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
Elis [28]
3 years ago
9

If p-3, p+3, 4p+3 are three consecutive terms of a geometric progression, find the possible values of p and the corresponding va

lue of the common ratio.​

Mathematics
2 answers:
fiasKO [112]3 years ago
8 0

Answer:  p = 6, r = 3       or       p = -1,  r = -1/2

<u>Step-by-step explanation:</u>

Since p - 3, p + 3, and 4p + 3 are consecutive terms in a geometric progression, then the proportion of the 2nd term over the 1st equals the 3rd term over the 2nd term.

<u>Step 1 is to find p.</u>

\dfrac{p+3}{p-3}=\dfrac{4p+3}{p+3}\\\\\\\underline{\text{Cross Multiply and solve for p:}}\\(p+3)(p+3)=(4p+3)(p-3)\\p^2+6p+9=4p^2-9p-9\\.\qquad \qquad 0=3p^2-15p-18\\.\qquad \qquad 0=3(p^2-5p-6)\\.\qquad \qquad 0=3(p-6)(p+1)\\.\qquad \qquad 0=p-6\qquad 0=p+1\\.\qquad \qquad \boxed{{p=6}}\qquad \quad\boxed{p=-1}}

<em>I will show that 3 is not valid below</em>

<u>Step 2 is to find r (common ratio).</u>

r=\dfrac{p+3}{p-3}\\\\\\\text{When p = 6} \rightarrow \quad \dfrac{6+3}{6-3}\quad =\dfrac{9}{3}\quad =\boxed{3}\\\\\text{When p = -1} \rightarrow \quad \dfrac{-1+3}{-1-3}\quad =\dfrac{2}{-4}\quad =\boxed{-\dfrac{1}{2}}

<u>Check:</u>

             <u>  p = 6     </u>                              <u>  p = -1    </u>

p - 3:       6 - 3 = 3                              -1 - 3 = -4

p + 3:      6 + 3 = 9                             -1 + 3 = 2

4p + 3:    4(6) + 3 = 27                      4(-1) + 3 = -1

3(3) = 9   \checkmark                                       -4(-1/2) = 2 \checkmark

9(3) = 27 \checkmark                                        2(-1/2) = -1 \checkmark

leva [86]3 years ago
6 0

Answer:

Step-by-step explanation:

hello :

look this solution :

You might be interested in
Express 18 as a fraction of 27. <br> Give your answer in its simplest form
den301095 [7]

Answer:

Thus, 2/3 is the simplified fraction for 18/27 by using the GCD or HCF method. Thus, 2/3 is the simplified fraction for 18/27 by using the prime factorization method

Step-by-step explanation:

hope l am not late!

6 0
3 years ago
50 POINTS
Marina86 [1]

vi is going in the positive direction (up). (That's my choice). a (acceleration) is going in the minus direction (down). The directions could be reversed.

Givens

vi = 160 ft/s

vf = 0 (the rocket stops at the maximum height.)

a = - 9.81 m/s

t = ????

Remark

YOu have 4 parameters between the givens and what you want to solve. Only 1 equation will relate those 4. Always always list your givens with these problems so you can pick the right equation.

Equation

a = (vf - vi)/t

Solve

- 32 = (0 - 160)/t Multiply both sides by t

-32 * t = - 160 Divide by -32

t = - 160/-32

t = 5

You will also need to solve for the height to answer part B

t = 5

vi = 160 m/s

a = - 32

d = ???

d = vi*t + 1/2 a t^2

d = 160*5 + 1/2 * - 32 * 5^2

d = 800 - 400

d = 400 feet

Part B

You are at the maximum height. vi is 0 this time because you are starting to descend.

vi = 0

a = 32 m/s^2

d = 400 feet

t = ??

formula

d = vi*t + 1/2 a t^2

400 = 0 + 1/2 * 32 * t^2

400 = 16 * t^2

400/16 = t^2

t^2 = 25

t = 5 sec

The free fall takes the same amount of time to come down as it did to go up. Sort of an amazing result.

6 0
3 years ago
Wendell wants to make a wooden lid for a decorative box. The lid needs to be 612inches wide and 812inches long with sides 2 inch
andriy [413]

Answer:

Step-by-step explanation:

A

3 0
2 years ago
$1800 at 6.5% for 30 months
nasty-shy [4]
1800×6.5%×30=b
b-1800=a

a) $1,710

b) $3,510
8 0
3 years ago
Jennifer is shopping with her mother. They pay $2 per pound of tomatoes.
elena-14-01-66 [18.8K]

Answer:

The constant of proportionality is 2

The equation is y=2x

Step-by-step explanation:

The unit price or unit rate is $2

Let y represent the price of tomatoes, then the price of x tomatoes is

y=2x dollars.

This represents a direct variation.

This equation is of the form y=kx, where k=2 is the constant of proportionality.

4 0
3 years ago
Other questions:
  • The equation for the circle is:
    12·1 answer
  • What is the square root of 432
    5·1 answer
  • Which equation could be used to find the cost of each Apple? 4x+3(0.89)=$7.15 , 3x+4(0.89)=$7.15 , $7.15-3x=0.89 , or 4x-3(0.89)
    8·1 answer
  • A confidence interval is constructed for an unknown population proportion, p. A sample is collected, and the 95% confidence inte
    12·1 answer
  • How much time does it take the car to complete one revolution around the track?
    15·1 answer
  • Kym used the integer tiles to find the sum of (–3) + 6. The line showed that the answer is negative 3. Which of the following do
    5·2 answers
  • I’ll give brainliest
    11·2 answers
  • Kareen correctly answered 85% of the questions on his math test. If he answered 34
    11·1 answer
  • Please help I don’t understand this
    11·1 answer
  • What is the absolute value of 1,123?​
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!