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
Citrus2011 [14]
2 years ago
7

Express p in terms of q if

Mathematics
1 answer:
Irina-Kira [14]2 years ago
8 0

p=x^2+\dfrac{1}{x^2}\\\\p=\dfrac{x^4}{x^2}+\dfrac{1}{x^2}\\\\p=\dfrac{x^4+1}{x^2}\qquad(*)

q=x+\dfrac{1}{x}\\\\q=\dfrac{x^2}{x}+\dfrac{1}{x}\\\\q=\dfrac{x^2+1}{x}\qquad\text{square both sides}\\\\q^2=\left(\dfrac{x^2+1}{x}\right)^2\\\\q^2=\dfrac{(x^2+1)^2}{x^2}\qquad\text{use}\ \ (a+b)^2=a^2+2ab+b^2\\\\q^2=\dfrac{(x^2)^2+2(x^2)(1)+1^2}{x^2}\\\\q^2=\dfrac{x^4+2x^2+1}{x^2}\\\\q^2=\dfrac{x^4+1}{x^2}+\dfrac{2x^2}{x^2}\\\\q^2=\dfrac{x^4+1}{x^2}+2\qquad\text{subtract 2 from both sides}\\\\q^2-2=\dfrac{x^4+1}{x^2}\\\\\text{From (*) we have}\\\\\boxed{p=q^2-2}

You might be interested in
Find the Geometric mean x of 5 and 20
Ugo [173]
Geometric mean =x=<span>√(5 × 20) 
                               =</span>√100
                               =10
8 0
3 years ago
The height h, in feet, of a ball that is released 4 feet above the ground with an initial velocity of 80 feet per second is a fu
gulaghasi [49]

Answer with Step-by-step explanation:

The height of the ball from the ground as a function of time is given by

h(t)=-16t^2+80t+4

The height of the ball at any instant of time can be found by putting the value of time 't' in the above relation as

Part a)

Height of ball after 2 seconds it is released is

h(2)=-16\times 2^2+80\times 2+4=100feet

Part b)

Height of ball after 4 seconds it is released is

h(4)=-16\times 4^2+80\times 4+4=68feet

4 0
3 years ago
Read 2 more answers
Sean made 3⁄4 pound of trail mix and put 3⁄8 pound in each bag. How many bags did Sean fill with trail mix?
ddd [48]

Answer:

It is 2 bags.

Step-by-step explanation:

You have to divide 3/4 and 3/8. The 3/4 goes first.

5 0
3 years ago
If you borrow $675 for 6 years at an interest rate of 10% how much interest will you pay
Artist 52 [7]
40.5 so 715.5 in all
8 0
3 years ago
Read 2 more answers
Worth 11 points and please actually help me instead of just taking the points
9966 [12]

Answer:

A' = (-6, -2)

Step-by-step explanation:

A is at ( -3,-1)

The dilation factor is 2 so multiply by 2

A' = (-3*2, -1*2)

A' = (-6, -2)

3 0
3 years ago
Read 2 more answers
Other questions:
  • GIVING BRAINLIEST PLSSSSS BE A GOD Jennifer is saving money to buy a bike. The bike costs $294. She has $107 saved, and each wee
    10·1 answer
  • I have no clue how to solve this and it’s really stressing me out! Can anyone help?
    7·1 answer
  • Billy has 2.4 m of ribbon for crafts. He wants to share it evenly with 12 friends. Billy has been making craft projects for seve
    11·1 answer
  • ما النتائج المترتبة على :-<br> ١- الاحتلال البريطاني لمصر.
    6·1 answer
  • Which of the following sets of numbers could represent the three sides of a right triangle
    8·1 answer
  • Anwser each question with yes or no
    11·2 answers
  • Use the drawing tools to form the correct answer on the pro
    8·1 answer
  • Another i-ready question! Sorry i am clueless and need a 100% Please help!
    12·1 answer
  • I’ll give you a lot of points for this
    13·2 answers
  • The graph of f(x) is shown below. Estimate and list the value of x where f(x) has a horizontal tangent.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!