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3 years ago

The length of a rectangle is 5cm more then the width. the perimeter of the rectangle is 38cm.what is the width of the rectangle?

Mathematics

1 answer:

Mazyrski [523]3 years ago

7 0

Answer:7

Step-by-step explanation:

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1. Express <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%282x%2B3%29%20%7D" id="TexFormula1" title="\frac{1}{x(2x+3) }" a

katovenus [111]

1. Let a and b be coefficients such that

$\dfrac1{x(2x+3)} = \dfrac ax + \dfrac b{2x+3}$

Combining the fractions on the right gives

$\dfrac1{x(2x+3)} = \dfrac{a(2x+3) + bx}{x(2x+3)}$

$\implies 1 = (2a+b)x + 3a$

$\implies \begin{cases}3a=1 \\ 2a+b=0\end{cases} \implies a=\dfrac13, b = -\dfrac23$

so that

$\dfrac1{x(2x+3)} = \boxed{\dfrac13 \left(\dfrac1x - \dfrac2{2x+3}\right)}$

2. a. The given ODE is separable as

$x(2x+3) \dfrac{dy}dx} = y \implies \dfrac{dy}y = \dfrac{dx}{x(2x+3)}$

Using the result of part (1), integrating both sides gives

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + C$

Given that y = 1 when x = 1, we find

$\ln|1| = \dfrac13 \left(\ln|1| - \ln|5|\right) + C \implies C = \dfrac13\ln(5)$

so the particular solution to the ODE is

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + \dfrac13\ln(5)$

We can solve this explicitly for y :

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3| + \ln(5)\right)$

$\ln|y| = \dfrac13 \ln\left|\dfrac{5x}{2x+3}\right|$

$\ln|y| = \ln\left|\sqrt[3]{\dfrac{5x}{2x+3}}\right|$

$\boxed{y = \sqrt[3]{\dfrac{5x}{2x+3}}}$

2. b. When x = 9, we get

$y = \sqrt[3]{\dfrac{45}{21}} = \sqrt[3]{\dfrac{15}7} \approx \boxed{1.29}$

8 0

3 years ago

a Car has a 15 gallon gas tank . I f a car gets 32 miles per gallon and travels 384 miles . how much gas will be left in the tan

Komok [63]

Answer:

so you would actually multiply 32 x 15=480 then subtract 480 - 384= it would have 96 miles left. then divide 96/32= 3

so your answer would be 3 gallons left

Step-by-step explanation:

4 0

3 years ago

Which expression is equivalent to 76x + 64?

Talja [164]

A.

4(19x + 16)

Hope this helps!

5 0

3 years ago

Hi! I just need help with the last problem, number 12. I did all of the rest. Please reply ASAP, thank you!

Fed [463]

Answer:

rocky???

Step-by-step explanation:

5/2 3/8

3 0

3 years ago

60% of what is 3. .

jasenka [17]

Answer:

Step-by-step explanation:

3 ÷ 0.6 = 5

7 0

3 years ago

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