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3 years ago

Direct Variation - Item 2845

Mathematics

1 answer:

Brums [2.3K]3 years ago

3 0

The equation of direct proportion is y = 62x

<h3>Direct variation</h3>

Two quantities are said to vary directly proportional to each other when an increase in one leads to an increase in the other or a decrease in one leads to a decrease in the other.

Direct variation is given by:

y = kx

where y, x are the variables and k is the constant of proportionality.

The equation of direct proportion is y = 62x

Find out more on Direct variation at: brainly.com/question/6499629

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Can somebody help me with math?<br> Answer ASAp

jeka57 [31]

Answer:

What is the question?

Step-by-step explanation:

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3 years ago

The sum of 3/4 and 18/19

SIZIF [17.4K]

The answer to this question is 2.

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3 years ago

Read 2 more answers

Suppose you would like to save P9000 invested at 8% compounded quarterly for 5 years and 6 months. (Note: Round off your answer

Sever21 [200]

Answer:

a) 13913

b) 4913.82

Step-by-step explanation:

The compound interest formula is given by:

$A(t) = P(1 + \frac{r}{n})^{nt}$

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

In this question:

Investment of 9000, so $P = 9000$

Interest rate of 8%, so $r = 0.08$

Compounded quarterly, so $n = 4$

5 years and 6 months, that is, 5 years and half, so $t = 5.5$

(a) How much would the value of her savings at the end of the term?

$A(t) = P(1 + \frac{r}{n})^{nt}$

$A(5.5) = 9000(1 + \frac{0.08}{4})^{4*5.5} = 13913.82$

(b) How much is the interest earned by your savings?

The amount subtracted by the principal. So

13913.82 - 9000 = 4913.82

5 0

3 years ago

Example 3 find the local maximum and minimum values and saddle points of f(x, y) = x4 + y4 − 4xy + 1. solution we first locate t

allsm [11]

$f(x,y)=x^4+y^4-4xy+1$

$\begin{cases}f_x=4x^3-4y\\f_y=4y^3-4x\end{cases}$

We have critical points whenever both partial derivatives vanish:

$4x^3-4y=0\implies x^3=y\implies x=y^{1/3}$
$4y^3-4x=0\implies y^3=x=y^{1/3}\implies y^6=y\implies y=0,y=-1,y=1$
$\begin{cases}y=0\implies x=0\\y=-1\implies x=-1\\y=1\implies x=1\end{cases}$

The Hessian is

$\mathbf H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}12x^2&-4\\-4&12y^2\end{bmatrix}$
$\det\mathbf H(x,y)=(12xy)^2-16$

At (0,0), we have $\det\mathbf H(0,0)=-16$ , so (0,0) is a saddle point.

At (-1, -1), we have $\det\mathbf H(-1,-1)=128>0$ and $f_{xx}(-1,-1)=12>0$ , so (-1, -1) is a local minimum.

At (1, 1), we have $\det\mathbf H(1,1)=128>0$ and $f_{xx}(1,1)=12>0$ , so (1, 1) is also a local minimum.

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3 years ago

Explain how to decide which is a better value. 4 greeting cards for $10 and 6 greeting cards for $14.

xxMikexx [17]

Answer:

I dont know if this is supposed to be solved a certain way for a class, but as a bargain shopper, this is what I would do to figure out the best value.

Step-by-step explanation:

First divide $10 by 4: 10.00/4=2.5 or $2.50 per card

Then, divide $14 by 6: 14.00/6=2.3333333 so about $2.33 per card

Now, just look at the two answers and see which one is less.

If you buy 4 cards for $10, you will pay $2.50 for each card and if you buy 6 cards for $14, you will pay about $2.33 for each card. Therefore, the better value would be the 6 cards for $14.

6 0

3 years ago