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3 years ago

How much water is being collected per day? (Think slope!)

Mathematics

1 answer:

Verizon [17]3 years ago

3 0

Answer:

1.5 liters

Step-by-step explanation:

we have

x ------> the number of days

y -----> the amount of water collected in liters

To find out how much water is collected by day, determine the slope of the linear equation

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

Observing the graph

we have

(0,2) and (4,8)

substitute the values in the formula

$m=\frac{8-2}{4-0}$

$m=\frac{6}{4}$

$m=1.5\frac{l}{day}$

therefore

The amount of water collected is 1.5 liter by day

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Step-by-step explanation:

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Alex787 [66]

Answer:

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Step-by-step explanation:

step 1

Find the $sin(\theta)$

we know that

Applying the trigonometric identity

$sin^2(\theta)+ cos^2(\theta)=1$

we have

$cos(\theta)=-\frac{\sqrt{2}}{3}$

substitute

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step 2

Find the sec(β)

Applying the trigonometric identity

$tan^2(\beta)+1= sec^2(\beta)$

we have

$tan(\beta)=\frac{4}{3}$

substitute

$(\frac{4}{3})^2+1= sec^2(\beta)$

$\frac{16}{9}+1= sec^2(\beta)$

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we know

0≤β≤π/2 ----> II Quadrant

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$sec(\beta)=\frac{5}{3}$

Remember that

$sec(\beta)=\frac{1}{cos(\beta)}$

therefore

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step 3

Find the sin(β)

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$tan(\beta)=\frac{sin(\beta)}{cos(\beta)}$

we have

$tan(\beta)=\frac{4}{3}$

$cos(\beta)=\frac{3}{5}$

substitute

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therefore

$sin(\beta)=\frac{4}{5}$

step 4

Find sin(θ+β)

we know that

$sin(A + B) = sin A cos B + cos A sin B$

In this problem

$sin(\theta + \beta) = sin(\theta)cos(\beta)+ cos(\theta)sin (\beta)$

we have

$sin(\theta)=-\frac{\sqrt{7}}{3}$

$cos(\theta)=-\frac{\sqrt{2}}{3}$

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substitute the given values in the formula

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3 years ago

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