Given that p varies directly as q and
[tex] \sqrt{q} [/tex]
varies inversely with t², show how p varies with t.​

Answers

Answer 1

Answer:

p varies inversely with t⁴

Step-by-step explanation:

Direct variation:

y = kx, where k is constant

Inverse variation:

y = k/x, where k is constant

Given:

p = kq   (1)

and

√q = k/t²    (2)

From the first equation we can see:

kq = p ⇒ q = (1/k)p ⇒ q = np, where n is a constant

It means if p varies directly as q, then q directly varies as p.

Square the second equation:

q = k²/t⁴ = m / t⁴, where m is constant

Since p varies directly as q and q varies inversely with t⁴, we can state p varies inversely with t⁴.


Related Questions

May I please get help i really dont understand, and would like some help

Please and thank you!

Answers

The answer is after 8 days

Answer:

8 days

Step-by-step explanation:

Every day, 1.26 stock is returned. You want to find the number of days until it reaches 10.08, so create an equation. x represents days.

1.26 * x = 10.08

x = 8

Graph the following features: Slope = 4 Y-intercept = 4​

Answers

Answer:

Step-by-step explanation:

Equation of the line

[tex]\\ \sf\longmapsto y=mx+b[/tex]

m=4b=4

[tex]\\ \sf\longmapsto y=4x+4[/tex]

x2-8x+12=0


Someone help me

Answers

[tex]\large\boxed{\tt\:Question}[/tex]

x² - 8x + 12 = 0

Hello meremyj! Here's your answer with explanation.

[tex]\large\boxed{\tt\:Answer\:with\:Explanation}[/tex]

[tex]x ^ { 2 } - 8 x + 12[/tex]

Use the biquadratic formula =》 [tex]x=\frac{-b±\sqrt{\left(-b\right)^{2}-4 ac}}{2}[/tex]

Now,

   b = 8    c = 12    a =  1

Using the biquadratic formula & substituting the values....

[tex]x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 12}}{2} \\x=\frac{-\left(-8\right)±\sqrt{64-4\times 12}}{2} \\x=\frac{-\left(-8\right)±\sqrt{64-48}}{2} \\x=\frac{-\left(-8\right)±\sqrt{16}}{2} \\x=\frac{-\left(-8\right)±4}{2} \\\underline{\underline{x=\frac{8±4}{2}} }[/tex]

Now, solve when  [tex]x=\frac{8+4}{2}[/tex]

[tex]x=\frac{8+4}{2}\\x=\frac{12}{2} \\\boxed{\bf\:x=6 }[/tex]

Now, solve when [tex]x = \frac{8-4}{2}[/tex]

[tex]x = \frac{8-4}{2}\\x = \frac{4}{2}\\\boxed{\bf\:x=2}[/tex]

______________

The value of  x  can be 6 & 2.

______________

Hope it'll help you!

Lucäžž

I need help finding this answer

Answers

y = -2x - 4

--> Swap sides so that all variable terms are on the left hand side

-2x - 4 = y

--> Add 4 to both sides

-2x = y + 4

--> Divide both sides by -2

-2x/-2 = y+4/-2

--> Dividing by -2 undoes the multiplication by -2.

x = y+4/-2

--> Divide y+4 by -2

x = -y /2 -2

-------------------------------------------------------------

y = 1/4x + 5

--> Swap sides so that all variable terms are on the left hand side.

1/4x + 5 = y

--> Subtract 5 from both sides.

1/4x = y - 5

--> Multiply both sides by 4.

1/4x 1/4 = y - 5/ 1/4

--> Dividing by 1/4 undoes the multiplication by 1/4.

x = y - 5/ 1/4

--> Divide y - 5 by 1/4 by multiplying y - 5 by the reciprocal of 1/4.

x = 4y - 20

Hope this helps you!

1) Order the numbers from least to greatest.
=2
3
3.5
2.5
2
NI
PLEASE HELP

Answers

Answer:

2, 2, 2.5, 3, 3.5

Step-by-step explanation:

Answer:

2, 2.5, 3, 3.5

Even thought there are two "2's", you only list one making it 2,2.5,3,3.5 instead of 2,2,2.5,3,3.5

here are 8 cardsthere is a number on each of these 6 cards

Answers

Answer:

I don't know

Step-by-step explanation:

sorry I apologize

Help me on this, please?

Answers

Answer:

angle 6 is 117

angle 7 is 63

Step-by-step explanation:

Find the value of x and y and each labeled
angle.

