Answer:
The linear approximation is ;
F(x,y) = x -5y - 1
Step-by-step explanation:
Here, we want to find the linear approximation of the given function at the indicated point.
We start by substituting the values then after wards finding the partial derivative with respect to x and then to y.
We finish by adding up these values after substituting the values of x and y into the differentiated partial equation. We then add up our results.
Please check attachment for complete solution and step by step explanation
9514 1404 393
Answer:
y = -3x +5
Step-by-step explanation:
The parallel line will have the same slope: m = -3.
The new y-intercept is ...
b = y -mx
y = -1 -(-3)(2) = -1 +6 = 5
Then the equation of the parallel line through (2, -1) is ...
y = -3x +5
![5N^2=2^2 \times 5^{7} \times x^{8}](https://tex.z-dn.net/?f=5N%5E2%3D2%5E2%20%5Ctimes%205%5E%7B7%7D%20%5Ctimes%20x%5E%7B8%7D)
Solution:
Given a number N in product of its prime factors.
![N=2 \times 5^{3} \times x^{4}](https://tex.z-dn.net/?f=N%3D2%20%5Ctimes%205%5E%7B3%7D%20%5Ctimes%20x%5E%7B4%7D)
Now, express
as a product of prime factors in index form.
Substitute
in place of N.
![5N^2=5\times(2 \times 5^{3} \times x^{4})^2](https://tex.z-dn.net/?f=5N%5E2%3D5%5Ctimes%282%20%5Ctimes%205%5E%7B3%7D%20%5Ctimes%20x%5E%7B4%7D%29%5E2)
Use exponential rule: ![\left(a^{m}\right)^{n}=a^{m n}](https://tex.z-dn.net/?f=%5Cleft%28a%5E%7Bm%7D%5Cright%29%5E%7Bn%7D%3Da%5E%7Bm%20n%7D)
Multiply the power 2 into the powers of factors of every number in the bracket.
![5N^2=5\times2^2 \times 5^{6} \times x^{8}](https://tex.z-dn.net/?f=5N%5E2%3D5%5Ctimes2%5E2%20%5Ctimes%205%5E%7B6%7D%20%5Ctimes%20x%5E%7B8%7D)
Arrange like terms together.
![5N^2=2^2 \times 5\times 5^{6} \times x^{8}](https://tex.z-dn.net/?f=5N%5E2%3D2%5E2%20%5Ctimes%205%5Ctimes%205%5E%7B6%7D%20%5Ctimes%20x%5E%7B8%7D)
Use exponential rule: ![a^{m} \times a^{n}=a^{m+n}](https://tex.z-dn.net/?f=a%5E%7Bm%7D%20%5Ctimes%20a%5E%7Bn%7D%3Da%5E%7Bm%2Bn%7D)
![5N^2=2^2 \times 5^{1+6} \times x^{8}](https://tex.z-dn.net/?f=5N%5E2%3D2%5E2%20%5Ctimes%205%5E%7B1%2B6%7D%20%5Ctimes%20x%5E%7B8%7D)
![5N^2=2^2 \times 5^{7} \times x^{8}](https://tex.z-dn.net/?f=5N%5E2%3D2%5E2%20%5Ctimes%205%5E%7B7%7D%20%5Ctimes%20x%5E%7B8%7D)
Hence
.
Answer:
Answer : 1,2,3,5,6,10,15,25,30,50,75,150, Related Links : Is 150 a rational number?
Step-by-step explanation:
The factors of 150.
Answer:
The average weight of new born otter was, ![1\frac{31}{40}](https://tex.z-dn.net/?f=1%5Cfrac%7B31%7D%7B40%7D)
Step-by-step explanation:
Let average weight of new born otter be x.
As per the given statement: At birth it's weight was 7/8 kilograms which is 9/10 kilogram less than the average weight of a new born otter in the aquarium
"
kg less than average weight of a new born otter" means ![x-\frac{9}{10}](https://tex.z-dn.net/?f=x-%5Cfrac%7B9%7D%7B10%7D)
As per the given information, we have;
![\frac{7}{8} = x -\frac{9}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B8%7D%20%3D%20x%20-%5Cfrac%7B9%7D%7B10%7D)
Add
both sides, we have;
![\frac{7}{8} + \frac{9}{10} = x](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B8%7D%20%2B%20%5Cfrac%7B9%7D%7B10%7D%20%3D%20x)
Take LCM of 8 and 10 is, 40
⇒![\frac{35+36}{40}=x](https://tex.z-dn.net/?f=%5Cfrac%7B35%2B36%7D%7B40%7D%3Dx)
Simplify:
![x = \frac{71}{40} = 1\frac{31}{40}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B71%7D%7B40%7D%20%3D%201%5Cfrac%7B31%7D%7B40%7D)
Therefore, the average weight of new born otter was, ![1\frac{31}{40}](https://tex.z-dn.net/?f=1%5Cfrac%7B31%7D%7B40%7D)