The equation of a curve is
[tex]y = 4x {}^{3} + 4px {}^{2} + 16x - 9[/tex]
Find the range of values of p such that y is an increasing function.

Answers

Answer 1

Let's solve for p.

[tex]y=4x3+4px2+16x−9[/tex]

Step 1: Flip the equation.

[tex]4px2+4x3+16x−9=y[/tex]

Step 2: Add -4x^3 to both sides.

[tex]4px2+4x3+16x−9+−4x3=y+−4x3[/tex]

[tex]4px2+16x−9=−4x3+y[/tex]

Step 3: Add -16x to both sides.

[tex]4px2+16x−9+−16x=−4x3+y+−16x[/tex]

[tex]4px2−9=−4x3−16x+y[/tex]

Step 4: Add 9 to both sides.

[tex]4px2−9+9=−4x3−16x+y+9[/tex]

[tex]4px2=−4x3−16x+y+9[/tex]

Step 5: Divide both sides by 4x^2.

4px² / 4x² = −4x³ − 16x + y + 9 / 4x²

Answer:

p = −4x³ − 16x + y + 9 / 4x²


Related Questions

Express in the form 1 : n Give n as a decimal 10 : 12

Answers

Answer:

1:1.2

Step-by-step explanation:

please give me a brainliest!!<3

Solve the inequality 3x-1 < 2x+5​

Answers

Answer:

x<6

Step-by-step explanation:

Solve for x

by simplifying both sides of the inequality, then isolating the variable.

Inequality Form:

x<6

Help please!!!!!!!! I need help with this ASAP!

Answers

9514 1404 393

Answer:

  2.89 m

Step-by-step explanation:

The attached shows the figure drawn accurately. It also shows that the angle of the line of sight is 102° -90° = 12° below the horizontal. The sine relation is useful in this situation.

The side opposite the angle in the triangle of interest is the difference in building heights, 5.3 -4.7 = 0.6 m. So, the useful relation is ...

  Sin = Opposite/Hypotenuse

  sin(12°) = (0.6 m)/(PR)

  PR = (0.6 m)/sin(12°) ≈ 2.886 m

  PR ≈ 2.89 m

The distance to the subject is about 2.89 meters.

Find Missing side lengths

Answers

Answer:

On the side length of the triangle

Step-by-step explanation:

On the side length of the triangle

First answer is correct

Can anybody help please I’ll mark brainlist!

Answers

182.5 times 0.12 is 2.19, so the answer is $2.19.

Show the different measuring instruments to be used in the economic/business system of the new civilization.

Answers

Answer:

The different measuring instruments to be used in the economic/business system of the new civilization is discussed below in detail.

Step-by-step explanation:

Economics is the research of how people allocate limited resources for generation, circulation, and consumption, both personally and collectively.

Two significant types of economics are microeconomics, which concentrates on the performance of individual customers and generators, and macroeconomics, which measures overall economies on a local, nationwide, or global scale.

Economics is especially concerned with performance in generation and exchange and practices models and opinions to assume how to generate incentives and procedures that will maximize productivity.

Economists formulate and announce numerous economic symbols, such as the Consumer Price Index (CPI). and gross domestic product (GDP).

Capitalism, communism, and socialism are examples of economic systems.

Mindy is saving money. She started with $0. After 6 weeks, she had $90 saved.

Mindy is not sure exactly how much money she saved each week. She assumes that she saved money at a constant rate from when she started saving money through week 6

Answers

Explain: you divide 90 by 6 (the weeks)
Answer: She mad $15 each week

x 0 1 2 3 y 8 1 −6 −13 Is the relationship a linear function? How do you know? A. No; the change in x and the change in y is not constant. B. Yes; the change in x is constant and the change in y is not constant. C. Yes; the change in x is constant and the change in y is constant. D. No; the change in x is not constant and the change in y is constant.

Answers

Answer:

The correct option is C) Yes; the change in x is constant and the change in y is constant.

Step-by-step explanation:

Consider the table shown.

x     y

0    8

1     1

2   -6

3   -13

Now observe the changes in x and y coordinates, if changes are constant then the given function is linear.

Consider the change in x coordinate.

1-0=1,  2-1=1 and 3-2=1

Now consider the change in y coordinate.

