The square of T varies directly with the cube of a and inversely with the square of d; T = 4 when a = 2 and d = 3

Answers

Answer 1
Question:

Write a general formula to describe each variation.

The square of T varies directly with the cube of a and inversely with the square of d; T = 4 when a = 2 and d = 3

Answer:

T² =  [tex]\frac{18a^3}{d^2}[/tex]

Step-by-step explanation:

Few things to note:

i. direct variation: When a variable x varies directly with another variable y, we write it in this form;

x ∝ y.

This can then be written as;

x = ky

Where;

k = constant of proportionality variation.

ii. inverse variation: When a variable x varies inversely with another variable y, we write it in this form;

x ∝ [tex]\frac{1}{y}[/tex]

This can then be written as;

x = k([tex]\frac{1}{y}[/tex])

Where;

k = constant of proportionality or variation

iii. combined variation: When a variable x varies directly with variable y and inversely with variable z, we write it in this form;

x ∝ ([tex]\frac{y}{z}[/tex])

This can then be written as;

x = k ([tex]\frac{y}{z}[/tex])

Where;

k = constant of proportionality or variation

From the question;

The square of T varies directly with the cube of a and inversely with the square of d.

Note that

square of T = T²

cube of a = a³

square of d = d²

Therefore, we can write;

T² ∝ [tex]\frac{a^3}{d^2}[/tex]

=> T² =  k ([tex]\frac{a^3}{d^2}[/tex])        -------------------(i)

Since;

T = 4 when a = 2 and d = 3

We can find the constant of proportionality k, by substituting the values of T=4, a = 2 and d = 3 into equation (i) and solve as follows;

(4)² =  k ([tex]\frac{2^3}{3^2}[/tex])

16 =  k ([tex]\frac{8}{9}[/tex])

8k = 16 x 9

8k = 144

k = [tex]\frac{144}{8}[/tex]

k = 18

Now substitute the value of k back into equation (i);

T² =  18 ([tex]\frac{a^3}{d^2}[/tex])

T² =  [tex]\frac{18a^3}{d^2}[/tex]

Therefore, the general formula that describes the variation is;

T² =  [tex]\frac{18a^3}{d^2}[/tex]


Related Questions

Two angles are complementary ( the sum of the two angles is 90°). The sum of the first angle plus twice the second angle is 150°. Find the measures of the angles.

Answers

Answer:

30 and 60

Step-by-step explanation:

Let x represent the first angle

(x) the sum of the first angle plus twice of the second angle 2(90 - x)

x + 180 - 2x = 150

180 - 150 = 2x - x (we export like terms to the same side of the equation)

30 = x is the measure of the first angle and since the second angle is complementary to this the measure of the second angle is 90 - 30 = 60

answer 1 or answer 2?

Answers

Answer:

2 Function B

Step-by-step explanation:

Answer:

Function B is greater

Step-by-step explanation:

The gradient of Function B is of 3 = m

Though the gradient of Function A  is of 1 = m, obviously being of the smaller size

If you didn't know, gradient is the same as the slope

Hope this helps

on an eight-question true-false quiz, a student guesses each answer. What is the proability that the student gets at least one of the answers correct

Answers

Answer:

0.9961

Step-by-step explanation:

Number of options per question = 2

P(success), p = 0.5

q = 1 - p = 0.5

Number of trials, n = 8

P(x ≥ 1) = p(x= 1) + p(x=2) +... + p(x = 8)

P(x = x) = nCx * p^x * q^(n-x)

Using a calculator to save computation time :

p(x ≥ 8) = 0.9961

which statement is true?

