Find the average rate of change for the function listed below on the interval [2,7].
f(x)=3x^2+2x+4

The volume of a pyramid with a square base is 3172.608 cubic meter.

Given that, the side length of the base is 14.4 m and the height of the pyramid is 15.3 m.

Formula to find the volume of the object is Volume = Area of a base × Height.

Here, volume = 14.4²×15.3

= 3172.608 cubic meter

Therefore, the volume of a pyramid with a square base is 3172.608 cubic meter.

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Answer:

YES

Step-by-step explanation:

A statistical question is a question that can be answered by collecting data that vary. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question.

Answer:

Step-by-step explanation:

[tex]4\frac{8}{9} . 1\frac{1}{3}\\= \frac{44}{9}.\frac{4}{3} \\= \frac{176}{27}[/tex]

The value of the expression is 1.

Given is an expression we need to solve it,

x - 1/2 = √1/4 x

x - 1/2 = 1/2 x

x - 1/2 x = 1/2

1/2 x = 1/2

x = 1

Hence the value of the expression is 1.

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The 8th term of the sequence is 2.

To find the 8th term of the given number sequence, we can observe that the sequence is decreasing by 3 with each term.

Starting from the first term, which is 23, we subtract 3 repeatedly to get the subsequent terms:

23 - 3 = 20

20 - 3 = 17

17 - 3 = 14

14 - 3 = 11

We can see that each term is obtained by subtracting 3 from the previous term.

To find the 8th term, we continue this pattern:

11 - 3 = 8

8 - 3 = 5

5 - 3 = 2

Therefore, the 8th term of the sequence is 2.

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The dimensionless product relating the torque, rotation rate, volume, and air density is:

Pi = (torque) * (rotation rate)² * (volume)^(1/3)

To find a dimensionless product relating the torque (ML²T⁻²) produced by an automobile engine, the engine's rotation rate (T⁻¹), the volume V of air displaced by the engine, and the air density p, we can make use of the Buckingham Pi theorem.

The Buckingham Pi theorem states that in a physical problem involving n variables with k fundamental dimensions, there will be n - k dimensionless quantities that can be formed as products of powers of the original variables.

In this case, we have 4 variables with 3 fundamental dimensions: torque (M L² T⁻²), rotation rate (T⁻¹), volume (L³), and air density (M L⁻³). Therefore, we expect to have 4 - 3 = 1 dimensionless product.

Let's define the dimensionless product (Pi) as:

Pi = (torque)ᵃ * (rotation rate)ᵇ * (volume)ᶜ * (air density)ᵈ

To determine the powers (a, b, c, d), we equate the dimensions on both sides of the equation:

M L² T⁻² = (M)ᵃ * (T⁻¹)ᵇ * (L³)ᶜ * (M L⁻³)ᵈ

Equating the dimensions of mass (M):

1 = a + d

Equating the dimensions of length (L):

2 = 3c - 3d

Equating the dimensions of time (T):

-2 = -b

Solving these equations, we find:

a = 1

b = 2

c = 1/3

d = 0

This dimensionless product captures the relationship between these variables, independent of their specific units and scaling factors.

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Answer:

[tex]36442 {e}^{.042t} = 75000[/tex]

[tex]t = 17.18 \: years[/tex]

Answer:

[tex]\\[/tex]

Step-by-step explanation:

We know that the total number of kids is 150. We can find the number of kids with green, brown, and gray eyes using the given percentages:

[tex]\sf\dashrightarrow Green\: eyes = 6\: kids[/tex]

[tex]\sf\dashrightarrow Brown\: eyes = 0.52 \times 150 = 78\: kids[/tex]

[tex]\sf\dashrightarrow Gray\: eyes = 0.16 \times 150 = 24\: kids[/tex]

[tex]\\[/tex]

To find the number of kids with blue eyes, we can subtract the number of kids with green, brown, and gray eyes from the total number of kids:

[tex]\sf\dashrightarrow Blue\: eyes = 150 - 6 - 78 - 24[/tex]

[tex]\sf\dashrightarrow Blue\: eyes = 42\: kids[/tex]

[tex]\\[/tex]

Finally, we can calculate the percentage of kids with blue eyes by dividing the number of kids with blue eyes by the total number of kids and multiplying by 100:

[tex]\sf\implies Percentage = \dfrac{42}{150} \times 100[/tex]

[tex]\sf\implies Percentage = \dfrac{4,200}{150}[/tex]

[tex]\sf\implies Percentage = \green{28\%}[/tex]

[tex]\\[/tex]

[tex]\\[/tex]

Therefore, 28% of the kids have blue eyes.

