`jae is costructing an open box froma piece of cardboard that is 9in. wide and 12in. long.

Answer:

a) A = 3π/16

b) A = ∑₂°° (π/n⁴) = π⁵/90 − π

Step-by-step explanation:

(a) The area between the curve and the x-axis is:

A = ∫ₐᵇ y (dx/dt) dt

x = ½ (1 − cos t) cos t

dx/dt = ½ (1 − cos t) (-sin t) + ½ sin t cos t

dx/dt = -½ sin t + ½ cos t sin t + ½ sin t cos t

dx/dt = -½ sin t + sin t cos t

dx/dt = -½ sin t (1 − 2 cos t)

y dx/dt = -½ sin t (1 − 2 cos t) × ½ (1 − cos t) sin t

y dx/dt = -¼ sin²t (1 − 3 cos t + 2 cos²t)

y dx/dt = -¼ sin²t + ¾ sin²t cos t − ½ sin²t cos²t

y dx/dt = ⅛ (-2 sin²t) + ¾ sin²t cos t − ½ (sin t cos t)²

y dx/dt = ⅛ (-1 + 1 − 2 sin²t) + ¾ sin²t cos t − ½ (½ sin(2t))²

y dx/dt = ⅛ (-1 + cos(2t)) + ¾ sin²t cos t − ⅛ sin²(2t)

y dx/dt = -⅛ + ⅛ cos(2t) + ¾ sin²t cos t + ¹/₁₆ (-2 sin²(2t))

y dx/dt = -⅛ + ⅛ cos(2t) + ¾ sin²t cos t + ¹/₁₆ (-1 + 1 − 2 sin²(2t))

y dx/dt = -⅛ + ⅛ cos(2t) + ¾ sin²t cos t + ¹/₁₆ (-1 + cos(4t))

y dx/dt = -⅛ + ⅛ cos(2t) + ¾ sin²t cos t − ¹/₁₆ + ¹/₁₆ cos(4t)

y dx/dt = -³/₁₆ + ⅛ cos(2t) + ¾ sin²t cos t + ¹/₁₆ cos(4t)

A = ∫₀ᵖⁱ [-³/₁₆ + ⅛ cos(2t) + ¾ sin²t cos t + ¹/₁₆ cos(4t)] dt

A = -³/₁₆ t + ¹/₁₆ sin(2t) + ¼ sin³t + ¹/₆₄ sin(4t) |₀ᵖⁱ

A = [-³/₁₆ π + ¹/₁₆ sin(2π) + ¼ sin³π + ¹/₆₄ sin(4π)] − [0 + ¹/₁₆ sin(0) + ¼ sin³0 + ¹/₆₄ sin(0)]

A = -³/₁₆ π

We got a negative answer because the graph traces to the left (x decreases as t increases).  So the area is simply ³/₁₆ π.

b) Each circle has radius 1/n², so the area is π (1/n)² = π/n⁴.

The sum of the areas from n=2 to n=∞ is:

A = ∑₂°° (π/n⁴)

A = ∑₁°° (π/n⁴) − π

A = π ∑₁°° (1/n⁴) − π

A = π (π⁴/90) − π

A = π⁵/90 − π

Answer:

Options 1) and 3) are correct.

Step-by-step explanation:

R={(A,B)|A⊆B}

Reflexive:

As A⊆A,  [tex](A,A)[/tex]∈ R.

So, R is reflexive

Symmetric:

Let [tex](A,B)[/tex]∈ R. So, A⊆B

Take [tex]A=\{1,2\}\,,\,B=\{1,2,3,4\}[/tex]

Here, A⊆B but B⊄A

So, [tex](B,A)[/tex]∉ R

R is not symmetric

Transitive:

Let [tex](A,B)[/tex]∈ R and [tex](B,C)[/tex]∈ R

So, A⊆B and B⊆C.

Therefore, A⊆C

So,

[tex](A,C)[/tex]∈ R

Hence, R is transitive.

Option 1) is correct.

Antisymmetric:

Let (A,B)∈R and (B,A)∈R

So, A⊆B and B⊆A

Hence, A = B

So, R is antisymmetric

Option 3) is also correct.

