [31]

please attach a diagram

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3 years ago

Your school's football team scored 49 points. Your team's score was 19 points more than the opponent's score s. Write and solve

solmaris [256]

Answer:

39 points

Step-by-step explanation:

Your school's football team scored 49 points.

Your team's score is 19 points more than the opponents score

The opponent score is represented as S

Since the total points that was scored is 49 and your team score is 19 then the equation can be written as follows

S+ 19= 49

Solve for S

S= 49-19

S= 30

Hence the opponent's score is 30 points

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3 years ago

What is one way that oak trees can spread to different areas

crimeas [40]

By dropping acorns, and spreading them to other areas by animals and wind.

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