Find two consecutive whole numbers that 7 lies between.

Mathematics

1 answer:

Wittaler [7]3 years ago

5 0

The answer is actually 3 and 4.

$\sqrt{7}$ lies between the two consecutive numbers 3 and 4.

I hope this helped! :))

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P is the point on the line 2x+y-10=0 such that the length of OP, the line segment from the origin O to P, is a minimum. Find the

nirvana33 [79]

The minimum distance is the perpendicular distance. So establish the distance from the origin to the line using the distance formula.
The distance here is: d2=(x−0)^2+(y−0)^2
 =x^2+y^2

To minimize this function d^2 subject to the constraint, 2x+y−10=0
If we substitute, the y-values the distance function can take will be related to the x-values by the line:y=10−2x
You can substitute this in for y in the distance function and take the derivative:
d=sqrt [x2+(10−2x)^2]

d′=1/2 (5x2−40x+100)^(−1/2) (10x−40)
Setting the derivative to zero to find optimal x,
d′=0→10x−40=0→x=4

This will be the x-value on the line such that the distance between the origin and line will be EITHER a maximum or minimum (technically, it should be checked afterward).
For x = 4, the corresponding y-value is found from the equation of the line (since we need the corresponding y-value on the line for this x-value).

Then y = 10 - 2(4) = 2.
So the point, P, is (4,2).

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3 years ago

What is the perimeter of a polygon with vertices at (3, 2) , (3, 9) , (7, 12) , (11, 9) , and (11, 2) ?

Furkat [3]

The perimeter of said polygon is 32.

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Please help me

GrogVix [38]

Answer:

Step-by-step explanation:

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