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soldi70 [24.7K]

2 years ago

9

The cylinder below has a diameter of 4.5 centimeters and a height of 7 centimeters. The shaded part represents the base of the c

ylinder.
Which is closest to the lateral surface area of this cylinder?

1 answer:

Butoxors [25]2 years ago

3 0

Step by step explanation

area= 2πrh
-> 2 * 3.14 * 2 * 9
-> 6.28 *18
-> 113.04

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Solve this please math problem asap please

Gennadij [26K]

Answer:

87

Step-by-step explanation:

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4 0

2 years ago

Read 2 more answers

Ryan planted flowers in a rectangular garden. The width of the garden is left parenthesis x minus 5 right parenthesis(x−5) feet

Nookie1986 [14]

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- The equation :

Area = length x width

- Substitute the values in :

Area = (x - 5)(x - 5 + 22)

(Note : the 'x' is for the algebraic expression x in the example above)

- Now you have to simplify the second parenthesis:

Area = (x - 5)(x + 17)

- Now expand :

Area = x^2 + 17x - 5x - 85

- Simplify by collecting like terms :

Area = x^2 + 12x - 85

(Note : x^2 means x squared)

Now you have your answer as:

x^2 + 12x - 85 feet^2

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- Ally ✧

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3 0

3 years ago

Help ASAP!!!!!!!!!!!! Show your work!!!!!!!!!!!

Mariulka [41]

Answer:

x = -0.846647 or x = -0.177346 or x = 0.841952 or x = 1.58204

Step-by-step explanation:

Solve for x:

5 x^4 - 7 x^3 - 5 x^2 + 5 x + 1 = 0

Eliminate the cubic term by substituting y = x - 7/20:

1 + 5 (y + 7/20) - 5 (y + 7/20)^2 - 7 (y + 7/20)^3 + 5 (y + 7/20)^4 = 0

Expand out terms of the left hand side:

5 y^4 - (347 y^2)/40 - (43 y)/200 + 61197/32000 = 0

Divide both sides by 5:

y^4 - (347 y^2)/200 - (43 y)/1000 + 61197/160000 = 0

Add (sqrt(61197) y^2)/200 + (347 y^2)/200 + (43 y)/1000 to both sides:

y^4 + (sqrt(61197) y^2)/200 + 61197/160000 = (sqrt(61197) y^2)/200 + (347 y^2)/200 + (43 y)/1000

y^4 + (sqrt(61197) y^2)/200 + 61197/160000 = (y^2 + sqrt(61197)/400)^2:

(y^2 + sqrt(61197)/400)^2 = (sqrt(61197) y^2)/200 + (347 y^2)/200 + (43 y)/1000

Add 2 (y^2 + sqrt(61197)/400) λ + λ^2 to both sides:

(y^2 + sqrt(61197)/400)^2 + 2 λ (y^2 + sqrt(61197)/400) + λ^2 = (43 y)/1000 + (sqrt(61197) y^2)/200 + (347 y^2)/200 + 2 λ (y^2 + sqrt(61197)/400) + λ^2

(y^2 + sqrt(61197)/400)^2 + 2 λ (y^2 + sqrt(61197)/400) + λ^2 = (y^2 + sqrt(61197)/400 + λ)^2:

(y^2 + sqrt(61197)/400 + λ)^2 = (43 y)/1000 + (sqrt(61197) y^2)/200 + (347 y^2)/200 + 2 λ (y^2 + sqrt(61197)/400) + λ^2

(43 y)/1000 + (sqrt(61197) y^2)/200 + (347 y^2)/200 + 2 λ (y^2 + sqrt(61197)/400) + λ^2 = (2 λ + 347/200 + sqrt(61197)/200) y^2 + (43 y)/1000 + (sqrt(61197) λ)/200 + λ^2:

(y^2 + sqrt(61197)/400 + λ)^2 = y^2 (2 λ + 347/200 + sqrt(61197)/200) + (43 y)/1000 + (sqrt(61197) λ)/200 + λ^2

Complete the square on the right hand side:

(y^2 + sqrt(61197)/400 + λ)^2 = (y sqrt(2 λ + 347/200 + sqrt(61197)/200) + 43/(2000 sqrt(2 λ + 347/200 + sqrt(61197)/200)))^2 + (4 (2 λ + 347/200 + sqrt(61197)/200) (λ^2 + (sqrt(61197) λ)/200) - 1849/1000000)/(4 (2 λ + 347/200 + sqrt(61197)/200))

To express the right hand side as a square, find a value of λ such that the last term is 0.

This means 4 (2 λ + 347/200 + sqrt(61197)/200) (λ^2 + (sqrt(61197) λ)/200) - 1849/1000000 = (8000000 λ^3 + 60000 sqrt(61197) λ^2 + 6940000 λ^2 + 34700 sqrt(61197) λ + 6119700 λ - 1849)/1000000 = 0.

Thus the root λ = (-3 sqrt(61197) - 347)/1200 + 1/60 (-i sqrt(3) + 1) ((3 i sqrt(622119) - 4673)/2)^(1/3) + (19 (i sqrt(3) + 1))/(3 2^(2/3) (3 i sqrt(622119) - 4673)^(1/3)) allows the right hand side to be expressed as a square.

