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2 years ago

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A gas station attendant has some antifreeze that is 40% alcohol and another type that is 60% alcohol. He wishes to make 1000 gal

lons of antifreeze that is 48% alcohol. How much of each kind should he use

1 answer:

Gennadij [26K]2 years ago

4 0

Answer:

600 Gallons of the 40% alcohol and 400 Gallons of the 60% alcohol

Step-by-step explanation:

N/A

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You need to convert your 3200 sq ft into yards which is 355.556 sq yards then you divide 355.556 by 25 to get 14.22224 bags of seed needed

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What is the equation of a line through the points (0, 9) and (3, 0)?

erastova [34]

Answer:

m = StartFraction 9 minus 0 Over 0 minus 3 EndFraction; y = –3x + 9

Step-by-step explanation:

The given points are the y-intercept and the x-intercept, so they can be used directly in the intercept form of the equation of a line.

x/(x-intercept) +y/(y-intercept) = 1

x/3 +y/9 = 1

Multiplying by 9 gives ...

3x +y = 9

This can be rearranged to the slope-intercept form ...

y = -3x +9

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The answer selection shown above is the only one that matches the slope and y-intercept of the line through the given points.

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2 years ago

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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).

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2 years ago

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