1-8=-7,  -6-1=-7  and -13-(-6)=-13+6=-7

Since the change in x and y is constant the given relationship is linear.

Therefore, the correct option is (C) Yes; the change in x is constant and the change in y is constant.

Multiple Choice: What method can be used to prove the triangles below are congruent? * Angle Side Angle (ASA) Angle Angle Side (AAS) Option 1 Option 2 Not Congruent Hypotenuse Leg (HL)​

Answers

Answer:

angle side angle

Step-by-step explanation:

A recipe calls for 3 cups of flour to make two batches of dinner rolls. One batch mix 15 rolls. Where is making dinner for 12 people and only needs one roll per person. What proportion will help Laura find how much flowers need to make 12 dinner rolls? A 3/30=x/12 B 3/2=x/12 C 3/15=x/12 D 12/15=x/3

Answers

Answer: A. [tex]\dfrac{3}{30}=\dfrac{x}{12}[/tex]

Step-by-step explanation:

According to the recipe,

For 2 batches, 3 cups of flour required.

One batch has 15 mix rolls

Then 2 batches will have 2 (15) = 30 rolls

Each person gets one roll, so 3 cups of flour is required for 30 people.

The quanity of flour is proportional to the number of people.

Let x be the quantity of flour required for 12 people.

By proportion,

[tex]\dfrac{\text{Quantity of flour}}{\text{Quanity of person}}=\dfrac{3}{30}=\dfrac{x}{12}[/tex]

Required proportion: [tex]\dfrac{3}{30}=\dfrac{x}{12}[/tex]

The correct option is A. [tex]\dfrac{3}{30}=\dfrac{x}{12}[/tex]

Please help me I need the answer now!!

Answers

Answer:

an ordered pair

the point where all the lines intersect (which is located by the ordered pair above)

No solutions (in case for example you have parallel lines, so no point there they intersect)

Infinitely Many Solutions (this is when for example you have one single equation, each point of the line is a solution and there are infinite points)

Step-by-step explanation:

basically a "system" means finding a solution that is valid for each equation, like a logical AND

so in this case it means finding a point that lies on each line, and that point can only exists (the intersection of those lines) or not exist (they are parallel)

if the system is made of one single linear equation then you have infinite solutions

A doctor collected data on how many hours children of different ages slept in a day. Data for 5 participants are
shown below.

Answers

The answers is the picture I posted. I did in khan academy and it was right.

The data values of the scatter plot are  (x,y) = (1,13), (2,11), (3, 10), (5,9) and (8,8)

How to represent the table on a scatter plot?

The table of values is given as:

x: 1  2  3  5  8

y: 13 11 10 9 8

This means that the data values are:

(x,y) = (1,13), (2,11), (3, 10), (5,9) and (8,8)

See attachment for the scatter plot

Read more about scatter plots at:

https://brainly.com/question/6592115

17.URGENT
Can someone please help me?​

Answers

Answer:

Answer choice D

Step-by-step explanation:

So we need to get r to the right side. First we can multiply by 3 to get rid of the fraction:

3V=4[tex]\pi[/tex][tex]r^{3}[/tex]

Then we can divide both sides by 4[tex]\pi[/tex] to get r by itself:

[tex]\frac{3V}{4\pi } = r^{3}[/tex]

Then cube both sides:

[tex]\sqrt[3]{\frac{3V}{4\pi } } =r\\[/tex]

Answer choice D

Consider I(p) = p(50 - p) , which gives the expected income in dollars from a bungee jump attraction when the ticket price is p dollars. What is I(20)?

Answers

Answer:

I(20) is 600 dollars

Step-by-step explanation:

From the given function, I(p) = p(50 - p)

Where I is the income in dollars and p is price dollars.

To determine I(20), that is, to determine the income in dollars when the ticket price is 20 dollars.

From

I(p) = p(50 - p)

When p = 20

Then,

I(20) = 20(50 - 20)

I(20) = 20(30)

I(20) = 20 × 30

I(20) = 600

Hence, I(20) is 600 dollars

That is, the income is 600 dollars when the ticket price is 20 dollars.



A train moves at a constant speed. The train travels 13 miles in 1/6hour What is the train's speed in miles per hour

Answers

Answer:

I think the answer is 78.

