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]
3 years ago
7

Express p in terms of q if

Mathematics
1 answer:
Irina-Kira [14]3 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
36×10 to the power of 5
Veseljchak [2.6K]
3600000, 3600000, 3600000 ur answer is <span>3600000</span>
5 0
3 years ago
If the circumference of a circle measures 3 4 π cm, what is the area of the circle in terms of π? A) 9 8 π cm2 B) 3 8 π cm2 C) 3
Paladinen [302]
O-o idk                          its hard             yesssssssssss                    
5 0
3 years ago
Read 2 more answers
Write an equation of the line in point-slope form that passes through the given points.
Sonja [21]

Answer:

y = 0.625x+3.625

Step-by-step explanation:

7 0
3 years ago
The cost of a bagel and a cup of coffee is $1.45. The cost of 3 bagels and a cup of coffee is $2.95. What is the cost of a cup o
seropon [69]

<em> </em><em>The</em><em> </em><em>answer</em><em> </em><em>is</em><em> </em><em>0</em><em>.</em><em>7</em><em>5</em><em>.</em><em>Hope</em><em> </em><em>this</em><em> </em><em>will</em><em> </em><em>help</em><em> </em><em>u</em><em>.</em><em>.</em><em>.</em><em>.</em>

8 0
3 years ago
Need help please help me
Ostrovityanka [42]
The solution is the point of intersection between the two equations.

Assuming you have a graphing calculator or a program to lets you graph equations (I use desmos) you simply put in the equetions and note down the coordinates of the point of intersection.

In the graph the first equation is in blue and the second in red.

The point of intersection = the solution = (-6 , -1)



If you dont have access to a graphing calculator you could draw the graphs by hand;

1) Draw a table of values for each equation; you do this by setting three or four values for x and calculating its image in y (you can use any values of x)

y = 0.5 x + 2 (Im writing 0.5 instead of 1/2 because I find its easier in this format)

x | y
-1 | 1.5 * y = 0.5 (-1) + 2 = 1.5
0 | 2 * y = 0.5 (0) + 2 = 2
1 | 2.5 * y = 0.5 (1) + 2 = 2.5
2 | 3 * y = 0.5 (2) + 2 = 3

y = x + 5

x | y
-1 | 4 * y = (-1) + 5 = 4
0 | 5 * y = (0) + 5 = 5
1 | 6 * y = (1) + 5 = 6
2 | 7 * y = (2) + 5 = 7

2) Plot these point on the graph
I suggest to use diffrent colored points or diffrent kinds of point markers (an x or a dot) to avoid confusion about which point belongs to which graph

3) Using a ruler draw a line connection all the dots of one graph and do the same for the other

4) The point of intersection is the solution

8 0
3 years ago
Read 2 more answers
Other questions:
  • Which is the equation of a line that has a slope of One-half and passes through point (2, –3)?
    15·2 answers
  • There are 216 forth graders. They took 3 buses to a field trip. How many 4th graders were on each bus?
    11·2 answers
  • A line has a slope of -4 and passes through the point (2,-5) <br> which is the equation of the line
    15·1 answer
  • An appropriate metric unit for the mass of an eyelash.
    11·1 answer
  • The solution for a system of two linear equations is (0, 0). Which equation below could be one of the equations in the system? A
    6·1 answer
  • Kenneth is 14 years younger than twice Sabrina’s age. Kenneth is 30 years old. How old is Sabrina?
    10·1 answer
  • (05.06 LC)
    11·1 answer
  • How do you start problem?!
    9·2 answers
  • What is the dot product of u = (11, 4, -2) and v = (-1, 3, 8)
    10·1 answer
  • Michelle is planting flowers in her garden. She wants the ratio of daisies to carnations to be 4 to 2. Michelle wants to plant a
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!