Suppose a wedge of cheese fills the region in the first octant bounded by the planes y=3z, y=12 and x=4. It is possible to divide the wedge into two equal pieces (by volume) if you sliced the wedge with the plane x=2. Instead, find a with 0

The correct option is B: V = π ∫[0,2] ((y + 2)/2 - 1)^2 dy

This integral will give us the Volume of the solid generated when region R is revolved about the vertical line x = 1.

The volume of the solid generated when region R is revolved about the vertical line x = 1, we can use the method of cylindrical shells.

The formula for the volume of a solid generated by revolving a region R about a vertical line is given by:

V = 2π ∫[a,b] x * f(x) dx

In this case, since we are revolving the region R about the vertical line x = 1, the limits of integration will be from y = 2 (where the horizontal line y = 2 intersects the graph y = 2x - 2) to y = 0 (where the graph y = 2x - 2 intersects the x-axis).

Let's analyze the options provided:

A. π ∫[1,2] ((y + 2)/2 - 1)^2 dy

B. π ∫[0,2] ((y + 2)/2 - 1)^2 dy

C. π ∫[1,2] (2 - (2x - 2))^2 dy

D. π ∫[0,2] ((y + 2)/2)^2 - 1^2 dy

Option A: The limits of integration are incorrect. We need to integrate with respect to y, not x.

Option B: This appears to be the correct integral setup, integrating with respect to y and using the correct limits of integration.

Option C: This option incorrectly uses the expression (2 - (2x - 2))^2, which doesn't match the function y = 2x - 2.

Option D: The limits of integration are incorrect. We need to integrate from y = 2 to y = 0.

Therefore, the correct option is B:

V = π ∫[0,2] ((y + 2)/2 - 1)^2 dy

This integral will give us the volume of the solid generated when region R is revolved about the vertical line x = 1.

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If we want to calculate the slope we have to do the following:

so the slope is -5/3

Answer:

The width of the garden is 7 feet.

Step-by-step explanation:

If the area is 56 feet, and the length is 8 feet, we can put this into the area equation.

Area = width * length

A = wl

Substitute variables.

56 = 8w

Divide by 8.

7 = w, or w = 7.

The width of the garden is 7 feet.

The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

From the question, we have the following parameters that can be used in our computation:

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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Answer:

2/3

Step-by-step explanation:

There are 3 odd numbers in a dice which equals 1/2. Then there is 1/6 of a chance of rolling a 3. So it would be 1/2 + 1/6=4/6 which simplifies to 2/3.

Answer: 20/3 = 40/6. These two fractions are known as equivalent fractions. Hope this helps ya.

Answer:

40

Step-by-step explanation:

20/3=40/6 the answer for the second fraction is just double the first fraction so your answer is c) 40

The length of arc JL is approximately 15.08 units.

We have,

The length of an arc in a circle can be calculated using the formula:

Arc Length = (θ/360) * 2πr

where θ is the central angle in degrees, r is the radius of the circle, and 2π is approximately 6.28.

In this case, we are given the central angle JKL = 144° and the radius JK = 6 units.

Plugging in the values, we have:

Arc Length = (144/360) * 2π * 6

Arc Length ≈ (0.4) * 6.28 * 6

Arc Length ≈ 15.072 units

Rounded to the nearest hundredth,

The length of arc JL is approximately 15.08 units.

Thus,

The length of arc JL is approximately 15.08 units.

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Answer:

less than

Step-by-step explanation:

.7 = 7/10

7/10 is less than 9/10

plz mark brainliest

Answer:

Greater

Step-by-step explanation:

0.7 is equal to \(\frac{7}{10}\), which is greater than \(\frac{9}{10}\).

~theLocoCoco

Answer:

Hello,

Answer A: 35 dimes and 5 nickels

Step-by-step explanation:

Let say

d the number of dimes

n the number of nickels

There are 25 coins: d+n=25

Total value : 0.1*d+0.05n=2.25

\(\left\{\begin {array} {ccc}d+n&=&40\\10*d+5*n&=&225\ multiplied\ by\ 100\\\end {array}\right.\\\\\\\left\{\begin {array} {ccc}n&=&40-d\\10*d+5*(40-d)&=&225\\\end {array}\right.\\\\\\\left\{\begin {array} {ccc}5*d&=&225-200\\n&=&40-d\\\end {array}\right.\\\\\\\left\{\begin {array} {ccc}5*d&=&25\\n&=&40-5\\\end {array}\right.\\\\\\\left\{\begin {array} {ccc}d&=&5\\n&=&35\\\end {array}\right.\\\\Proof:\\5*0.1+35*0.05=0.5+1.75=2.25\\\)

Answer:

150+25x = 600

Step-by-step explanation:

Hope this helped!

