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

*URGENT* I NEED HELP WITH THIS QUICK

Answers

The function:
f ( x ) = x * 0.965^t
where x is the initial amount and t is the number of the years
80 = x * 0.965^3
80 = x * 0.89632
x = 80 : 0.89632 ≈ 89
Answer:
The initial amount of animals was 89.

Hope this helps!
Have a nice day :)

What is 7x-4y+2x+8y in distributive form? I will give brainliest and 100 points. Thank you.

Answers

Answer:

4(2 1/4x + y)

Step-by-step explanation:

Just factor

In this cae no GCF

So just divide By 4 becuase its easy

If you solve it

You’d get 9x+4y

WHich is the combined term of the expression given

Answer:

4(2 1/4x + y)

Step-by-step explanation:

Just factor

In this cae no GCF

So just divide By 4 becuase its easy

If you solve it

You’d get 9x+4y

WHich is the combined term of the expression given

For lawn mowing, Jeremy charges a flat fee of $5 plus $10 per hour. Write an equation for cost and hours of lawn mowing. What is the slope?

Answers

Answer:

y = 10x+5

Slope is 10 dollars per hour

Step-by-step explanation:

y = mx+b where m is the slope and b is the y-intercept or flat fee, here.

b = 5

10 per hour means m = 10

Please help ASAP i really need help

Answers

Answer:

X= 0

X= -4

x1= -4, x2=0

Step-by-step explanation:

Answer:

Step-by-step explanation:

Please help me with this quadratic equation question! I always give out 5 stars, thanks and brainliest to people that help me with a good explanation.

Find the values of p and q given that 12x² - 13x - 7175 = (x-p) (qx + 287)

Answers

Answer:

[tex]p=25,\\q=12[/tex]

Step-by-step explanation:

In [tex](ax+b)(cx+d)=acx^2+bcx+dax+bd[/tex], notice the third term of the quadratic in standard form is formed entirely by [tex]b\cdot d[/tex].

Therefore, in [tex]12x^2 - 13x - 7175 = (x-p) (qx + 287)[/tex]:

[tex]-p\cdot287=-7175,\\-p=\frac{-7175}{287},\\p=\fbox{$25$}[/tex].

Now that we found [tex]p[/tex], we must find [tex]q[/tex]. The first term of the quadratic in standard form is formed entirely by [tex]ax\cdot cx[/tex]. Therefore:

[tex]1\cdot q=12, \\q=\fbox{$12$}[/tex].

An invertible function is represented by the values in the table.
Which graph shows the inverse of this function?

Answers

Answer:

your answer should be c

Hope this helps!

Step-by-step explanation:

Use synthetic division and the Remainder Theorem to find P(a).
P(x)= x^4+ x^3- 5x^2 + 9x-6; a=3

Answers

Answer:

Since i'm only substituting 3 with x, why am using synthetic division and the remainder theorem?

tho, putting 3 in, it would be

81 + 27 -45 + 27-6

= 108 -51 +27

=84

Step-by-step explanation:

please answer this 2 questions fast step by step ❤️​

Answers

Answer:

4). [tex]-\frac{27}{28}[/tex]

5). Amount payable by the customer = 1416 Rs.

Step-by-step explanation:

4). [tex](\frac{3}{7})\times (-\frac{5}{8})\div (\frac{1}{3}\times \frac{5}{6})[/tex]

   = [tex](-\frac{15}{56})\div (\frac{5}{18})[/tex]

   = [tex](-\frac{15}{56})\times \frac{18}{5}[/tex]

   = [tex]-\frac{54}{56}[/tex]

   = [tex]-\frac{27}{28}[/tex]

5). Cost of the item = Rs 1200

   G.S.T. applicable on this item = 18%

   Amount to be paid for G.S.T.= 1200 × [tex]\frac{18}{100}[/tex]

                                                   = Rs 216

    Total amount payable by the customer = Cost + G.S.T.

