Cylinder A has a radius of 7 inches and a height of 5 inches. Cylinder B has a volume of 490π. What is the percentage change in volume from cylinder A to cylinder B?
50% decrease
75% increase
150% decrease
100% increase

Answer:

[tex]\boxed{47.089 \;meters} \\\\[/tex]

Step-by-step explanation:

For any function f(x), the maximum or minimum value can be determined by 1. Finding the first derivative f(x) with respect to x i.e. f'(x)

2. Setting this first derivative to 0, solving for x

3. Substituting for x in the original function to get the maximum/minimum value

[tex]\textrm{The equation for the function f(t) is }\\f(t) = -4.9t^2 + 20.58t + 25.48\\\\[/tex]

[tex]\textrm{The first derivative of this function with respect to t is }\\\\f'(t) = - 2\cdot 49t + 20.58\\= -9.8t + 25.48\\\\[/tex]

[tex]\textrm{Setting this first derivative equal to 0 gives:}\\\\-9.8t + 20.58 = 0\\\\-9.8t = -20.58 \;\;\;\;\;\textrm{(Subtracting 20.58 from both sides)}\\\\9.8t = 20.58 \;\;\;\;\;\; \textrm{ (Multiplying both sides by -1)}[/tex]

[tex]\textrm{Therefore }\\\\t = \dfrac{20.58}{9.8}\\\\t= 2.1 \textrm{ seconds}[/tex]

[tex]\textrm{Therefore, at = 2.1 seconds, the ball will reach its maximum height.}[/tex]

To find what this maximum height is, substitute t = 2.1 in the original equation and solve for h(t)

[tex]h(t)\;at\;t=2.1 \\h(2.1) = 4.9\cdot \:2.1^2+20.58\cdot \:2.1+25.48=47.089 \;meters\\\\[/tex]

[tex]\textrm{ The maximum height the ball achieves before landing is } \boxed{47.089 \;meters} \\\\[/tex]

[tex]\textrm {This occurs 2.1 seconds after launch }[/tex]

Answer: 75m^3

Step-by-step explanation:

First, find the scale factor:

5/2 = 2.5

Multiply figure A's volume by the scale factor:

2.5 * 30

= 75 m^3

the ordered pair that represents the number of years elapsed when the trees are at the same height is (8,5). We were then asked to find the number of years elapsed when the trees are at the same height.

In this problem, we were given two different trees, one that is 3 feet tall and growing at a rate of 1 foot per year, and another that is 5 feet tall and growing at a rate of 0.75 feet per year. The ordered pair (3,1) represents the 3-foot tall tree growing at a rate of 1 foot per year and the ordered pair (5,0.75) represents the 5-foot tall tree growing at a rate of 0.75 feet per year.

To find the number of years elapsed when the trees are at the same height, we need to solve the equation:

3 + 1t = 5 + 0.75t

t = (5 - 3)/(1 - 0.75) = 2/0.25 = 8

So the ordered pair that represents the number of years elapsed when the trees are at the same height is (8,5).

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To calculate how many flowers of each kind Marisol created, use the formulae x+y=96 and x+3y=192. Marisol used 48 tulips in total to produce Garden Delight bouquets on Monday and Tuesday.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

Let x be Spring Mix bouquets and y be the Garden Delight bouquets.

x+y=96

x+3y=192

2y=96

y=48

x=48

The system of equations that you can use to find how many bouquets of each type Marisol made is x+y=96 and x+3y=192. The total number of tulips Marisol used to make Garden Delight bouquets on Monday and Tuesday is 48.

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Answer:

A step to step solution

Step-by-step explanation:

The measure of all these angles is just adding up the remote interior angles (the 2 angles that are shown in every triangle in this worksheet)

Find the sum, and that is your answer.

The first solution is 49+80 = 129

Therefore, the answer for #1 is 129 degrees

But to see one’s own face essential that the light emitted by it is either bounced back into our eyes (intimate a mirror - or something very much like it) - or that the light is recorded, captured and then played back into our eyes.

Did you know that shapes have a face? No, this face does not mean a face with two eyes, a nose, and a mouth. I mean a face of a shape, or the flat surface of a shape that you can trace and see. This face is known as a face in math.

Plane shapes in math mean any closed, flat, two-dimensional shape. All plane shapes have a face, because you can trace the shape of all plane shapes.

A triangle has a triangle face.

A rectangle has a rectangle face.

A diamond has a diamond face.

A circle has a circle face.

A square has a square face.

An oval has an oval face.

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Answer:

Step-by-step explanation:

just do - x + = -

- x - = +

so the answer is + i think

The product of r and s to the fourth power is written as

In math, the term exponent refers to the number of times a certain number multiplies it self.

