We are given with the expression y<span> = b cos t + t2 sin t and is asked to differentiate the function in terms of t. Based in the power law and law of products, we apply these to the given expresssion. the derivative is y' = -b sin t + t^2 * (cos t) + sin t * 2t. This is equal to </span>y' = sin t (-b +2t) + t^2 cos t.
Answer: ![3ab\sqrt[3]{b^4}](https://tex.z-dn.net/?f=3ab%5Csqrt%5B3%5D%7Bb%5E4%7D)
Step-by-step explanation:
Given the following expression:
![\sqrt[3]{27a^3b^7}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B27a%5E3b%5E7%7D)
You need to apply the Product of powers property, which states that:

Then, you can rewrite the expression as following:
![=\sqrt[3]{27a^3b^4b^3}](https://tex.z-dn.net/?f=%3D%5Csqrt%5B3%5D%7B27a%5E3b%5E4b%5E3%7D)
The next step is to descompose 27 into its prime factors:

Now you must substitute
inside the given root. Then:
![=\sqrt[3]{3^3a^3b^4b^3}](https://tex.z-dn.net/?f=%3D%5Csqrt%5B3%5D%7B3%5E3a%5E3b%5E4b%5E3%7D)
You need to remember that, according to Radicals properties:
![\sqrt[n]{a^n}=a^{\frac{n}{n}}=a^1=a](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Ba%5En%7D%3Da%5E%7B%5Cfrac%7Bn%7D%7Bn%7D%7D%3Da%5E1%3Da)
Therefore, the final step is to apply this property in order to finally get the expression is its simplest form. This is:
![=3^{\frac{3}{3}}a^{\frac{3}{3}}b^{\frac{4}{3}}b^{\frac{3}{3}}=3ab^{\frac{4}{3}}b=3ab\sqrt[3]{b^4}](https://tex.z-dn.net/?f=%3D3%5E%7B%5Cfrac%7B3%7D%7B3%7D%7Da%5E%7B%5Cfrac%7B3%7D%7B3%7D%7Db%5E%7B%5Cfrac%7B4%7D%7B3%7D%7Db%5E%7B%5Cfrac%7B3%7D%7B3%7D%7D%3D3ab%5E%7B%5Cfrac%7B4%7D%7B3%7D%7Db%3D3ab%5Csqrt%5B3%5D%7Bb%5E4%7D)
Answer:
Slope=4
x−intercept=−
4
16
=−4
b−intercept=
1
16
=16.0000
Step-by-step explanation:
The answer is 24. because you multiply 8 and 6 <span />
Answer:
2.8, 8.8, and -17 respectively.
Step-by-step explanation:
We need to find roots of the equation.