Answer:

y=5x+200

Step-by-step explanation:

x=number of handbags

y-intercept=200

slope=5

please give me brainly since I'm trying to level up!

The soccer ball reaches a maximum height of approximately 34.8 feet.

The parametric equations for the motion of the soccer ball are:

x(t) = 39*cos(44°)t ≈ 26.9t

y(t) = \(39\sin(44)*t - 16t^2\) ≈ \(22.7t - 16t^2\)

where t is the time elapsed since the ball was kicked.

To find the maximum height of the ball, we need to find the vertex of the parabolic trajectory given by y(t).

The maximum height occurs at the vertex, which is at the time t = -b/2a, where a = -16 and b = 39*sin(44°).

So, t = -b/2a ≈ 1.1 seconds.

Substituting this value of t into the equation for y(t), we get the maximum height:

y(max) = \(39*\sin(44)1.1 - 16(1.1)^2 = 34.8 feet.\)

Therefore, the soccer ball reaches a maximum height of approximately 34.8 feet.

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Answer:

£735,000

Step-by-step explanation:

we can keep the first three numbers and then round the rest (284). since the first number (2) is less than 5, we round to 0. thus, 284 -> 000 and 735,284 -> 735,000. note that the first 3 numbers do not include a zero, so we don't have to do anything fancy here.

The Surface area of the given cuboid is found to be 872 sq, in.

Three-dimensional shapes with length, breadth, and height are called cuboids. Six of the cuboid's sides are referred to as faces.

Surface area of a cuboid is = 2(lw + 2lh + hw0

S.A = 2[(17)*(8) + (8)*(12) +(12)*(17)]

S.A = 2*436

S.A = 872

Thus, the Surface area of the given cuboid is found to be 872 sq, in.

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Answer:

(2, –3) is a solution to the system of linear equations.

Step-by-step explanation:

Given: Equations:

3x - y = 9 --------(1),

4x + y = 5 --------(2),

Add Equation (1) + Equation (2),

3x + 4x = 9 + 5

7x = 14  ( Combine like terms )

x = 2   ( Divide both sides by 7 ),

From equation 1:

3(2) - y = 9

6 - y = 9

-y = 9 - 6    ( Subtraction 6 on both sides )

-y = 3

y = - 3     ( Multiplying -1 on both sides )

A characteristic of the classical approach to probability include the following: D. probabilities assume outcomes of an experiment are equally likely.

In Science, an experiment is a scientific investigation which typically involves the process of manipulating an independent variable (the cause), in order to determine or measure the dependent variable (the effect).

In Mathematics and statistics, an expected value is sometimes referred to as the long-term mean (average) of a discrete random variable, E(X) and it can be calculated by taking the weighted average of all the outcomes of the discrete random variable with respect to their probabilities.

In this context, we can logically deduce that a characteristic of the classical approach to probability is that most times probabilities assume outcomes (results) of an experiment are equally likely.

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The probability of choosing a green sweet at random is 7/9.

Given information:

A bag of sweets contains only 1 pink sweet, 7 green sweets, and 1 orange sweet

There are 7 green sweets out of a total of 9 sweets in the bag.

So the probability of choosing a green sweet at random is:

= the total number of green sweets / total number of sweets

=7/9.

This is already in its simplest form, so the final answer is:

7/9.

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Answer:

6

Step-by-step explanation:

12 + 42 = 54 then 54 divided by 9 = 6.

Answer:

Point slope form is the best form to use for this particular question.

We reflect point slope form as:  \(y-y_{1} =m(x-x_1)\)

M reflects the slope, and the X and Y values are the coordinates given.

M = -2, X = 4, Y = 2

This should result in an equation that looks like this:

\(y-2=-2(x-4)\)

Now, if we want to turn this equation into slope-intercept form, we have to do some calculations. First of all, we have to multiply -2 with (x-4) to get

\(y-2=-2x+8\)

Next, we add two on both sides to isolate the Y variable.

Therefore, the slope-intercept equation would be: \(y=-2x+10\)

Answer:

4/5

Step-by-step explanation:

hope it helped :)

When a\(_{n}\) = \(2^{n}\)+ n,  a₀ = 1,  a₁ = 3,  a₂ = 6, and a₃ = 11  

When a\(_{n}\) = n^(n+1)!,  a₀ = 0,  a₁ = 2,  a₂ = 2⁶, and a₃ = 3²⁴  

When a\(_{n}\) =  [n/2], a₀ = 0,  a₁ = 1/2,  a₂ = 1, and a₃ = 3/2      

When a\(_{n}\) = [n/2] + [n/2], a₀ = 0,  a₁ = 1,  a₂ = 2, and a₃ = 3/2  

Number sequence

A number sequence is a progression or a list of numbers that are directed by a pattern or rule.