Answers

Answer:

The y-intercept of function a is greater than the y intercept of function b

Step-by-step explanation:

function a:

y = 4x + 2

function b:

y = 2x + 1

ou want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 99% confident that you esimate is within 0.1% of the true population proportion. How large of a sample size is required

Answers

Answer: the required sample size =1658944

Step-by-step explanation:

When the prior population proportion for the study is unknown , then the formula for sample size is [tex]Sample \ size = 0.25(\dfrac{z^*}{Margin\ of \ error})^2[/tex]

z-value for 99% confidence = 2.576

[tex]Sample \ size = 0.25(\dfrac{2.576}{0.001})^2\\\\=0.25(2576)^2\\\\=1658944[/tex]

Hence, the required sample size =1658944

If 50% of the students in your class are men and 20% of the men have blond hair, which of the following describes the percentage of students in your class who are men with blond hair?

Answers

.50 x .20 = .10 so 10% of the class are men with blonde hair

Answer:

10%

Step-by-step explanation:

10% of the Male students have blonde hair

What is the slope of the line described by the equation below?

y-5=-3(x - 17)

O A. -3
O B. 3
O c. 5
O D. -5
PLEASE HELP ME

Answers

Answer:

A

Step-by-step explanation:

Hi there!

The given equation of the line is in slope-point form, which is y-y1=m(x-x1), where (x1,y1) is a point and m is the slope

the given equation is y-5=-3(x - 17)

-3 is in the place of where m is, so -3 is the slope. Remember that the sign is part of the slope, so it can't be B (3). Therefore, the answer is A

Hope this helps!

What is the slope of the line through (-5, -10) and (-1, 5)

Answers

Answer:

Slope = 15/4

Step-by-step explanation:

Use the slope formula and you'll get the same answer.

Hope this helps:)

Select the points that are solutions to the system of inequalities. Select all that apply A. (-12, 0) B. (1, 2) C. (0, 0) D. (-10, 1)

Answers

Answer:

B. (1, 2)

D. (-10, 1)

Step-by-step explanation:

Both points land in the highlighted area.

Hope this helps! :)

Answer:

The correct answer would be

A. (–12, 0) & D. (–10, 1)

1 ÷ 7


pls help me
hi)

Answers

Answer:

7 lol

Step-by-step explanation:

self explanatory-

but you divide 1 by 7 you get 7

Use the given values to complete each table.
PLEASE HELP.

Answers

Number 5. Is 15, 19, 23
Number 6. Is 1, 6, 13

Number 7 is: Rosa’s horse is 60in tall.

Why are unit fractions important?

Answers

Answer:

Unit fractions play an important role in modular arithmetic, as they may be used to reduce modular division to the calculation of greatest common divisors. Specifically, suppose that we wish to perform divisions by a value x, modulo y. In order for division by x to be well defined modulo y, x and y must be relatively prime.

Step-by-step explanation:

determine the value of a in the figure shown

Answers

Answer:

d

Step-by-step explanation:

180-149= 31.

31+ 122= 153

180-153= 27

a= 27

The length of a rectangle is 4 meters more than the width of the rectangle. The perimeter of the rectangle is 40 meters. What are the length and the width of the rectangle? *

Answers

Answer:

Length = 12 m, Width = 8 m

Step-by-step explanation:

Let the width of the rectangle is b.

Length, l = 4+b

The perimeter of the rectangle = 40 m

We know that,

Perimeter of rectangle = 2(l+b)

2(4+b+b) = 40

4+2b = 20

Subtract 2 from boths sides,

2b = 16

b = 8

Width = 8 m

Length = 4+8 = 12 m

Hence, the length and the width of the rectangle is 12 m and 8 m respectively.

Question 6,7 I needed the answer

Answers

Answer:

6.n/4

7.3/4time G or 0.75G

Step-by-step explanation:

6.3m+n/12-m-n/4=3m-3m+n+3n=4n/12=n/4

7.G=0.9a/1.2b G=3/4*a/b

Paul signs up for a new cell phone plan. He is offered a discount for the first five months. After this period, his rate increases by $8.50 per month. His total cost at the end of the year is $245.50. Paul wrote the following equation to represent his plan. 5x + 7(x + 8.50) = 245.50

Answers

Answer:

The first 5 months Paul paid $ 15.50, and in the next 7 months he paid $ 24.