The number that is being multiplies is referred to as the base number while the number of times it multiplies itself is the exponents

In the problem, the multiplication of r and s is done as follows

= r * s

= rs

In this case, the base number is rs and raise to the fourth power implies that rs multiplies it self four times

= rs * rs * rs * rs

= (rs)⁴

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Answer:

(rs)^4

Step-by-step explanation:

The other addend is from the arithmetic operation is 14

The act of combining two or more objects is known as an addition. The process of computing the sum of two or more integers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently utilized in daily life.

The addends are the figures that are added. Between the addends is the plus sign (+), which represents addition.

Given that:

7 + x = 21

Then;

x = 21 - 7

x = 14

Therefore, we can conclude that if one addend is 7, the other will be 14 to make a sum of 21.

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a). The sequence as represented in question a). is not an arithmetic sequence and hence, does not have a common difference.

b). The sequence formed by recording the daily odometer reading of a car after driving 15 miles each day does not have a negative common difference.

It follows from the task content that the sequence which has a negative common difference be determined.

It follows that the common difference, by definition is the difference between successive terms a (n) of the sequence.

Therefore, common difference is usually given by; a (n) - a (n-1).

a). Since the given sequence is; 64, 32, 16, 8, ....

Since The common difference is; 32 - 64 ≠ 16 - 32 ≠ 8 - 16.

Hence, the sequence does not have a common difference and hence, is not an arithmetic sequence.

b). For a sequence involving the daily odometer reading of a car after driving 15 miles every day.

It follows that the recursive function for such a sequence would take the form; a (n) = a (n-1) + 15.

By comparison with the standard recursive function for arithmetic sequences, a (n) = a (n-1) + 15, it follows that the common difference, d = 15.

On this note, the common difference for the sequence is not a negative number.

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The expression that represents the cost (in dollars) of renting a paddleboard for h hours is r + xh

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

Cost of rents:

Charging a rental fee plus an hourly rate.

Using the above as a guide, we have the following:

Initial rental fee = r

Hourly rate = x

The cost for h hours can then be represented as

C(h) = Initial rental fee + Hourly rate * Number of hours

Substitute the known values in the above equation, so, we have the following representation

C(h) = r + x * h

Evaluate

C(h) = r + xh

Hence, the expression is r + xh

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r is called as radius in the formula  A=πr^2

A large part of the field of operations research is the use of statistical equations to solve problems in business or military operations.

Music, linguistics, and philosophy all use mathematical models (for example, intensively in analytic philosophy).

A model is, for example, the method for the area of a circle, πr2.

Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'. This quantity has importance in almost all circle-related formulas. The area and circumference of a circle are also measured in terms of radius.

Α= pi r^2

Divide each side by pi

A / pi = r^2

Take the square root of each side

sqrt( A / pi ) = sqrt(r^2)

sqrt( A / pi ) =r

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Answer:

0

Step-by-step explanation:

h(x) = 3 – 3/x

h(3) = 3 – 3/3

h(3) = 0/3

h(3) = 0

i hope this helped

Answer: you learn more, and it looks good on job applications, but you have to go to more school and use up more of your time

Step-by-step explanation:

B. MLYZ and C. LN = XZ are not true, since these letters do not correspond to any sides or angles in the given triangles.

CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." Given the statement "ALMN = AXYZ," we can assume that triangle ALMN is congruent to triangle AXYZ.

With that in mind, the following congruences are true:

A. ZX=ZN (Corresponding parts of congruent triangles)

D. MN = YZ (Corresponding parts of congruent triangles)

E. ZY ZMo (not a valid statement)

F. ZZ = ZL (not a valid statement)

B. MLYZ and C. LN = XZ are not true, since these letters do not correspond to any sides or angles in the given triangles.

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Distance is a measure of how far an object has traveled from a starting point. Displacement is the change in position from the starting point.

It is the total distance an object has moved and is the sum of all the displacements an object has made. The formula for calculating distance is distance = speed x time. For example, if a car has traveled at a speed of 50 km/h for 4 hours, then the distance traveled is 200 km (50 km/h x 4 h = 200 km).

Displacement is the change in position from the starting point. It is the shortest distance between the starting point and the final point and does not take into account the direction of motion. The formula for calculating displacement is displacement = final position – initial position. For example, if a car starts at point A and travels to point B, the displacement is the distance between A and B (B – A).

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Answer:

Solution: Sine is a trigonometric function of an angle defined as the ratio of the length of the perpendicular(opposite) side to the hypotenuse. Thus, the value of sin 2A = √3 / 2.

⤠is the symbol for the euro, while ⥠is the symbol for the Japanese yen.

The euro, represented by the symbol â¤, is the official currency of 19 of the 28 member states of the European Union. It was introduced in 1999, and is the second-most traded currency in the world after the US dollar. The euro is managed and administered by the European Central Bank and the Eurosystem.

