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The width of a rectangular flower shop is 20 feet less than twice the length. The perimeter is more than 70 feet. Which inequali

Schach [20]

Answer:

what is it

Step-by-step explanation:

7 0

3 years ago

The length of a rectangle is eight more than twice its width. The perimeter is 96 feet. Find the dimensions of the rectangle

blagie [28]

Step-by-step explanation:

Length = L

Width = W

L=8 more than 2W

L = 8 * 2W

L = 16W

Perimeter = 96

perimeter is the lengths of all sides added together

so

2L + 2W = 96

we have

L = 16W

2L + 2W = 96

let's do substitution

put what L = into 2L + 2W = 96

so

2(16W) + 2W = 96

can you rearrange that to get w

put answer in comment

4 0

2 years ago

Guys I need the RUGHT ANSWER ASAP PLZ IS IT

mrs_skeptik [129]

Answer = 4 ft

Radius = Circumference / (pi x 2)

Radius = 8 / (4 x 2)

Radius = 4

8 0

3 years ago

Set up the integral that represents the arc length of the curve f(x) = ln(x) + 5 on [1, 3], and then use Simpson's Rule with n =

marta [7]

Answer:

The integral for the arc of length is:

$\displaystyle\int_1^3\sqrt{1+\frac{1}{x^2}}dx$

By using Simpon’s rule we get: 1.5355453

And using technology we get: 2.3020

The approximation is about 33% smaller than the exact result.

Explanation:

The formula for the length of arc of the function f(x) in the interval [a,b] is:

$\displaystyle\int_a^b \sqrt{1+[f'(x)]^2}dx$

We need the derivative of the function:

$f'(x)=\frac{1}{x}$

And we need it squared:

$[f'(x)]^2=\frac{1}{x^2}$

Then the integral is:

$\displaystyle\int_1^3\sqrt{1+\frac{1}{x^2}}dx$

Now, the Simposn’s rule with n=4 is:

$\displaystyle\int_a^b g(x)}dx\approx\frac{\Delta x}{3}\left( g(a)+4g(a+\Delta x)+2g(a+2\Delta x) +4g(a+3\Delta x)+g(b) \right)$

In this problem:

$a=1,b=3,n=4, \displaystyle\Delta x=\frac{b-a}{n}=\frac{2}{4}=\frac{1}{2},g(x)= \sqrt{1+\frac{1}{x^2}}$

So, the Simposn’s rule formula becomes:

$\displaystyle\int_1^3\sqrt{1+\frac{1}{x^2}}dx\\\approx \frac{\frac{1}{3}}{3}\left( \sqrt{1+\frac{1}{1^2}} +4\sqrt{1+\frac{1}{\left(1+\frac{1}{2}\right)^2}} +2\sqrt{1+\frac{1}{\left(1+\frac{2}{2}\right)^2}} +4\sqrt{1+\frac{1}{\left(1+\frac{3}{2}\right)^2}} +\sqrt{1+\frac{1}{3^2}} \right)$

Then simplifying a bit:

$\displaystyle\int_1^3\sqrt{1+\frac{1}{x^2}}dx \approx \frac{1}{9}\left( \sqrt{1+\frac{1}{1^2}} +4\sqrt{1+\frac{1}{\left(\frac{3}{2}\right)^2}} +2\sqrt{1+\frac{1}{\left(2\right)^2}} +4\sqrt{1+\frac{1}{\left(\frac{5}{2}\right)^2}} +\sqrt{1+\frac{1}{3^2}} \right)$

Then we just do those computations and we finally get the approximation via Simposn's rule:

$\displaystyle\int_1^3\sqrt{1+\frac{1}{x^2}}dx\approx 1.5355453$

While when we do the integral by using technology we get: 2.3020.

The approximation with Simpon’s rule is close but about 33% smaller:

$\displaystyle\frac{2.3020-1.5355453}{2.3020}\cdot100\%\approx 33\%$

8 0

3 years ago

Factorize completely <br> 81k^2 - m^2

Genrish500 [490]

81k^2 - m^2 factors to

(9k + m)(9k - m)

Prove this by FOILing.

First - 81k^2

Outer - (-9km)

Inner - 9km

Last - (-m^2)

Put it into equation form

81k^2 - 9km + 9km - m^2

And combine terms to get the original equation,

81k^2 - m^2.

⭐ Answered by Hyperrspace (Ace) ⭐

⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐

⭐ If you have questions, leave a comment, I'm happy to help! ⭐

7 0

3 years ago

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