Step-by-step explanation:

Since Paul signs up for a new cell phone plan, and he is offered a discount for the first five months, and after this period, his rate increases by $ 8.50 per month, and his total cost at the end of the year is $ 245.50, and Paul wrote the following equation to represent his plan: 5x + 7 (x + 8.50) = 245.50; To determine the value of X, the following calculation must be performed:

5X + 7 x (X + 8.50) = 245.50

5X + 7X + 59.50 = 245.50

12X + 59.50 = 245.50

12X = 245.50 - 59.50

12X = 186

X = 186/12

X = 15.50

Therefore, the first 5 months Paul paid $ 15.50, and in the next 7 months he paid $ 24.

Can y’all help me on question 1?! Have a good day everyone!

Answers

Answer:

54 square inches

Step-by-step explanation:

9 times 12 is 108. That is the area of a rectangle with the same length and width/height. A right triangle is half of that. So 108/2=54

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

Option B  

»»————- ★ ————-««  

Here’s why:  

An area of a triangle is half the value of the product of the triangle's base and height.

⸻⸻⸻⸻

[tex]\boxed{\text{Area of A Triangle:}}\\\\---------\\\frac{b*h}{2}\\\\\boxed{\text{Key:}}\\\\\text{b - base}\\\text{h - height}[/tex]

⸻⸻⸻⸻

[tex]\boxed{\text{Finding the area of the Triangle:}}\\\\-------------\\\ \frac{9*12}{2}\\\\\rightarrow\frac{108}{2}\\\\\rightarrow \boxed{54}\\\\\text{The area should be 54 square inches.}}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

Use the net to find the surface area of the regular pyramid.

Answers

Answer:

D

Step-by-step explanation:

Base perimeter = side x 5 = 8 x 5 = 40 cm

LA = (base perimeter x slant height)/2 = (40 x 9)/2 = 180 cm^2

SA  = base area + lateral area = 110.1 + 180 = 290.1 cm^2

Which of the following figures has reflectional symmetry?


Help !!

Answers

Answer:

Figure D. (A)

When you flip the figure across like a mirror, it remains the same shape as the other side. An easy way to determine this is by cutting a line down the middle.

Reflectional symmetry states that if there exists at least one line that divides a figure into two halves such that one-half is the mirror image of the other half.

Edit: Typo!

A cone-shaped paper drinking cup is to be made to hold 24 cm3 of water. Find the height and radius of the cup that will use the smallest amount of paper. (Round your answers to two decimal places.)

Answers

Answer:

I. Radius, r = 2.90 cm

II. Height, h = 4.10 cm

Step-by-step explanation:

Given the following data;

Volume of cone = 24 cm³

To find the height and radius of the cup that will use the smallest amount of paper;

Mathematically, the volume of a cone is given by the formula;

[tex] V = \frac{1}{3} \pi r^{2}h[/tex]  ......equation 1

Where;

V is the volume of the cone.

r is the radius of the base of the cone.

h is the height of the cone.

Substituting into the formula, we have;

[tex] 36 = \frac{1}{3} \pi r^{2}h[/tex]

Multiplying both sides by 3, we have;

[tex] 108 = \pi r^{2}h[/tex]

Making radius, r the subject of formula, we have;

[tex] r^{2} = \frac {108}{ \pi h} [/tex]

Taking the square root of both sides, we have;

[tex] r = \sqrt { \frac {108}{ \pi h}} [/tex]

Mathematically, the lateral surface area of a cone is given by the formula;

[tex] LSA = \pi rl [/tex]  ......equation 2

Where;

r is the radius of a cone

l is the slant height of a cone.