Here,

a₀, a₁, a₂, and a₃ are terms of a sequence

from option a, a\(_{n}\) = \(2^{n}\)+ n

⇒ a₀  = 2⁰+ 0 = 1+0 = 1

⇒ a₁  = 2¹+ 1 = 2+1 = 3

⇒ a₂, = 2²+ 2 = 4+2 = 6

⇒ a₃  = 2³+ 3 = 8 +3 = 11  

from option b, a\(_{n}\) = n^(n+1)!

⇒ a₀  = 0^(0+1)! = 0

⇒ a₁  = 1^(1+1)! = 2² = 2

⇒ a₂, = 2^(2+1)! = 2^(3)! = 2⁶          [ ∵ 3! = 6 ]

⇒ a₃  = 3^(3+1)! = 3^(4)! = 3²⁴         [ ∵ 4! = 24 ]

from option c, a\(_{n}\) =  [n/2]          

⇒ a₀  = [0/2] = 0

⇒ a₁  = [1/2] = 1/2

⇒ a₂, = [2/2] = 1

⇒ a₃  = [3/2] =  3/2  

from option d, a\(_{n}\) = [n/2] + [n/2]

⇒ a₀  =  [0/2] + [0/2] = 0

⇒ a₁  =  [1/2] + [1/2] = 1/2 + 1/2 = 1

⇒ a₂, = [2/2] + [2/2] = 1 + 1 = 2

⇒ a₃  =  [3/2] + [3/2] = 6/4 = 3/2

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The Complete Question is -

What are the terms a₀, a₁, a₂, and a₃ of the sequence {a\(_{n}\)}, where a\(_{n}\) is where a\(_{n}\) equals

a. \(2^{n}\) + n                    b. n^(n+1)!

c. [n/2]                      d. [n/2] + [n/2]

Answer:

378 Euros

Step-by-step explanation:

A good way to estimate is to round to the nearest whole number or 10th and then multiply:

8.70 --> 9.00 (since 7 > 5 you round up to the nearest whole number, in this case 9)

then you multiply. A good way to do this in your head is doing:

split 42 into 2 numbers:
40, 2

then multiply by nine:

9 * 4 = 36 (9 * 40 = 360) added a zero since we multiplied by 40, its just easier to multiply by smaller numbers

9 * 2 = 18

then add the two numbers together:

360 + 18 = 378 Euros

The actual answer with a calculator is 365.4 Euros, so for an estimation its fairly close.

Another way you could solve it is to just round 8.70 --> 10 (rounding to the nearest 10th)

then:

10 * 42 = 420 (nice)

I don't recommend it since its way too off from the original value, but could be good for quick estimations.

hope this helped you :)

Step-by-step explanation:

\( \underline{ \underline{ \text{Given}}} : \)

\( \underline{ \underline{ \text{To \: find}}} : \)

\( \underline{ \underline{ \text{Solution}}} : \)

\( \tt{16\% \: of \: 400}\)

⟷ \( \tt{ \frac{16}{100} \times 400}\)

⟷ \( \tt{ £ 64}\)

\( \pink{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline { \tt{James \: saves \: \boxed { \: £\: 64}}}}}}}}\)

Hope I helped ! ♡

Have a wonderful day / night ! ツ

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Answer:

x is 46.67

y is 28.4°

Step-by-step explanation:

To solve for x we use sine

sin ∅ = opposite / hypotenuse

AC is the opposite

x is the hypotenuse

so we have

sin 59° = 40 / x

x sin 59 = 40

Divide both sides by sin 59

x = 40/sin 59

x = 46.67

To solve for y we also use sine

sin y = 30/ 63

y = sin^-1(30/63)

y = 28.4°

Hope this helps you

The volume of the shape Q is 25,920 cm³.

The isoperimetric inequality describes the relationship between a sphere's volume and surface area. This inequality indicates that the sphere has the biggest volume among all forms with a fixed surface area. The sphere also has the lowest surface area among all forms with a fixed volume. Due to its ability to increase volume while reducing surface area, the sphere is sometimes referred to as the "most efficient" form.

Let us suppose the scale factor = k.

Given that, total surface area of shape P is 240 cm².

Then surface area of Q can be written as:

k² × surface area of shape P = surface area of shape Q

k² × 240 cm² = 2160 cm²

k² = 9

k = 3

The volume of shape Q is:

k³ × volume of shape P = volume of shape Q

3³ × 960 cm³ = 27 × 960 cm³ = 25,920 cm³

Hence, the volume of the shape Q is 25,920 cm³.

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