Use the definition of the derivative to find the slope of the tangent line to the graph of the given function at any point. Show your work by completing the four-step process. (Simplify your answers completely for each step.) f(x) = 4x² + 7x Step 1: Step 2: Step 3: Step 4: f'(x) = lim h→0 f(x + h) = 4(x + h)² +7(x+h) f(x + h)-f(x) = h(4(2x+h)+7) f(x + h) − f(x) = h f(x+h)-f(x) h 4(2x+h) +7 8x + 7 X X (Expand your answer completely.) (Factor your answer completely.)
Let f(x) = x² + 5x. (a) Find the derivative f' off by using the definition of the derivative. Show your work by completing the four-step process. (Simplify your answers completely for each step.) f(x + h) = (x + h) +5(x+h) (b) Step 1: Step 2: Step 3: Step 4: f'(x) = _lim_ h→0 f(x +h)-f(x) = f(x+h)-f(x) h f(x +h)-f(x) h (Expand your answer completely.) X (Factor your answer completely.) Find an equation of the tangent line to the graph of f at the point (1,4). Give your answer in the slope-intercept form.

Answer:

its 36 dollars

Step-by-step explanation:

27 + x = 62

x = 62 - 27

x = 36

Answer:

Step-by-step explanation:

How do location and population density affect ways of life in Central Africa? Tropical forests have low population densities since they are not fertile areas. More densely populated areas are countries in which the capital city is an economic, political, and cul- tural hub.

Answer:

A. trust me I did it and got 100

Answer:

D

since all the other 1st elements (Domains) of each ordered pairs are repeated in all options except D they are not functions.

In conclusion, a function is defined as a set of ordered pairs with wich each element of the domain has one unique y value.

infinite sequences of arithmetic expressions can have a value of 4

Step-by-step explanation:

infinite sequences of arithmetic expressions can have a value of 4

Answer:

Original angle = 122*

Supplementary angle = 58*

Step-by-step explanation:

A supplementary angle is one of two angles that make up 180*

If one angle is 30*, its supplementary angle is 150*. 30 + 150 = 180.

So in this case we have two angles, the original and the supplementary angle. The original angle is 64* more than the supplementary angle. The key word is MORE.

The formula to figure it out would look like this:  x + (x + 64) = 180

x is the supplementary angle

x + 64 is the original angle (64 MORE than its supplementary angle)

180 is the total measure of the two angles because they are supplementary and we know that supplementary angles always equals 180* when added together.

Take the formula and do a little algebra.

x + (x + 64) = 180

Subtract 64 from both sides

x + x = 116

Combine the x's

2x = 116

Divide both side by 2

x = 58

Remeber we know that the original angle is 64 more than the supplementary angle, so we'll add the 64 to the value of x and we get 122.

x + 64 = 122

Check our work:

x + (x + 64) = 180

58 + 58 + 64 = 180

Given :

⠀

To Find :

⠀

Solution :

Now,

⠀

According to the Question :

⠀

\(\longrightarrow\qquad \sf{{x + (x + 64) {}^{ \circ} = {180}^{ \circ} }}\)

⠀

\(\longrightarrow\qquad \sf{{x + x + 64 {}^{ \circ} = {180}^{ \circ} }}\)

⠀

\(\longrightarrow\qquad \sf{{2x + 64 {}^{ \circ} = {180}^{ \circ} }}\)

⠀

\(\longrightarrow\qquad \sf{{2x = {180}^{ \circ} - 64 {}^{ \circ}}}\)

⠀

\(\longrightarrow\qquad \sf{{2x = {116}^{ \circ} }}\)

⠀

\(\longrightarrow\qquad \sf{{x = \dfrac{{116}^{ \circ}}{2} }}\)

⠀

\(\longrightarrow\qquad \mathfrak{\pmb{{x = {58}^{ \circ} }}}\)

⠀

Therefore,

⠀

Henceforth ,

The perimeter of the entire figure is 62.8 cm.

Given, that the diameter of the inner semicircles is 9 cm and the width between the outer and inner semicircles is 2 cm.