To find the slant height, we would apply the Pythagorean' theorem;

[tex] l = \sqrt {r^{2} + h^{2}} [/tex]

Substituting r into the above equation, we have;

[tex] l = \sqrt {\frac {108}{\pi h} + h^{2}} [/tex]

Substituting the values of r and l into eqn 2, we have;

[tex] LSA = \pi * \sqrt { \frac {108}{ \pi h}} * \sqrt {\frac {108}{\pi h} + h^{2}} [/tex]

Simplifying further, we have;

[tex] LSA = \sqrt {108} * \sqrt { \frac {\pi h^{3} + 108}{\pi h}} [/tex]

[tex] LSA = \sqrt {108} * \sqrt { \frac {108}{ h^{2}} + \pi h}} [/tex]

Next, to find the value of h, we differentiate the above mathematical equation with respect to h;

[tex] \frac {dS}{dh} = \sqrt {108} * (\pi - \frac {216}{h^{3}}) * (\pi h + \frac {108}{h^{2}}) [/tex]

Limiting [tex] \frac {dS}{dh} [/tex] w.r.t 0;

[tex] \frac {dS}{dh} = 0 [/tex]

[tex] (\pi - \frac {216}{h^{3}}) = 0 [/tex]

Rearranging the equation, we have;

[tex] \pi = \frac {216}{h^{3}} [/tex]

We know that π = 3.142

[tex] 3.142 = \frac {216}{h^{3}} [/tex]

Cross-multiplying, we have;

[tex] 3.142h^{3} = 216 [/tex]

[tex] h^{3} = \frac {216}{3.142} [/tex]

[tex] h^{3} = 68.75 [/tex]

Taking the cube root of both sides, we have;

Height, h = 4.10 cm

Lastly, we find the value of r;

[tex] r = \sqrt { \frac {108}{ \pi h}} [/tex]

[tex] r = \sqrt { \frac {108}{3.142 * 4.10}} [/tex]

[tex] r = \sqrt { \frac {108}{12.88}} [/tex]

[tex] r = \sqrt {8.39} [/tex]

Radius, r = 2.90 cm

The height and radius of the cup that will use the smallest amount of paper is;

Radius = 2.52 cm

Radius = 2.52 cmHeight = 3.58 cm

Let us first state some relevant formulas;

Volume of a cone is;

V = ⅓πr²h

Surface area of a cone is;

S = πrL

Where L is Slant height and has a formula;

L = √(h² + r²)

We are told that the cone is to hold 24 cm³. Thus; V = 24 cm³

24 = ⅓πr²h

πr²h = 72

r = √(72/πh)

Putting √(72/πh) for r in the Slant height equation gives;

L = √(h² + (72/πh))

Thus;

S = π × √(72/πh) × √(h² + (72/πh))

Differentiating with respect to h gives;

dS/dh = √72 × (π - 144/h³) × 1/√(πh + 72/h²)

At dS/dh = 0,we will have;

(π - 144/h³) = 0

Thus;

h³ = 144/π

h = 3.58 cm

Thus, from r = √(72/πh);

r = √(72/(π × 3.58))

r = 2.52 cm

Read more at; https://brainly.com/question/4405937

I am one of Jehovah's Witnesses reply if you are to

Answers

Nope but I respect what you are

Answer:

I am

Step-by-step explanation:

PLEASE HELP !!! WILL MARK WHOEVER GETS IT RIGHT AS BRAINLIEST !!

Answers

Answer:

Last one (x + 4, y - 1).

Step-by-step explanation:

From the point, you go right 4 (going right on a graph is positive).

From there, you go down 1 (going down on a graph is negative).

If each 2 cm on the scale drawing below equals 9 feet, what is the actual area of the shape in square units?

Answers

Answer: 18 cm

Step-by-step explanation: 9 feet x 2

Please answer and explain.

