a thin, 120 g disk with a diameter of 8.00 cm rotates about an axis through its center with 0.18 j of kinetic energy.

The rate of change of the surface area when the radius is 6 inches and the height is 18 inches is 979.68 in² per minute.

Given:

radius of a right circular cylinder is increasing at a rate of 6 inches per minute, and the height is decreasing at a rate of 4 inches per minute.

we are asked to find the rate of change of the surface area when the radius is 6 inches and the height is 18 inches.

we have dr/dt = 6 in/min and dh/dt = -4 in/min

Volume, V = πr²h

Differentiate the above expression to get:

dV/dt = 2πrh dr/dt + πr² dh/dt

SUbstitute the value we get:

dV/dt = 2π(6)(18)(6) + π(6)²(-4)

= 4069.44 - 452.16

= 3617.28 in³ per minute.

The volume is increasing at a rate of  3617.28 in³ per minute.

Area = 2πr(h+r)

Differentiate the above expression:

dA/dt = 2π {(h+r) dr/dt + r (dh/dt + dr/dt)}

dA/dt = 2π {(18+6)(6) + 6(-4+6)}

= 2π(144 + 12)

= 312π

= 979.68 in² per minute.

The area is increasing at a rate of 979.68 in² per minute.

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The rate of change of the surface area when the radius is 6 inches and the height is 18 inches is 979.68 in² per minute.

Given:

The radius of a right circular cylinder is increasing at a rate of 6 inches per minute, and the height is decreasing at a rate of 4 inches per minute.

We are asked to find the rate of change of the surface area when the radius is 6 inches and the height is 18 inches.

We have dr/dt = 6 in/min and dh/dt = -4 in/min

In geometry, it is defined as a three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the volume of the cylinder is given by:

Volume, V = πr²h

Differentiate the above expression to get:

dV/dt = 2πrh dr/dt + πr² dh/dt

Substitute the value we get:

dV/dt = 2π*6*18*6 + π*6² * -4

= 4069.44 - 452.16

= 3617.28 in³ per minute.

The volume is increasing at a rate of 3617.28 in³ per minute.

Area = 2πr(h+r)

Differentiate the above expression:

dA/dt = 2π {(h+r) dr/dt + r (dh/dt + dr/dt)}

dA/dt = 2π {(18+6)(6) + 6(-4+6)}

= 2π(144 + 12)

= 312π

= 979.68 in² per minute.

The area is increasing at a rate of 979.68 in² per minute.

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Answer:

33

Step-by-step explanation:

                                              Difference from

Day     Number of apples      previous day              

1           1                                   -

2          2                                  1

3          3                                  1  

4          5                                 2

5          7                                 2

6          9                                 2

7           12                               3

8           15                               3

9           18                               3

10          22                             4

11           26                             4

12         30                              4

13          35                             5

14          40                             5

15          45                             5

16          51                              6

17           57                            6

18           63                            6

19           70                            7

20          77                             7

21           84                            7

The differences between consecutive days started at 1, then 2, then 3, etc. The last day of any specific difference is a multiple of 3.

For example, day 3 was the last day of a difference of 1.

Day 6 was the last day of a difference of 2.

Day 9 was the last day of a difference of 3.

Day 12 was the last day of a difference of 4.

In each case, 6/2 = 3; 9/9 = 3; 12/4 = 3.

99 is a multiple of 3, so it will be the last day with a difference of 99/3 = 33

Answer: 33

(x+x/2)*3=105 is the equation for "three times the sum of a number and half the number equals 105."

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 sentence with two equal sides separated by an equal sign is called an equation. 4 + 6 = 10 is an example of an equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept.

Here,

Three more than twice the sum of a number and half the number equals 105,

The equation will be,

(x+x/2)*3=105

The equation for "Three more than twice the sum of a number and half the number equals 105" will be (x+x/2)*3=105.

