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:
the answer would be exactly 63
Step-by-step explanation: no explanation need
The answer to this is .15%
Answer:
A
Step-by-step explanation:
We are given that:
And we want to find:
Remember that tangent and cotangent are co-functions. In other words, they follow the cofunction identities:
Therefore, since tan(θ) = 1.3 and cot(90° - θ) = tan(θ), then cot(90° - θ) must also be 1.3.
Our answer is A.
Answer:
11 or -16
Step-by-step explanation:
The square of a number increased by 5 times the number is equal to 176.
Let the number be x
Then, x²+5x=176
x²+5x-176=0
We use splitting the middle term method
x²+16x-11x-176=0
x(x+16)-11(x+16)=0
(x-11)(x+16)=0
i.e. either x-11=0 or x+16=0
i.e. either x=11 or x=-16
Hence, the number is either 11 or -16
