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Ratling [72]
3 years ago
10

Evaluate the expression below if m = 350. 3.5m =

Mathematics
1 answer:
Lena [83]3 years ago
8 0

Answer:

1,225

Step-by-step explanation:

3.5×350=1225

its saying m is 350 and the question is asking 3.5 times 350

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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

7 0
3 years ago
Find the equation of the line through the point (2, 5) that cuts off the least area from the first quadrant. Give your answer us
Amanda [17]

The equation of the line would be

y = mx+b 

where m is the slope, b is the y intercept. 

<span>The line will form a triangular region in the first quadrant. Its area would be 1/2 base times height. The height is the y intercept and the base is y intercept divided by slope. Therefore,</span>

A = b^2/2m

At point (2,5)

5 = 2m+b

Substitute that in the area

A = b^2/5-b to find the least area, differentiate the area with respect to the height and equate it to 0 

dA/db = 0

<span>find b and use that to find m. Then, you can have the equation of the line.</span>


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sattari [20]
C would be the answer as x^{4} is the same thing as x * x * x * x.
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Answer:

B

Step-by-step explanation:

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