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The weighted arithmetic mean price per ton is $72.33

Given that, a purchasing agent placed the three orders for coal. tons of coal 1,200 3,000 500 price per ton $28.50, $87.25 and $88.00, we need to find the weighted arithmetic mean price per ton,

So, the mean = 28.50x1200+87.25x3000+88x500 / 1200+3000+500

= 339950 / 4700 = 72.33

Hence, the arithmetic mean price per ton is $72.33

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The required conversion of the 15 cm/year is given as 0.5 inches per month.

Given that,
15 cm/year converted to inches per month is to be determind.

Conversion of the units is defined as the multiplying the original value with the unit factor.

Here,
1 cm = 0.4 inch
1 year = 12 month,
Substitute these values in the expression = 15 cm / year
= 15 × 0.4 / 12
= 0.5 inches per month.

Thus, the required conversion of the 15 cm/year is given as 0.5 inches per month.

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Answer:

1/3

Step-by-step explanation:

rise/run is rate of change

16/25 as a percentage is 64%.

The number in the denominator is the one below the fraction line, while the number in the numerator is the one above the fraction line.

When we talk about percentages, we really mean that it's a subset of 100. Since the word "percent" refers to a hundred, 50% is equivalent to expressing 50/100 or 5/10 in fractional form.

Therefore, since 25 is the denominator in 16/25, we might change the fraction so that 100 is the denominator.

To do that, we divide 100 by the denominator:

100/25 = 4

Once we have that, we can multiply both the numerator and denominator by this multiple:

[tex]\frac{16}{25}[/tex] × [tex]\frac{4}{4}[/tex] = [tex]\frac{64}{100}[/tex]

Now we can see that our fraction is 64/100.

Thus, 16/25 as a percentage is 64%.

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Answer:

I belive it would be 102

Step-by-step explanation:

Answer:

306 cm

Step-by-step explanation:

the opposite side is the same as the shaded side

18 x 17 = 306 cm

The statement made by Erin about the triangles is false

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

As a general rule of dilation (i.e. scale factors),

The area of the image of the dilation is the square of the scale factor multiplied by the area of the pre-image shape

Mathematically, this is represented as

Area of the image of the dilation = scale factor² * Area of the pre-image shape

Using familiar terms, we have

Area of ∆XYZ = (31)² * the area of ∆ABC.

The above statement is true and it is not the same as Erin's statement

Hence, Erin is incorrect

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Answer:

question 1: T
question 2: F
question 3: C

Step-by-step explanation:

Answer:

1. True

2. False

3. D. {2,4,9,16}

Step-by-step explanation:

⭐What is a function?

Therefore, #1 is a function because for every x-value, there is 1 y-value.

Therefore, #2 is NOT a function because 6 has 2 y-values, and 12 has 2 y-values.

⭐What is the range of a function?

Therefore, {2,4,9,16} is the range of #3 because it lists all of the y-values in ascending order.

The value of the x in g(h(x)) = 4 is 4 if the g⁻¹(4) = 2 and at x = 4 h(x) = 2 option (C) is correct.

The correct value of x when g(h(x)) = 4 is,

⇒ x = 4

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The relation is,

g (h (x)) = 4

Now, Substitute x = 4;

LHS;

g (h (x)) = g (h (4))

            = g (2)

           = 4

Thus, The correct value of x when g(h(x)) = 4 is,

⇒ x = 4

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Answer:

Step-by-step explanation:

1)Option A)

2)Option B)

Answer:

V = 5πX^2 + 50πX + 75π

Step-by-step explanation:

The volume of a cylinder with radius r and height h is given by the formula:

V = πr^2h

Substituting the values for the radius and height of the cylinder in this formula, we get:

V = π(5X + 5)^2(5X + 3)

This can be written in standard form as:

V = 5πX^2 + 50πX + 75π

So, the polynomial in standard form that best describes the total volume of the cylinder is:

