Which student found the total surface area of a cylinder with a height that was two times greater than its radius?

By answering the presented question, we may conclude that As a result, function the value of f'(-1) is -9.

Mathematicians examine numbers and their variations, equations and associated structures, forms and their locations, and prospective positions for these things. The term "function" refers to the relationship between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs in which each input leads to a single, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible functions are on functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions.

We are given the function f(x) = -3x3 - 4 and asked to calculate the value of f' (-1).

To determine f'(-1), calculate the derivative of f(x) with respect to x and evaluate it at x = -1.

f(derivative )'s is provided by:

[tex][-3x3 - 4] f'(x) = d/dx = -9x^2[/tex]

We can now calculate f'(-1) by entering x = -1:

[tex]f'(-1) = -9(-1) (-1)\\a^2 = -9[/tex]

As a result, the value of f'(-1) is -9.

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Answer:763.02

Step-by-step explanation:

r=9

R=r+9=18

[tex]A=R^{2}\pi-r^{2}\pi = \pi (R^{2}-r^{2})=\pi =243\pi \\\pi =3.14\\243\pi=763.02[/tex]

Answer:

763.02

Step-by-step explanation:

Area of a circle is πr²

so the area of the whole circle is the sum of both radius

9+9 = 18

so Area = 3.14 × 18² = 1017.36

then we subtract the white part to leave the shaded part

area of the white circle = 3.14 × 9² = 254.34

then 1017.36 - 254.34 = 763.02

Answer:

Amount of benzoic acid in the solvent phase = 0.303 kg/L * 100 L/min * 20 min = 606 g.

Step-by-step explanation:

To determine the amount of benzoic acid that has passed into the solvent phase after 20 minutes, we need to use the given simplifications to set up a mass balance equation.

Let's express the stream-flow rates on a solute-free basis, which means that we consider only the flow rate of the solvent (water) and the flow rate of the toluene (ignoring the mass of benzoic acid in each stream). Let Fw be the flow rate of water and Ft be the flow rate of toluene.

Since the toluene and water are immiscible, we can assume that the volume of the two phases leaving the tank is the same as the volume of the mixture entering the tank (which is 100 L/min). Let V be this volume, which is also equal to the volume of the tank (120 L).

Let x be the concentration of benzoic acid leaving the stage in the organic phase (i.e., the solvent phase), and y be the mass concentration of benzoic acid in the aqueous phase.

From the given simplification, we have:

y = 5x

Let's use the mass balance equation to relate the flow rate of benzoic acid entering the tank to the flow rate of benzoic acid leaving the tank:

FtCt,in = VxCt,out + (FwCw,in - Fw*Cw,out)*y

where Ct,in and Cw,in are the concentrations of benzoic acid in the toluene and water entering the tank, respectively, and Ct,out and Cw,out are the concentrations of benzoic acid in the toluene and water leaving the tank, respectively.

We can assume that the feed concentration is constant, so Ct,in = 0.12 kg/L. We also know that the flow rate of the toluene and water entering the tank are 100 L/min and 110 L/min, respectively.

The concentration of benzoic acid in the water leaving the tank is given by:

Cw,out = y/5 = x/5

Since the flow rate of each phase is steady, we can assume that the concentration of benzoic acid in the toluene leaving the tank is the same as the concentration of benzoic acid in the toluene entering the tank, which is also 0.12 kg/L.

Substituting these values into the mass balance equation, we get:

1000.12 = 120x*0.12 + (110 - 120)*y

Simplifying, we get:

12 = 14.6x + 10y

Substituting y = 5x, we get:

12 = 39.6x

x = 0.303 kg/L

Therefore, the concentration of benzoic acid leaving the tank in the organic phase is 0.303 kg/L.

To find the amount of benzoic acid that has passed into the solvent phase after 20 minutes, we need to multiply the concentration by the flow rate of the toluene:

Amount of benzoic acid in the solvent phase = 0.303 kg/L * 100 L/min * 20 min = 606 g.

