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castortr0y [4]

3 years ago

Mathematics

1 answer:

Ymorist [56]3 years ago

5 0

12x - 5(x+4) = -20
12x - 5x - 20 = -20
7x = 0
x = 0
and since y = x + 4, y = 4
(0,4) is answer

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If a1 = 2 and an - 2an-1 then find the value of 06.<br><br><br>need help with these please

anygoal [31]

Answer:

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7 0

3 years ago

Find the value of the following expression 100 - 2(x + 5) when x = 10 *

Ede4ka [16]

Answer:

Step-by-step explanation:

100 - 2(x + 5) = 100 - 2x - 10 = 90 -2x

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3 years ago

Read 2 more answers

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

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

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3 years ago

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pickupchik [31]

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Samantha drove 440 km in 5 hours. She drove part of the way at 80 km/h and the rest at 100 km/h. What distance did she drive at

jarptica [38.1K]

Answer:

She drove 200km at 100km/hr and she drove 240km at 80km/hr

Step-by-step explanation:

2×100km/hr=200km and 80km/hr×3=240km/hr

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5 0

4 years ago

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