The radius of the inner semicircle =4.5 cm and the radius of outer semicircle =5.5 cm (∵Diameter=9+2=11 cm)

We need to find the perimeter of the entire figure.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference.

We know that, the circumference of a semicircle=πr and the circumference of two semicircles=2πr

Thus, the circumference of inner semicircles=2×3.14×4.5=28.26 cm

The circumference of outer semicircles=2×3.14×5.5=34.54 cm

The perimeter of the entire figure=28.26+34.54=62.8 cm

Therefore, the perimeter of the entire figure is 62.8 cm.

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The perimeter of whole path is 12.56 cm

Perimeter is the distance around the edge of a shape.

r1= 4.5cm, r2= 6.5cm

Perimeter of semicircle 1,

=πr1

= 3. 14 * 4.5

= 14.13 cm

Perimeter of semicircle 2

=πr2

= 3. 14 * 6.5

= 20.41 cm

Perimeter of path = 20.41 - 14.13 =6.28 cm

Perimeter of whole path = 2 * 6.28 =12.56

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Answer:

B)

Step-by-step explanation:

625:250=2.5

so i think it is B

Answer:

A 2:3

Step-by-step explanation:

625-250= 375 which is the number of boys in the school now it's 375 and 250

250:375

= 250/375

Dividing by 5/5, we have,

50/75

Again, Dividing by 5/5, we have,

10/15

Again, Dividing by 5, we have,

2/3

Hence, the ratio 250:375 in the simplest form will be 2:3

Answer:

16.49

Step-by-step explanation:

21^2 - 13^2 = 272

square root 272 = 16.49

The equation that can be used to find the unknown number is 9x - 5 = 40

Let's assume the unknown number is represented by the variable "x".

According to the given information, "9 times a number" can be expressed as "9x" and "5 more than 9 times a number" can be expressed as "9x + 5".

The problem states that the difference between "9 times a number" and 5 is 40.

Mathematically, this can be written as:

9x - 5 = 40

To find the unknown number, we can solve this equation for "x".

Adding 5 to both sides of the equation:

9x - 5 + 5 = 40 + 5

9x = 45

Dividing both sides of the equation by 9:

(9x)/9 = 45/9

x = 5

Therefore, the unknown number is 5.

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Answer:

13 meters.

Step-by-step explanation:

We can use the formula for the volume of a rectangular prism, which is:

Volume = length x width x height

We are given that the base area (length x width) of the prism is 54 m², so we can write:

length x width = 54 m²

We are also given that the volume of the prism is 702 m³, so we can write:

Volume = length x width x height = 702 m³

We want to find the height of the prism, so we can rearrange the formula for the volume to solve for height:

height = Volume / (length x width)

Substituting the given values, we get:

height = 702 m³ / 54 m²

Simplifying this expression, we can divide both the numerator and the denominator by the greatest common factor of 54 and 702, which is 18:

height = (702/18) m / (54/18) m = 39 m / 3 m

height = 13 meters

Therefore, the height of the rectangular prism is 13 meters.

Answer:

1:eaxctly two factors  2:more than two factors  3:neither prime nor composite

Step-by-step explanation:

I GOT IT RIGHT!

Answer:

Answer time!!

1. exactly 2 factors

2. more than 2 factors

3. niether prime nor compisite

Answer:

f(3) = 15

Step-by-step explanation:

to evaluate f(3) substitute x = 3 into f(x)

f(3) = 2(3)² - 3 = 2(9) - 3 = 18 - 3 = 15

We evaluate the integral over the given region by plugging in the limits of integration for θ and r. The limits of integration for \(θ are 0 to π/2,\) and the limits for r depend on the equation of the circle\(x^2 + y^2 = r^2.\)

To evaluate the given integral, we can change to polar coordinates. In polar coordinates, we express points in terms of their distance from the origin (r) and the angle they make with the positive x-axis (θ).

The region enclosed by the circle \(x^2 + y^2 = r^2\) in the first quadrant corresponds to\(0 ≤ θ ≤ π/2 and 0 ≤ r ≤\) the radius of the circle (which can be determined from the equation of the circle).