Answer:

A, c(x)=5+21x

Step-by-step explanation:

`

Answer:

Sarah multiplied the denominator by the denominator and the numerator by the numerator instead of finding the cross products. The equation should be 5x = 42, so the cost should be $8.40.

Step-by-step explanation:

Can I get brainliest?

Answer:

the answer is £1.44

Step-by-step explanation:

hope this helps

Answer:

I think it is 6.24

Step-by-step explanation:

not really sure

Answer:

150

Step-by-step explanation:

Answer:

Your answer is that X=1

Answer:

The answer is 1.

Step-by-step explanation:

12x-15-4x+1 = -6

8x = 8

Therefore x = 1

Answer:

The medium is the middle of something. More like math thought. So what even the numbers are it will be the middle.

Step-by-step explanation:

Answer: Any item that can be traded for another item.

Step-by-step explanation: took the quiz

Answer:

4 5/12

Step-by-step explanation:

Convert to mixed fraction 7/4 + 8/3

Find common denominator, 12

21/12 + 32/12

add numerators  (21+32)/12 = 53/12

reduce fraction 4 5/12

Answer: The unit rate is

116 ​calorie(s) per cup

and

There are 464 calories in 4 cups of the cereal

Answer:

Step-by-step explanation: C. 2x+3=1/2(4x+2)+2 hopes this helps:)

The equations that are identities are option B x – 4(x + 1) = –3(x + 1) + 1 and option C 2x + 3 = 1/2(4x + 2) + 2.

To check which equation is an identity, we need to simplify each equation and see if it is true for all values of x.

A. 3(x – 1) = x + 2(x + 1) + 1

Expanding the right side:
3(x – 1) = x + 2x + 2 + 1
3x – 3 = 3x + 3-3 = 3

This is a contradiction and cannot be true for any value of x. Therefore, option A is not an identity.

B. x – 4(x + 1) = –3(x + 1) + 1
Expanding both sides:
x – 4x – 4 = –3x – 3 + 1
-3x – 3 = -3x – 3

This equation simplifies to -3x - 3 = -3x - 3, which is true for all values of x. Therefore, option B is an identity.

Similarly,

Option C is an identity.

Option D is not an identity.

Learn more about equations here:

brainly.com/question/10413253

#SPJ7

Answer:

Step-by-step explanation:

Let the number be x

Then we have the equation

let the number be "x" .

now according to the given question ;

Answer:

0,4

Step-by-step explanation:

Answer:

Option (A)

Step-by-step explanation:

Graph attached shows a function that models the value V of a stock portfolio as a function of time.

y-values on the graph shows the value of V and x-values represent the time.

Lowest point of the curve shows the minimum value of V and highest point of the curve shows the maximum value.

Maximum value of the function → 6.93 at t = 4

Minimum value of the function → 1.05 at t = 15

Therefore, Option (A) will be the answer.  

Answer:

  translated (x, y) → (x - 2, y + 2) and rotated 90° counterclockwise about the origin

Step-by-step explanation:

The image point is in the 3rd quadrant, and the pre-image point is in the first quadrant. This means there has been any of ...

The only answer choice involving the appropriate rotation is ...

  translated (x, y) → (x - 2, y + 2) and rotated 90° counterclockwise about the origin

__

Checking this, we have

  (x, y) ⇒ (x -2, y +2) . . . . translation left 2, up 2

  (x -2, y +2) ⇒ (-y -2, x -2) . . . . followed by 90° CCW rotation

  J(9, 1) ⇒ J'(-3, 7) . . . . . consistent with the given image point

5.) x>20

11.)x≤−15

13.)x≥−21

2.)x≤−7

6.)x≤−45

10.)x≤10

12.)x≥−12

16.)x≤−4

Answer:

2. x ≤ -7

5. x > 36

6. x ≤ -40

10. x ≤ 10

11. x ≤ -15

12. x ≥ -12

13. x ≥ -21

16. x ≤ -4

Step-by-step explanation:

2. x ≤ -7 (You want to add 8 to both sides like any equation, but don't forget it is an inequality, not an equation!)

