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rosijanka [135]

2 years ago

8

Find the midpoint of (6, -1) (0,5)

1 answer:

insens350 [35]2 years ago

7 0

Answer:

(3, 2)

Step-by-step explanation:

Use the midpoint formula, add the 2 x values up and divide by 2, and then add the 2 y values up and divide by 2

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The population of a town is 32600 about 27% are over 60 years old about 19% are 16 or under how many are between 16 and 60

r-ruslan [8.4K]

Answer: 17604

Explanation: In order to find a percentage, mulptiply the population by the percentage with a decimal in front. Like this:

32600 • .46

I got 46 because 27 + 19 = 46

Once you get that answer, subtract it from the original total

32600 - 14996 = 17604

You're done! Hope this helps

3 0

2 years ago

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

2 years ago

disa [49]

Answer:

A 29 is the answer to the problem

5 0

3 years ago

C(x) = -5x^2+x<br> Find c(4)

Alchen [17]

Answer:

c(4) = -76

Step-by-step explanation:

c(x) x=4 so plug 4 in for x

-5(4)² + (4)

Do parentheses first so... 4² = 16

-5(16) + 4

-5(16) = -80

-80+4 = -76

c(4) = -76

7 0

3 years ago

A. Explain why the point (100,2) is on the graph.

Crazy boy [7]

Answer:

the log function is the "inverse" function of an exponential function

by definition $log_{a} b = c$ then $a^{c} = b$

in this problem you have $log_{10} 100$

thus what x solves this ? $10^{x} = 100$ the answer is $10^{2}$

thus (100,2)

B) the x intercept is when y = 0

$10^{0} = 1$

x intercept at (1,0)

C) at 100, the curve will hit y = 5000

Step-by-step explanation:

4 0

3 years ago