V = 5πX^2 + 50πX + 75π

Answer:17cm x 19cm

Step-by-step explanation:

Answer: length is 19 inches  

               width is 17 inches

Step-by-step explanation:

Let the length and the width are x>0 and (x+2)>0

Hence,

x(x+2)=323

x²+2x=323

x²+2x-323=0

x²+(19x-17x)-323=0

(x²+19x)-(17x+323)=0

x(x+19)-17(x+19)=0

(x+19(x-7)=0

x+19=0

x=-19∉ (x>0)

x-17=0

x=17 inches

x+2=17+2

x+2=19 inches

Answer: 4ft/s

Step-by-step explanation:

I think

2 + 6 = 8

8 / 2 = 4

The slope of the line is  4/3

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

Without actually using a compass, determining a line's slope in a coordinate plane can aid in determining whether the line is parallel, perpendicular, or not.

In the slope marked,

vertical length = change in y values = number of unit squares = 4

Horizontal length = change in x values = number of unit squares = 3

Slope= ( change in y values  )/ ( change in x values ) = 4/3

Thus, the slope = 4/3

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Answer:

Step-by-step explanation:

The Function value of f(-2) is -4

What are Function?

Exactly each element of Y is assigned to each element of X in a mathematical function from the a set X to a set Y. Both the set X as well as the set Y are referred to as the function's domain and codomain, respectively. Al-Biruni as well as Sharaf al-Din al-Tusi were two Persian mathematicians who are credited with developing the earliest known method for approaching the concept of function. The original conception of functions was the relationship between varying quantities and other variables. An illustration of this is how time affects a planet's position. The idea was developed historically at the conclusion of the 17th century with the development of infinitesimal calculus, and up to until nineteenth century, the functions taken into consideration were differentiable.

Solution:

Given: f(x) = 3x + 2

To find: Value of f(-2)

To solve this problem we will simply replace the value of x in Function with -2

f(-2) = 3*(-2) + 2

f(-2) = -6 + 2

f(-2) = -4

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He utilized about 39.9 KG of clay per pot, or 38% of the 315 KG of clay, using 119.7 KG for 3 pots.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. Percentage, a relative value indicating hundredth parts of any quantity, is a relative value that indicates how many questions on a test you correctly answered out of 100 (75/100). Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

Here,

Weight of clay=315 KG

Weight of clay he used,

=38%*315

=119.7 KG

Number of pots=3

Clay used in each pot,

=119.7/3

=39.9 KG

He used around 39.9 KG of clay to make each pot using 119.7 KG of clay for  3 pots out of 38% of 315 KG of clay.

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The standard deviation of the team members' heights is 2.35.

A z-score is a number that indicates how far an observation deviates from the mean and in which direction.

A z-score is a common name for a standardized number.

The standardized value of x is: If x is an observation from a distribution with known mean and standard deviation :

z = (x - mean) / Standard Deviation

Given in question,

z = -0.85

x = 74

mean = 76

Let the Standard deviation be s.

By putting the values in the equation,

-0.85 = (74 - 76)/s

s = -2/-0.85

  = 2/0.85

  = 2.35

Hence, the standard deviation of the team members' heights is 2.35.

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Answer:

  82.4 mg/mm²

Step-by-step explanation:

You want to convert 8.24 g/cm² to units of mg/mm².

Multiply by the conversion factors that cancel the unwanted units, leaving the wanted units.

  [tex]\dfrac{8.24\text{ g}}{\text{cm}^2}=\dfrac{8.24\text{ g}}{\text{cm}^2}\cdot\dfrac{1000\text{ mg}}{\text{g}}\cdot\left(\dfrac{1\text{ cm}}{10\text{ mm}}\right)^2=\dfrac{8.24\cdot1000\text{ mg}}{100\text{ mm}^2}\\\\=\boxed{82.4\text{ mg/mm$^2$}}[/tex]

A test's large p-value does not necessarily mean that the null hypothesis should be accepted.

