Mathematics High School

Write an equation for the statement. Then, solve the equation:
The volume of a can varies jointly as the height of the can and the square of its radius. A can with an 8 inch
height and 4 inch radius has a volume of 402.12 inches cubed. What is the volume of a can that has a 2 inch
radius and a 10 inch height?

PLZZ help

Answers

Answer 1

Answer:

V = 125.6 in³

Step-by-step explanation:

let V be volume, h the height and r the radius, then the equation relating the quantities is

V = khr² ← k is the constant of variation

To find k use the condition V = 402.12, h = 8, r = 4

402.12 = k × 8 × 4² = 128k ( divide both sides by 128 )

3.14 = k [ note 3.14 is π )

V = 3.14hr² ← equation of variation [ V = πr²h ]

Given r = 2 and h = 10, then

V = 3.14 × 10 × 2² = 3.14 × 40 = 125.6

Related Questions

I got some money for my birthday. I save and spend in the ratio 2:3. I save £32. How much money did I receive for my birthday?

Answers

Answer:

80 i think

Step-by-step explanation:

32.3=80

Step-by-step explanation:

Amount of money saved : spent = 2 : 3.

Since amount of money saved = £32,

Amount of money spent = £32 * (3/2) = £48.

Total amount of money = £32 + £48 = £80.

Therefore I received £80 for my birthday.

An airplane ascended into the sky to a steady altitude of 35000 feet. The same plane descended to a steady altitude of 32000 feet. How many feet did the airplane descend

Answers

Answer:

3000 feets

Step-by-step explanation:

Given that :

Initial Ascent to steady altitude = 35,000 feets

Descent to steady altitude = 32,000 feets

Number of feets the plane descend :

(Initial ascent to steady altitude - descent to steady altitude)

(35000 - 32000) feets = 3,000 feets

What is the y-intercept of y = -3x

Answers

Answer:

Step-by-step explanation:

The y-intercept of y = -3x is zero.

Answer:

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

m - slope b - y-intercept

Step-by-step explanation:

Step 1: Define

y = -3x

Step 2: Break Function

Identify Parts

Slope m = -3

y-intercept b = 0

*We assume that if the variable isn't there, it is 0 or being multiplied by 0.

Can someone substitute this? Please and thank you

Answers

Step-by-step explanation:

soln

given

y=2x+3 -----(i)

y=-x-9 ------(ii)

now, putting value of equation (i) in (ii)

y= -x-9

or, 2x+3 = -x-9

or, 2x+x = 9-3

or, 3x = 6

or, x = 6/3

or, x = 2

again,

y = 2x+3

or, y = 2×2+3

or, y = 7

therefore, value of X and Y are 2 and 7 respectively.

2 questions,Neeed helpppp assssaaaappp!!!

Answers

Answer:

(i) (x + 3) is a factor of p(x)= x⁴ + 4x³ + 4x² + 4x + 3 and the remaining factors are (x + 1) and ( x² + 1).

(ii) (x + 1) is not a factor of p(x)= 2x⁴ - 5x² - 2 and the remainder is -5.

Step-by-step explanation:

(i) Given;

Polynomial, p(x)= x⁴ + 4x³ + 4x² + 4x + 3

Factor, = x + 3

x = -3

if (x + 3) is a factor of the polynomial, then p(-3) = 0

p(-3) = (-3)⁴ + 4(-3)³ + 4(-3)² + 4(-3) + 3

= 81 -108 + 36 - 12 + 3

= 0

(x + 3) is a factor of the given polynomial and the remainder is 0.

The remaining factors can be obtained as follows;

x³ + x² + x + 1

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

x + 3 √x⁴ + 4x³ + 4x² + 4x + 3

- ( x⁴ + 3x³)

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

x³ + 4x² + 4x + 3

-(x³ + 3x²)

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

x² + 4x + 3

-(x² + 3x)

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

x + 3

-(x + 3)

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

Further divide x³ + x² + x + 1 by x + 1

x² + 1

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

x + 1 √x³ + x² + x + 1

-(x³ + x²)

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

x + 1

-( x + 1)

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

Thus, the factors of x⁴ + 4x³ + 4x² + 4x + 3 = (x + 3)(x + 1)( x² + 1)

(ii) Given;

Polynomial, p(x)= 2x⁴ - 5x² - 2

Factor, = x + 1

x = -1

if (x + 1) is a factor of the polynomial, then p(-1) = 0

p(-1) = 2(-1)⁴ - 5(-1)² - 2

= 2 - 5 - 2

= -5

Thus, (x + 1) is not a factor of the given polynomial and the remainder is -5.

2.
.
X + 3
X + 18
X +4
X=

Answers

x = -1,-16,-2.

