Given f(x)= 2x^2+5x-12 over x+4 what are the domain and range

Answer:

603 Hours

Step-by-step explanation:

Volume of the cylinder is the area of the base times the height.

Base

a = \(\pi\)\(r^{2}\)

a = \(\pi\)(\(4x^{2}\))

a = 16\(\pi\)

Volume = 16\(\pi\)h

V = 16\(\pi\)(6)

v = 96\(\pi\)

There are 6

Total volume is 96\(\pi\)(6)

576\(\pi\)

1810  Rounded to the nearest whole number

1810/3

603 hours.  Rounded to the nearest hour

Answer:

there are 5 boys

Step-by-step explanation:

Answer:

waitttttttttttttttt- MY DAD IS A TEACHER!?!?!?!??!?!??!??!?!?!?!?

Step-by-step explanation:

I DIDNT KNOW MY DAD WAS A TEACHER-

Answer:

y= - 3cosx - 2

Step-by-step explanation:

Our max here is at 1, and the minimum is at - 5

The distance between the x-axis and these points are 1 and 5. 5 + 1/2 = 6/2 = 3, our amplitude. But let's double check. Our middle point is - 2 so...

- 5 - (- 2) = - 5 + 2 = - 3

The amplitude is rather - 3.

f(x) = Acos(Bx + C) + D

Using this we know B = 0, D = - 2 (the middle point), C = 0, and A = - 3 (amplitude). B = 0, and C = 0, as there is no horizontal/vertical shift

f(x) = Acos(Bx + C) + D

f(x) = - 3cosx + (- 2)

f(x) = - 3cosx - 2

Answer:

y= - 3cosx - 2

Step-by-step explanation:

Just Answered on A P E X Practice Assignment

Answer:

The compound inequality which is used to model the normal rage of pH values of water is:

x>6.5 and x<8.5    (6.5<x<8.5)

Step-by-step explanation:

It is given that:

Normal drinking water needs to have a pH of less than 8.5 and greater than 6.5.

This means that the pH level of the water will lie in the range in between 6.5 and 8.5 excluding them.

Hence, if the pH level is less than or equal to 6.5 or greater than or equal to 8.5 then it could not be used for drinking purpose.

If x represent the pH of the normal drinking water then:

                 6.5 < x < 8.5

i.e. x>6.5 and x<8.5

the relationship between the no.of towers and customers is proportional. As you can see fr each data sets, 1 (thousand) customer for every 48 towers can be calculated.

Ex. 5.25 cust/ 252 towers = 1/48

the same is true for the other data sets, so the data are proportional

The expression 8x1+9x1/100+5x1/1000 in decimal form is 8.095.

An expression is combination of variables, numbers and operators.

The given expression is

8x1+9x1/100+5x1/1000

Eight into 1 plus nine into one by hundred plus five into one by thousand.

Let us solve the expression

8+9/100+5/1000

8+0.09+0.005

Add 8, 0.09 and 0.005

8.095

Hence the expression 8x1+9x1/100+5x1/1000 in decimal form is 8.095.

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Answer:

30.6

Step-by-step explanation:

if the decimal previous is 5 or above, round it up

if the decimal previous is 4 or below, leave it as it is

Answer:

31

Step-by-step explanation:

Because since .9 is a big number it would round up 5 into a 6 so the 6 would round up 30 into 31

Answer:

The blanks are 18 and 20

equivalent ratios

Step-by-step explanation:

With angle of depression = 48°, the horizontal distance from the base of the skyscraper to the ship is approximately 1239.8 feet.

An angle of depression is an angle formed by a horizontal line and a line of sight that is directed downward to an object or point below the horizontal line. In other words, it is the angle between a horizontal line and a line of sight that is directed downward from an observer to an object that is at a lower level than the observer.

Now,

We know that the tangent of the angle of depression A is equal to the opposite side (h) divided by the adjacent side (the distance from the observation deck to the ship). So we can set up an equation:

tan(A) = h / x

where x is the distance from the base of the skyscraper to the ship (the adjacent side).

x = h / tan(A)

A = 48 degrees (angle of depression)

h = unknown

x = unknown

tan(48) = 1.1106 (tangent of 48 degrees)

Using the equation above, we can solve for h:

h = x * tan(A)

h = 969 ft / tan(48)

h ≈ 1239.8 ft

So the horizontal distance from the base of the skyscraper to the ship is approximately 1239.8 feet.

