5 consecutive even integers: 2n, 2n+2, 2n+4, 2n+6, 2n+8 for any integer n The sum of the two smallest of five consecutive even integers is 50 less than the sum of the other three integers: 2n + 2n+2 = 2n+4 + 2n+6 + 2n+8 - 504n + 2 = 6n -3234 = 2nn = 17 <span>The smallest integer in our sequence is 2n = 2*17 = 34</span> Check:2n + 2n+2 = 2n+4 + 2n+6 + 2n+8 - 5034 + 36 = 38 + 40 + 42 - 5070 = 120 - 5070 = 70
Answer:
- g(2.95) ≈ -1.8; g(3.05) ≈ -0.2
- A) tangents are increasing in slope, so the tangent is below the curve, and estimates are too small.
Step-by-step explanation:
(a) The linear approximation of g(x) at x=b will be ...
g(x) ≈ g'(b)(x -b) +g(b)
Using the given relations, this is ...
g'(3) = 3² +7 = 16
g(x) ≈ 16(x -3) -1
Then the points of interest are ...
g(2.95) ≈ 16(2.95 -3) -1 = -1.8
g(3.05) ≈ 16(3.05 -3) -1 = -0.2
__
(b) At x=3, the slope of the curve is increasing, so the tangent lies below the curve. The estimates are too small. (Matches description A.)
Answer:
Step-by-step explanation:
So there we have it, <A=135° and <B=45°. This should check when you add them together ("<A and <B are supplementary which means that together their angles equal 180°"). Does 135°+45=180°? YES!
I Really hope it helps
Answer:
40 rubber bands are needed
5 rubber bands will be left from 5 bags of of rubber band
Step-by-step explanation:
Each student will need five rubber bands.
There are eight students
Total rubber bands needed = rubber bands per student × number of students
= 5 × 8
= 40
Total rubber bands needed = 40
Rubber bands come in bags of nine.
Number of bags needed = Total rubber bands needed / number of rubber bands in each bag
= 40 / 9
= 4.44 bags
It is impossible to get decimal number of rubber bands bag, so, the next whole number after 4 is 5
5 rubber bands bags will be bought which = 5 × 9
= 45 rubber bands
Only 40 rubber bands are needed
Left over rubber bands = 45 - 40
= 5 rubber bands
Answer:
10.1 years.
Step-by-step explanation:
It is given that,
Principal = 9000
Rate of interest = 5%
No. of times interest compounded = 2 times in an year
Amount after certain time = 14800
The formula for amount:
where, P is principal, r is rate of interest, n is no. of times interest compounded in an year and t is time in years.
Substitute the given values in the above formula.
Taking log both sides.
![[\because \log a^b=b\log a]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Clog%20a%5Eb%3Db%5Clog%20a%5D)
Therefore, the required time is 10.1 years.