Answer:

y = [tex]\frac{2}{3}[/tex] x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 6, 0) and (x₂, y₂ ) = (0, 4) ← 2 points on the line

m = [tex]\frac{4-0}{0-(-6)}[/tex] = [tex]\frac{4}{0+6}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]

the line crosses the y- axis at (0, 4 ) ⇒ c = 4

y = [tex]\frac{2}{3}[/tex] x + 4 ← equation of line

Answer:

h = 4 units

Step-by-step explanation:

Given equation:

[tex]\text{A}_{\text{trapezoid} } = \dfrac{1}{2}(h)(b_{1} + b_2)[/tex]

Given numerical values:

Plug in all values into the equation and simplify it to find the height:

[tex]\implies \text{28} = \dfrac{1}{2}(h)(6 + 8)[/tex]

[tex]\implies\text{28} = (h)(3 + 4) = 7h[/tex]

[tex]\implies h = \dfrac{28}{7} = 4[/tex]

Therefore, the measure of the height is 4 units.

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The option that describes the rigid transformation that take AEFD to CFEB are:

To rotate a form 180°, turn it about its center point such that it faces the opposite way. This is accomplished by tracing the form on a sheet of paper and then folding it in half so that the two sides of the shape line up. The form is now rotated 180 degrees.

A rigid transformation (also known as a Euclidean transformation or Euclidean isometry) in mathematics is a geometric transformation of a Euclidean space that retains the Euclidean distance between each pair of points.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

The information which would be enough to prove the triangles to be congruent are either DE = RP or ∠F = ∠Q.

Given two triangles,

ΔDEF and ΔRPQ.

If ΔDEF is congruent to ΔRPQ, then the corresponding vertices of D, E and F are R, P and Q respectively.

Already we have from the figure,

∠D = ∠R

DF = RQ

Now, it is enough to prove either DE = RP or ∠F = ∠Q.

When DE = RP, by SAS congruence theorem, corresponding two sides and the included angle of each triangle are equal and thus triangles are congruent.

When ∠F = ∠Q, by ASA congruence theorem, corresponding two angles and the included side of each triangle are equal and thus triangles are congruent.

Hence the information required are either DE = RP or ∠F = ∠Q.

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The interval on which f(x) is increasing is (-∞, -1) and (3, ∞).

To find the interval on which the function f(x) = x³ - x² - 9x + 3 is increasing, we need to determine where the derivative of the function is positive.

First, let's find the derivative of f(x):

f'(x) = 3x² - 6x - 9

3x² - 6x - 9 = 0

3(x - 3)(x + 1) = 0

x - 3 = 0 or x + 1 = 0

x = 3 or x = -1

These are the critical points of the function.

Let's test a value from each interval:

For x < -1, let's use x = -2:

f'(-2) = 3(-2)² - 6(-2) - 9 = 12 + 12 - 9 = 15 > 0

For -1 < x < 3, let's use x = 0:

f'(0) = 3(0)² - 6(0) - 9 = -9 < 0

For x > 3, let's use x = 4:

f'(4) = 3(4)² - 6(4) - 9 = 12 - 24 - 9 = -21 < 0

From these test values, we can see that f(x) is increasing on the interval (-∞, -1) and (3, ∞).

Therefore, the interval on which f(x) is increasing is (-∞, -1) and (3, ∞).

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Based on the information provided in the table, Jack has 4h yellow marbles.

To determine the number of yellow marbles in the jar of 275 marbles, we can use the information from the table to find the proportion of yellow marbles in the first pouch.