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Answer:

Proved

Step-by-step explanation:

Given

\((2 * 10^2) * (3 * 10^5) = 3.5 * 10^7 + 2.5 * 10^7\)

Required

Prove

On the right hand side, we have:

\(2 * 10^2 * 3 * 10^5 = 3.5 * 10^7 + 2.5 * 10^7\)

Rewrite:

\(2 * 3* 10^2 * 10^5 = 3.5 * 10^7 + 2.5 * 10^7\)

\(6* 10^2 * 10^5 = 3.5 * 10^7 + 2.5 * 10^7\)

Apply law of indices

\(6* 10^{2+5} = 3.5 * 10^7 + 2.5 * 10^7\)

\(6* 10^7 = 3.5 * 10^7 + 2.5 * 10^7\)

Express 6 as 3.5 + 2.5

\((3.5 + 2.5)* 10^7 = 3.5 * 10^7 + 2.5 * 10^7\)

Open bracket

\(3.5 *10^7+ 2.5*10^7 = 3.5 * 10^7 + 2.5 * 10^7\)

Proved

The component form of the following vectors is Option A. V = (38.3, 32.1).

To find the component form of a vector given its magnitude and direction angle, we can use trigonometry.

The component form of a vector in two dimensions is represented as (x, y), where x is the horizontal component and y is the vertical component.

In this case, the magnitude of the vector is given as 50, and the direction angle θ is 50°. We can use this information to calculate the horizontal and vertical components.

The horizontal component (x) can be found using the formula x = magnitude * cos(θ), and the vertical component (y) can be found using y = magnitude * sin(θ).

Let's calculate the components:

x = 50 * cos(50°) ≈ 38.3

y = 50 * sin(50°) ≈ 32.1

Rounding the answers to the nearest tenth, we get the component form of the vector V as (38.3, 32.1).

Therefore, the correct answer is A. V = (38.3, 32.1).

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The question is incomplete. Find the full content below:

Find the component form of the following vectors. Round your answers to the tenth.

Magnitude of v = 50, direction angle θ = 50°

A. V = (38.3, 32.1)

B. V = (33.8, 31.2)

C. V = (32.1, 38.3)

D. V = (31.2, 33.8)

The value of the ratio a:b is (a)13 : 25

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

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

Ratio = a : b

So, we have

Ratio = 65 : 125

Simplify the ratio

Ratio = 13 : 25

Hence, the ratio is (a)13 : 25

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Answer:10

Step-by-step explanation:

The ratio of apple oranges and bananas cannot be calculated with the given information

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

Fruits = Orange, Bananas and Apple

Total number of fruits = 48

The available parameters is not enough to determine the ratio

Assuming that we have

Banana = 10

Orange =  20

Apple = 18

Then the ratio would be:

Apple : oranges : bananas = 18 : 20 : 10

Simplify

Apple : oranges : bananas = 9 : 10 : 5

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Answer:

Here's an interesting project idea for mathematics that can relate three different topics:

Topic 1: Fractals

Topic 2: Chaos Theory

Topic 3: Differential Equations

Research Question: Can fractals be used to model chaotic systems described by differential equations?

In this project, you can explore the concept of fractals and their applications in modeling complex systems. You can also delve into chaos theory and differential equations to understand how they are used to describe chaotic systems. By combining these three topics, you can investigate whether fractals can provide a better understanding of chaotic systems by modeling them more accurately.

Your research paper can cover the following areas:

Introduction: Provide an overview of fractals, chaos theory, and differential equations, and explain their relevance to the research question.

Fractals: Discuss the properties of fractals and how they can be used to model complex systems. Provide examples of fractals in nature and technology.

Chaos Theory: Explain the concept of chaos and how it is described by differential equations. Discuss the importance of chaos theory in understanding complex systems.

Differential Equations: Provide an overview of differential equations and their applications in physics, engineering, and other fields. Explain how differential equations are used to model chaotic systems.

Combining the three topics: Explain how fractals can be used to model chaotic systems described by differential equations. Provide examples of fractals used in modeling chaotic systems and compare the results to traditional methods.

Conclusion: Summarize the findings of your research and discuss the implications of using fractals to model chaotic systems.

Overall, this project can be a challenging and rewarding exploration of the interplay between three different mathematical topics.

Step-by-step explanation:

5 weeks do Newton and Descartes spend at home. This can be solved using the concept of fractions.

In mathematics, the portion or component of the complete item is represented by a fraction. It stands for the equal components of the whole. Both the numerator and denominator are components of a fraction. The top number is referred to as the numerator, while the bottom number is referred to as the denominator.

Given that,

Newton and Descartes have a 70-day summer vacation

They go to camp for 23/70 of their vacation

= 70 × (23/70)

= 23

Next, they travel for 6/35 of their vacation

= 70 × (6/35)

= 12

So, they stay home the rest of their vacation

= 70 - 23 - 12

= 35

Now, they stay home (35 ÷ 7) = 5 weeks.

Therefore, 5 weeks do Newton and Descartes spend at home.

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Let's begin by listing out the information given to us:

This is a parallelogram. One of the characteristics of a parallelogram is that consecutive angles sum up to 180 degrees

11.

We thus have this:

Hi :)

I'd start by adding 5 to both sides of the equation. That would make the equation easier.