Now, let's express the integral in polar coordinates.

Since \(x = rcos(θ) and y = rsin(θ),\)

we have:
\(∫∫ rye^xdA = ∫∫ (r*sin(θ))*(re^rcos(θ))*rdrdθ\)

To evaluate this double integral, we can separate it into two integrals: one with respect to r and the other with respect to θ.
First, we integrate with respect to r:
\(∫ (r*sin(θ))*(re^rcos(θ))*rdr = ∫ r^3e^rcos(θ)*sin(θ)dr\)

To integrate this, we can use integration by parts.

Let's choose\(u = r^3 and dv = e^rcos(θ)*sin(θ)dr.\)

Then, we have \(du = 3r^2dr and v = -e^rcos(θ).\)

Using the formula for integration by parts, we get:
\(∫ r^3e^rcos(θ)*sin(θ)dr = -r^3e^rcos(θ) - 3∫ r^2e^rcos(θ)dr\)

Next, we integrate with respect to θ:\(-3∫ r^2e^rcos(θ)dr = -3(e^rcos(θ))∫ r^2dr = -3(e^rcos(θ))(r^3/3)\)

Substituting this result back into the previous integral, we have:

\(∫ (r*sin(θ))*(re^rcos(θ))*rdr = -r^3e^rcos(θ) + (e^rcos(θ))(r^3)\)
After performing the necessary substitutions and calculations, we find the value of the integral.

This is a general approach to evaluating the given integral by changing to polar coordinates. Remember to check the limits of integration and perform the necessary substitutions depending on the specific problem.

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Answer:

B. 20

Step-by-step explanation:

Using the Pythagorean Theorem, you have:

\(a^2 + b^2 = c^2\\24^2 + 32^2 = c^2\\576 + 1024 = c^2\\1600 = c^2\\c = 40\)

So you know side AB is 40 inches long. It asks the length of the midpoint to point A, so you have to do 40/2 = 20 inches

Answer:  approximately 4.7368 minutes

This decimal value is the result of computing 90/19

=====================================================

Explanation:

Let's find the LCM of 6, 9 and 15. First, list out the prime factorization of each value.

The unique prime factors are 2, 3, and 5. We have 2 show up at most once, 3 show up at most twice, and 5 show up at most once. The LCM is 2^1*3^2*5^1 = 2*9*5 = 18*5 = 90.

We'll use this LCM value to set up an example below.

---------------

Consider the tank to be 90 gallons. If we only use tap A, keep tap B closed, and don't open pipe C, then tap A fills the tank at a rate of 90/6 = 15 gallons per minute since it needs 6 minutes to completely fill the tank.

If we have tap B do all the work (keep tap A and pipe C closed), then the rate is 90/9 = 10 gallons per minute for this tap.

Keeping pipe C closed, the two taps A and B work together to have a combined rate of 15+10 = 25 gallons per minute.

Now we consider pipe C being opened. This drains the tank and can do so in 15 minutes (assume the taps A and B aren't open). If we're dealing with a full 90 gallon tank, then its rate is 90/15 = 6 gallons per minute.

The net rate is 25-6 = 19 gallons per minute. We can think of it as a tug of war where the taps A and B ultimately win out despite the fact that pipe C is draining the water. The two taps fill the tank faster than the pipe can drain the tank.

In other words, the tank ultimately gets filled up rather than drained out over the long run. That net speed is at 19 gallons per minute.

The amount of time needed is approximately 90/19 = 4.7368 minutes.

Side note: you can start with any size tank. It doesn't have to be 90 gallons. I picked on this value because it works cleanly with the original given numbers 6, 9 and 15.

Answer:

\(x=\frac{90}{19}\) = 4.73 minutes

\(\frac{1}{6}x +\frac{1}{9}x - \frac{1}{15} x = 1\)

\(\frac{135}{810}x +\frac{90 }{810}x - \frac{54}{810} x = 1\)

\(\frac{171}{810}x = 1\)

x = 4.73 minutes

Step-by-step explanation:

Answer:

− 0.018  ( \(7x^{3}\) − 450 )

Step-by-step explanation:

because math

In the trapezoid ABCD, the midpoints S and T divide the legs into equal segments. By setting up equations based on the fact that S and T are midpoints, we can solve for the value of x. We find that x equals 0, which means that the legs of the trapezoid have equal lengths.