Answer:

Answer is 2

Step-by-step explanation:

Because The other answers dont punctuation and answer 2 explains as the president

solve please -3x-27=

Answers

Answer:

−3(x+9)

Step-by-step explanation:

The answer is -3(x-27)

The amount sabrina earns varies directly with the number boxes of cookies she sells.How much does Sabrina earn for eah box of cookies that she sells?

Answers

The question is incomplete :

The amount sabrina earns varies directly with the number boxes of cookies she sells.How much does Sabrina earn for eah box of cookies that she sells?

Earning (y) : ____ 5 ____ 10 ____ 15 ____ 20

Boxes sold (x) :__ 2 ____ 4 _____ 6 ____ 8

Answer:

$2.5

Step-by-step explanation:

Given:

Earning varies directly as the number of boxes of cookies sold

y α x

y = kx - - - (1)

k = constant of proportionality (earning per box of cookies sold)

Taking any 2 points :

y = 10 ; x = 4

10 = k4

10 = 4k

Divide both sides by 4

10/4 = 4k/4

2.5 = k

Hence, the amount earned per box of cookies sold is $2.5

Find the unknown sides and angles of this triangle using the Law of Cosines.
Round to the nearest hundredth.
Now, I know side C is 10.35, but I couldn't get the angles for A or B. I'm uncertain if this is a bug or what, but could someone help me out? I'd appreciate a well written explanation as well.

Answers

Answer:

side c-10.35 Angle a-50.88 Angle B-94.12

Step-by-step explanation:

I found the answers on a khan academy thing. I just took the quiz and got a 100%

21 points.

List the vocabulary word given in each diagram.

Answers

Answer:

1. Median

2. Point of Concurrency

3. Centroid

4. Incenter

5. Concurrent Lines

6. Circumcenter

7. Altitude

8. Orthocenter  

9. Vertices

(I'm not sure if the entirety of the vocabulary words are accurate, but they make sense.)

Please help-
Tell which postulate, if any, make the triangles congruent

Answers

Answer:

the answer is SAS

side angle side

HEEEEEEEEEEELPPPPPPPPP PLEASEEEEEEE URGENT 15 POINTS+ MORE

Answers

Answer:

y - 70, x - 73 should be the answer

Step-by-step explanation:

Solve the following system using the Elimination Method; 6x+y=10 and 2x+y=12.

Answers

Hey there!

The solution to the system is [tex](\frac{1}{2}, 13)[/tex]

To solve the system, we can multiply the second equation by -1:

[tex]-2x - y = -12[/tex]

Then, we add the two equations together, and solve for x:

[tex]4x = -2[/tex]

[tex]x = \frac{-1}{2}[/tex]

Now, we plug the x value into one of the equations, and solve for y:

[tex]2(\frac{1}{2} ) + y = 12[/tex]

[tex]-2 + y = 12[/tex]

[tex]y = 13[/tex]

Now we know that the solution to the system is [tex](\frac{1}{2}, 13)[/tex]

Hope it helps and have an amazing day!

Answer:

(-1/2, 13)

Step-by-step explanation:

Multiply the 2nd equation by -1, obtaining the following system:

6x + y = 10

-2x  - y = -12

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

Combine like terms, obtaining:

6x + y = 10

-2x  - y = -12

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

4x     = -2

Dividing both sides by 4 yields x = -2/4, or x = -1/2

Substituting -1/2 for x in the second equation yields:

2(-1/2) + y = 12, or

-1 + y = 12.  Then y = 13, and the solution is

(-1/2, 13)

DUE IN 27 minutes PLEASE HELP EASYY

Answers

Answer:

6 + 0 = 0 + 6 = 6

12 X (3 X 9)

2 + 6x

3 + 7 + 8 = 7 + __ + 3

27 - 108

-15 - 5m

(6 + 5) + 1

8x + 28

26 X 1 = 1 X 26 = 26

24 + 4s

Step-by-step explanation:

i hope this helps :))

Solve the following systems by Elimination

1) 4x+6y=32
3x-6y=3

2) -3+5y=-11
3x+7y=-1

Answers

Answer:

The solutions for both system of equations are as follows:

(5,2)(2,-1)

Step-by-step explanation:

The first set of equations is:

