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2 years ago

You may remember that the perimeter of a rectangle is P=2(W+L) where W is the width and L is the length.

Mathematics

1 answer:

s344n2d4d5 [400]2 years ago

6 0

Step-by-step explanation:

So, x=width and the width=13+L. The formula for perimeter is 2(L)+2(W) and the total perimeter in this question is 62 feet. That means 2(L)+2(13+L)=62 feet. Solve for L and that's going to be your length. Add the length plus 13 and you'll have the width. Double check the equation by plugging the width and length back into the equation. (Does that help?)

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For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate limn→[

Ivenika [448]

Answer:

The following are the solution to the given points:

Step-by-step explanation:

Given value:

$1) \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\2) \sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}$

Solve point 1 that is $\sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\$ :

when,

$k= 1 \to s_1 = \frac{1}{1+1} - \frac{1}{1+2}\\\\$

$= \frac{1}{2} - \frac{1}{3}\\\\$

$k= 2 \to s_2 = \frac{1}{2+1} - \frac{1}{2+2}\\\\$

$= \frac{1}{3} - \frac{1}{4}\\\\$

$k= 3 \to s_3 = \frac{1}{3+1} - \frac{1}{3+2}\\\\$

$= \frac{1}{4} - \frac{1}{5}\\\\$

$k= n^ \to s_n = \frac{1}{n+1} - \frac{1}{n+2}\\\\$

Calculate the sum $(S=s_1+s_2+s_3+......+s_n)$

$S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....\frac{1}{n+1}-\frac{1}{n+2}\\\\$

$=\frac{1}{2}-\frac{1}{5}+\frac{1}{n+1}-\frac{1}{n+2}\\\\$

When $s_n \ \ dt_{n \to 0}$

$=\frac{1}{2}-\frac{1}{5}+\frac{1}{0+1}-\frac{1}{0+2}\\\\=\frac{1}{2}-\frac{1}{5}+\frac{1}{1}-\frac{1}{2}\\\\= 1 -\frac{1}{5}\\\\= \frac{5-1}{5}\\\\= \frac{4}{5}\\\\$

$\boxed{\text{In point 1:} \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2} =\frac{4}{5}}$

In point 2: $\sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}$

when,

$k= 1 \to s_1 = \frac{1}{(1+6)(1+7)}\\\\$

$= \frac{1}{7 \times 8}\\\\= \frac{1}{56}$

$k= 2 \to s_1 = \frac{1}{(2+6)(2+7)}\\\\$

$= \frac{1}{8 \times 9}\\\\= \frac{1}{72}$

$k= 3 \to s_1 = \frac{1}{(3+6)(3+7)}\\\\$

$= \frac{1}{9 \times 10} \\\\ = \frac{1}{90}\\\\$

$k= n^ \to s_n = \frac{1}{(n+6)(n+7)}\\\\$

calculate the sum: $S= s_1+s_2+s_3+s_n\\$

$S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(n+6)(n+7)}\\\\$

when $s_n \ \ dt_{n \to 0}$

$S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(0+6)(0+7)}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{6 \times 7}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{42}\\\\=\frac{45+35+28+60}{2520}\\\\=\frac{168}{2520}\\\\=0.066$

$\boxed{\text{In point 2:} \sum ^{\infty}_{k = 1} \frac{1}{(n+6)(n+7)} = 0.066}$

8 0

3 years ago

What are the solution(s) of –x2 + 2x + 3 = x2 – 2x + 3?

Leviafan [203]

-x^2+2x+3=x^2-2x+3 add x^2 to both sides

2x+3=2x^2-2x+3 subtract 2x from both sides

3=2x^2-4x+3 subtract 3 from both sides

2x^2-4x=0 factor

2x(x-2)=0

So x=0 and 2

3 0

3 years ago

Read 2 more answers

Need some help on this. any help is appreciated :) !!

kirza4 [7]

If we think about a normal curve / bell curve and the 68-95-99.7 rule, we know that the majority of data will lie within 1, 2, or 3 standard deviations from the mean. The mean is in the center of the curve, and to each side of the mean, 34% of the data lies 1 standard deviation on either side of the mean. Therefore, we need to add and subtract one standard deviation from the mean.

85 + 12 = 97

85 - 12 = 73

Correct Answer: B. 73 - 97

Hope this helps!! :)

7 0

3 years ago

Describe how to transform the quantity of the fifth root of x to the seventh power, to the third power into an expression with a

MrRa [10]

Fifth root of x is x^1/5 as an exponential expression. . This to the 7th power is

x ^(1/5 * 7) which is x^(7/5). Bringing this to the third power is x^ (21/5) which is your answer.

6 0

3 years ago

Help! i need the answer to this question plsss NO LINKS AND NO DOING IT JUST FOR THE POINTS Will give brainliest to the first se

Alex_Xolod [135]

2745

Step-by-step explanation:

solve it like simultaneously

180x+120y greater than 5145

180x+120y greater than 2400

eliminate x

y will now be greater than 2745

5 0

3 years ago