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3 years ago

Systems of equations by substitution

Mathematics

1 answer:

Korolek [52]3 years ago

6 0

Could you please clarify the question please by putting a question to be solved? Or are you asking for the definition?

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What is the apparent slope of the line graphed below

maria [59]

I think the answer would be -2.5 because 0-5=-5 and 4-2=2 you subtract the perfect points X1-x2 with y2-y1

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3 years ago

Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that it forms a pile in the shap

11Alexandr11 [23.1K]

Answer:

0.25 feet per minute

Step-by-step explanation:

Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.

$\dfrac{dV}{dt}=20$ ft^3/min$

$\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h$

Since base diameter = Height of the Cone

Radius of the Cone = h/2

Therefore,

$\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}$

$\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}$

Therefore: $\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=20$

We want to determine how fast is the height of the pile is increasing when the pile is 10 feet high.

$h=10$ feet$\\\\\dfrac{3\pi *10^2}{12}\dfrac{dh}{dt}=20\\25\pi \dfrac{dh}{dt}=20\\ \dfrac{dh}{dt}= \dfrac{20}{25\pi}\\ \dfrac{dh}{dt}=0.25$ feet per minute (to two decimal places.)$

When the pile is 10 feet high, the height of the pile is increasing at a rate of 0.25 feet per minute

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3 years ago

The graphs of the equations Ax + By =15 and Ax - By =9 intersect at (2, 1). Find A and B. Show or explain your reasoning

iVinArrow [24]

Hi here’s the answers hope this helps

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3 years ago

Hodel just got her driver's license. Her parents offer her two options. 1. They'll buy her a used car that will cost her $0.50 p

Romashka-Z-Leto [24]

Answer:

The second option will cost her less than the first one.

Step-by-step explanation:

In order to solve this problem we will create two functions to represent the cost of the car in function of the miles drove by her.

For the first option we have:

$cost_1(x) = 0.5*x$

For the second option we have:

$cost_2(x) = 5000 + 0.1*x$

Since she intends to drive it for 10,000 miles per year for 6 years, then the total mileage she intends to drive her car is 60,000 miles. Applying this to the formula of each car and we have:

$cost_1(60000) = 0.5*60000 = 30000$

$cost_2(60000) = 5000 + 60000*0.1 = 11000$

The second option will cost her less than the first one.

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3 years ago

Joe is making a recipe that calls for 3/4 teaspoon of cinnamon. His only measuring spoon holds 1/8 teaspoon. How many times will

allochka39001 [22]

He will need to fill his measuring cup 8 times

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3 years ago