That particular binomial expression can be simplified to . . . . . <em>1.03 t</em>
Answer: my teacher did this with me today.
Step-by-step explanation:
Explanation in picture
Answer:
![L(x)=\sqrt{10}+\frac{\sqrt{10}}{20}x](https://tex.z-dn.net/?f=L%28x%29%3D%5Csqrt%7B10%7D%2B%5Cfrac%7B%5Csqrt%7B10%7D%7D%7B20%7Dx)
Step-by-step explanation:
We are asked to find the tangent line approximation for
near
.
We will use linear approximation formula for a tangent line
of a function
at
to solve our given problem.
![L(x)=f(a)+f'(a)(x-a)](https://tex.z-dn.net/?f=L%28x%29%3Df%28a%29%2Bf%27%28a%29%28x-a%29)
Let us find value of function at
as:
![f(0)=\sqrt{10+x}=\sqrt{10+0}=\sqrt{10}](https://tex.z-dn.net/?f=f%280%29%3D%5Csqrt%7B10%2Bx%7D%3D%5Csqrt%7B10%2B0%7D%3D%5Csqrt%7B10%7D)
Now, we will find derivative of given function as:
![f(x)=\sqrt{10+x}=(10+x)^{\frac{1}{2}}](https://tex.z-dn.net/?f=f%28x%29%3D%5Csqrt%7B10%2Bx%7D%3D%2810%2Bx%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D)
![f'(x)=\frac{d}{dx}((10+x)^{\frac{1}{2}})\cdot \frac{d}{dx}(10+x)](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Cfrac%7Bd%7D%7Bdx%7D%28%2810%2Bx%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%29%5Ccdot%20%5Cfrac%7Bd%7D%7Bdx%7D%2810%2Bx%29)
![f'(x)=\frac{1}{2}(10+x)^{-\frac{1}{2}}\cdot 1](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Cfrac%7B1%7D%7B2%7D%2810%2Bx%29%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%5Ccdot%201)
![f'(x)=\frac{1}{2\sqrt{10+x}}](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Cfrac%7B1%7D%7B2%5Csqrt%7B10%2Bx%7D%7D)
Let us find derivative at ![x=0](https://tex.z-dn.net/?f=x%3D0)
![f'(0)=\frac{1}{2\sqrt{10+0}}=\frac{1}{2\sqrt{10}}](https://tex.z-dn.net/?f=f%27%280%29%3D%5Cfrac%7B1%7D%7B2%5Csqrt%7B10%2B0%7D%7D%3D%5Cfrac%7B1%7D%7B2%5Csqrt%7B10%7D%7D)
Upon substituting our given values in linear approximation formula, we will get:
![L(x)=\sqrt{10}+\frac{1}{2\sqrt{10}}x-0](https://tex.z-dn.net/?f=L%28x%29%3D%5Csqrt%7B10%7D%2B%5Cfrac%7B1%7D%7B2%5Csqrt%7B10%7D%7Dx-0)
![L(x)=\sqrt{10}+\frac{\sqrt{10}}{20}x](https://tex.z-dn.net/?f=L%28x%29%3D%5Csqrt%7B10%7D%2B%5Cfrac%7B%5Csqrt%7B10%7D%7D%7B20%7Dx)
Therefore, our required tangent line for approximation would be
.
Answer:
<A = 35degrees
<B =90degrees
<C = 55degrees
Step-by-step explanation:
Given the ratios of a triangle as 7:18:11
Total ratio = 7+18+11
Total ratio = 36
Since the smallest angle is 35degrees, hence <A = 35degrees
Get angle B;
<B = 18/36 * 180 (sum of angle in a triangle is 180degrees)
<B = 1/2 * 180
<B = 90degrees
Get angle C;
<C = 11/36 * 180
<C = 11 * 5
<C = 55degrees
Hence the value of A, B and C are 35, 90 and 55 degrees repectively
Answer:
The answer is B.
Step-by-step explanation:
The answer would be B because dividing 250,000 would get you 25,000 which would be 10% of the total cost. Dividing by 10 again would get you 2500 which would be 1% of the total cost. Divide 2500 by 2 and you'll get 1250. 1250 + 2500 would be 1.5% of the total cost.