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
IgorLugansk [536]
2 years ago
9

Find the 5th term of the GP is 48 and it 8th term is 384. find the first term and the common​

Mathematics
1 answer:
rewona [7]2 years ago
7 0

Answer:

\text{1st term} = 3\\\\\text{Common ratio} = 2

Step by step explanation:

\text{Given that,}\\\\\text{5th term} = ar^{5-1} = ar^4 = 48~~~~~~~~...(i)\\ \\\text{8th term} = ar^{8-1} = ar^7 = 384~~~~~~~...(ii)\\\\\text{1st term,}~ a = ?\\\\\text{Common ratio,}~ r = ?\\\\(ii) \div (i):\\\\~~~~~~\dfrac{ar^7}{ar^4}=\dfrac{384}{48}\\\\\implies r^{7-4} = 8\\\\\implies r^3 = 8\\\\\implies r^3 = 2^3\\\\\implies r =2\\\\\text{Substitute r = 2 in eq (i):}\\\\~~~~~~a\cdot 2^4 = 48\\\\\implies 16a  =48\\\\\implies a = \dfrac{48}{16}\\\\\implies a = 3\\

You might be interested in
<img src="https://tex.z-dn.net/?f=5x%3D%5Csqrt%7B10%2B15x%7D" id="TexFormula1" title="5x=\sqrt{10+15x}" alt="5x=\sqrt{10+15x}" a
sashaice [31]
Don’t now the answer sorry
3 0
3 years ago
I need help I don’t understand this
Hatshy [7]

Answer:

Step-by-step explanation:

lets say "a" for the empty line,

for small triangle; y^2 = 2^2 + x^2

right triangle; we say a for empty line, a^2= 6^2 + x^2

and big triangle covering both triangles, 8^2 = y^2 + a^2

lets add left sides and right sides in each;

x^2 + 4 + x^2 + 36 + y^2 + a^2 = y^2 + a^2 + 64 and we can delete same things for both sides

y^2 and a^2 can be deleted and 4+36 - 64

2(x^2)=24

x^2= 12

and x will be √12

so, y^2 = x^2 + 2^2 which means y^2 = 12+4 y=16

4 0
3 years ago
<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%20%7B%7D%5E%7B2%7D%20-%204%20%7D%7B%20%5Csqrt%7Bx%20%7B%7D%5E%7B2%7D%20-%206x%2
Nimfa-mama [501]

First of all, we can observe that

x^2-6x+9 = (x-3)^2

So the expression becomes

\dfrac{x^2-4}{\sqrt{(x-3)^2}} = \dfrac{x^2-4}{|x-3|}

This means that the expression is defined for every x\neq 3

Now, since the denominator is always positive (when it exists), the fraction can only be positive if the denominator is also positive: we must ask

x^2-4 \geq 0 \iff x\leq -2 \lor x\geq 2

Since we can't accept 3 as an answer, the actual solution set is

(-\infty,-2] \cup [2,3) \cup (3,\infty)

7 0
3 years ago
if a tree 20 meters tall casts a shadow 30 meters long, what is the angle of elevation from the shadow to the tip of the tree, t
inn [45]

sketch the situation

a trigonometric function that is a relation between the angle of elevation and the 2 sides of the rectangles is the tan

\tan \theta=\frac{opp}{adj}\tan \theta=\frac{20}{30}=\frac{2}{3}

find the inverse

\begin{gathered} \tan ^{-1}(\frac{2}{3})=\theta \\ \theta=33.69º \end{gathered}

after rounding the angle of elevation is 34º.

6 0
1 year ago
X + 4 = 11
mojhsa [17]

Answer:

A. Subtraction

B. Subtraction

C. x+4=11

      -4  -4

D. x=7

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • You thought the balance in your checking account was $68 when you check your online account you realize that you forgot to recor
    11·2 answers
  • He radius of a sphere is 6 centimeters. Which is the volume of the sphere?
    6·1 answer
  • 32% as a fraction in lowest terms
    11·1 answer
  • Can somebody please help me with this question??<br>10=10(k-9)
    15·2 answers
  • Paula can spend no more than $500 for a photographer to take specialty photos for the dinner. Aerial photos from a drone cost $2
    12·1 answer
  • Please answer this asap
    15·1 answer
  • I like this game some people dont
    9·2 answers
  • URGENT! I need this answered today!
    15·2 answers
  • The coordinate grid represents a map of Yvon's town.
    7·2 answers
  • A shopkeeper bought 24 bottles of fruit juice for $63 dollars.
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!