If a varies jointly as b and c,
and a=6 when b=2 and a=3.
Find the variation constant and
the equation of variation.​

Answers

Answer 1

Given:

a varies jointly as b and c.

a=6 when b=2 and a=3.

To find:

The variation constant and the equation of variation.

Solution:

a varies jointly as b and c.

[tex]a\propto bc[/tex]

[tex]a=kbc[/tex]              ...(i)

Where, k is the constant of proportionality.

a=6 when b=2 and a=3.

[tex]6=k(2)(3)[/tex]

[tex]6=6k[/tex]

[tex]\dfrac{6}{6}=k[/tex]

[tex]1=k[/tex]

The value of k is 1.

Putting k=1 in (i), we get

[tex]w=1xy[/tex]

[tex]w=xy[/tex]

Therefore, the variation constant is 1 and the equation of variation is [tex]w=xy[/tex].


Related Questions

Guys help I’ve been trying to solve this problem for the past 40 minutes.

Answers

Answer:

56 degrees since you set the two equations equal to each other and then plug the value of p (which is 11) back in to find the answer.

The stock of Company A gained 5% today to $54.60. What was the opening price of
the stock in the beginning of the day?

Answers

Answer: $51.85

Step-by-step explanation:

To find the answer, you would divide $54.60 by 100. You do that to figure out the amount of money for 1%. Then you multiply 5 to figure out 5%. Lastly, you would subtract the answer by $54.60 since your finding out how much it was at the beginning of the day. Equation: $54.60 ÷100= $.546 x 5= 2.73. 54.60- 2.75 =51.85

$51.85

To find the answer, you would divide $54.60 by 100. You do that to figure out the amount of money of 1%

Then you multiply 5 to figure out 5%. Subtract the answer by $54.60 since your finding out how much it was at the beginning of the day.

Equation: $54.60 ÷100= $.546 x 5= 2.73. 54.60- 2.75 =51.85.

Final result: $51.85

In a certain year, the average e-mail user sent or received 111 e-mails each day. The number of e-mails received was 3 more than twice the number
sent. How many were sent and how many were received each day?

Answers

Answer:

Number of sent mail = 36

Number of received mail = 75

Step-by-step explanation:

Let,

x be the number of mails sent

y be the number of mails received

According to given statement;

x + y = 111      Eqn 1

y = 2x + 3     Eqn 2

Putting value of y from Eqn 2 in Eqn 1

x + 2x + 3 = 111

3x = 111 - 3

3x = 108

Dividing both sides by 3

[tex]\frac{3x}{3}=\frac{108}{3}\\x = 36[/tex]

Putting x = 36 in Eqn 2

y = 2(36) + 3

y = 72 + 3 = 75

Hence,

Number of sent mail = 36

Number of received mail = 75

What is the measure of angle P?

Answers

Answer:

60

Step-by-step explanation:

step 1: 180°-130°= 50

step 2: 180-110= 70

step 3: 70+50= 120

step 4: 180°-120°= 60

using pythagoras theorem if a = 3, b = 4 what is c?

3
4
5
6
3.6

Answers

Answer:

5

Step-by-step explanation:

[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ \\ {3}^{2} + {4}^{2} = {c}^{2} \\ \\ 9 + 16 = {c}^{2} \\ \\ {c}^{2} = 25 \\ \\ c = \sqrt{25} \\ \\ c = 5[/tex]

Which of the following expressions will result in a product less than zero?
А
6.4 x (-3.5)
B
-7.1 x (2.5)
С
-2.3 (-1.9)
D
9.2 x (4.0)

Answers

Answer:

All of the except for D and C

Step-by-step explanation:

A negative times a positive is always negative

Answer:

A,B

Step-by-step explanation:

please help i’ll give you and thanks and brainliest

Answers

Answer:

105

160

150

Step-by-step explanation:

This is just simple subtraction.

180-75=105

180-20=160

180-30=150

Find the missing side of the right triangle. Write the value only.

Answers

The missing side is 30

reduce to the simplest form[tex]\frac{286}{858}[/tex]

Answers

Answer:

143 over 428

Step-by-step explanation:

Classify 5x5 - 5x3 + 2x2 by degree.

Answers

Answer:

295 is the answer... god bless

Answer25

Step-by-step explanation:

The ordered pairs (8,12). (16, 24), (x, 21), (26, y) represent a proportional relationship

Find the value of x and the value of y.

Select the two correct answers.