To find the value of x in the trapezoid ABCD, we need to use the fact that S and T are midpoints of the legs.

First, let's label the points:
- A is one endpoint of the shorter base
- B is the other endpoint of the shorter base
- C is one endpoint of the longer base
- D is the other endpoint of the longer base
- S is the midpoint of AB
- T is the midpoint of CD

Given that AB = 3x, ST = 15, and CD = 9x, we can set up an equation based on the fact that S and T are midpoints.
Since S and T are midpoints, the lengths of AS and SB must be equal, and the lengths of CT and TD must also be equal.
Therefore, AS = SB and CT = TD.

From this information, we can set up the following equation:
AS + ST + TB = AB

Since ST = 15, AS = SB, and AB = 3x, the equation becomes:
AS + 15 + SB = 3x
Since AS = SB, we can rewrite the equation as:
2AS + 15 = 3x
Similarly, we can set up an equation for CT and TD:
CT + ST + TD = CD

Since ST = 15, CT = TD, and CD = 9x, the equation becomes:
CT + 15 + TD = 9x

Since CT = TD, we can rewrite the equation as:
2CT + 15 = 9x

Now we have two equations:
2AS + 15 = 3x
2CT + 15 = 9x

To find the value of x, we can solve this system of equations. Subtracting the first equation from the second equation gives us:
2CT + 15 - (2AS + 15) = 9x - 3x

Simplifying both sides gives us:
2CT - 2AS = 6x

Now we can substitute AS and CT with their respective values:
2(TD) - 2(SB) = 6x
Since TD = CT and SB = AS, we have:
2TD - 2SB = 6x
Since we know that SB = AS and TD = CT, we can rewrite the equation as:
2(TD) - 2(AS) = 6x
Simplifying gives us:
2TD - 2AS = 6x

Since TD = CT and AS = SB, we have:
2CT - 2SB = 6x
Substituting the values of CT and SB gives us:
2(9x) - 2(3x) = 6x
Simplifying gives us:
18x - 6x = 6x
Combining like terms gives us:
12x = 6x
Dividing both sides by 6 gives us:
x = 0

Therefore, the value of x in the trapezoid ABCD is 0.

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Check the picture below.

Answer:

14.1

Step-by-step explanation:

You add all of your numbers up, and then you divide by how many numbers you have.

Answer:

x = 16

Step-by-step explanation:

Answer:

x=16

Step-by-step explanation:

3/4x +2=5/4x-6

subtract the 3/4x from both sides

2=2/4x-6

add 6 to add sides

8=2/4x

2/4x simplifies to 1/2x

8=1/2x

x=16

Option (A) Names of TV shows taped in New York are an example of qualitative data. Qualitative data is descriptive in nature and does not involve numerical values or measurements.

It deals with qualities or attributes that cannot be expressed numerically. In this case, the names of TV shows are characteristics that describe the nature of the data. Quantitative data, on the other hand, is numerical data that can be measured and expressed in numbers. A parameter is a measurable factor or variable that can be used to define a system, while statistics is a branch of mathematics that deals with data collection, analysis, and interpretation. In conclusion, since the names of TV shows are descriptive in nature and do not involve numerical values, they are an example of qualitative data.

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Answer: => 56.52 cm²

Step-by-step explanation:

Answer:

0.15 cents

Step-by-step explanation:

1.80 (price) divided by 12 (amount) = 0.15 cents per pencil

The probability of X being within the range (1, 3) is 3.