\(\boldsymbol{\sqrt{2x}-5=3}}\)

\(\boldsymbol{\sqrt{2x}=2}\)

The next step is to get rid of the radical sign.

Which operation will undo the square root? Squaring.

So that's why we square both sides:

\(\boldsymbol{2x=4}\)

And Now we just divide both sides by 2

\(\boldsymbol{x=2}\)

~\(\textit{\textbf{Learn More; Work Harder}}\)~

:)

Answer:

See answers below

Step-by-step explanation:

Given that sin theta = √3/√7

Opposite =√3

Hypotenuse = √7

Get the adjacent

Adj² = (√7)²-(√3)²

Adj² = 7-3

Adj² = 4

Adj = √4

Adj = 2

Cos theta = adj/hyp = 2/√7

csc theta= 1/sin theta = 1/(√3/√7) =

√7/√3

sec theta= 1/costheta = 1/(2/√7) = √7/2

tan theta= opp./adj = √3/2

cot theta =1/tan theta = 1/(√3/2) = 2/√3

= 2√3/3

Answer:

8/2 or 4

Step-by-step explanation:

y^2 - y^1 / x^2 - x^1

The average access time for a cache miss is decreased from 61 cycles to 116 cycles by using critical-word first and early restart, which is a considerable improvement.

Critical-word first and early restart are two approaches we can employ to enhance the L2 cache's performance.

The first word in the cache block is accessed first when using the critical-word first strategy to reduce latency. In our scenario, getting the first 8-byte word requires 100 cycles. So, to speed up access when a cache miss occurs, the critical word should be fetched first.

The number of blocks in the cache can be determined using the formula below, assuming a 1 MB L2 cache with 64-byte blocks:

1 MB = 1024 * 1024 bytes

Number of blocks = 1 MB / 64 bytes = 16384

The first 8 bytes from memory must be retrieved in 90 cycles, and each subsequent 8 bytes must be retrieved in 10 cycles. The duration needed to fetch the complete block therefore is:

Time to fetch block = 90 cycles + 7 * 10 cycles = 160 cycles

Now, With the critical-word first and early restart, let's compute the average access time for a cache miss with and without these features.

Without critical-word first and early restart:

The probability of referencing the first word in a block is 30%.

The probability of referencing the remaining words in a block is (1 - 0.3) / 7 = 0.1.

So, When a cache miss occurs without using critical-word first and an early restart, the average access time is:

Average access time = probability of referencing first word * time to fetch critical word + probability of referencing remaining words * time to fetch block

= 0.3 * 90 cycles + 0.1 * 160 cycles

= 45 cycles + 16 cycles

= 61 cycles

With critical-word first and early restart:

The essential word is retrieved first, which requires 100 cycles.

As soon as the required data is made available, we begin accessing it.

In the background, the remaining words in the block are fetched.

With critical-word first and an early restart, the average access time for a cache miss is as follows:

Average access time = time to fetch critical word + probability of referencing remaining words * time to fetch block

= 100 cycles + 0.1 * 160 cycles

= 100 cycles + 16 cycles

= 116 cycles

Therefore, The average access time for a cache miss is decreased from 61 cycles to 116 cycles by using critical-word first and early restart, which is a considerable improvement.

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Answer:

Step-by-step explanation:

Area of one base:

  \(A=\pi r^2=\pi (3.2)^2 =10.24\pi cm^2\)

Perimeter of circle base:

  \(P=2\pi r=2\times \pi \times 3.2 =6.4 \pi cm\)

Height of cylinder:

  \(h=8.7cm\)       (given in question)

Total surface area:

\(SA=\) area 2 circles + area rectangle

     \(=(2\times 10.24 \pi) +(6.4\pi\times 8.7)\)           (Area rectangle = cylinder height x

                                                              circle perimeter)

     \(=239.26cm^2\)

Answer:

\(\frac{28 + 6a}{a}\)

Step-by-step explanation:

Lets draw a picture of the penny-farthing bicycle:

where x is the diameter of the back wheel. Since the ratio is 3 to 1, we have

By moving 48 to the right hand side, we have

This means that the diameter of the back wheel is 16 inches. Now, the circunference formula is

where d is the diameter. Then, the circunference of the back wheel is

What is the circumference of the back wheel? 50.24 inches

The quartic function with only two real zeros of x=0 and x=4 is x² - 4x = 0

A quartic function is a quartic polynomial, that is, a polynomial with integer coefficients whose highest degree is four. The coefficient of the variable to the fourth degree cannot be zero. Examples of quartic functions include

From the roots;

a = 0 ; b = 4

From the polynomial expressions

x² - (a +b)x + ab = 0

x² - (0 +4 )x + 0*4 = 0

x² - 4x = 0

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Answer:

33 nickels and 11 dimes

Step-by-step explanation:

11*3= 33

11 + 33 = 44