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katrin [286]
2 years ago
14

the sum of two numbers is 49.Twice the smaller number is 97 less than 3 times the larger number.What are the numbers. help mee I

'm on homework and its due soon
Mathematics
1 answer:
kondaur [170]2 years ago
7 0

Answer:

smaller number is 10

larger number is 39

Step-by-step explanation:

a = small number

b = larger number

a + b = 49

2a = 3b - 97

substitute 49-a into second equation for b

2a = 3(49-a) - 97

2a = 147 - 3a - 97

5a = 50

a = 10

b = 39

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Answer:

b is the answer

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2 years ago
17. A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49 cm. Find
Pavlova-9 [17]

Answer:

r = 3.74cm

Step-by-step explanation:

Given

Hemisphere

Radius = 7cm

Cone

Height = 49m

Required

Determine the radius of the cone

First, we calculate the volume (V1) of the hemisphere.

V_1 = \frac{2}{3}\pi r^3

Substitute 7 for r

V_1 = \frac{2}{3}\pi * 7^3

V_1 = \frac{2}{3}\pi * 343

V_1 = \frac{686}{3}\pi

Volume (V2) of a cone is:

V_2 = \frac{1}{3}\pi r^2h

Because the lead is cast into a cone, then they have the same volume.

So, we have:

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Substitute 49 for h

686 =  r^2 * 49

Divide both sides by 49

r^2 = \frac{686}{49}

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3 years ago
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