If = cos + (3 − 2

2

) − (3 + 2), find

2

​

Answer:

[tex]r=\dfrac{2}{3}\ yards[/tex]

Step-by-step explanation:

Given that,

The volume of a sphere is, [tex]V=\dfrac{32}{81}\pi[/tex] cubic yards

We need to find the radius of the sphere. The formula for the volume of a sphere is given by :

[tex]V=\dfrac{4}{3}\pi r^2[/tex]

Put all the values,

[tex]\dfrac{32}{81}\pi=\dfrac{4}{3}\pi r^3\\\\r^3=\dfrac{8}{27}\\\\r=\dfrac{2}{3}\ yards[/tex]

So, the radius of the sphere is equal to [tex]\dfrac{2}{3}\ yards[/tex].

Answer:

[tex]x^{3} - x^{2} - 7x -2[/tex]

Step-by-step explanation:

Give me brainllest

Answer:

[tex] {x}^{3} - {x}^{2} - 7x - 2[/tex]

Step-by-step explanation:

[tex](x + 2)( {x}^{2} - 3x - 1)[/tex]

Multiply the first term.

[tex]x \times {x}^{2} = {x}^{3} [/tex]

Multiply x by everything on the right, dont do x squared we already done that.

[tex]x \times - 3x = - 3 {x}^{2} [/tex]

[tex]x \times - 1 = - x[/tex]

Multiply 2 by everything on the left expect -1. ( that our next step).

[tex]2 \times {x}^{2} = 2 {x}^{2} [/tex]

[tex]2 \times - 3x = - 6x[/tex]

Multiply the last term, 2 and -1.

[tex]2 \times - 1 = - 2[/tex]

Add like with like.

[tex] {x}^{3} - {x}^{2} - 7x - 2[/tex]

Answer:

a) The total engine volume is 30.3265 in³

b) the mass of air contained in the engine is 0.00129 lbm

c) The efficiency of the engine is 55.6%

Step-by-step explanation:

Given the data in the question;

The configuration is in line with four-stroke, four-cylinder engine.

Bore ( d ) = 3.17 in

Stroke ( L ) = 3.48 in

compression ratio ( r ) = 10.6 : 1

First, we calculate the swept Volume V₁ = π/4 × d²L

we substitute

V₁ = π/4 × (3.17 )² × (3.48) = 27.4655 in³

Now, Compression Ration; r = Vs + Vc / Vc

r = (V₁ + V₂) / V₂

we substitute

10.6 = (27.4655 + V₂) / V₂

10.6V₂ = 27.4655 + V₂

10.6V₂ - V₂ = 27.4655

9.6V₂ = 27.4655

V₂ = 2.861 in³

So

a) total engine volume

[tex]V_{BDC[/tex] = V₁ + V₂

we substitute

[tex]V_{BDC[/tex] = 27.4655 in³ + 2.861 in³

[tex]V_{BDC[/tex] = 27.4655 in³ + 2.861 in³

[tex]V_{BDC[/tex] = 30.3265 in³

Therefore, The total engine volume is 30.3265 in³

b) The mass of air

given that; T = 540°R, P = 14.7 psia

we know that; PV = mRT   { R is constant }

we solve for m

m = PV / RT

we substitute

m = (14.7 × 30.3265)  / ( 0.3704 × 1728 )540

m = 445.79955 / 345627.648

m = 0.00129 lbm

Therefore, the mass of air contained in the engine is 0.00129 lbm

c) The efficiency

from table { properties of air}

At 540°R; u₁ = 92.04 BTu/lbm, u[tex]_r[/tex]₁ = 144.32

Now process 1 - 2 ( Isentropic )   u[tex]_r[/tex]₁ / u[tex]_r[/tex]₂  = V₁/V₁ = r

so,  u[tex]_r[/tex]₁ / u[tex]_r[/tex]₂ = r

144.32  / u[tex]_r[/tex]₂ = 10.6

u[tex]_r[/tex]₂ = 144.32/10.6

u[tex]_r[/tex]₂ = 13.61

Thus, at u[tex]_r[/tex]₂ = 13.61, u₂ = 235 BTU/lbm, T₂ = 1340°R

Now, we know that;

