MATHEMATICS MIDDLE SCHOOL

7) Given that Sn=3-2^(-4n)is the sum of the first n terms of a sequence.
Un is the n term.
a) Express Un+1 in terms of n.
b) Deduce that the
sequence is a geometric progression.
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Answers

Answer 1
Answer:

Answer:

Step-by-step explanation:

s_(n)=3-2^(-4n)\ns_(n+1)=3-2^(-4(n+1))=3-2^(-4n) *2^(-4)\ns_(n+1)-s_(n)=3-2^(-4n)*2^-4-3+2^(-4n)

=2^(-4n)-2^(-4n)*2^(-4)\n=2^(-4n)(1-2^(-4))\n=2^(-4n)((2^4-1)/(2^4))\n=2^(-4n)(15)/(16)\nU_(n+1)=15*2^(-4(n+1))

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the tank is 600 cubic meters. the height of tank is 6 meters. the base of the tank is square. what is the area of the base?

Answers

100 squre meters because the base is square so both sides are equal in length so if you divide volume on hight so the area will come which is 100 and lcm is 10

A store has apples on sale for $3.00 for 2 pounds. How many pounds of apples can you buy for $9? If an apple is approximately 5 ounces, how many apples can you buy for $9? Explain your reasoning.

Answers

we know that

A store has apples on sale for $3.00 for 2 pounds

Part a) How many pounds of apples can you buy for $9?

by using proportion

(3)/(2)(usd)/(pound) =(9)/(x) (usd)/(pound) \n \n 3x=9*2\n \n x=(18)/(3) \n \n x=6 pounds

therefore

the answer Part a) is

6 pounds

Part b) If an apple is approximately 5 ounces, how many apples can you buy for $9?

we know that

1 pound=16 ounces

step 1

convert ounces to pounds

1apple=(5)/(16)pounds

by using proportion

(1)/((5)/(16))\ (apples)/(pounds) =(x)/(6) (apples)/(pounds)\n \n x(5)/(16) =6\n \n x=(16*6)/(5) \n \n x=19.2 apples

therefore

the answer part b) is

about 19 apples
Since 2 pounds is $3 and you have $9, you would do: 

(3)/(2) = (9)/(x) , x= # of pounds of apples

You do cross multiplication to get:

3x=18

x=6      

1 lb= 16 oz

So 6*16=96   to get the number of ounces you can buy for $9.

Then divide 96 by 5, so that is ABOUT 19 APPLES.

What is the divisor of 33 3/4

Answers

33 ÷ 3/4 = 33 × 4/3 = 44
the correct  answer is 44 hope this helps

PLEASE HELP ME WITH THIS QUESTION I AM VERY CONFUSED PLEASE HELP ME ONLY ON QUESTION 20

Answers

The diagonal of a rectangle forms a right triangle with the length and the width. So the square of the diagonal is the length squared plus the width squared.

How to factorise 6ac-12

Answers

Common is 6 so it would be 6 on the outside of the brackets.
Therefore it would be ac inside with a -2 because there is 2 6's in 12 :) 
6 (ac - 2) 
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Solve for x.
−7.8(x+6.5)=−25.74
Enter your answer, as a decimal, in the box.

Answers

−7.8(x+6.5)=−25.74
-7.8x - 50.7 = -25.74
-7.8x = -25.74 + 50.7
-7.8x = 24.96
      x = 24.96/-7.8
      x = -3.2
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