(This value will be substituted later):

(y^2 + sqrt(61197)/400 + λ)^2 = (y sqrt(2 λ + 347/200 + sqrt(61197)/200) + 43/(2000 sqrt(2 λ + 347/200 + sqrt(61197)/200)))^2

Take the square root of both sides:

y^2 + sqrt(61197)/400 + λ = y sqrt(2 λ + 347/200 + sqrt(61197)/200) + 43/(2000 sqrt(2 λ + 347/200 + sqrt(61197)/200)) or y^2 + sqrt(61197)/400 + λ = -y sqrt(2 λ + 347/200 + sqrt(61197)/200) - 43/(2000 sqrt(2 λ + 347/200 + sqrt(61197)/200))

Solve using the quadratic formula:

y = 1/40 (sqrt(2) sqrt(400 λ + 347 + sqrt(61197)) + sqrt(2) sqrt(347 - sqrt(61197) - 400 λ + 172 sqrt(2) 1/sqrt(400 λ + 347 + sqrt(61197)))) or y = 1/40 (sqrt(2) sqrt(400 λ + 347 + sqrt(61197)) - sqrt(2) sqrt(347 - sqrt(61197) - 400 λ + 172 sqrt(2) 1/sqrt(400 λ + 347 + sqrt(61197)))) or y = 1/40 (sqrt(2) sqrt(347 - sqrt(61197) - 400 λ - 172 sqrt(2) 1/sqrt(400 λ + 347 + sqrt(61197))) - sqrt(2) sqrt(400 λ + 347 + sqrt(61197))) or y = 1/40 (-sqrt(2) sqrt(400 λ + 347 + sqrt(61197)) - sqrt(2) sqrt(347 - sqrt(61197) - 400 λ - 172 sqrt(2) 1/sqrt(400 λ + 347 + sqrt(61197)))) where λ = (-3 sqrt(61197) - 347)/1200 + 1/60 (-i sqrt(3) + 1) ((3 i sqrt(622119) - 4673)/2)^(1/3) + (19 (i sqrt(3) + 1))/(3 2^(2/3) (3 i sqrt(622119) - 4673)^(1/3))

Substitute λ = (-3 sqrt(61197) - 347)/1200 + 1/60 (-i sqrt(3) + 1) ((3 i sqrt(622119) - 4673)/2)^(1/3) + (19 (i sqrt(3) + 1))/(3 2^(2/3) (3 i sqrt(622119) - 4673)^(1/3)) and approximate:

y = -1.19665 or y = -0.527346 or y = 0.491952 or y = 1.23204

Substitute back for y = x - 7/20:

x - 7/20 = -1.19665 or y = -0.527346 or y = 0.491952 or y = 1.23204

Add 7/20 to both sides:

x = -0.846647 or y = -0.527346 or y = 0.491952 or y = 1.23204

Substitute back for y = x - 7/20:

x = -0.846647 or x - 7/20 = -0.527346 or y = 0.491952 or y = 1.23204

Add 7/20 to both sides:

x = -0.846647 or x = -0.177346 or y = 0.491952 or y = 1.23204

Substitute back for y = x - 7/20:

x = -0.846647 or x = -0.177346 or x - 7/20 = 0.491952 or y = 1.23204

Add 7/20 to both sides:

x = -0.846647 or x = -0.177346 or x = 0.841952 or y = 1.23204

Substitute back for y = x - 7/20:

x = -0.846647 or x = -0.177346 or x = 0.841952 or x - 7/20 = 1.23204

Add 7/20 to both sides:

Answer: x = -0.846647 or x = -0.177346 or x = 0.841952 or x = 1.58204

3 0

2 years ago

Convert 35 inches to yards. Explain or show how you got your answer.

Gwar [14]

Answer:

0.972222 yards

Step-by-step explanation:

35/36= 0.972222

7 0

3 years ago

Suppose that x and y are both differentiable functions of t and are related by the given equation. Use implicit differentiation

stepan [7]

Answer:

Let z = f(x, y) where f(x, y) =0 then the implicit function is

$\frac{dy}{dx} =$ $\frac{-δ f/ δ x }{δ f/δ y }$

Example:- $\frac{dy}{dx} = \frac{-(y+2x)}{(x+2y)}$

Step-by-step explanation:

<u>Partial differentiation</u>:-

Let Z = f(x ,y) be a function of two variables x and y. Then

$\lim_{x \to 0} \frac{f(x+dx,y)-f(x,y)}{dx}$ Exists , is said to be partial derivative or Partial differentiational co-efficient of Z or f(x, y)with respective to x.

It is denoted by δ z / δ x or δ f / δ x

Let Z = f(x ,y) be a function of two variables x and y. Then

$\lim_{x \to 0} \frac{f(x,y+dy)-f(x,y)}{dy}$ Exists , is said to be partial derivative or Partial differentiational co-efficient of Z or f(x, y)with respective to y

It is denoted by δ z / δ y or δ f / δ y

<u>Implicit function</u>:-

Let z = f(x, y) where f(x, y) =0 then the implicit function is

$\frac{dy}{dx} =$ $\frac{-δ f/ δ x }{δ f/δ y }$

The total differential co-efficient

d z = δ z/δ x + $\frac{dy}{dx}$ δ z/δ y

<u>Implicit differentiation process</u>

differentiate both sides of the equation with respective to 'x'

move all d y/dx terms to the left side, and all other terms to the right side

factor out d y / dx from the left side
Solve for d y/dx , by dividing

Example : $x^2 + x y +y^2 =1$

solution:-

differentiate both sides of the equation with respective to 'x'

$2x + x \frac{dy}{dx} + y (1) + 2y\frac{dy}{dx} = 0$

move all d y/dx terms to the left side, and all other terms to the right side

$x \frac{dy}{dx} + 2y\frac{dy}{dx} = - (y+2x)$

Taking common d y/dx

$\frac{dy}{dx} (x+2y) = -(y+2x)$

$\frac{dy}{dx} = \frac{-(y+2x)}{(x+2y)}$

7 0

3 years ago