1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
den301095 [7]
3 years ago
5

Write a polynomial f (x) that satisfies the given conditions. Polynomial of lowest degree with zeros of -4 (multiplicity 3), 1 (

multiplicity 1), and with f(0) = 320.​
Mathematics
2 answers:
yuradex [85]3 years ago
8 0

Answer:

Step-by-step explanation:

Polynomial f(x) has the following conditions: zeros of -4 (multiplicity 3), 1 (multiplicity 1), and with f(0) = 320.

The first part zeros of -4 means (x+4) and multiplicity 3 means (x+4)^3.

The second part zeros of 1 means (x-1) and multiplicity 1 means (x-1).

The third part f(0) = 320 means substituting x=0 into (x+4)^3*(x-1)*k =320

(0+4)^3*(0-1)*k = 320

-64k = 320

k = -5

Combining all three conditions, f(x)

= -5(x+4)^3*(x-1)

= -5(x^3 + 3*4*x^2 + 3*4*4*x + 4^3)(x-1)

= -5(x^4 + 12x^3 + 48x^2 + 64x - x^3 - 12x^2 - 48x - 64)

= -5(x^4 + 11x^3 + 36x^2 + 16x -64)

= -5x^3 -55x^3 - 180x^2 - 80x + 320

Anuta_ua [19.1K]3 years ago
6 0

Answer:

Step-by-step explanation:

-4 is a root for 3 times and 1 is root for once

so (x+4)^3 * (x-1) is part of f(x)

the constant term there is 4^3*(-1)=-64

so there is a multiplier of 320/-64=-5

f(x) = -5 * (x+4)^3 * (x-1)

You might be interested in
What is the value of y for the line that had a slope of -3/2 and passes through the points (3,5) and (7,y)?
Leni [432]

\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{y}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{y-5}{7-3}=\stackrel{\stackrel{slope}{\downarrow }}{-\cfrac{3}{2}}\implies \cfrac{y-5}{4}=-\cfrac{3}{2} \\\\\\ 2y-10=-3y\implies 5y-10=0\implies 5y=10\implies y=\cfrac{10}{5}\implies y=2

7 0
3 years ago
A circle has a circumfernce of 13 it has a arc length of 11. What is the central angle of the arc in degrees
tatiyna

Answer: 304.6°

Step-by-step explanation:

First of all, using the circumference of the circle formula to find the radius of the circle.

Circumference of the circle = 13, ie

2πr = 13,

r = 13/2π ---------------------------- 1

Now getting the radius of the circle now, you now substitute for this in the formula for finding the length of an arc to get the central angle.

Arc length = 11 , ( 2πr0°/360) or (πr0°/180), so

πr0°/180 = 11 ------------------------ 2

Now solve for 0°, the central angle of the angle by making it the subject of the formula.

πr0° = 180 x 11

0° = 180 x 11

----------- ----------------- 3

πr

Now, put equation 1 in equation 3 and solve.

0° = 1980

--------

π x 13/2π

= 1980 x 2π

-----------

π.x. 13

= 1980 x 2

----------

13

= 3960/13

= 304.6°

Therefore, the central angle of the arc is 304.6°

Please be meticulous and understand the way I change the r in the denominator. It was the rule in fraction when dividing.

5 0
3 years ago
3. The graph y = x2 - 3 is translated down 6 units. What would be the new function rule? Y=8² - 9 À​
SIZIF [17.4K]

Answer:

a= −1/9y+64/9

3 0
3 years ago
Estimate plz:<br> 137,638+52,091<br> Explain plz how to do it
IceJOKER [234]
The best way to estimate it is to do "written addition" in your head, adding 1+8, then 9+3, all the way until you get to the front. the actual answer is 189,459, so your answer should be somewhere close to that.
7 0
3 years ago
Read 2 more answers
Y=9x-5 in standard form
Mkey [24]
Y equals nine x minus five I’m sorry I don’t know if I did the right thing but yeah
3 0
3 years ago
Other questions:
  • What is 363 feet below sea level ?
    11·1 answer
  • Simplify quantity 6 x plus 9 over 15 x squared all over quantity 16 x minus 12 over 10 x to the fourth power.
    7·2 answers
  • 38 please and thank u because I’m so bad at doing mad
    6·2 answers
  • –8=1.5x−2.3x What is x?
    14·2 answers
  • When 40% of a number is added to the number and the result is 126 , what is the number ?
    13·1 answer
  • What is the expected value of the spinner? And is the game fair? Correct answer gets brainiest!
    8·1 answer
  • What happens to the slope when a line with a positive slope gets close to the vertical
    15·1 answer
  • What is a reflection of point R(-2,9) first across the y-axis and then across the x-axis?
    13·2 answers
  • Find the range of the relation.
    13·1 answer
  • HELP PLEASE WILL GIVE BRAINLIEST
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!