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3 years ago

Write an equation that is parallel to y=-4x+5 and passes through the point (-2,-1)

Mathematics

1 answer:

marta [7]3 years ago

8 0

The equation of line parallel to y=-4x+5 is y = -4x-9

Further explanation:

Given equation of line is:

y = -4x+5

Comparing it with the standard form of equation

$y=mx+b\\Then\\m = -4$

As the slopes of parallel lines is equal, the slope of the line parallel to given line will be same. Putting the value of slope in standard equation.

$y = mx +b\\y = -4x +b$

To find the value of b, the given point will be put in the equation

$-1 = -4x -2\\-1 = -4(-2) +b\\-1 = 8 +b\\-1 -8 = b\\-9 = b$

Putting the values of b and m in standard form

$y = -4x -9$

So, the equation of line parallel to y=-4x+5 is y = -4x-9

Keywords: Slope, Equations of lines, Point-slope equation of line

Learn more about point-slope form at:

#LearnwithBrainly

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Answer:

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3 years ago

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Answer:

Therefore the rate at which water level is dropping is $\frac{11}{21}$ in per minute.

Step-by-step explanation:

Given that,

The diameter of cylindrical bucket = 12 in.

Depth is increasing at the rate of = 4.0 in per minutes.

i.e $\frac{dh_1}{dt}=4$

$h_1$ is depth of the bucket.

The volume of the bucket is V = $\pi r^2 h$

$=\pi \times 6^2\itimes h_1$

$\therefore V=36\pi h_1$

Differentiating with respect yo t,

$\frac{dV}{dt}=36\pi \frac{dh_1}{dt}$

Putting $\frac{dh_1}{dt}=4$

$\therefore\frac{dV}{dt}=36\pi\times 4$

The rate of volume change of the bucket = The rate of volume change of the aquarium .

Given that,The aquarium measures 24 in × 36 in × 18 in.

When the water pumped out from the aquarium, the depth of the aquarium only changed.

Consider h be height of the aquarium.

The volume of the aquarium is V= ( 24× 36 ×h)

V= 24× 36 ×h

Differentiating with respect to t

$\frac{dV}{dt}=24\times 36 \times \frac{dh}{dt}$

Putting $\frac{dV}{dt}=36\pi\times 4$

$36\pi\times 4= 24\times 36\times \frac{dh}{dt}$

$\Rightarrow \frac{dh}{dt}=\frac{36\pi \times 4}{24\times 36}$

$\Rightarrow \frac{dh}{dt}=\frac{11}{21}$

Therefore the rate at which water level is dropping is $\frac{11}{21}$ in per minute.

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See attached image

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