5. x > 36 (You need to multiply by 2, to get rid of the division. So multiply both sides by 2, that gets rid of the 2 on the one side, and you get 36 on the other side when you multiply 18 by 2).

6. x ≤ -40 (You need to multiply by -5. REMEMBER: When you multiply or divide by a negative, you switch the sign. So if it is a < then it would be a > and same with if you had ≤ then it would be ≥ instead).

10. x ≤ 10 (You need to divide by -2. And once again you switch the signs).

11. x ≤ -15 (Add 8, like you did in number 2).

12. x ≥ -12 (Multiply by 6. REMEMBER: Do NOT switch the signs if you the number you are dividing by is in the numerator, or if you multiply and the negative number is first, UNLESS you have 2 negatives.

13. x ≥ -21 (Multiply by 7).

16. x ≤ -4 (Divide by 10).

The speed of the train in kilometer per hour is 68.9km/hr.

The rate of change of position of an object in any direction.

[tex]speed = \frac{distance}{time}[/tex]

According to the given question

Distance travelled by commuter train = 21km

Time taken by a train to travel 31 km = 27 minutes = [tex]\frac{27}{60} =0.45hour[/tex]

Therefore, the speed of the train in kilometer per hour is given by

[tex]speed = \frac{31}{0.45}[/tex]

⇒[tex]speed = 68.9km/hr[/tex]

Hence, the speed of the train in kilometer per hour is 68.9km/hr.

Find out more information about speed distance and time here:

https://brainly.com/question/4978052

#SPJ2

Answer:

Yes

Step-by-step explanation:

Answer:

The probability of an event can only be between 0 and 1 and can also be written as a percentage. ... If P ( A ) > P ( B ) P(A) > P(B) P(A)>P(B)P, left parenthesis, A, right parenthesis, is greater than, P, left parenthesis, B, right parenthesis, then event A has a higher chance of occurring than event B.

so that means yes

Answer:

1

Step-by-step explanation:

The bars around the j mean absolute value, meaning any number inside those brackets, you make it positive. So, 6-5=1

Answer:

3/4 of a banana

Step-by-step explanation:

3 divided by 4 = 3/4

Answer:

1/15

Step-by-step explanation: Just equate the values like my last ans

Answer:

Step-by-step explanation:

Step 1:

Put value of b = 5/6

1/(12(5/6)+5

1/60/6 +5

1/10+5

Answer:

1/15 or 0.06666

Answer:

1. 10 nickels and 34 dimes

Step-by-step explanation:

Answer:

PQ

Step-by-step explanation:

Parallel lines are a pair of lines in a plane that do not meet/intersect

Answer:

900,000

Step-by-step explanation:

Answer:

D. NM=12; mK=70°

Step-by-step explanation:

KN≈KM so they have the same 55° and then

180°-55°-55°=70° and

6*2=12

Answer:

Explained below.

Step-by-step explanation:

The rules of the deal are as follows:

(a)

The correct option is: "the money you win".

(b)

The random variable X denotes the amount won or lost.

(c)

The value of X are as follows:

X = {-$6, $5 and $10}

(d)

The probability function of X is as follows:

P (X = 10) = 1/6

P (X = 5) = 1/3

P (X = -6) = 1/2

(e)

Compute the expected value as follows:

[tex]E(X)=\sum x\times P(X=x)\\[/tex]

         [tex]=(10\times\frac{1}{6})+(5\times\frac{1}{3})+(-6\times\frac{1}{2})\\\\=0.333333\\\\\approx $0.33[/tex]

Thus, the average winnings per game is $0.33.

(f)

Since the expected value of the game is a positive amount, the deal will not  lead to me paying up.

Thus, you take the deal.

Answer:

y = 1/2x + 2.5

Step-by-step explanation:

First we want to plug it into the [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. This gets us 6-2/7-(-1) which solves to 4/8 which simplifies to 1/2. This gives us the slope. Now, when using slope intercept form y = mx + b, we can plug our newly found slope in for m and get y = 1/2x + b. To find b plug in any point on the line into the equation, I chose (7,6) because we are given that, and both numbers are positive. Now plug those in for x and y. 6 = 1/2(7). Solve, and get 2.5. are final equation is

y = 1/2x + 2.5