The Japanese yen, represented by the symbol â¥, is the official currency of Japan and is the third most traded currency in the world. It is issued and managed by the Bank of Japan, the country's central bank. The yen is used as a reserve currency by central banks and is often seen as a safe-haven asset during times of economic or political uncertainty.

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The value of CE in the segment is 30 units.

The value of x in the segment is 1 units.

A line segment is bounded by two distinct points on a line. Therefore, point D is located on the segment CE. Hence,

CD = 24 and DE = x

CE = 5x

Therefore, the measurement of the segment CE can be found as follows:

CE = CD + DE

5x = 24 + x

5x - x = 24

4x = 24

divide both sides of the equation by 4

x = 24 / 4

x = 6

Finally,

CE = 5(6) = 30

The segment XZ is bisected by the point Y. Hence,

XY = 12x

XZ = 18x - 6

Hence, let's find x

Therefore,

2XY = XZ

2(12x) = 18x - 6

24x = 18x - 6

24x - 18x = -6

-6x = -6

x = -6 / -6

x = 1

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When there are 25 students in the group, the number of people who not like non-fiction will be A. 15 people.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

From the information, three fifths of the students in the reading group like non-fiction books. If there are 25 students in the group, the number of people who not like non-fiction will be:

= 3/5 × 25

= 15

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Calculating the total VMT or VKT for all road segments during a certain time period by multiplying the daily traffic volume on each segment by its length.

The average automobile is around 15 feet long, so if you multiply 5280 by this number, you get about 350 cars, assuming they are all touching. Just over 284 million automobiles were on the road in the second quarter of 2022 in the United States. Though estimating the overall number of automobiles on the planet is not a precise science, the number is rising quickly.

Given that the ACS estimated there were 150 million workers in 2016, there are at least 115 million automobiles and trucks on American roads every day. Congestion is expected to be so bad during morning and afternoon rush hours. A balance between the demand for using the system and the infrastructure's capabilities can be achieved by creating digital twins of the transportation system and using them to optimise flows.

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The lessons we get from book that discuss applied regression analysis and other multivariable is that it can be used in real-life problems such as prediction and forecasting.

As a very effective and practical statistical technique, regression analysis has numerous applications to the field of nursing science. It allows scientists to explain, forecast, and quantify the correlations between variables, and form credible conclusions about the underlying causes of any phenomenon under study.

Regression analysis is a reliable way for determining which variables have an impact on a particular topic of interest. The method of doing a regression allows you to safely establish which elements are most important, which factors may be ignored, and how these factors influence each other.

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The solution of equation: 2y + 8x = 2(y + 4)x.

For the stated equation:

= 2y + 8x

As. 2y and 8x both are divisible by 2 .

So, Taking two common from both.

= 2(y + 4x)

Thus, the solution of the equation becomes: 2(y + 4x).

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Answer:

parallelogram

The required reflection of the points N(-3, 1), G(0, 4), B(-1, 1) across the y-axis are N(3, 1),  G(0, 4), B(1, 1) .

Point (x, y) is reflected across the x-axis as (x, -y). The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse.

We have,

N(-3, 1), G(0, 4), B(-1, 1)

While, find reflected points we are considering y-axis as mirror,

Then,

Reflection of point N(-3, 1) across the y-axis

⇒ N(3, 1)

Reflection of point G(0, 4) across the y-axis

⇒ G(0, 4)

Reflection of point B(-1, 1) across the y-axis

⇒ B(1, 1)

Thus, required reflected points are  N(3, 1),  G(0, 4), B(1, 1) .

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The slope of the line passing through the equation 4x - 3y = 12 is given by Slope m = -3/4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

4x - 3y = 12   be equation (1)

Now , on simplifying the equation , we get

Adding 3y on both sides of the equation , we get

3y + 12 = 4x

Subtracting 12 on both sides of the equation , we get

3y = 4x - 12

Divide by 3 on both sides of the equation , we get

y = ( 4/3 )x - 4

It is of the form y = mx + b where m is the slope and b is the y-intercept

So , slope m₁ = 4/3

Now , the line is perpendicular to the line y = ( 4/3 )x - 4

So , the product of their slopes is -1

And , m₁ x m₂ = -1

Substituting the values in the equation , we get

m₂ = ( 3/4 ) x -1

m₂ = -3/4

Hence , the slope of the line is -3/4

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The graph that represents the solution to the inequality is a number line with closed point at 10 with arrow pointing left

You should be aware that inequality is is a mathematical statement showing that two opposite things are not equal.  The graph is a diagram that illustrates the statement.

The given inequality is 2(b + 2) > 24

Opening the brackets to get

2b+4≥24

2b≥24-4

This implies that 2b≥20

Making b the subject

b≥20/2

b≥10

Conclusively the graph is a number line with closed point at 10 with arrow pointing left

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