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3 years ago

M is directly proportional to r3When r = 4, M = 160a) Work out the value of M when r = 2.

Mathematics

2 answers:

Natali [406]3 years ago

6 0

Answer:

M = 20

Step-by-step explanation:

Given that M is directly proportional to r³ then the equation relating them is

M = kr³ ← k is the constant of proportion

To find k use the condition when r = 4, M = 160, that is

160 = k × 4³ = 64k (divide both sides by 64 )

2.5 = k

M = 2.5r³ ← equation of proportion

When r = 2, then

M = 2.5 × 2³ = 2.5 × 8 = 20

aliya0001 [1]3 years ago

4 0

Answer:

M<varies>r³

M=kr³(k= constant)

when M=160,r=4

160=k(4)³

160=64k

k=2.5

therefore,M=2.5r³

when r=2

M=2.5r³

M=2.5(2)³

M=2.5(8)

M=20

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One of the local homeless shelters received a donation of 852 blankets to help support the homeless population during the harsh

Arte-miy333 [17]

Answer:

Each shelter would get 121 blankets

And there would be 5 blankets left over

Step-by-step explanation:

One of the local homeless shelters received a donation of 852 blankets to help support the homeless population during the harsh winter months. They plan on distributing them to all 7 of the local shelters. How many blankets will each shelter get? Will there be any leftover? If so, how many?

From the above question

7 local shelters = 852 blankets

1 local shelters = x blankets

Cross Multiply.

7x = 852 blankets

x = 852 blankets/7

x = 121 5/7 blankets

Therefore, Each shelter would get 121 blankets

And there would be 5 blankets left over

7 0

2 years ago

This should be easy for you Please help me

Alik [6]

Explanation:

a. The line joining the midpoints of the parallel bases is perpendicular to both of them. It is the line of symmetry for the trapezoid. This means the angles and sides on one side of that line of symmetry are congruent to the corresponding angles and sides on the other side of the line. The diagonals are the same length.

b. We observe that adjacent pairs of points have the same x-coordinate, so are on vertical lines, which have undefined slope. KN is a segment of the line x=1; LM is a segment of the line x=3. If the trapezoid is isosceles, the midpoints of these segments will be on a horizontal line. The midpoint of KN is at y=(3-2)/2 = 1/2. The midpoint of LM is at y=(1+0)/2 = 1/2. These points are on the same horizontal line, so the trapezoid is isosceles.

c. We observed in part (b) that the parallel sides are KN and LM. The coordinate difference between K and L is (1, 3) -(3, 1) = (-2, 2). That is, segment KL is the hypotenuse of an isosceles right triangle with side lengths 2, so the lengths of KL and MN are both 2√2.

_____

For part (c), we used the shortcut that the hypotenuse of an isosceles right triangle is √2 times the leg length.