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fomenos
3 years ago
10

The sum of the first 5 terms of an AP is 30 and the sum of the four term from T6 to T9 (inclusive) is 69. Find the AP​

Mathematics
1 answer:
Ainat [17]3 years ago
7 0

Answer: The AP = 1, ⁷/₂, 6, ¹⁷/₂, 11 ..............

Step-by-step explanation:

From the first statement,

S₅ = ⁵/₂(2a + ( n - 1 )d }    = 30

       5(2a  + 4d )d           = 60

       10a    + 20d             = 60

reduce to lowest term to easy calculation by dividing through by 10

                      a + 2d       = 6 -----------------------------------1

second statement

sum of the next 4 terms inclusive

T₉  = ⁹/₂(2a + 8d )   = 69

        9(2a  + 8d )    = 30 + 69

            18a + 72d   = 99 x 2

            18a + 72d   = 198

divide through by 18 to reduce to lowest time

                a  + 4d    = 11 ------------------------------------------2

Now solve the two equation simultaneously to find a and d

                 a + 2d = 6

                 a + 4d = 11

                     -2d  = -5

                          d = ⁵/₂.

Now substitute  for d to get a

               a  + 2(⁵/₂) = 6

                a + 5       = 6

                           a   = 6 - 5

                            a = 1.

Therefore the AP = 1 , ⁷/₂ , 6 , ¹⁷/₂ , 11 , ..............

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Triangle ABC has the side lengths 6 in., 9 in., and 11 in.
andriy [413]

Answer:

The BEST statement describes how the triangle could be altered in order to make it a right triangle

B.

One inch could be removed from the 9 in. leg and a new hypotenuse could be drawn.

Step-by-step explanation:

Triangle ABC has the side lengths 6 in., 9 in., and 11 in.

The only condition is that satisfy to become Δ ABC a Right angle triangle is

Longer leg (one inch remove) = 9 - 1 = 8 inch

New hypotenuse = 10 inch

So that Pythagoras theorem must satisfy

(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}

So (Hypotenuse)² = 10² = 100

     (Shorter leg)²  = 6² = 36

     (Longer leg)² = 8² = 64

So we have,

(Shorter leg)² + (Longer leg)² = 36 + 64

                                                = 100

                                                 = (Hypotenuse)²

Therefore, Δ ABC is right Triangle By Converse of Pythagoras Theorem.

Therefore,

The BEST statement describes how the triangle could be altered in order to make it a right triangle

B.

One inch could be removed from the 9 in. leg and a new hypotenuse could be drawn.

4 0
3 years ago
Why is <img src="https://tex.z-dn.net/?f=lim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7Bx%7D%7Bln%20x%7D" id="TexFormula1" title="li
aleksklad [387]

The first limit is infinity since x>\ln(x) for all x>0.

The second limit is zero since 2^x converges to 0 as x\to-\infty, while x^2 is very large and positive.

8 0
1 year ago
How do I solve this question?
olya-2409 [2.1K]

Hello,

we can simplify as below

\dfrac{(2p^3q^4)^4}{(-3q^5)^2}*\dfrac{9}{(4p^2q)^2}=\dfrac{2^4p^{12}q^{16}3^2}{3^2q^{10}4^2p^4q^2}=p^{12-4}q^{16-10-2}=p^{8}q^{4}=p^{a+b}q^{b-a}

So it means that

8 = a+b

4 = b-a

8+4 = a+b+b-a=2b

2b = 12

b = 6

and a = 6 - 4 = 2

hope this helps

7 0
3 years ago
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