We can use the mass balance equation to solve this problem. Let x be the concentration of benzoic acid leaving the stage in the organic phase (in kg/L) and y be the concentration of benzoic acid in the aqueous phase (in kg/L). Then we have:

Mass of benzoic acid entering the stage per minute = Mass of benzoic acid leaving the stage per minute

The mass of benzoic acid entering the stage per minute is:

100 L/min x 0.12 kg/L = 12 kg/min

The mass of benzoic acid leaving the stage per minute can be expressed in terms of x and y as:

100 L/min x (0.12 kg/L - x) + 110 L/min x y = (100 + 110) L/min x m x x

Simplifying and using the given linear relationship between y and x, we get:

12 - 100x + 110(5x) = 210x

Solving for x, we get:

x = 0.034 kg/L

Therefore, the concentration of benzoic acid in the organic phase after 20 minutes is 0.034 kg/L.

Answer:

x ≤ 4

Step-by-step explanation:

5x-12 ≤3x-4

collect like terms

5x - 3x ≤ -4 + 12

2x ≤ 8

2x/2 ≤ 8/2

x ≤ 4

Answer:

x [tex]\leq[/tex] 4

Step-by-step explanation:

5x - 12 [tex]\leq[/tex] 3x - 4  Subtract 3x from both sides

2x - 12 [tex]\leq[/tex] -4  Add 12 to both sides

2x [tex]\leq[/tex] 8  Divide both sides by 2

x [tex]\leq[/tex] 4

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

To simplify the expression 24 + b/b + 24 x 53.72,

we first need to substitute the given value of b into the expression.

For example, if b is equal to 5, we can replace all instances of b with 5 to get 24 + 5/5 + 24 x 53.72.

Next, we can simplify the division by evaluating 5/5, which equals 1.

Then, we can multiply 24 and 53.72 to get a product of 1288.28.

Finally, we can add the simplified terms to get a final result of 1312.28.

Therefore, the simplified expression, given that b is equal to 5, is 1312.28.

(a) OIne critical number that is x = 1

(b) Function is decreasing on the interval (-∞,1) and increasing on the interval (1,∞).

(c) at x = 1, this critical number corresponds to a relative minimum.

(d) The graph is given in the attachment.

The rate change of the function at a specific point

a) The values of x where the derivative of the function equals zero or does not exist.

f'(x) = -4x + 4

Setting f'(x) equal to zero gives:

-4x + 4 = 0

-4x = -4

x = 1

So the critical number is x = 1.

(b) we need to examine the sign of the derivative on either side of the critical number.

When x < 1, f'(x) is negative, indicating that the function is decreasing.

When x > 1, f'(x) is positive, indicating that the function is increasing.

Therefore, the function is decreasing on the interval (-∞,1) and increasing on the interval (1,∞).

(c) all relative extrema, we examine the sign of the derivative in the neighborhood of the critical number x = 1. Since f'(x) changes sign at x = 1, this critical number corresponds to a relative minimum.

(d) The graph is given in the attachment.

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Answer: We can start by noticing that the total number of small cubes used is 64, which is the same as the total number of unit squares on the surface of the large cube. To maximize the white surface area, we want to arrange the cubes in a way that maximizes the number of white faces on the surface.

Each small cube has 6 faces, so there are a total of 6 x 64 = 384 faces. Half of these faces are white and half are black, since we have an equal number of white and black cubes. Therefore, there are 192 white faces and 192 black faces.

Now, let's consider how the small cubes can be arranged to maximize the white surface area. If we arrange all the white cubes together in a 4 x 4 x 4 block, then all the faces of this block that are adjacent to a black cube will be black, and all the faces that are adjacent to another white cube will not contribute to the surface area. This leaves only 16 white faces that contribute to the surface area.

On the other hand, if we alternate white and black cubes in each layer of the cube, then all the faces that are adjacent to a black cube will be white, and all the faces that are adjacent to another white cube will be black. This maximizes the white surface area. Specifically, there are 6 layers of the cube, and each layer has 16 white faces (4 along the top and bottom and 4 along each side). Therefore, there are a total of 6 x 16 = 96 white faces that contribute to the surface area.

So the fraction of the surface that is white is:

96 white faces / 384 total faces = 1/4

Therefore, one quarter of the surface area of the cube is white.

Step-by-step explanation:

Answer:

Step-by-step explanation:

its 10.7

1x1 *why is that ok  ut number

The expression that represents the product of t and 9 is 9t

The product of t and 9 can be represented by the following expressions:

All three of these expressions represent the same thing: the result of multiplying t and 9 together.

The expression "t * 9" uses the multiplication operator (*) to indicate that t and 9 are being multiplied.