Answers

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The required values are ~

[tex]\fbox \colorbox{black}{ \colorbox{white}{x} \:  \:  \:   \:  \:  \:  \: \: \colorbox{white}{=}  \:  \:  \:  \:  \:   + \colorbox{white}{40 \degree}}[/tex]

[tex]\fbox \colorbox{black}{ \colorbox{white}{y} \:  \:  \:   \:  \:  \:  \: \: \colorbox{white}{=}  \:  \:  \:  \:  \:   + \colorbox{white}{80 \degree}}[/tex]

[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]

From the given figure, we can infer that ~

3x - 20° + 2x = 180°

(by linear pair)

now, let's solve for x ~

[tex]5x - 20 \degree = 180 \degree[/tex]

[tex]5x = 180 \degree + 20 \degree[/tex]

[tex]5x = 200 \degree[/tex]

[tex]x = 200 \degree \div 5[/tex]

[tex]x = 40 \degree[/tex]

And, we can see that 2x = y (by alternate interior angle pair)

So, let's find the value of y ~

[tex]2x[/tex]

[tex]2 \times 40 \degree[/tex]

[tex]80 \degree[/tex]

Answer:

x = 40

3x - 20 = 100

2x = 80

y = 80

2x - 15 = 65

Step-by-step explanation:

The angles 3x - 20 and 2x are a linear pair, so they are supplementary. Their measures has a sum of 180°.

Angles 2x and y are alternate interior angles, so they are congruent.

Once we find the value of x, we can find the measure of angle 2x - 15.

3x - 20 + 2x = 180

5x = 200

x = 40

3x - 20 = 3(40) - 20 = 120 - 20 = 100

2x = 2(40) = 80

y = x = 80

2x - 15 = 2(40) - 15 = 80 - 15 = 65

how do you solve this I'm on a time crunch

Answers

Answer:

19.59≈20

Step-by-step explanation:

Have a nice day

Using Pythagoras Theorem we can find the 3rd side of a right angled triangle.

Steps are there in the image I attached.

Hope it helps you...

Please mark as Brainlliest!!!

A number is 5 less than 2 times another number. Their sum is 25. What are the 2 numbers ?

Answers

Answer:

I don't understand the question but I think the answer is either 10 or 30

expand and simplify a(a+2)

Answers

Answer:

a²+2a

Step-by-step explanation:

multiple a with a and 2

Please help im in a hurry

Answers

Answer:

I can't explain this discrepancy other than to suggest that they are talking about 2 different groups.  The boss has included his salary in the average, but the employee is only concerned about the wage of the average worker.

Step-by-step explanation:

Nadine received the same score on each turn in an online game. Her score on each turn was −24. She had 4 turns.

What was Nadine's final score?

Answers

Answer:

Step-by-step explanation:

-24 x 4 = -96

Write the following phrase as an algebraic expression. Use k for the unknown.

"The product of 20 and a number"

Answers

Answer: 20k

Step-by-step explanation: product means to multiply. Use k for the unknown number. 20 times k can be written as 20k.

a. For y = 5+ 80 when x = 4, what does y equal?
b. For a = 3 - 5c when c = -0.5, what does a equal?
c. For n = 2d2 – 5 when d = -2, what does n equal?
n
d. For v = -3(1 – 3) when r = -1, what does v equal?

Answers

a. y = 5x + 80 = 5*4 + 80 = 20 + 80  = 100

b. a = 3-5c = 3 - 5*(-0.5) = 3 - (-2.5) = 3 + 2.5 + 5.5

c. n = 2d² - 5 = 2*(-2)² - 5 = 2* 4 - 5 = 8 - 5 = 3

d. v = -3(1-3r) = -3(1-3(-1)) = -3(1+3) = -3*4=-12

A group of 3 adults and 10 children bought tickets to watch a dance performance.Each adult ticket cost $7 more than each child ticket.The group paid a total of $125.Find the child ticket cost.

Answers

Answer:

8$

Step-by-step explanation:

$54= adults $71=kids which would equal $125 in total and when you divide $71 by 10 because there’s 10 kids you should get $7

What multiple of five is also a factor of five

Answers

Hello, hope you are having a remarkable day. :)

These are the multiples of 5:

5, 10, 15, 20, 25, 30, 35...

These are the factors of 5:

1, 5

As we can see, the number 5 is both a multiple of 5 and a factor of 5.

Hope it helps. Ask me if you have any queries.

~An emotional teen who helps others with joy

Good luck.

Compare the fractions.


​10\14,3\7​


Enter the correct inequality in the box.

Answers

Answer:

10/14 > 3/7

Step-by-step explanation:

L.C.D of these two fractions is 14:

10/14 = 10/14

3/7 = 6/14

10 is bigger than 6.

Please help and NO LINKS!

Answers

Answer:

2/100 is the answer to the question

Answer:

B

Step-by-step explanation:

I need help please !

Answers

Answer:

y column: 1st = -7 , 2nd = -5 , 3rd = -3 , 4th = -1 , 5th = 1

Harper is knitting a scarf for her cousin's birthday. She plans to knit every night, making the scarf 5 centimeters longer each night. Write an equation that shows the relationship between the number of nights Harper spends knitting, x, and the length of the scarf in centimeters, y.