A y=56

B. x= 14

C. x=7

D. y=39

Ex= 9

F. y = 42

Answers

Answer: B. x= 14

D. y=39

Step-by-step explanation:

First and foremost, we need to calculate the constant of proportionality. This will be:

(8,12).

y = kx.

12 = 8k

k = 12/8

k = 1.5

(16, 24),

y = kx

24 = 16k

k = 24/16

k = 1.5

(x, 21),

y = kx

x = y/k

x = 21/1.5

x = 14

(26, y)

y = kx

y = 26 × 1.5

y = 39

Not drawn
accurately
AB is parallel to CD.
LMN and PMQ are straight lines.
MQ = MN
B
Work out the value of x. *
(3 Points)
Diagram not drawn accurately.
-D
The value must be a number

Answers

so first u want to get a ruler to measure each sides, there gonna seem big at first so divide what you get on the ruler by 2 so its smaller, then do it for all sides.

HURRY
1/12 is the same as 1÷12. What is the exact quotient in decimal form of 1÷12?

Answers

Answer: Yes 1/12 is the same as 1 ÷ 12

decimal form is 0.083333333333333333(3 is repeating)

Step-by-step explanation:

Answer:

0.08333333333

Step-by-step explanation: since i helped can i have brainlist please :D

The. Ordered pair?

Is this a function yes or no?

Answers

Yes. It is a function I don’t know why but I know it is

Solve for u. m/u^2+r=−k−y

Answers

9514 1404 393

Answer:

  u = ±√(-m/(k+r+y))

Step-by-step explanation:

Subtract r, rearrange, then take the square root.

  [tex]\dfrac{m}{u^2}+r=-k-y \qquad\text{given}\\\\ \dfrac{m}{u^2}=-k-y-r\\\\-\dfrac{m}{k+r+y}=u^2\\\\ \boxed{u=\pm\sqrt{-\dfrac{m}{k+r+y}}}[/tex]

Answer: +/- sqrt(m/-k-y-r)

Step-by-step explanation:

Graph y-4=2x and identify
the slope and y-intercept.

Answers

Answer:

slope is 2 and y-intercept is (0, 4)

Step-by-step explanation:

Answer:

s- 2       y int- 4

Step-by-step explanation:

If GEOM is a square, find m2GQE.

Answers

Answer:

90 is correct answer of it question

can someone please help me?

Answers

First off, a triangle will be 180 all together, so, x + 59 + x + 51 = 180, 59 + 51 is 110, x + x is 2x, 180 - 110 is 70 so you have 2x = 70, now divide both sides by two, The left will cancel out to x and the other will be 35, x = 35, now you are looking for angle a, in order to find this, you have to plug in your X, so 51+35 is 86, that should be your answer, I hope this helps!

Jada had read 2/3 of a book . She has read 60 pages so far . How many pages are in the whole book?

Answers

90 pages in the whole book

Find the missing side of each right triangle. Side c is the hypotenuse. Sides a and bare
the
legs. Round your answers to the nearest tenth if necessary.
a = 8.8 ft, b = 9 ft

Answers

Answer:  12.6 ft

Step-by-step explanation:

a = 8.8 ft

b = 9 ft

c = ?

Since it is a right triangle, we can use the Pythagorean Theorem to solve for missing side c, the hypotenuse.

a^2 + b^2 = c^2

(8.8)^2 + (9)^2 = c^2

158.44 = c^2

(158.44)^(1/2) = c

12.5873 = c

c = 12.6 ft (rounded to the nearest tenth)

What hazard is present in this image?

Select the best option.


A mat that has upturned edges


Hair clippings on the floor


Tool cord left out


Spills on floor

Answers

Answer:

spills on the floor

Step-by-step explanation:

there is liquid of some sort someone could slip and hurt themselves. hope this helps

please solve for b

a=b/c

Answers

Answer:

b = ac

Step-by-step explanation:

Solve for b by simplifying both sides of the equation, then isolating the variable.

Answer:

b= ac

Solve for b by simplifying both sides of the equation, then isolating the variable.

2x + y = 11

3x - y = 4

Answers

Answer:

[tex]x=3,y=5[/tex]

Step-by-step explanation:

Add the equations together and solve for x.

[tex](2x + y )+ (3x - y) = 11 + 4[/tex]

[tex]5x=15[/tex]

[tex]x=3[/tex]

Use equation [tex]2x+y=11[/tex]  to solve for y.

[tex]2(3) +y=11[/tex]

[tex]6+y=11[/tex]

[tex]y=11-6[/tex]

[tex]y=5[/tex]

Need Help with this please!!