Answers

Answer:

x = 13

Step-by-step explanation:

The sum of the exterior angles of a 4 sided polygon is 360

139+ 6x+9x+2x = 360

Combine like terms

139+17x=360

Subtract 139 from each side

17x = 360-139

17x = 221

Divide each side by 17

17x/17 = 221/17

x = 13

the answer is x = 13

14. Anna, Bella, Claire, Dora and Erika meet at a party. Each pair who know each other shake hands exactly once.
Anna shakes hands only once, Bella twice, Claire three times and Dora four times. How many people does Erika
shake hands with?
(A) 1
(B)2
(C) 3
(D) 4
(E) 5

Answers

Answer:

(B) part is the answer which means he shook hands with 2.

Step-by-step explanation:

Since Dora shook hands four time with: Alan, Bella, Claire, Erik. Then Erik shook hands only with Dora. Claire shook hands three times with Bella, Claire and Dora. Then Bella shook hands with two people Claire and Dora. Now Erik would shook hands only with those who shook hands with him. 2 people Claire and Dora

The required handshake Erika had is given as 2. Option B is correct.

What are permutation and combination?

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Here,
According to the question,

Dora shake hands 4 times,
So Dora shakes hands with Anna, Bella, Claire, and Erika.

Anna shake hands 1 time,
From the above combination.
Dora shakes hands with Anna,
Implies Anna does not shake hands with Erika,

Clair shakes hands 3 times,
So Clair shakes hands with Bella, Claire, and Erika.

Bella shake hands 2 times,
So Bella shakes hands with Bella and Claire.

From the above reasoning, Erika shakes hands with Dora and Clair.


Learn more about permutations and combinations here: https://brainly.com/question/2295036
#SPJ2

11
Akhtar gets a bonus of 20% of £70
Karl gets a bonus of £26
Work out the difference between the bonus Akhtar gets and the bonus Karl gets.


help

Answers

Answer:

8.8

Step-by-step explanation:

Akhtar's bonus = 20% × £70 = £14

karl's bonus = 20% × £26 = £5.2

Difference = £14 - £5.2 = 8.8

**I'm not sure about the answer sorry, please get it checked.

What is the y-intercept of the graph of the line whose equation is y = -2/5x + 4?
1) - 5/2
2) - 2/5
3) 0
4) 4

I’ve been stuck on this question for so long I need help with it.

Answers

Answer:

4

Step-by-step explanation:

in y=mx+b, the "b" is the y-intercept

Answer:

4

it's in y = mx + b form, where b is the y-intercept

factorise fully 16c^4p^2+20cp^3​

Answers

Answer:

4cp^2 ( 4c^3+5p

Step-by-step explanation:

See image below:)

The factored form of the expression will be [tex]4cp^2 (4c^3+5p)[/tex]

Factorization:

Given the expression  16c^4p^2+20cp^3​

Get the factor for each term

[tex]16c^4p^2 = 4 * 4 * c^3 * c * p^2 \\20cp^3= 4 * 5 * c * p^2 * p[/tex]

From the factors, you can see that 4cp^2 is common to both terms. Hence the factored form of the expression will be:

[tex]4cp^2 (4c^3+5p)[/tex]

Learn more on factored form here: https://brainly.com/question/25948667

In angle ABC, AB = 2.5 m, BC = 3.2 m and AC = 2.9 m. Use the Cosine Law to find
, to the nearest degree.

Answers

9514 1404 393

Answer:

  ∠A ≈ 72°

Step-by-step explanation:

Fill in the given numbers and do the arithmetic.

  cos A = (2.9² +2.5² -3.2²)/(2(2.9)(2.5)) = 4.42/14.5

The inverse cosine function is used to find the angle, given its cosine.

