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3 years ago

A bathtub can hold 80 gallons of water. The faucet flows at a rate of 4

Mathematics

2 answers:

svetlana [45]3 years ago

8 0

Answer:

32% of the tub will be filled after 8 minutes. Hope this helps!

Step-by-step explanation:

4x8= 32

telo118 [61]3 years ago

5 0

Answer: The percentage of the tub that is filled after 8 minutes is is the 40%

Step-by-step explanation:

the 100% of the bathtub is 80 gallons of water.

the rate per minute is 4 gallons, so in 8 minutes, the amount of water in the bathtub will be:

4*8 gallons = 32 gallons

the percentage that will be filled of the bathtu is:

(32 gallons/80 gallons)*100% = 0.4*100% = 40%

The percentage of the tub that is filled after 8 minutes is is the 40%

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Prove algebraically that r = 10/2+2sinTheta is a parabola

Xelga [282]

Answer:

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Step-by-step explanation:

We want to prove algebraically that:

$r = \frac{10}{2 + 2 \sin \theta}$

is a parabola.

We use the relations

${r}^{2} = {x}^{2} + {y}^{2}$

and

$y = r \sin \theta$

Before we substitute, let us rewrite the equation to get:

$r(2 + 2 \sin \theta) = 10$

$r(1+ \sin \theta) = 5$

Expand :

$r+ r\sin \theta= 5$

We now substitute to get:

$\sqrt{ {x}^{2} + {y}^{2} } + y = 5$

This means that:

$\sqrt{ {x}^{2} + {y}^{2} }=5 - y$

Square:

${x}^{2} + {y}^{2} =(5 - y)^{2}$

Expand:

${x}^{2} + {y}^{2} =25 - 10y + {y}^{2}$

${x}^{2} =25 - 10y$

${x}^{2} - 25 = - 10y$

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This is a parabola (0,2.5) and turns upside down.

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3 years ago

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Answer:

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Step-by-step explanation:

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