The expression "9 * t" is equivalent, as multiplication is commutative and the order of the factors doesn't affect the result.

The expression "9t" is a shorthand way of writing the product, using the distributive property of multiplication.

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Answer:

One example of an irrational number between 5.25 and 5.26 is:

√139 ≈ 11.78982612...

Since the decimal representation of √139 goes on forever without repeating, it is an irrational number.

Step-by-step explanation:

The simple rate of return for the investment (rounded to the nearest tenth of a percent) is: 0.1572 or 15.7%.

Simple rate of return is a financial metric used to measure the profitability of an investment, calculated as the ratio of net income to the initial investment.

To calculate the simple rate of return for the investment, we need to first calculate the average annual net cash inflow.

Annual net cash inflow = Annual cash inflows - Annual depreciation expense

The annual depreciation expense can be calculated as:

Depreciation expense = (Initial cost - Salvage value) / Life of investment

Depreciation expense = ($34,000 - $0) / 15 years = $2,266.67 per year

Therefore, the average annual net cash inflow is:

Annual net cash inflow = $7,600 - $2,266.67 = $5,333.33

The simple rate of return can now be calculated as:

Simple rate of return = Average annual net cash inflow / Initial investment

Simple rate of return = $5,333.33 / $34,000 = 0.1572 or 15.7% (rounded to the nearest tenth of a percent)

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Step-by-step explanation:

the total cost is $200.

the given function calculates the total costs.

so, all we need to do is set the function result and calculate backwards to the necessary value of m :

200 = 0.75m + 50

150 = 0.75m

m = 150/0.75 = 200

the van must have been rented for 200 miles to have cost $200.

If you own 4 stocks, there are 81 possibilities that could occur, according to the provided assertion.

In most cases, the probability is described as the ratio of favourable outcomes to all results in the survey region. Probability of an occurrence P(E) = (Number of positive events) is how it is stated (Sample space).

For each of the 4 stocks, there are 3 possibilities - up, down, or unchanged. Therefore, the total number of possibilities for owning 4 stocks is 3 x 3 x 3 x 3, which is equal to 81.

So there are 81 possible scenarios if you own 4 stocks.

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The unit rate of 24t = 98 is A. 24 feet per year.

Unit rate is the rate of increase or decrease of a unit of item

Now, since a 984-foot tree has grown at a constant rate each year. Since we have the equation 24t = 984, wheret is the age of the tree in years.

To determine the unit rate, we compare it with the function y = mx where m = gradient

Now, the gradient is the rate of change of y per unit of x.

Now, comparing y = mx with 24t = 984,

Since m = 24 which is the gradient which is also the unit rate.

So, the unit rate of 24t = 98 is A. 24 feet per year.

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Answer:

405$

Step-by-step explanation:

First we need to find out what is the price of one unit:

330 units - 495$

1 unit - x $

Use the property of proportion to find x:

x = 1 × 495 / 330 = 1,5$ (for one unit)

Then multiply this price by 270 (since it's the new quantity of units):

270 × 1,5 = 405$

Answer:

18.2 square miles

Step-by-step explanation:

r = radius of circle

 = 4 miles

Area of shaded region = Area of sector

                                        = [tex]\frac{AngleOfSector}{360}[/tex] ×[tex]\pi r^{2}[/tex]

                                       = [tex]\frac{130}{360}[/tex] × [tex]\pi (4)^{2}[/tex]

                                       = 18.2 [tex]mi^{2}[/tex] (Rounded to 3 significant figures)

The fοrmula fοr the circumference (C) οf a circle with radius (r) is C = 2πr.

The perimeter οf a circle οr ellipse is its circumference. That is, if the circle were οpened up and straightened οut tο a line segment, the circumference wοuld be the length οf the arc.

The equatiοn C/d = π relates the circumference (C) οf a circle tο its diameter (d) using the cοnstant pi (π).

we can use the relatiοnship between the diameter and the radius:

d = 2r

We can substitute 2r fοr d in the equatiοn C/d = π, giving us:

C/(2r) = π

We can then multiply bοth sides by 2r tο isοlate C:

C = 2πr

Therefοre, the fοrmula fοr the circumference (C) οf a circle with radius (r) is C = 2πr.

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Step-by-step explanation:

To calculate the amount of wood needed to create a raised bed, you will need to know the dimensions of the bed.

Assuming the raised bed is rectangular, you will need to know the length and width of the bed, as well as the height of the bed.