  A = arccos(4.42/14.5)

  ∠A ≈ 72°

Trig how do you do I do not know

Answers

9514 1404 393

Answer:

  a) 2π radians

  b) 10π inches

  c) 5/4π inches per minute

Step-by-step explanation:

The formulas are fairly straightforward. Use the given values in each.

a) θ = ωt

  θ = (π/4 radians/min)(8 min) = 2π radians

__

b) s = rθ

  s = (5 in)(2π radians) = 10π in

__

c) v = s/t

  v = (10π in)/(8 min) = 5/4π in/min

Other Questions
Can someone Please help meeee Monopoly in the competitive environment a. is enjoyed by few organizations as sole suppliers of a good or service. b. is typical of public utilities -- even more so now than twenty years ago. c. cannot be achieved temporarily even through the use of patents and similar legal devices. d. is the logical extension of a firm's control of its production and labor resources. e. is, all in all, the most common type of competition in the U.S. market. Emma wants to buy a new cell phone. She commits to saving 10% of the costeach month. Let p be the percent she has saved after m months. Why were the ancient Egyptians able to farm in the desert?A) They grew crops that did not need much water.B) The Nile River fertilized the soil along its banks.C) The pharaohs used slave labor to carry water down from the mountains.D) They got water out of cactus and other large plants in the desert. Despite the reports Columbus gave Ferdinand and Isabella of finding great riches, he mostly foundtimber and wool.plants and animals.salt and hawks bells.wine and glass beads. Which of the following pieces of evidence would best support the argument that humans are more evolutionarily related to fish than they are to insects? (1 point) The early stages of embryo development in fish and humans look strikingly similar while insects develop very differently compared to both fish and humans, O All these organisms require oxygen to survive. O The earliest fish fossils are found in the lowest strata of sedimentary rocks, followed by insects, and then humans. O Fossils of ancient fish and human ancestors have been discovered in the same sedimentary rock layers. A municipal electrical utility charges customers a $15 per month fee plus 12 cents per kilowatt-hour of energy used. Write an equation for a customer's monthly costs, C (in dollars) for electric service as a function of x, the kilowatt-hours used. Which rhetorical appeal is used in the text, One of the worst cases was a young mother of two who was diagnosed with early stage skin cancer?logos, an appeal based on logicethos, an appeal based on the authors characterpathos, an appeal based on emotionno rhetorical appeal is used An author published a book which was being sold online. The first month the author sold 14400 books, but the sales were declining steadily at 5% each month. If this trend continues, how many total books would the author have sold over the first 23 months, to the nearest whole number? solve for x and y in the system of equationy=x-4x2x-y=2I'll mark brainliest Who are famous for their spider-web fishing nets? To make punishment more effective, it should be 44.7When Xavier places his hands near a light bulb, he notices that certain areas around the light bulb are warmer thanothers. Which best explains this?The areas to the sides of the light bulb are warmest because of conduction,O The areas to the sides of the light bulb are warmest because of convection,The area directly above the light bulb is warmest because of conduction,The area directly above the light bulb is warmest because of convection.Save and ExitSubmitMark this and retumNex I need help on this please! What are the possible gametes (sperms) that would be produced from a male carrying balanced translocation between chromosomes 11 and 22, if it occurs in 2:2 Segregation: adjacent segregation If i left Raleigh at 9:30 am and drove and drove 6 1/2 hours what time would it be What are the domain and range of the function f(x)=-3(x-5)2 +4?domain: (-00, 5)range: (-00,00)domain: (-0,4]range: -00,00)domain: (-0,5]range:(-0,4]O domain: (-0,00)range: (-0,4] President Roosevelt and members of his administration gave speeches thatwarned of Japan's rising power in the Pacific. What was the point of thesespeeches?O The administration used the speeches to make a case for going to war.O The speeches made the case that Japan was greater threat than Germany.o The speeches gave Americans hope that diplomatic relations would help theUnited States avoid war with Japan.O The administration used these speeches to explain military strategy, if and whenthe United States went to war. Which greenhouse gas is produced when fossil fuels are burned for energy?A. PetroleumB. MethylamineC. HeliumD. Carbon dioxide Why are classical allegories not regarded as realistic fiction?