Answer:
Step-by-step explanation:
5x + 4y = 20
You need to express y in terms of x.
isolate the y term
4y = -5x + 20
divide both sides by the coefficient of y
y = (-5/4)x + 5
f(x) = (-5/4)x + 5
The length of the function y = 3x over the given interval [0, 2] is 3.2 units
For given question,
We have been given a function y = 3x
We need to find the length of the function on the interval x = 0 to x = 2.
Let f(x) = 3x where f(x) = y
We have f'(x) = 3, so [f'(x)]² = 9.
Then the arc length is given by,
![\int\limits^a_b {\sqrt{1+[f'(x)]^2} } \, dx\\\\= \int\limits^2_0 {\sqrt{1+9} }\, dx\\\\=\sqrt{10}\\\\ =3.2](https://tex.z-dn.net/?f=%5Cint%5Climits%5Ea_b%20%7B%5Csqrt%7B1%2B%5Bf%27%28x%29%5D%5E2%7D%20%7D%20%5C%2C%20dx%5C%5C%5C%5C%3D%20%5Cint%5Climits%5E2_0%20%7B%5Csqrt%7B1%2B9%7D%20%7D%5C%2C%20dx%5C%5C%5C%5C%3D%5Csqrt%7B10%7D%5C%5C%5C%5C%20%3D3.2)
This means, the arc length is 3.2 units.
Therefore, the length of the function y = 3x over the given interval [0, 2] is 3.2 units
Learn more about the arc length here:
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Answer:
There are 22.5 meters of silver yarn
Step-by-step explanation:
Gold yarn : bronze yarn : silver yarn
10 : 7 : 3
Gold yarn = 10
bronze yarn = 7
silver yarn = 3
Total ratio = 20
Total meters = 150 meters
How much silver yarn is in the magic carpet?
Quantity of silver yarn in the carpet = silver yarn ratio / Total ratio × total meters of yarn
= 3 / 20 × 150
= 450 / 20
= 22.5 meters
There are 22.5 meters of silver yarn
Bronze yarn = bronze yarn ratio / Total ratio × total meters of yarn
= 7 / 20 × 150
= 1,050 / 20
= 52.5 meters
Bronze yarn = 52.5 meters
Quantity of gold yarn in the carpet = gold yarn ratio / Total ratio × total meters of yarn
= 10 / 20 × 150
= 1500 / 20
= 75 meters
Gold yarn = 75 meters
Answer:
(1,3) (2,6) (3,9) (4,12)
Step-by-step explanation:
Meanwhile the x value increases by 1, the y value increases by 3.
Answer:
B
Step-by-step explanation:
The slope is -3/7. Use the point-slope form to write the equation.
(y-8)=-3/7(x-5)
