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4 years ago

0.74 as a fraction in simplest form

Mathematics

2 answers:

aliya0001 [1]4 years ago

3 0

The answer is 37/50......

vova2212 [387]4 years ago

3 0

0.74.....the last digit (4) is in the hundredths place...so put it over 100

74/100 reduces to 37/50 <==

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Compute the second partial derivatives ∂2f ∂x2 , ∂2f ∂x ∂y , ∂2f ∂y ∂x , ∂2f ∂y2 for the following function. f(x, y) = 2xy (x2 +

blsea [12.9K]

Answer with step-by-step explanation:

We are given that a function

$f(x,y)=2xy(x^2+y^2)^2$

Differentiate partially w.r.t x

Then, we get

$\frac{\delta f}{\delta x}=2y(x^2+y^2)^2+8x^2y(x^2+y^2)=(x^2+y^2)(2x^2y+2y^3+8x^2y)=2(5x^2y+y^3)(x^2+y^2)$

Differentiate again w.r.t x

$\frac{\delta^2f}{\delta x^2}=2(10xy)(x^2+y^2)+4x(5x^2y+y^3)=20x^3y+20xy^3+20x^3y+4xy^3=40x^3y+24xy^3$

Differentiate function w.r.t y

$\frac{\delta f}{\delta y}=2x(x^2+y^2)^2+2xy\times 2(x^2+y^2)\times 2y$

$\frac{\delta f}{\delta y}=(x^2+y^2)(2x^3+2xy^2+8xy^2)=2(x^2+y^2)(x^3+5xy^2)$

Again differentiate w.r.t y

$\frac{\delta^2f}{\delta x^2}=2(2y)(x^3+5xy^2)+20xy(x^2+y^2)=4x^3y+20xy^3+20x^3y+20xy^3=24x^3y+40xy^3$

Differentiate partially w.r.t y

$\frac{\delta^2f}{\delta y\delta x}=2(2y(5x^2y+y^3)+(x^2+y^2)(5x^2+3y^2))=10x^4+36x^2y^2+10y^4$

$\frac{\delta^2f}{\delta y\delta x}=10x^4+36x^2y^2+10y^4$ $\frac{\delta^2f}{\delta x\delat y}=2(2x(x^3+5xy^2)+(3x^2+5y^2)(x^2+y^2))=10x^4+36x^2y^2+10y^4$

$\frac{\delta^2f}{\delta x\delat y}=10x^4+36x^2y^2+10y^4$

Hence, if f(x,y) is of class $C^2$ (is twice continuously differentiable), then the mixed partial derivatives are equal.

i.e $\frac{\delta^2f}{\delta y\delta x}=\frac{\delta^2f}{\delta x\delta y}$

8 0

4 years ago

Please, solve for x!

AlekseyPX

Answer:
x= 232

Explanation:
The angle I think is 180 degrees, meaning both sides have to add up to 180. sorry i might be wrong

5 0

4 years ago

Suppose you and a partner want to make a recipe for 25 friends. Adjust the amount of each ingredient below to 25 servings.

mel-nik [20]

Well, we are starting with 100 servings, and we're trying to find the amount of ingredients necessary to create 25 servings. To do this, we must first simply divide 25 by 100 to see what the ratio would be, and when we do this, we can see that

25 / 100 = $\frac{25}{100}$ = $\frac{1}{4}$

Now, all we have to do is multiply all of the ingredients by the ratio to find out how much we would use for only a quarter of the amount that the original recipe calls for.

In order to multiply by a whole number by a fraction, you just need to make sure that the numerator is lined up with the whole number, and then put a 1 below the whole number to turn it into a fraction. Then, you can divide the numerators and denominators together, respectively.

1.) 100 * $\frac{1}{4}$ = $\frac{100}{1} * \frac{1}{4}$ = $\frac{100 * 1}{1 * 4}$ = $\frac{100}{4}$ = 25

2.) 72 * $\frac{1}{4}$ = $\frac{72}{1} * \frac{1}{4}$ = $\frac{72 * 1}{1*4}$ = $\frac{72}{4}$ = 18

3.) 14 * $\frac{1}{4}$ = $\frac{14}{1} * \frac{1}{4}$ = $\frac{14 *1}{1*4}$ = $\frac{14}{4}$ = 3 $\frac{1}{2}$

4.) 6 * $\frac{1}{4}$ = $\frac{6}{1} * \frac{1}{4}$ = $\frac{6*1}{1*4}$ = $\frac{6}{4}$ = 1 $\frac{1}{2}$ 

5.) 24 * $\frac{1}{4}$ = $\frac{24}{1} * \frac{1}{4}$ = $\frac{24*1}{1*4}$ = $\frac{24}{4}$ = 6

6.) 80 * $\frac{1}{4}$ = $\frac{80}{1} * \frac{1}{4}$ = $\frac{80*1}{1*4}$ = $\frac{80}{4}$ = 20

7.) 50 * $\frac{1}{4}$ = $\frac{50}{1} * \frac{1}{4}$ = $\frac{50*1}{1*4}$ = $\frac{50}{4}$ = 12 $\frac{1}{2}$

And there you have the recipe ingredients necessary for 25 servings.
Hope that helped! =)

5 0

4 years ago

Read 2 more answers

Scientists are examining two different strains of a particular bacteria. The length of one strain of the bacteria measures 0.000

vesna_86 [32]

Scientists are examining two different strains of a particular bacteria. The length of one strain of the bacteria measures 0.000000368

mm, while the length of the second strain measures 0.000000064 mm. How much larger is the first strain than the second?

We can figure this out using scientific notation.

$0.000000368 - 0.000000064$