Answers

Answer:

A is 85 degrees

work out 1/5 of 80 =

Answers

Answer:

16

Step-by-step explanation: your welcome

what is the slope of the form of (1,2) m= -2​

Answers

Answer:

m = -2

Step-by-step explanation:

slope is m in y = mx + b

You already said what m is

Work out the PED for each, and comment on your result. The price of a smartphone is currently £200, and the quantity demanded is 4m. Next year the price falls to £180 and the quantity demanded rises to 6m. The price of pens today is £1, and the quantity demanded is 1m. Next year the price rises to £1.10 and the quantity demanded falls to 950,000. The price of a daily newspaper today is £1.50p, and the quantity demanded is 2m. Next year the price falls by 30p and the quantity demanded rises to 2.2m Question 2

Answers

Answer:

a.) PED = 5

b.) PED = 5

c.) PED = 0.05

Step-by-step explanation:

Here , PED = Price elasticity of demand

a.)

Given - The price of a smartphone is currently £200, and the quantity demanded is 4m. Next year the price falls to £180 and the quantity demanded rises to 6m.

PED = (Change in quantity demanded)×[tex]\frac{Initial Price}{Initial Quantity demanded}[/tex]

Now,

Change in quantity demanded = [tex]\frac{6 - 4}{180 - 200}[/tex] = [tex]\frac{2}{20} = \frac{1}{10}[/tex]

⇒PED = [tex]\frac{1}{10}[/tex]×[tex]\frac{200}{4}[/tex] = 5

b.)

Given -The price of pens today is £1, and the quantity demanded is 1m. Next year the price rises to £1.10 and the quantity demanded falls to 950,000.

Change in quantity demanded = [tex]\frac{1000000 - 950000}{1.10- 1}[/tex] = [tex]\frac{50000}{0.10} = 500000[/tex]

⇒PED = [tex]500000[/tex]×[tex]\frac{1}{1000000}[/tex] = 5

c.)

Given -The price of a daily newspaper today is £1.50p, and the quantity demanded is 2m. Next year the price falls by 30p and the quantity demanded rises to 2.2m

Change in quantity demanded = [tex]\frac{2.2 - 2}{30 - 1.50}[/tex] = [tex]\frac{0.2}{28.50} = \frac{20}{2850} = \frac{2}{285}[/tex]

⇒PED = [tex]\frac{2}{285}[/tex]×[tex]\frac{1.50}{2}[/tex] = [tex]\frac{15}{2850}[/tex]= [tex]\frac{1}{190}[/tex] = 0.005

please help me or dont

Answers

Answer:

pentegan easy

Step-by-step explanation:

I need to write an equation for the triangle and solve for x

Answers

You know that the sum of angles of line CX has to be 180 degrees. Therefore, because you know angle EDX equals 134 degrees, and 180-134= 46, you know that angle CDE equals 46 degrees. Because you know the 3 interior angles of a triangle equals 180 degrees, if you subtract 180 - 46 - 105 = 2x-13. This simplified is 29= 2x-13. Further simplified, 42=2x. Therefore x=21 degrees.

Jamal wants to install a rectangular 2025 cm² window in his garden shed. That area of window comes in several length/width combinations, and he wants to minimize the perimeter to prevent drafts. What is the least perimeter possible for the window?

Answers

Answer:

The ideal size will be a 45cmx45cm square, giving you a perimeter of 180cm.

Step-by-step explanation:

The shortcut answer here is that the square will always be the most efficient rectangle for border to area, so the sides should be the square root of 2025 cm, or 45 cm each, giving you a total of 180 minimum perimeter.

The full solution is to express the perimeter as a function of the length and width, define either length or width as a function of the other, take the entire expression's derivative and solve for zero.  Let's do it:

So first the area:

2025 = wl

l = 2025 / w

Now the sides:

[tex]p = 2w + 2l\\p = 2w + 2(2025 / w)\\p = 2w + 4050 / w[/tex]

Then we can take its derivative with respect to w

[tex]p = 2w + 4050\frac{1}{w}\\\frac{dp}{dw} = 2 + 4050\frac{-1}{w^2}\\[/tex]

Now we can set the derivative to zero, and solve for w:

[tex]\frac{dp}{dw} = 2 + 4050\frac{-1}{w^2}\\0 = 2 + \frac{-4050}{w^2}\\-2 = \frac{-4050}{w^2}\\2w^2 = 4050\\w^2 = 2025\\w = \sqrt{2025}\\w = 45[/tex]

So the width being 45, we can get the length by dividing the area by that amount, which of course is also 45.

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