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:
A. Complete the missing entries in this Excel Regression tool output. Enter negative values as negative numbers. ANOVA df SS MS F Significance F Regression 2 .8811 52.4464 Residual 7 .1179 .0168 Total Coefficients Standard Error t Stat P-value Intercept X1 X2.
Answer:
[0,∞), {y|y≥0}
Step-by-step explanation:
Answer:
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We are given two sides and their included angle. Using the side-angle-side method we can find the Area of the triangle using the following formula:
Area = 0.5 ab sin(γ)
a = Measure of first side = 3.2 feet
b = Measure of second side = 4.7 feet
γ = Angle between the two sides = 62 degrees
Using the values in the above formula, we get:
Area = 0.5 x ( 3.2) x (4.7) x (sin(62))
Area = 6.64 square feet (rounded to nearest hundredth)
Thus, the Area of the given triangle is 6.64 square feet
