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pav-90 [236]
3 years ago
12

A system of equations consists of a line s of the equation y = x – 5 and a line t that passes through the points (0, 2) and (8,

–4). Answer the questions about line t to write the equation. What is the slope of line t? What is the y-intercept of line t? What is the equation in slope-intercept form of line t?
Mathematics
2 answers:
Anit [1.1K]3 years ago
9 0

Answer:

-0.75

2

y=-0.75x+2

Step-by-step explanation:

because e D g E n U i T y

GenaCL600 [577]3 years ago
5 0

Answer:

\text{The slope of the line t:}\ m=-\dfrac{3}{4}\\\\\text{The y-intercept of the line t:}\ b=2\\\\\text{The equation of a line t in the slope-intercept form:}\ y=-\dfrac{3}{4}x+2

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y=mx+b

m - slope

b - y-intercept → (0, b)

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

We have two points (8, -4) and (0, 2) → b = 2.

Calculate the slope:

m=\dfrac{2-(-4)}{0-8}=\dfrac{6}{-8}=-\dfrac{3}{4}

Therefore the equation of a line t in the slope-intercept form is:

y=-\dfrac{3}{4}x+2

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A cylindrical tank with radius 3 m is being filled with water at a rate of 4 m3/min. How fast is the height of the water increas
Fittoniya [83]

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<h3>How to solve?</h3>

With related rates, we need a function to relate the 2 variables, in this case it is clearly volume and height. The formula is:

#V=pi r^2 h#

There is radius in the formula, but in this problem, radius is constant so it is not a variable. We can substitute the value in:

#V=pi (5m)^2 h#

Since the rate in this problem is time related, we need to implicitly differentiate wrt (with respect to) time:

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In the problem, we are given #3(m^3)/min# which is #(dV)/(dt)#.

So we need to substitute this in:

#(dh)/(dt)=(3m^3)/(min (25m^2) pi)=3/(25 pi)m/(min)#

Hence,  Height of the water increasing is at rate of  #(dh)/(dt)=3/(25 pi)m/(min)#

<h3>Formula used: </h3>

#V=pi r^2 h#

To Learn more visit:

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4 0
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6 0
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kow [346]
Correct answer:
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