Once you have these dimensions, you can calculate the surface area of the raised bed by multiplying the length and width of the bed together. This will give you the area of the bottom of the bed.

To calculate the total surface area of the bed, including the sides, you will need to multiply this area by 2 (since there are two sides) and add this to the area of the bottom.

So the formula for calculating the total surface area of the raised bed is:

Total surface area = (2 x length x height) + (2 x width x height) + (length x width)

Once you have this total surface area, you can then calculate how much wood you need by multiplying it by the thickness of the wood.

For example, if the total surface area of the bed is 100 square feet and you plan to use 2-inch-thick boards, you would need 200 cubic feet of wood.

It's worth noting that this calculation assumes that the raised bed has straight sides and right angles. If the bed has a more complex shape, the calculation will be more difficult.

Answer:

3 hours

Step-by-step explanation:

65 - 85x = 320

85x = 320 - 65

85x = 255

x = 255 / 85

x = 3

Answer:

multiply all of them then add all of them then divide by the lowest number

12:1 is the scale factor

3.5 ÷ 3.5 = 1 and 142 ÷ 3.5 =123.5 so 42:123.5 ratio simplified is 12:1

Looking at the question, to find the scale factor we are going to divide 42 by 3.5 which is 12. To check our work we will do 1 times 3.5 which is 42.

Why is it not 147:1? Well, scale factoring means that in two similar geometric figures, the scale factor is the ratio of their corresponding sides, dividing the two corresponding lengths of the sides will gives the ratio

To check go to:

https://www.ginifab.com/feeds/cm_to_inch/scale_factor_calculator.html

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Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle

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Answer idek

Step-by-step explanation: why

By using scale and prοpοrtiοn, the dimensiοns οf the actual painting are 144 inches² by 216 inches².

Scale refers tο the relatiοnship between the dimensiοns οf a scaled οbject and the cοrrespοnding dimensiοns οf the οriginal οbject. If an οbject is scaled dοwn tο half its οriginal size, then the dimensiοns οf the scaled οbject will be half οf the dimensiοns οf the οriginal οbject.

Prοpοrtiοn, οn the οther hand, refers tο the relatiοnship between twο οr mοre quantities that have the same ratiο. In οther wοrds, if twο quantities are in prοpοrtiοn, then their ratiο is cοnstant.

Tο find the dimensiοns οf the actual painting, we need tο "undο" the 6:1 scale.

If the scaled painting is 6 times smaller than the actual painting, then the actual painting is 6 times larger than the scaled painting.

Sο we can find the actual dimensiοns by multiplying the scaled dimensiοns by 6:

Actual width = 24 inches x 6 = 144 inches

Actual height = 36 inches x 6 = 216 inches

Therefοre, the dimensiοns οf the actual painting are 144 inches² by 216 inches².

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The end behavior of the function f(x) = -1/x - 4 is given as follows:

As x -> ∞, f(x) -> -4.

The end behavior of a function refers to the behavior of the function as the input variable (usually denoted as "x") approaches positive or negative infinity. To obtain the end behavior of a function, we look at the highest degree term in the function, which will determine the general shape of the graph.

The function for this problem is defined as follows:

f(x) = -1/x - 4.

As x goes to infinity, the term 1/x goes to zero, hence the end behavior of the function is defined as follows:

f(x) = 0 - 4

f(x) = 4.

The problem is incomplete, hence I found the end behavior of the function f(x) = -1/x - 4.

You should use the same procedure to find the end behavior of the function in your problem.

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The function S (m) = 105m represents the amount of steps after m minutes.

What is a function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable) is known as a function.

We are given two functions.

Tim's function : S (m) = [tex]105^{m}[/tex]

This function cannot be used to find the amount of steps taken after m minutes.

Each minute, they take an additional 105 steps. Equal differences represent a linear relationship.

Kristin's function: S (m) = 105m

This function can be used to find the amount of steps taken after m minutes.

For every minute that passes, 105 more steps are take.

Hence, the function S (m) = 105m represents the amount of steps after m minutes.