[tex]4x+6y=32\\3x-6y=3\\[/tex]

It can clearly be seen that the coefficients of y are already same in magnitude with different signs so we have to add both equations

So adding both equations, we get

[tex]4x+6y+3x-6y = 32+3\\7x = 35\\\frac{7x}{7} = \frac{35}{7}\\x = 5[/tex]

Putting x=5 in equation 1

[tex]4(5)+6y = 32\\20+6y = 32\\6y = 32-20\\6y = 12\\\frac{6y}{6} = \frac{12}{6}\\y = 2[/tex]

The solution is (5,2)

The second set of simultaneous equations is:

[tex]-3x+5y=-113x+7y=-1[/tex]

We can see that the coefficients of x in both equations are same in magnitude with opposite signs so

Adding both equations

[tex]-3x+5y+3x+7y = -11-1\\12y = -12\\\frac{12y}{12} = \frac{-12}{12}\\y = -1[/tex]

Putting y= -1 in first equation

[tex]-3x+5(-1)=-11\\-3x-5=-11\\-3x=-11+5\\-3x=-6\\\frac{-3x}{-3} = \frac{-6}{-3}\\x = 2[/tex]

The solution is: (2,-1)

Hence,

The solutions for both system of equations are as follows:

(5,2)(2,-1)

If h = 12 units and r= 4 units, what is the volume of the cone shown above?
Use 3.14 for .
A.
12.56 cubic units
B.
50.24 cubic units
C.
200.96 cubic units
D. 602.88 cubic units

Answers

C because you have to multiply and estimate
C, 200.96 cubic units I’m pretty sure

HELPPPPP PLEASEEEE!!!!

Answers

Answer:

pretty sure x is 60 because 60+25 is 80 and its the same as N so 80

Step-by-step explanation:

12.
Line ( is parallel to line m. Line 1 is a transversal
with angle measures as indicated below.
(3x + 42)
(5x – 22)
m
Note: The figure is not drawn to scale.
7 Pt
What is the value of x?

A 16
B. 20
C.25
D. 32

Answers

3x + 42 + 5x -22 = 180

8x + 20 = 180

8x = 180-20

8x = 160

Divide on both sides

X = 20

Answer is B

Solve the following system of equations:
y = 2x +1
y=-x+ 4

x=?
y=?​

Answers

Answer:

x = 1, y = 3

Step-by-step explanation:

Given the 2 equations

y = 2x + 1 → (1)

y = - x + 4 → (2)

Substitute y = 2x + 1 into (2)

2x + 1 = - x + 4 ( add x to both sides )

3x + 1 = 4 ( subtract 1 from both sides )

3x = 3 ( divide both sides by 3 )

x = 1

Substitute x = 1 into (1) and evaluate for y

y = 2(1) + 1 = 2 + 1 = 3

Then solution is x = 1, y = 3

A circle has a diameter of 48 feet. Which of the following expressions shows how to find the radius of the circle?

Answers

Answer:

r = d/2

Step-by-step explanation:

The radius is always the diameter divided by 2. Hope this helps :)

Answer:

48/2 or d/2

Step-by-step explanation:

radius is half the diameter because its starts from the center. so if the diameters 48 feet, you have to divide it by 2 and get 24 feet.

The price of a watch was increased by 20% to £162.
What was the price before the increase?​

Answers

The original price is 135
Step-by-step explanation:
Write equation. Let o be original price, r be rate of increase, P be the increased price. o+ro=P
Substitute values. Original price (o) is unknown, so that will stay as it is; we know that the increased price (P) is 162; we know that the rate of increase (r) is 20%, which in decimal form is 0.20 o+0.20o=162
Add like terms. o is the same as 1o. So 1+0.20 is 1.20. 1.20o=162
Isolate the variable (o). To isolate o, you need to divide both sides by 1.20. 1.20 divided by 1.20 is the same as 1. 162 divided by 1.20 is 135. o=135
Check your work. Plug in the values into the equation and check if it is correct: o+ro=P becomes (135)+(.20)(135)=162. That is simplified into 135+27=162, which is further simplified into 162=162
It’s correct, the answer is 135

Answer:

£129.60

Step-by-step explanation:

10% =  £16.2

20% = £32.4

£162 - £32.40 = £129.60

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