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PtichkaEL [24]
3 years ago
7

Find the simplified form of the expression. give your answer in scientific notation (8x10^4)(9x10^-8)

Mathematics
1 answer:
allochka39001 [22]3 years ago
6 0
You multiply the 2 values together and B is the correct answer
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se the function to show that fx(0, 0) and fy(0, 0) both exist, but that f is not differentiable at (0, 0). f(x, y) = 9x2y x4 + y
alexandr1967 [171]

Answer:

It is proved that f_x, f_y exixts at (0,0) but not differentiable there.

Step-by-step explanation:

Given function is,

f(x,y)=\frac{9x^2y}{x^4+y^2}; (x,y)\neq (0,0)

  • To show exixtance of f_x(0,0), f_y(0,0) we take,

f_x(0,0)=\lim_{h\to 0}\frac{f(h+0,k+0)-f(0,0)}{h}=\lim_{h\to 0}\frac{\frac{9h^2k}{h^4+k^2}-0}{h}\\\therefore f_x(0,0)=\lim_{h\to 0}\frac{9hk}{h^4+k^2}=\lim_{h\to 0}\frac{9k}{h^3+\frac{k^2}{h}}=0    exists.

And,

f_y(0,0)=\lim_{k\to 0}\frac{f(h,k)-f(0,0)}{k}=\lim_{k\to 0}\frac{9h^2k}{k(h^4+k^2)}=\lim_{k\to 0}\frac{9h^2}{h^4+k^2}=\frac{9}{h^2}   exists.

  • To show f(x,y) is not differentiable at the origin cheaking continuity at origin be such that,

\lim_{(x,y)\to (0,0)}\frac{9x^2y}{x^4+y^2}=\lim_{x\to 0\\ y=mx^2}\frac{9x^2y}{x^4+y^2}=\frac{9x^2\times m x^2}{x^4+m^2x^4}=\frac{9m}{1+m^2}  where m is a variable.

which depends on various values of m, therefore limit does not exists. So f(x,y) is not continuous at (0,0). Hence it is not differentiable at (0,0).

4 0
3 years ago
Adam used 1072.4 gallons of water over the course of 7 days. How much water did Adam use, on average, each day?
Shkiper50 [21]

Answer:

153.2 gallons per day

Step-by-step explanation:

To find out how much water he used each day, take the amount of water he used and divide by the number of days

1072.4 gallons / 7 days

153.2 gallons per day

4 0
3 years ago
Hello! I need help please answer these correctly thanks in advance
lana [24]

Answer:

1a  the square root of 37

1b the same as a

2 y=3x+2

Step-by-step explanation:

a and b use the distance formula

for number 2 use rise over run to find the slope and find where the line intersects to find the y intercept.

Hope this helps :)

8 0
2 years ago
Beth poured the same amount of juice into 10 glasses. She used 2 quarts of juice. How much juice is in each glass?
tia_tia [17]

Answer:

6.4 ounces

Step-by-step explanation:

If you divide 2 quarts by 10 you get 0.2 quarts per glass. That converts to 6.4 ounces.

5 0
3 years ago
Read 2 more answers
Similar triangles are congruent.
Alex Ar [27]

Answer:

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion . In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
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