P₁V₁/T₁ = P₂V₂/T₂  ⇒ (P₁/V₁)r = P₂/T₂

⇒ ( 14.7 / 540 )10.6 = P₂/1340

P₂ = 386.664 psia  

process 2 - 3; constant volume heat addition;

Now, At T₃ = 3600°R, u₃ = 721.44 BTU/lbm, u[tex]_r[/tex]₃ = 0.6449

so, [tex]q_{in[/tex] =  u₃ -  u₂

we substitute

so, [tex]q_{in[/tex] =  721.44  -  235  = 486.44 BTU/lbm

Next, process 3 - 4; Isentropic  

u[tex]_r[/tex]₄/u[tex]_r[/tex]₃ = V₄/V₃ = r

u[tex]_r[/tex]₄ / 0.6449  = 10.6

u[tex]_r[/tex]₄ = 6.8359

At u[tex]_r[/tex]₄ = 6.8359; u₄ = 308 BTU/lbm

∴

Heat Rejection [tex]q_{out[/tex] = u₄ - u₁ = 308 - 92.04 = 215.96 BTU/lbm

so, [tex]W_{net[/tex] = [tex]q_{in[/tex] - [tex]q_{out[/tex]

[tex]W_{net[/tex] = 486.44 - 215.96

[tex]W_{net[/tex] = 270.48 BTU/lbm

so the efficiency; η[tex]_{thermal[/tex] = ([tex]W_{net[/tex] / [tex]q_{in[/tex] ) × 100%

η[tex]_{thermal[/tex] = ( 270.48 / 486.44  ) × 100%

η[tex]_{thermal[/tex] = ( 0.55604  ) × 100%    

η[tex]_{thermal[/tex] = 55.6%

Therefore, The efficiency of the engine is 55.6%

Answer:

[tex]Corn = \alpha_1 *price + \beta_1 * income + \mu_1[/tex] --- Demand

[tex]Corn = \alpha_2 *price + \beta_2 * rainfall + \gamma * rainfall_2 + \mu_2[/tex] --- Supply

Step-by-step explanation:

Given

[tex]Corn = \alpha_1 *price + \beta_1 * income + \mu_1[/tex]

[tex]Corn = \alpha_2 *price + \beta_2 * rainfall + \gamma * rainfall_2 + \mu_2[/tex]

Required

Identify the demand and the supply equation.

To identify which is the demand equation and which is the supply equation, we simply look through the constraints of the equation.

For (1):

[tex]Corn = \alpha_1 *price + \beta_1 * income + \mu_1[/tex]

We have: Price and Income

For (2):

[tex]Corn = \alpha_2 *price + \beta_2 * rainfall + \gamma * rainfall_2 + \mu_2[/tex]

We have: Price and Rainfall

In (1), price and income determines the demand of a product.

Hence, (1) represents the demand equation

In (2), price and weather condition (rainfall) determines the supply of a product.

Hence, (2) represents the supply equation.

Answer: Tom has run 9 miles so far

Step-by-step explanation:

3/4 of 12 if equal to 9

Answer:

9 miles

Step-by-step explanation:

3 is 25 percent of 12.

to figure out how much he runs in 755 of two miles you multiply 3x3=9.

Answer:

Consider matrix A.

What is the inverse of A? Fill in the missing elements in the matrixs.

Step-by-step explanation:

Consider matrix A.

What is the inverse of A? Fill in the missing elements in the matrixs.

Answer:

Hello! Your answer would be, 600

Step-by-step explanation:

if we start backwards, the value of 6 in 6000 is equal to 1/1000. If you want to find what is 10 times that, multiply 1/1000 with ten and you get 1/100. That is equal to 6/600. The value of 6 is 600.

Hope I helped! Brainiest plz!♥ Have a nice morning! Hope you make a 100%! -Abby

Answer:

H) 7x² + 8x - 2

Step-by-step explanation:

Answer:

$900

Step-by-step explanation:

$180 divided by 0.20 is $900

A percentage is a way to describe a part of a whole. The original cost of the laptop is $900.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Let the original cost of the laptop be represented by x.

Given that you saved $180 on your new laptop, which is a 20% saving from the original price. Therefore, the percentage can be written as,

20% of original price = $180

(20/100) × x = $180

x = ($180×100)/20

x = $900

Hence, the original cost of the laptop is $900.