In a test, a low P-value will favor rejecting the null hypothesis.

The P-value approach evaluates whether something is "likely" or "unlikely," assuming that the null hypothesis is correct, by calculating the probability of observing a test statistic that is more extreme in the direction of the alternative hypothesis than the one actually seen. If the P-value is low, such as less than, it is "unlikely" (or equal to) α.

The null hypothesis is disregarded in favor of the alternative hypothesis if the P-value is less than (or equal to) α. Additionally, the null hypothesis is not disproved if the P-value is higher than α.

As a result, the right response is false.

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The correct option A: graph A, shows the logarithmic function;

f(x) = log₃x + 1

f(x) = log₃x + 1

f(1) = log₃1 + 1

f(1) = 0 + 1

f(1) = 1

(1, 1)

f(3) = log₃3 + 1

f(3) = 1 + 1

f(3) = 2

(3, 2)

Thus, the graph must contain the points   (1, 1), (3, 2).

Therefore, graph A define the given logarithmic function;

f(x) = log₃x + 1.

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Answer:

It looks like you have an inequality equation with one variable, but the equation is incomplete. In order to solve the inequality, we need to have a complete equation with a left-hand side and a right-hand side.

For example, if we wanted to solve the inequality 8y - 5 < 3, we could complete the equation by adding 5 to both sides:

8y - 5 + 5 < 3 + 5

8y < 8

Then, we could divide both sides of the inequality by 8 to solve for y:

8y/8 < 8/8

y < 1

Therefore, the solution to the inequality 8y - 5 < 3 is y < 1.

A line chart is the best chart to show trends over time. It shows trends and data variables clearly.

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.  

The points on the graph often represent the relationship between two or more things.

We can deduce that a line chart is the best chart to show trends over time as it shows trends and data variables clearly and also assists readers with making predictions for the future. However, for a data set comparison being useful, you must use the same scale on both axes.

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The given equation is a linear equation.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

We have,

g(x) = 1/3x - 6

We need to identify whether the given equation is Linear, Quadratic, Exponential, or None and why.

g(x) is the term that shows the rate of change with respect to x.

1/3 is the coefficient of the variable x

and the 6 is the constant term in the equation.

so, comparing the given equation with standard form of linear equation,

y = mx + c.

we can say here,

y = g(x)

m = 1/3,

c = 6

Hence, the given equation is a linear equation.

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The  distance between the shortstop and the pitcher calculated as per the given data is 63.6.

Distance between two consecutive bases = 90 feet

Halfway distance between them will be = 45 feets

therefore, halfway distance between first base and second base = 45 feet

and that between second base and third base = 45 feet

So the distance between the  shortstop and the pitcher using pythagoras theorem

= >SP² = PQ² + QS²

           = 45²  + 45²

            =4050

SP = 63.6

Therefore , the required distance is 63.36feets.

The Pythagorean Theorem, often known as Pythagoras Theorem, is a crucial concept in mathematics that describes how the sides of a right-angled triangle relate to one another. Pythagorean triples are another name for the sides of the right triangle

In essence, the Pythagorean theorem is used to determine a triangle's angle and length of an unknown side. We can derive the base, perpendicular, and hypotenuse formulas using this theorem.

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The length of AB will be 32

Given that,

AC=32

AD=8

∠ABC=90 degree

From the diagram, we can see that it is a right-angle triangle so we can use that trigonometry to find the value of AB.

We know that,

                     sinФ=[tex]\frac{perpendicular}{hypotenuse }[/tex]

Now using this formula we can find the value of AB. And we know that the value of sin90= is 1.

sin90=AB/AC

⇒1=AB/32

⇒32=AB

⇒AB=32

So the length of AB mean x is 32

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Answer:

Triangle perimeter = 12 + x + (x - 4) = 26 which is the equation you can use to find out the value of x.

Step-by-step explanation: