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AveGali [126]
3 years ago
12

A vegetable garden and it's around a pasta shaped like a square that together are 12 ft wide. A path is 1 feet wide. If one bag

of gravel covers 9 square feet, how many bags are needed to cover the path? Round your answers to the nearest tenth.
​

Mathematics
1 answer:
Nat2105 [25]3 years ago
7 0

The overall width of the path and garden is 12 feet.

The area of the entire garden and path is 12 x 12 = 144 square feet.

The path is 1 foot wide, so the garden would be 12 - 2 = 20 feet wide.

The area of the garden only would be 10 x 10 = 100 square feet.

The area of the path only = 144 - 100 = 44 square feet.

1 bag covers 9 square feet:

44 / 9 = 4.88

You would need 5 bags.

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Now, lets evaluate the same integral using power series. first, find the power series for the function f(x = \frac{32}{x^2+4}. t
BlackZzzverrR [31]
No idea what the previous part of the problem is, but you have

f(x)=\dfrac{32}{x^2+4}=\dfrac8{1-\left(-\frac{x^2}4\right)}=\displaystyle8\sum_{n\ge0}\left(-\frac{x^2}4\right)^n
f(x)=\displaystyle8\sum_{n\ge0}\left(-\dfrac14\right)^nx^{2n}

which is valid for \left|-\dfrac{x^2}4\right|, or |x|. So the integral from 0 to 2 is

\displaystyle\int_0^2f(x)\,\mathrm dx=\int_0^28\sum_{n\ge0}\left(-\frac14\right)^nx^{2n}\,\mathrm dx
=\displaystyle8\sum_{n\ge0}\left(-\frac14\right)^n\int_0^2x^{2n}\,\mathrm dx

Note that since the power series only converges on the interval if x is strictly less than 2, which means we have to treat this as an improper integral.

=\displaystyle8\sum_{n\ge0}\left(-\frac14\right)^n\lim_{t\to2^-}\int_0^tx^{2n}\,\mathrm dx[/tex]
=\displaystyle8\sum_{n\ge0}\left(-\frac14\right)^n\lim_{t\to2^-}\frac{x^{2n+1}}{2n+1}\bigg|_{x=0}^{x=t}
=\displaystyle8\sum_{n\ge0}\frac{(-1)^n}{2^{2n}(2n+1)}\lim_{t\to2^-}t^{2n+1}
=\displaystyle16\sum_{n\ge0}\frac{(-1)^n}{2n+1}
=16-\dfrac{16}3+\dfrac{16}5-\dfrac{16}7+\dfrac{16}9+\cdots
6 0
3 years ago
Ginger Yiu has a principal of $900 in her savings account with a 6% APR. The simple interest is calculated quarterly. What is th
Bezzdna [24]
A=p (1+rt)
A future value ?
p Principle 900
R interest rate 0.06
T time 9/12

A=900×(1+0.06×(9÷12))
A=940.5
3 0
3 years ago
Solve c= 8a-3b for a
Vesnalui [34]

Answer:

(c+3b)/8 = a

Step-by-step explanation:

c= 8a-3b

Add 3b to each side

c+3b= 8a-3b+3b

c+3b = 8a

Divide each side by 8

(c+3b)/8 = 8a/8

(c+3b)/8 = a

6 0
3 years ago
If the original quantity is 8 and the new quantity is ​,2 what is the percent​ decrease?
azamat

Answer: 75%

Step-by-step explanation:

75% of 8 is 6.

8 was decreased by 6 to get 2.

8 was decreased by 75% of its initial value to get 2.

Hope this helped!

3 0
3 years ago
Read 2 more answers
Solve the following system of equations using the elimination method. 5x + y = 9 –10x + 7y = 18 Question 6 options: A) (2,–6) B)
Leya [2.2K]

Answer:

Step-by-step explanation:

5x + y = 9

-10x + 7y = 18

10x + 2y = 18

-10x + 7y = 18

9y = 36

y = 4

5x + 4 = 9

5x = 5

x = 1

(1,4)

answer is D

4 0
3 years ago
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