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kirza4 [7]
4 years ago
15

Plz help question below

Mathematics
1 answer:
vladimir2022 [97]4 years ago
6 0
1.2/0.5 because as x increases by 0.5, y increases by 2.5
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Find the area of the shape shown below.
Shtirlitz [24]

Answer:

6 + 2 = 8 x 2 = 16 divided by 2 = 8

Step-by-step explanation:

Formula of a trapezoid:

B1(base 1) + B2(base 2) x H (Height) x 1/2 (basically dividing by 2)

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What is 170 one tenth of
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17.17 is one tenth of 170. 

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The midpoint of AB
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Explain the meaning of the following: A scale on a map is 1 cm to 20 mi.
ycow [4]

Each centimeter on the map represents 20 miles in real life. Similarly, every twenty miles in real life would be represented as 1 centimeter on the map.

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3 years ago
7(x^2 y^2)dx 5xydyUse the method for solving homogeneous equations to solve the following differential equation.
aivan3 [116]

I'm guessing the equation should read something like

7(x^2+y^2) \,dx + 5xy \, dy = 0

or possibly with minus signs in place of +.

Multiply both sides by \frac1{x^2} to get

7\left(1 + \dfrac{y^2}{x^2}\right) \, dx + \dfrac{5y}x \, dy = 0

Now substitute

v = \dfrac yx \implies y = xv \implies dy = x\,dv + v\,dx

to transform the equation to

7(1+v^2) \, dx + 5v (x\,dv + v\,dx) = 0

which simplifies to

(7 + 12v^2) \, dx + 5xv\,dv = 0

The ODE is now separable.

\dfrac{5v}{7+12v^2} \, dv = -\dfrac{dx}x

Integrate both sides. On the left, substitute

w = 7+12v^2 \implies dw = 24v\, dv

\displaystyle \int \frac{5v}{7+12v^2} \, dv = -\int \frac{dx}x

\displaystyle \dfrac5{24} \int \frac{dw}w = -\int \frac{dx}x

\dfrac5{24} \ln|w| = -\ln|x| + C

Solve for w.

\ln\left|w^{5/24}\right| = \ln\left|\dfrac1x\right| + C

\exp\left(\ln\left|w^{5/24}\right|\right) = \exp\left(\ln\left|\dfrac1x\right| + C\right)

w^{5/24} = \dfrac Cx

Put this back in terms of v.

(7+12v^2)^{5/24} = \dfrac Cx

Put this back in terms of y.

\left(7+12\dfrac{y^2}{x^2}\right)^{5/24} = \dfrac Cx

Solve for y.

7+12\dfrac{y^2}{x^2} = \dfrac C{x^{24/5}}

\dfrac{y^2}{x^2} = \dfrac C{x^{24/5}} - \dfrac7{12}

y^2= \dfrac C{x^{14/5}} - \dfrac{7x^2}{12}

y = \pm \sqrt{\dfrac C{x^{14/5}} - \dfrac{7x^2}{12}}

8 0
2 years ago
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