Learn more about Percentages here:

https://brainly.com/question/6972121

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Answer:

Do you see the lines and how they are named? I am going to try and explain this in less words than I can. Where it says XS you have to match it up with the lines. But if it says that you have to find XSU (which it does not) you would have to go up all the way but you stop where it says the S so you wont go all  the way up to the U. I hope this helps!

Answer:

13/52

Step-by-step explanation:

Answer:

21 students ride the bus

Answer:

x=5

Step-by-step explanation:

2(x-1)=x+3

x=5

(5-1)=4

4*2=8

5+3=8

ANSWER 5

Have a great day!

answer:

$14

step-by-step explanation:

the formula for simple interest is-

i=prt

meaning interest=principal (the starting amount of money) * rate * time

=200*0.01*7

(we have to turn 1% into a decimal so 1/100=0.01)

=14

i=14

good luck :)

i hope this helps

brainliest would be highly appreciated

have a nice day!

After 7 years and a 1% interest rate, Brendan will have a total of 214$.

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.

Given, Brendan has $200 in a saving account with a 1% interest rate.

The simple interest is given as

Interest = (PRT/100)

where

P = Amount deposited = 2,00

R = Rate = 1%

T= Time = 7 years

Interest = (PRT/100)

Interest = (200 × 7 × 1/100)

Interest = 14

Total amount = SI + principal amount

Total amount = 14 + 200 = 214

Therefore, Brendan will have 214 $ after 7 years and a 1% interest rate.

Learn more about simple interests here:

https://brainly.com/question/29210957

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According to the given data,

By adding the probabilities, we get

→ [tex]P (D \leq = 2) = 0.301+0.176[/tex]

                     [tex]= 0.477[/tex]

Thus the response above is appropriate.

Learn more about probability here:

https://brainly.com/question/16790640

Answer:

0.097

Step-by-step explanation:

1) "First digit greater than 7" means that the first digit is 8 or 9.

2) P(first digit greater than 7)=0.051+0.046=0.097

3) 0.097

Answer:

First we need to see how many times 65% will make the price go up by 100%. We can see this by dividing 100 by 65. 100 divided by 65 is 1.53846153846. Now we can multiply 40 by 1.53846153846 and see what we get. 40x1.53846153846=$61.5384615384.

This is a lot of decibal numbers so if you seek more help then contact me on discord at Mousycritter#2842 for free advice!

Step-by-step explanation:

Answer:

The area would be 15.75 feet squared!

(4+5/2)(3.5) = 15.75

Answer:

Solve each inequality and combine solutions:

Combination of the two is:

or

Answer: <0<x<10/3

Step-by-step explanation:

Given:

CDEF is dilated by a scale factor of [tex]\dfrac{3}{4}[/tex] to form the quadrilateral C'D'E'F'.

To find:

The measure of side E'F'.

Solution:

If a figure is dilated by a scale factor of k, then the side of dilated figure is k times of corresponding side of original figure.

CDEF is dilated by a scale factor of [tex]\dfrac{3}{4}[/tex] to form the quadrilateral C'D'E'F'. So,

[tex]E'F'=\dfrac{3}{4}\times EF[/tex]

From the given figure it is clear that [tex]EF=12[/tex]. So,

[tex]E'F'=\dfrac{3}{4}\times 12[/tex]

[tex]E'F'=9[/tex]

Therefore, the measure of side E'F' is 9 units.

Answer:

Entras a una tienda ropa y hay un pantalón que valia 150 y ahora vale 90 y una camiseta que valia 40 ahora vale 24 ¿ tienen el mismo porcentaje de rebaja ? Justifica tu respuesta

Answer:

2 x 2 x 11 or 2^2 x 11

Prime factorization: 44 = 2 x 2 x 11, which can also be written 2² x 11.26

9514 1404 393

Answer:

  11

Step-by-step explanation:

X'Y' = 2XY . . . . lengths are related by the dilation factor

22 = 2XY . . . substitute the given value

11 = XY . . . . . divide by 2

The measure of side XY is 11.

Answer:

Theatre A has the greatest percent

Answer:

1/6, 3/7, 2/3, 4/5

Step-by-step explanation: