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2 years ago

If y varies directly as x, and y is 20 when x is 4, what is the constant of variation for this relation?

Mathematics

2 answers:

Mekhanik [1.2K]2 years ago

7 0

Answer:

[DATA EXPUNGED]

Step-by-step explanation:

[REDACTED]

solong [7]2 years ago

7 0

Answer:

Step-by-step explanation:their are many vbarity

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Use Lagrange multipliers to find the maximum and minimum values of

marusya05 [52]

The Lagrangian is

$L(x,y,\lambda)=x+8y+\lambda(x^2+y^2-4)$

It has critical points where the first order derivatives vanish:

$L_x=1+2\lambda x=0\implies\lambda=-\dfrac1{2x}$

$L_y=8+2\lambda y=0\implies\lambda=-\dfrac4y$

$L_\lambda=x^2+y^2-4=0$

From the first two equations we get

$-\dfrac1{2x}=-\dfrac4y\implies y=8x$

Then

$x^2+y^2=65x^2=4\implies x=\pm\dfrac2{\sqrt{65}}\implies y=\pm\dfrac{16}{\sqrt{65}}$

At these critical points, we have

$f\left(\dfrac2{\sqrt{65}},\dfrac{16}{\sqrt{65}}\right)=2\sqrt{65}\approx16.125$ (maximum)

$f\left(-\dfrac2{\sqrt{65}},-\dfrac{16}{\sqrt{65}}\right)=-2\sqrt{65}\approx-16.125$ (minimum)

5 0

3 years ago

Ashley, Bob, Claire, and Daniel are among 13 students who entered a lottery to win a free vacation to Paris.

AlladinOne [14]

Answer:

0.0014 = 0.14% probability that Ashley, Bob, Claire, and Daniel will be chosen.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the students are chosen is not important, so the combinations formula is used to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Desired outcomes:

4 students from a set of 4(Ashley, Bob, Claire, and Daniel). So

$D = C_{4,4} = \frac{4!}{4!(4-4)!} = 1$

Total outcomes:

4 students from a set of 13(number of students in the lottery). So

$T = C_{13,4} = \frac{13!}{4!(13-4)!} = 715$

Probability:

$p = \frac{D}{T} = \frac{1}{715} = 0.0014$

0.0014 = 0.14% probability that Ashley, Bob, Claire, and Daniel will be chosen.

7 0

2 years ago

A book costs $ 25.00. You have a coupon for 30 % off. Calculate the final price of the book with a 5% GST. (Begin by finding the

guapka [62]

Answer:

$18.375 or rounded = $18.38 (brainliest if correct)

Step-by-step explanation:

25.00- 7.5 = $17.5

5% of 17.5 = 0.875

17.5 +0.875 = 18.375

6 0

2 years ago

Calculate the following absolute value |-1-1+2|-|-1+2|-|-2|

Softa [21]

Answer:

-3

Hope This Helps!

8 0

2 years ago

Factorize 3ac-6ad-2bc+4bd

KatRina [158]

Answer:

(c - 2d) (3a - 2b)

Step-by-step explanation:

if you need the steps just ask me in the comments and I’ll type them lol

7 0

1 year ago