Michael needs at least $150 to buy a new pair of Jordans shoes. He has already

Mathematics

1 answer:

damaskus [11]3 years ago

3 0

Y=15x+45
150=15x+45
-45 -45
105=15x
105/15=15x/15
7=x
7 hours

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1.) The island shown has a population of 12,175 people. Find the population

miv72 [106K]

Answer:

Population density = $148.22\ \text{people per square kilometer}$

Step-by-step explanation:

The attached figure shows the dimension of an island.

Population density is equal to total population per unit land area.

Firstly we will find the area of the triangle using Pythagoras theorem as follows :

$H^2=B^2+P^2$

H is Hypotenuse, B is base and P is perpendicular

$B=\sqrt{H^2-P^2} \\\\B=\sqrt{(18.5)^2-(11.1)^2} \\\\B=14.8\ km$

Area of triangle is given by :

$A=\dfrac{1}{2}\times b\times P\\\\A=\dfrac{1}{2}\times 14.8\times 11.1\\\\A=82.14\ km^2$

$\text{Population density}=\dfrac{\text{Total population}}{\text{land area}}\\\\=\dfrac{12175 }{82.14}\\\\=148.22\ \text{people per square kilometer}$

Hence, the population density is $148.22\ \text{people per square kilometer}$ .

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ale4655 [162]

Answer:

0.01

Steps:

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The general solution of 2 y ln(x)y' = (y^2 + 4)/x is

Sav [38]

Replace $y'$ with $\dfrac{\mathrm dy}{\mathrm dx}$ to see that this ODE is separable:

$2y\ln x\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{y^2+4}x\implies\dfrac{2y}{y^2+4}\,\mathrm dy=\dfrac{\mathrm dx}{x\ln x}$

Integrate both sides; on the left, set $u=y^2+4$ so that $\mathrm du=2y\,\mathrm dy$ ; on the right, set $v=\ln x$ so that $\mathrm dv=\dfrac{\mathrm dx}x$ . Then