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
son4ous [18]
2 years ago
11

The numbers 2/1/3,h,k,7/7/8 firm a geometric progression. find the value of h and of k

Mathematics
1 answer:
taurus [48]2 years ago
8 0

\text{We have }\ 2\dfrac{1}{3},\ h,\ k,\ 7\dfrac{7}{8}.\\\\\text{Convert the mixed numbers to the improper fractions}\\\\2\dfrac{1}{3}=\dfrac{2\cdot3+1}{3}=\dfrac{7}{3}\\\\7\dfrac{7}{8}=\dfrac{7\cdot8+7}{8}=\dfrac{63}{8}\\\\\text{If}\ a_1,\ a_2,\ a_3,\ a_4\ \text{is a geometric seqence, then:}\\\\\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=r\\\\a_2=a_1r\\\\\text{and}\ \dfrac{a_4}{a_1}=r^3\\\\\text{Substitute:}

r^3=\dfrac{\frac{63}{8}}{\frac{7}{3}}\\\\r^3=\dfrac{63}{8}\cdot\dfrac{3}{7}\\\\r^3=\dfrac{9\cdot3}{8\cdot1}\\\\r^3=\dfrac{27}{8}\to r=\sqrt[3]{\dfrac{27}{8}}\\\\r=\dfrac{3}{2}\\\\h=2\dfrac{1}{3}\cdot\dfrac{3}{2}=\dfrac{7}{3}\cdot\dfrac{3}{2}=\dfrac{7}{2}\\\\k=\dfrac{7}{2}\cdot\dfrac{3}{2}=\dfrac{21}{4}\\\\Answer:\ \boxed{h=\dfrac{7}{2}=3\dfrac{1}{2}\ and\ k=\dfrac{21}{4}=5\dfrac{1}{4}}

You might be interested in
You have $5600. The best interest rate you can find is 3%
EleoNora [17]

Answer:

18 years

Step-by-step explanation:

The formula for computing accrued amount A for a principal of P at an interest rate of r(in decimal) compounded n times in a year for t years is given by

A = P(1 + \frac{r}{n})^{nt}

Note that r is percentage converted to decimal. So 3% = 3/100 = 0.03

We can rearrange the above equation to:

\frac{A}{P} = (1 + \frac{r}{n})^{nt}

Taking logs on both sides

log(\frac{A}{P}) = log(1 + \frac{r}{n})^{nt}

This gives

log(\frac{A}{P}) =nt \times log(1 + \frac{r}{n})\\So,\\nt = \frac{log(\frac{A}{P})}{ log(1 + \frac{r}{n})}

In this particular problem, n = 4, , A= 9600, P = 5600, r =0.03, so r/n = 0.03/4 = 0.0075

1 + r/n = 1+0.0075 = 1.0075

4t = log(9600/5600)/log(1.0075) = log(1.714) / log(1.0075) = 0.234 /0.00325 = 72

t = 72/4 = 18 years

4 0
2 years ago
I need help asap :):):):
Kamila [148]

Answer:

its the second one

Step-by-step explanation:

6 0
3 years ago
The melting point of substance X is -20 degrees Celsius and the boiling point is 90 degrees Celsius. How many Celsius degrees ar
Kazeer [188]
To find the distance between 2 numbers you must take the absolute value of the difference

|90-(-20)|
|110|
110

110 degrees celsius 
3 0
2 years ago
Read 2 more answers
Please help.........
Schach [20]

Answer: what the heck do you have to answer

Step-by-step explanation:

3 0
3 years ago
The graph shows f(x) = (1/2)^x and its translation, g(x). Which describes the translation of f(x) to g(x)?
rosijanka [135]
<span>translation of four units up </span>
8 0
3 years ago
Read 2 more answers
Other questions:
  • What is the solution of the equation 1.6m - 4.8 = -1.6m
    5·1 answer
  • Describe how to convert 2 liters per hour to milliliters per second. First convert liters to milliliters by multiplying by . The
    5·1 answer
  • At a certain middle school, there are 26 students per teacher in every homeroom. Is the total number of students proportional to
    6·1 answer
  • Write twelve and sixteen thousand as a mixed decimal
    10·1 answer
  • Kathy lives directly east of the park. The football field is directly south of the park. The library sits on the line formed bet
    12·2 answers
  • What is the following following product 4 square 7 • 4 square root 7• 4 square root 7 •4 square root 7
    12·1 answer
  • 0.04(y - 9) +0.16y = 0.12y-0.5<br> y=<br> (Type an integer or a decimal.)
    10·1 answer
  • A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it co
    12·1 answer
  • The following questions are adding and subtracting polynomials
    9·1 answer
  • I need some help by today or tomorrow how can I express the ratio of 500 miles to 50 gallons of gas as a unit rate?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!