A continuous random variable is one that can take on any value within a given range, rather than just a few discrete values. This range is typically expressed as an interval such as (a, b) or [a, b] where a and b are two real numbers. It is usually denoted by the letter X. The probability of a continuous random variable X taking on any particular value is always zero - P(X = x) = 0. However, the probability of X being within a certain range [a, b] can be calculated using the following formula:

\(P(a < X < b) = ∫baf(x)dx\)

where f(x) is the probability density function (PDF). This formula is derived from the area under the PDF curve for the given range of values. For example, if X is a continuous random variable with PDF f(x) = 2x, then the probability of X being within the range (1, 3) is

\(P(1 < X < 3) = ∫3f(x)dx = ∫32x dx = [x2]3 - 12 = 4 - 1 = 3\)

In other words, the probability of X being within the range (1, 3) is 3.

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sin(2x) = -24/25, cos(2x) = 7/25, and tan(2x) = -24/7 based on the given information about cos(x) and csc(x). These values represent the sine, cosine, and tangent of twice the angle x.

To find sin(2x), cos(2x), and tan(2x) from the given information, we will utilize the identities and relationships between trigonometric functions.

Given information: cos(x) = 4/5 csc(x) < 0 First, let's find sin(x) using the identity \(sin^2(x) + cos^2(x)\) = 1:

\(sin^2(x) = 1 - cos^2(x)\\sin^2(x) = 1 - (4/5)^2\\sin^2(x) = 1 - 16/25\\sin^2(x) = 9/25\)

sin(x) = ±√(9/25)

Since csc(x) = 1/sin(x), we can determine the sign of sin(x) by looking at csc(x) < 0. Since csc(x) is negative, sin(x) must be negative. Therefore, sin(x) = -3/5.

Using double-angle trigonometric identities, we can find sin(2x), cos(2x), and tan(2x): sin(2x) = 2sin(x)cos(x) sin(2x) = 2(-3/5)(4/5) sin(2x) = -24/25

\(cos(2x) = cos^2(x) - sin^2(x)\\cos(2x) = (4/5)^2 - (-3/5)^2\\cos(2x) = 16/25 - 9/25\\cos(2x) = 7/25\)

tan(2x) = sin(2x) / cos(2x) tan(2x) = (-24/25) / (7/25) tan(2x) = -24/7 Therefore, sin(2x) = -24/25, cos(2x) = 7/25, and tan(2x) = -24/7 based on the given information about cos(x) and csc(x). These values represent the sine, cosine, and tangent of twice the angle x.

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Answer:

2 /-9

Step-by-step explanation:

We can see here that the solutions to the triangles are:

1. 62.2°.

2. 35.9°

3. 61.9°

4. 53.1°

We can see here that using trigonometric ratio formula, we find the values of x.

We see the following:

1. Cos x = 7/15 = 0.4666

x = \(cos^{-1}\) 0.4666 = 62.2°.

2. Sin x = 27/46 = 0.5869

x° = \(sin^{-1}\)  0.5869  = 35.9°

3. Sin x = 30/34 = 0.8823

x° = \(sin^{-1}\) 0.8823 = 61.9°

4. Tan x = 8/6 = 1.3333

x° = 1.3333 = 53.1°

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To parametrize the surface of the first-octant portion of the cone between the planes z = 0 and z = 3, we can use cylindrical coordinates.

Let's denote the cylindrical coordinates as (r, θ, z), where r represents the distance from the z-axis, θ represents the azimuthal angle in the xy-plane, and z represents the height.

The equation of the cone in cylindrical coordinates can be written as:

z = √(r^2)/2

To restrict the cone to the first octant, we can set the ranges for the coordinates as follows:

0 ≤ r ≤ √(6)

0 ≤ θ ≤ π/2

0 ≤ z ≤ 3

Now, we can express the surface parametrically as:

x = r * cos(θ)

y = r * sin(θ)

z = √(r^2)/2

This parametrization satisfies the equation of the cone in the given range of coordinates. The parameter r varies from 0 to √(6), θ varies from 0 to π/2, and z varies from 0 to 3, covering the first-octant portion of the cone between the planes z = 0 and z = 3.

Therefore, the parametrization of the surface is:

(r * cos(θ), r * sin(θ), √(r^2)/2)

where 0 ≤ r ≤ √(6), 0 ≤ θ ≤ π/2, and 0 ≤ z ≤ 3.

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