TIE FIGHTERS GO ZOOOOOOOM

Translate the given phrase to an expression.
The quotient of 15 and 2
The expression is (Do not simplify)

Answers

I doubt your teacher would want you to evaluate the whole thing but if they do leave a comment

A square with a perimeter of 20 units is graphed on a coordinate grid. The square is dilated by a scale factor of 0.4 with the origin as the center of dilation. If (x , y ) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square

Answers

Answer:

its 20x20

Step-by-step explanation:

ty for point also i did the test

Answer: I just did the test so the answer would be (20x,20y)

Step-by-step explanation: hoped this help thx for the points :D

Help!!!!!! Please and thanks

Answers

Answer:

HI I am back thanks for zooming in I would say your answer would be D sorry if i am wrong but that should be correct I am 98% sure. Plz let me know if it is correct or not! (Brainliest Plz)

Step-by-step explanation:

(PLz give me Brainliest)

Y varies with x. When y=39, x=3. Find the value of y when x=2

Answers

Answer:

[tex] \frac{39}{y} = \frac{3}{2} \\ y = \frac{39 \times 2}{3} \\ \boxed{y = 26}[/tex]

26 is the right answer.

A shoe salesperson sold 20 pairs of shoes for $640. A brown pair of shoes sells for $30 and a black pair for $35. How many brown pairs were sold? A. 12 B. 14 C. 15 D. 8

Answers

Answer:

12 pairs

Step-by-step explanation:

Represent Brown with B and Black with A

So:

[tex]A + B = 20[/tex] --- Pairs sold

[tex]30B + 35A = 640[/tex] --- Amount

Required

Solve for B (the brown pairs)

Make A the subject in the first equation

[tex]A = 20 - B[/tex]

Substitute 20 - B for A in the second

[tex]30B + 35(20-B) = 640[/tex]

Open bracket

[tex]30B + 700 - 35B = 640[/tex]

Collect Like Terms

[tex]30B - 35B = 640 -700[/tex]

[tex]-5B = -60[/tex]

Divide both sides by -5

[tex]B = \frac{-60}{-5}[/tex]

[tex]B =12[/tex]

Howie works at a petting zoo. He fed a piglet 1/5 of a bottle of milk then gave 3/4 of what was left to the calf. How much of the bottle of milk did the calf drink

Answers

Answer:

[tex]\frac{3}{5}[/tex]th part of the bottle will be drunk by the calf.

Step-by-step explanation:

Part of the bottle fed by the piglet = [tex]\frac{1}{5}[/tex]

Milk left in the bottle = 1 - [tex]\frac{1}{5}[/tex]

= [tex]\frac{5-1}{5}[/tex]

= [tex]\frac{4}{5}[/tex]

Milk drunk by the calf = [tex]\frac{3}{4}[/tex]th of the left part

= [tex]\frac{3}{4}\times \frac{4}{5}[/tex]

= [tex]\frac{3}{5}[/tex]th part of the bottle

Therefore, [tex]\frac{3}{5}[/tex]th part of the bottle will be drunk by the calf.

f f(x)=4x^(2)-9, find f(-1)

f(-1)= ?

Answers

Answer:

[tex]f(-1)=-5[/tex]

Step-by-step explanation:

Numeric Value of a Function

Given:

[tex]f(x)=4x^2-9[/tex]

It's required to find f(-1).

It can be calculated by substituting the value x=-1 in the function:

[tex]f(-1)=4(-1)^2-9[/tex]

Calculating:

[tex]f(-1)=4*1-9[/tex]

[tex]f(-1)=4-9[/tex]

[tex]\boxed{f(-1)=-5}[/tex]

take like 10 secs. im just not smart

Answers

Answer:

Step-by-step explanation:

Answer:

hope it helps...........

3-7/8

please answer :p

Answers

Answer:

2.125 is your answer!! pls give brainlist (:

Step-by-step explanation:

Please help :( im struggling

Answers

Answer:

a= 9/4

Step-by-step explanation:

2m^(5/2)/m^(1/4)

2m^(5/2 -1/4)

2m^(9/4)

Hope you find this helpful <3

f(x) = (1)
What is the x intercept

Answers

Answer:

There is no x-intercept, only a y-intercept, which would be 1

The price of a technology stock was $9.70 yesterday. Today, the price fell to $9.59 Find the percentage decrease. Round your answer to the nearest tenth of a percent.

Answers

Answer:

round it to 20×10 there's you answer

Which table does NOT show a proportional relationship?
1 point

A
B
C
D

Answers

The answer is Either ‘A’ or ‘D’

I think it’s C or A I don’t know but I say A or C

Who can answer this? .. if u dk it don’t comment thanks ♡︎ .

Answers

The answer is D.

It is the only one that has an intercept of -2 and a negative slope.

Please Help Fast It’s Pretty Easy a sew both question please and thank you

Answers

Answer:

5x-10=60 being vertically plopposite angle .

Answer:

14; vertical

Step-by-step explanation:

since these are vertical angles, they will equal the same;

5x - 10 = 60

add 10

5x = 70

divide by 5

x = 14

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