Answers

The equation that shows the relationship between x and y is:

y = 5x

A linear equation is in the form:

y = mx + b

where m is the rate of change and b is the initial value of y, y, x are variables.

Let x represent the number of nights knitting and y represent the length of the scarf.

The equation that shows the relationship between x and y is:

y = 5x

Find out more at: https://brainly.com/question/13911928

Johnny has a bag full of marbles that he keeps in his desk. He has 35 red marbles and 25 green marbles. Find the ratio of red marbles to green marbles, and put it in its simplest form.​

Answers

Answer:

7:5

Step-by-step explanation:

Ratio between red and green marbles is simply the number of red marbles to the number of green marbles.

---------------------

35:25

To simplify it, you divide both of them by 5 (which is the highest common factor) to get

--------------------

7:5

Owen's score in a card game is 6
points away from zero. If David's score
is the opposite of Owen's and is a
positive value, what is David's score?

Answers

Answer:

aaa is easy you can pitch the ball

Owen's score will be (-6) and David's score will be opposite to that of Owen's score and a positive value, which will be (+6).

What is absolute value of a number?

The absolute value of a number is the magnitude of number. Absolute value describes the distance from zero that a number is on the number line, without considering direction.

We have Owen's score in a card game is 6 points away from zero. David's score is the opposite of Owen's and is a positive value.

For a number [x], such that [x] < 0, the absolute value would be -

v[a] = -x

A number cannot be negative and positive at the same time, therefore, Owens score is 6 points away from 0, but in the negative direction of number line. So, Owen's score will be (-6) and David's score will be opposite to that of Owen's score and a positive value, which will be (+6).

Therefore, Owen's score will be (-6) and David's score will be opposite to that of Owen's score and a positive value, which will be (+6).

To solve more questions on number line, visit the link below-

https://brainly.com/question/24402764

#SPJ2

I lowered the points because people were stealing them.

Answers

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

Domain ~

[tex] - 6 \leqslant x \leqslant - 1[/tex]

Range ~

[tex] - 5 \leqslant x \leqslant - 3[/tex]

Domain and range are correct in the other answer. Slope is -2/5 (negative two fifths), and y-intercept is not applicable because the line segment does not cross the y axis, however if you need an answer the line would keep going and would cross the y axis at 5.4 or 27/5 (not sure which form you need)

8 less than 4 times a number is 76. Find the number.

Answers

Answer:

the answer is twenty one

what is the value of a in a/5 + 3= 8

Answers

Answer:

Step-by-step explanation:

what is the value of a in a/5 + 3= 8

a/5 + 3= 8

a/5 = 8 - 3

a/5 = 5

a = 5 * 5

a = 25

Answer: a= 25

Step-by-step explanation:

first, you'll have to write the opposite of the + symbol which is - and then you'll have to lose the 3 by substracting it with, so the equation will look like this: a/5= 8-3 not 8+3

a/5=5

after that step you'll have to multiply 5 from the equal sgin with the 5 that is divided by a, so the final equation looks like this:

a=5x5

a=25

now let's make a verification:

25/5+3=8

5+3=8

a=25

hope I helped you :)

2315 x 584 / 591 x 841

Answers

Answer:

About 2.72 rounded

Step-by-step explanation:

PEMDAS

:))

The product of a number t and 3 decreased by 1 is 11.Write an equation that models the verbal sentence. Solve the equation. What is the number?

Answers

3t-1=11
Add one on both sides
3t=12
Divide 3 on both sides
t=4

volume of a cube is 343 cm cube . find the edge​

Answers

Answer:

Edge: 7 cm

Step-by-step explanation:

Cubic root of 343 = 7

Can someone please help me with this

Answers

Answer:

f(x) = 3x +4f(x) = 5x +2f(x) = -4x +11f(x) = -4x +11 (same table as problem 3)

Step-by-step explanation:

To write the equation for f(x) in slope-intercept form, you need to know the slope and the y-intercept. The y-intercept is the value of f(x) when x=0. You can read this directly from the table.

The slope is the ratio of the change in f(x) to the change in x. It can be computed using the formula ...

  m = (y2 -y2)/(x2 -x1)

where (x1, y1) and (x2, y2) are any two pairs of numbers from the table. You can use the first two table rows, for example.

__

1. m = (10 -4)/(3 -0) = 6/3 = 2; y-intercept = 4 (from ordered pair (0, 4))

  y = mx +b . . . . line with slope m and y-intercept b

  f(x) = 2x +4

__

2. m = (2 -(-3))/(0 -(-1)) = 5/1 = 5

  f(x) = 5x +2

__

3. m = (11 -19)/(0 -(-2)) = -8/2 = -4

  f(x) = -4x +11

__

4. same as 3.

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