                                                                      = 1200 + 216

                                                                      = Rs 1416

Measure of angle CXF

Answers

50°

angle CXF and DXF are complementary which means they add to 90°

to 40° + x = 90
x = 50

In 1990 the cost of tuition at a state university was 4300. The tuition increased at a rate of 4% each year.

a) How much would it cost to attend in 2010?
b) How much will it cost to attend in 2025?​

Answers

Answer:

10

20

Step-by-step explanation:

For questions 1 - 8, find f-'(x), the inverse of f(x). 1. f(x)= x + 12 2. f(x)= -2 3. f(x)=2x +12 4. f(x)= 3x -4 5. f(x)= 2x + 3 6 6. f(x)=​

Answers

Answer:

1) inverse: x - 12

2) inverse: 3x + 6

3) inverse: x/2 - 6

4) inverse: x/3 + 4/3

5) inverse: 3x - 3/2

6) inverse: -3x/2 + 15/2

7) inverse: x/5 - 3

8) inverse: 2x/5 + 1/5

The force, F newtons, exerted by a magnet on a metal object is inversely
proportional to the square of the distance d cm.
When d = 2 cm, F= 50 N.
Express F in terms of d.

Answers

Answer:

F = 200/d^2

Step-by-step explanation:

F is inversely proportional to d^2

The equation is;

F = k/d^2

K = F•d^2

so to get k, we substitute the given values

K = 50 * 2^2

K = 50 * 4

K = 200

So we have that;

F * d^2 = 200

F = 200/d^2

What is the value of 15 + x2 when the value of x is 3? also there's a tiny 2 above the 15

Answers

Answer:

231

Step-by-step explanation:

So the tiny 2 above the 15 means 15 is squared

15 squared = 225

225 + x(2)

If x = 3, then simply plug that into the equation

225 + 3(2)

225 + 6

231 is your answer

Answer:

231

Step-by-step explanation:

I put the equation as 15^2+2(3) I'm guessing the x was suppose to be after the 2 because it doesn't make sense putting x in front of the two....

Find sin(90°).

45°
A.0
В.1
C. square 2
D. square 2 / 2

Answers

Answer:

sin90° = 1.

Step-by-step explanation:

Using the diagram, we notice that the side opposite of the 90° angle is the hypotenuse itself.

Therefore sin90° = Hypotenuse/Hypotenuse = 1.

2/5 minute = ____ seconds
3/5 hour =_______ minutes
3/5 meter =_____centimeters

Answers

Answer:

24 second

36 minutes

60 centimeters

Answer:

A: 24 second

B: 36 minutes

C: 60 centimeters

I have the same map test lol

Answers

If you need help let me know

x
3
4
5
6

y
9
12
15
8

Answers

Answer: (x34, y912)

Step-by-step explanation: Because (x34, y912) equals (x34, y912) :)

Answer:

x = 2, y = 6

Step-by-step explanation:

I'm assuming you're finding the pattern and then finding x and y, in which case it would be:

In the first one (x, 3, 4, 5, 6) you can see it goes up by 1 each time so x is just 2.

In the second one (y, 9, 12, 15, 18) it goes up by 3 each time so y = 9-3 = 6.

Solve for h in the following equation: — 6 (h + 2) = 72
10
-10
76
-14

Answers

Answer:

-6h -12 = 72

-6h = 72 + 12

-6h = 84

h = -14

what is the quotient (3x^2 + 8x -3) divided by (x + 3)

Answers

Answer:

Quotient = (3x-1)

Step-by-step explanation:

we need to find the quotient when (3x² + 8x -3) is divided by (x+3)

It means we need to divide (3x² + 8x -3) by (x+3).

We can write it as follows :

[tex]\dfrac{3x^2 + 8x -3}{(x+3)}[/tex]

Applying middle term splitting on the numerator.

[tex]\dfrac{3x^2 +9x-x-3}{(x+3)}\\\\=\dfrac{3x(x+3)-1(x+3)}{(x+3)}\\\\=\dfrac{(3x-1)(x+3)}{(x+3)}\\\\=(3x-1)[/tex]

So, the required quotient is (3x-1)

The distance between Beth's
house and her friend Tristan's
house is 8,000 cm. How many
meters is this?

Answers

Answer: 80 meters

Step-by-step explanation:

There are 100cm in one meter.

Do 8,000/100 and you will get 80.

There are 80 meters.