According to the table, there are 4 yellow marbles out of a total of 25 marbles in the first pouch.

Therefore, the proportion of yellow marbles in the first pouch is 4/25.

To find the number of yellow marbles in the jar of 275 marbles, we can multiply this proportion by the total number of marbles in the jar.

Number of yellow marbles = (4/25) x 275 = 44

Therefore, there are 44 yellow marbles in the jar of 275 marbles.

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Answer:0.03125

Step-by-step explanation:

GOO*OOGLE

Step-by-step explanation:

(1/2)^5   = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 =   1/32

The values of r for which y = e^(rx) satisfies the differential equation y″ - 64y = 0 are r = 8 and r = -8.

First, differentiate y twice:

y' = [tex]re^{rx}[/tex]

y'' = r²[tex]e^{rx}[/tex]

y'' - 64y = r²[tex]e^{rx}[/tex] - 64[tex]e^{rx}[/tex] = 0

[tex]e^{rx}[/tex] * ([tex]r^{2}[/tex] - 64) = 0

[tex]r^{2}[/tex] - 64 = 0:

Solving this quadratic equation gives:

[tex]r^{2}[/tex] = 64

r = ±8

Therefore, the values of r that satisfy the differential equation are r = 8 and r = -8.

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Let y″−64y=0.

Find all values of r such that y=kerx satisfies the differential equation. If there is more than one correct answer, enter your answers as a comma separated list.

Answer:

Step-by-step explanation:

In order from top to bottom:

3

2

1

4

A) The algebraic expression will be 12d + 7 = 91

B) He drives 7 miles per day to work.

For 11 days straight, Ms. Chung drove the same distance every day going to and coming from work.

The distance she drove on Saturday was; 0.9 miles.

The number of miles she drives per day:

84 miles/12

= 7 miles per day

Let the number of miles she travels be day = d

12d + 7 = 91 miles

12d + 7 = 91

12d = 91 - 7

12d = 84

d = 84/12

d = 7 miles per day

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5m is the height of a cone with a diameter of 12 m whose volume is 188 m³.

To find the height of a cone, we can use the formula for the volume of a cone and solve for the height.

The formula for the volume of a cone is:

V = (1/3)× π × r² × h

Given that the diameter of the cone is 12 m, the radius (r) is half of the diameter, which is 6 m.

We are also given that the volume of the cone is 188 m³.

Using the formula, we can rearrange it to solve for the height (h):

h = (3V) / (πr²)

Plugging in the values:

h = (3 × 188) / (3.14 × 6²)

h = 564 / (3.14 × 36)

h = 564 / 113.04

h =4.9916

h=5

Therefore, the height of a cone with a diameter of 12 m whose volume is 188 m³ is 5 m.

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The force of gravity on the rocket is 30 N/kg, the mass of the rocket stays constant while its weight varies

The force of gravity is the force exerted on an object by the earth or a planet.

Given that the force of gravity on an object when it is launched is 30 N/kg. This is three times larger than Earth's gravity. To determine what happens to the mass and weight of the object when gravity is 30 N/kg, we proceed as follows.

We know that weight, W = mg where

Since gravity g = 30 N/kg, we have that

W = mg

= m × 30 N/kg

= 30m

Now, we know that mass is an intrinsic property and weight is an extrinsic property. This means that the mass of the object is constant but its weight can change based on the object's position and depends on the amount of mass.

So, since the force of gravity on the rocket is 30 N/kg, the mass of the rocket stays constant while its weight varies

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The surface area of the larger solid is approximately 172 mm sq. approx

Given

The volume of the smaller solid = 540 mm cube

The volume of the larger solid = 857.5 mm cube

The surface area of the smaller solid = 108 mm sq.

Required to find the surface area of the larger solid =?

Let the surface area of the larger solid be x.

(surface area of smaller solid) / (volume of smaller solid) = (surface area of larger solid) / (volume of larger solid)

Putting the values in the above formula we get the value of x.