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Answer:

Option C

Step-by-step explanation:

Answer:

2 √3

Step-by-step explanation:

The value of sin 90° is 1, so we can simplify the expression as:

16 sin 10° sin 30° sin 50° sin 70° sin 90° = 16 sin 10° sin 30° sin 50° sin 70°

We can use the identity sin (90 - x) = cos x to rewrite sin 70° as cos 20°:

16 sin 10° sin 30° sin 50° sin 70° = 16 sin 10° sin 30° sin 50° cos 20°

We can use the identity sin (180 - x) = sin x to rewrite sin 170° as sin 10°:

16 sin 10° sin 30° sin 50° cos 20° = 8 sin 10° [2 cos 20° sin 30° sin 50°]

We can use the identity sin (2x) = 2 sin x cos x to simplify the expression inside the brackets:

8 sin 10° [2 cos 20° sin 30° sin 50°] = 8 sin 10° [sin 100° - sin 20°]

We can use the identity sin (180 - x) = sin x to rewrite sin 20° as sin 160°:

8 sin 10° [sin 100° - sin 20°] = 8 sin 10° [sin 100° - sin 160°]

We can use the identity sin (x + y) = sin x cos y + cos x sin y to rewrite sin 100° as sin (60° + 40°):

8 sin 10° [sin 100° - sin 160°] = 8 sin 10° [sin 60° cos 40° + cos 60° sin 40° - sin 160°]

We can use the identity sin (180 - x) = sin x to rewrite sin 160° as sin 20°:

8 sin 10° [sin 60° cos 40° + cos 60° sin 40° - sin 20°] = 8 sin 10° [sin 60° cos 40° + cos 60° sin 40° - sin 20°]

Now, we can use the values of sin 60°, cos 40°, and sin 20°, which are:

sin 60° = √3/2

cos 40° = √[(1+cos 80°)/2] = √[(1+sin 10°)/4]

sin 20° = sin (60° - 40°) = sin 60° cos 40° - cos 60° sin 40° = (√3/2)(√[(1+sin 10°)/4]) - (1/2)sin 10°

Substituting these values into the expression, we get:

8 sin 10° [sin 60° cos 40° + cos 60° sin 40° - sin 20°]

= 8 sin 10° [√3/2 × √[(1+sin 10°)/4] + 1/2 × sin 10° - (√3/2) × √[(1+sin 10°)/4]]

= 2 √3 sin 10° √[(1+sin 10°)/2]

Therefore, the value of the expression is:

16 sin 10° sin 30° sin 50° sin 70° sin 90° = 2 √3

Answer:

Step-by-step explanation:

Without the graph or any additional information, it is not possible to determine the formula for the quadratic function f(x). The graph provides visual information about the shape and characteristics of the function, but not enough details to determine the exact coefficients of the quadratic expression.

To find the formula for a quadratic function, we need to know three coefficients: a, b, and c. These coefficients are determined by the specific shape and features of the graph, such as the vertex, intercepts, and symmetry.

If you can provide more information about the graph, such as the coordinates of some key points or any additional characteristics, I can help you find the formula for the quadratic function f(x).

The graph of the system of linear inequality is attached below

a. Graphing the system of linear inequality, the solutions are (0.7, -3.35)

b. To prove that the inequality remains true at any given point, we can use a test point. We will choose the point (0,0) as our test point.

For the first inequality, plugging in (0,0) gives:

4(0) + 8(0) ≤ -24

0 ≤ -24

This is clearly false, so (0,0) is not a solution to the first inequality. This means that any point below the line 4x + 8y = -24 will not satisfy the inequality.

For the second inequality, plugging in (0,0) gives:

12(0) - 4(0) < 5

0 < 5

This is true, so (0,0) is a solution to the second inequality. This means that any point to the left of the line 12x - 4y = 5 will satisfy the inequality.

Therefore, the system of inequalities will only be satisfied by points that are both below the line 4x + 8y = -24 and to the left of the line 12x - 4y = 5. We can verify this visually by graphing the two lines and shading in the appropriate regions. Any point in the shaded region will satisfy both inequalities, and any point outside of the shaded region will not satisfy at least one of the inequalities.

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To estimate how many Boomers prefer to shop in-store, we can use the percentage given and apply it to the sample size of 75 people.

84% of 75 = 0.84 x 75 = 63

Therefore, we can estimate that approximately 63 Boomers out of a sample size of 75 prefer to shop in-store.

To represent this data visually, we can create a simple bar graph. The x-axis can represent the different generations and the y-axis can represent the percentage of people who prefer to shop in-store. We can then plot the data for Boomers as a bar that reaches 84% on the y-axis.