(give brainliest)

80 meters :) the answer is 80

please help with 11 & 12

x=12
y=8
z=3

Answers

Answer:

11. 24

12. 253

hope it's helpful ❤❤❤❤

THANK YOU

Mia can finish her math homework in 30 minutes. Every night there are 45 problems for homework. How many problems can she finish in 4 minutes?​

Answers

Hi ☁️

45 problems 30 minutes

x problems 4 minutes

____________________

[tex] \frac{45.4}{30} = \frac{180}{30} = 6[/tex]

We learnt this way in Turkey.

Answer: 6 problems in 4 minutes

Step-by-step explanation: If there are 45 problem and she can do them in 30 minutes, then you divide 45 by 30 to see how many problems she can do in one minute. 45 problems/30 minutes = 1.5 problems per minute. Then, you multiply 1.5 by 4, because you need to see the 4 minute mark, and 1.5 x 4 = 6. So, your answer is 6 problems.

(brainly pls)

Ok this ones is rll hard and I need help! the question is:
Whats 3+3?
A: Triangle
B: Purple
C: Flowers
D: 6
Im in 8th grade so good luck on figuring this one out guys its rll hard

Answers

Seems like the answer could be D) 6
uhhh i’m in between c and d but i think d!

What is the product of (y + 3) and (7y – 1)?

Answers

Answer: =7y^2+20y−3

Step-by-step explanation:

A group of friends were working on a student film. They spent $256 on equipment, which was 32% of their total budget. What was the total budget for their student film?

Answers

the total budget for their student film is $337.92

Answer:

800

Step-by-step explanation:

I got it correct on delta math.

There is a square with a perimeter of
412
what is the length of the diagonal?

Answers

Answer:

hhjbvft

Step-by-step explanation:

jojo giving kbjvuvuvvuvugubibbibiogg

Which equation shows this formula solved for m?
P=5(m+10) need help asap will give brainest
a. m=[tex]m=\frac{p-5}{10}[/tex]
b.m=[tex]\frac{p}{5}-50[/tex]
c.m=[tex]\frac{p-50}{5}[/tex]
d.m=5p-50

Answers

Answer:

viariables

Step-by-step explanation:

Ben made a sundial in his backyard by placing a stick with height 6 in. straight into the ground, and marking the hours in the grass. To test it, he checks the time each day when the sun makes an angle of 30 degrees or 60 degrees with the ground. Select all the possible lengths of the shadow when Ben checks the sundial.

a) 12 in.
b)2 rad 3 in.
c)8 in.
d)6 rad 3 in.
e)2 rad 2 in.

Answers

Answer:

B and D

Step-by-step explanation:

Answer:

The answer is 6√3in and 2√3in. Just finished taking the quiz, hope this gives you some conformation! :)

Use inverse operations to solve the equation.

−4x = 52

Answers

Answer:

x=-13

Step-by-step explanation:

divide 52 by -4 to get x=-13

Answer:

x = -13

Step-by-step explanation:

−4x = 52

Divide both sides by -4 to isolate the variable

-4x/-4 = 52/-4

x = - 13

Check:

Substitution

-4 (-13) = 52

52 = 52

* 2 negatives make a positive

Hope this helped!

Hardest hw question on the Homework can you solve it?

the ratio of the heights of two similar pyramids is 2:5 in the volume of the smaller pyramid is 100 cubic feet, find the volume of the large pyramid ​

Answers

Volume is a cubic measurement.

Set up a ratio of volume to the ratio of the height:

100/v2 = 2^3/5^3

V2 = 100 x 5^3/2^3 = 100 x 125/8 = 1,562.5 cubic feet

The volume of large pyramid is 1,562.5 cubic feet, by using ratio of heights.

Volume of pyramid based problem:

What information do we have?

Ratio of heights of two similar pyramids = 2:5

Volume of smaller pyramid = 100 cubic feet

Volume of smaller pyramid / Volume of large pyramid = Height of smaller pyramid³ / Height of large pyramid³

100 / Volume of large pyramid = 2³ / 5³

Volume of large pyramid = 125(100) / 8

Volume of large pyramid = 1,562.5 cubic feet

Find out more information about 'Pyramid'.

https://brainly.com/question/13057463?referrer=searchResults

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