108 mm^2 / 540 mm^3 = x / 857.5 mm^3

x = 171.5 mm sq

Thus, the surface area of the larger solid is approximately 172 mm sq

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Answer:

same side interior

Step-by-step explanation:

they are on the SAME SIDE as the transversal (diagonal line) which means that they can't be alternate. also, they are inside (interior) of the two horizantal parallel lines. this means that they must be same side interior

[tex]a^2-b^2=(a-b)(a+b)[/tex]

Therefore

[tex]f(x)=x^4-16\\f(x)=(x^2-4)(x^2+4)\\f(x)=(x-2)(x+2)(x^2+4)[/tex]

[tex](x-2)(x+2)(x^2+4)=0\\x=2 \vee x=-2[/tex]

Answer:

x = 2

y = -3

Step-by-step explanation:

y = x - 5

x + y = -1

To solve the given system of equations, we can use the method of substitution.

That is, you can replace y with ( x - 5 ).

x + y = -1

x + (x - 5 ) = -1

x + x - 5 = -1

Combine like terms.

2x - 5 = - 1

Add 5 to both sides.

2x = - 1 + 5

2x = 4

Divide both sides by 2.

x = 2

And now let us find the value of y by replacing x with 2.

y = x - 5

y = 2 - 5

y = -3

The value of all three angles, A , B and C is 60°

All sides , a,b, and c are 7.5 inches

From Cosine Rule :

CosA = (b² + c² - a²)/(2bc)

CosA = (7.5² + 7.5² - 7.5²)/(2 × 7.5 × 7.5)

CosA = 56.25/112.5

CosA = 0.5

A =

[tex] {cos}^{ - 1} (0.5) = 60[/tex]

From Sine Rule a/sinA = b/sinB

7.5/Sin60° = 7.5/SinB

cross multiply

7.5SinB = 7.5(Sin60°)

sinB= 6.495/7.5

SinB = 0.866

B =

[tex] {sin}^{ - 1} (0.866) = 60[/tex]

A + B + C = 180

60 + 60 + C = 180

C = 180 - 120

C = 60°

Therefore , all three angles A,B and C are 60° each.

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The farmer sold 3.6 kilograms of apples at the farmers market.

To find the weight of apples the farmer sold at the farmers market, we need to subtract the weight of pears from the total weight.

We have,

3/5 of the weight is pears, the weight of pears

= (3/5) x 7.2 kilograms.

= 3.6 Kg

Since the remaining weight is apples, we can calculate the weight of apples by subtracting the weight of pears from the total weight:

Weight of apples = Total weight - Weight of pears

= 7.2 - 3.6

= 3.6 kilograms

Therefore, the farmer sold 3.6 kilograms of apples at the farmers market.

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The data set is approximately periodic with a period of 3 and an amplitude of about 7.5.

The period is the length of time it takes for the data to repeat itself. In this case, the data repeats itself every 3 hours. The amplitude is the distance between the highest and lowest values in the data set. In this case, the amplitude is about 7.5 cars.

Hour | Number of cars

------- | --------

1     | 90

2     | 52

3     | 76

4     | 75

5     | 91

6     | 104

7     | 89

8     | 105

9     | 119

10    | 103

11    | 121

12    | 135

As you can see, the data repeats itself every 3 hours. The highest value in the data set is 135 cars, and the lowest value is 52 cars. The difference between these two values is 83 cars, which is about 7.5 times the average number of cars (90 cars). Therefore, the amplitude of the data set is about 7.5 cars.

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The height of the cone in this problem is given as follows:

h = 16.4 units.

The volume of a cone of radius r and height h is given by the equation presented as follows:

V = πr²h/3.

The parameters for this problem are given as follows:

V = 2325 π, r = 15.

Hence the height is obtained as follows:

2325 = π x 15² x h/3

h = 2325 x 5/(15² x π)

h = 16.4 units.

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Answer:

V = lwh

Step-by-step explanation:

The volume of a rectangular prism or a rectangle stretched is the basic rectangle area formula ( wh ) multiplied by the new factor, the length ( l ). This makes the formula V = lwh
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