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3 years ago

7

Help with math!!!!!!!!!!!!!!!!

1 answer:

cricket20 [7]3 years ago

7 0

Answer:

7

Step-by-step explanation:

Because 7 x 1 = 7 (you have to multiply the numerator if the denominators are the same number)

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1. Determine the degree of homogeneity of the function S(x,y) = x^2 y + xy^2, and show that Euler's Theorem holds. 24 zvy

Dmitrij [34]

Answer:

Degree $k=3$

Step-by-step explanation:

The function that you have is a homogeneous function of degree $k=3$ . In fact, if $\lambda \in \mathbb{R}$ and $(x,y) \in \mathbb{R}^{2}$ we have that:

$s(\lambda x, \lambda y)=(\lambda y)(\lambda x)^{2}+(\lambda x)(\lambda y)^{2}=\lambda^{3}x^{2}y+\lambda^{3}xy^{2}=\lambda^{3}s(x,y)$

To verify that the Euler Theorem holds we need to show that:

$x\frac{\partial s}{\partial x}+y\frac{\partial s}{\partial y}=3 s(x,y)$ .

To do that let's compute the partial derivatives:

$\frac{\partial s}{\partial x}=2xy+y^2$

$\frac{\partial s}{\partial y}=x^2+2xy$

Then,

$x\frac{\partial s}{\partial x}+y\frac{\partial s}{\partial y}=2x^{2}y+xy^{2}+yx^{2}+2xy^{2}=3xy^{2}+3x^{2}y=3(x^{2}y+xy^{2})=3s(x,y).$

6 0

4 years ago

Suppose there are 8 runners competing in the 400 meter race. The fastest three runners will win a ribbon. In how many ways can r

yKpoI14uk [10]

Answer:

$^8C_3=336way$

Step-by-step explanation:

From the question we are told that

Number of runners $N=8$

Distance $d=400m$

Generally the top three places can be determined mathematically as

$^8C_3$

$^8C_3=336way$

therefore the top three can be determined in 336ways

6 0

3 years ago

The half-life of Radium-226 is 1590 years. If a sample contains 400 mg, how many mg will remain after 2000 years?

Assoli18 [71]

Answer:

167.27 mg.

Step-by-step explanation:

We have been given that the half-life of Radium-226 is 1590 years and a sample contains 400 mg.

We will use half life formula to solve our given problem.

$N(t)=N_0*(\frac{1}{2})^{\frac{t}{t/2}$ , where N(t)= Final amount after t years, $N_0$ = Original amount, t/2= half life in years.

Now let us substitute our given values in half-life formula.

$N(2000)=400*(\frac{1}{2})^{\frac{2000}{1590}$

$N(2000)=400*(0.5)^{1.2578616352201258}$

$N(2000)=400*0.4181633028874878239$

$N(2000)=167.26532115499512956\approx 167.27$

Therefore, the remaining amount of Radium-226 after 2000 years will be 167.27 mg.

3 0

3 years ago

PLEASE ANSWER ASAP!!

aliya0001 [1]

Answer is D

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Y=10x+16 looks like what on a graph

lakkis [162]

Here is my graph. Hope it helps

7 0

3 years ago