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3 years ago

Solve the inequality and graph the solution on the line provided. 8x-11>-27

Mathematics

1 answer:

andrezito [222]3 years ago

3 0

Answer:

x>-2

on a number line you would put a circle on -2 and draw a line going to the right since x is greater than -2

Step-by-step explanation:

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Find the solution of the initial value problem<br><br> dy/dx=(-2x+y)^2-7 ,y(0)=0

Leokris [45]

Substitute $v(x)=-2x+y(x)$ , so that $\dfrac{\mathrm dv}{\mathrm dx}=-2+\dfrac{\mathrm dy}{\mathrm dx}$ . Then the ODE is equivalent to

$\dfrac{\mathrm dv}{\mathrm dx}+2=v^2-7$

which is separable as

$\dfrac{\mathrm dv}{v^2-9}=\mathrm dx$

Split the left side into partial fractions,

$\dfrac1{v^2-9}=\dfrac16\left(\dfrac1{v-3}-\dfrac1{v+3}\right)$

so that integrating both sides is trivial and we get

$\dfrac{\ln|v-3|-\ln|v+3|}6=x+C$

$\ln\left|\dfrac{v-3}{v+3}\right|=6x+C$

$\dfrac{v-3}{v+3}=Ce^{6x}$

$\dfrac{v+3-6}{v+3}=1-\dfrac6{v+3}=Ce^{6x}$

$\dfrac6{v+3}=1-Ce^{6x}$

$v=\dfrac6{1-Ce^{6x}}-3$

$-2x+y=\dfrac6{1-Ce^{6x}}-3$

$y=2x+\dfrac6{1-Ce^{6x}}-3$

Given the initial condition $y(0)=0$ , we find

$0=\dfrac6{1-C}-3\implies C=-1$

so that the ODE has the particular solution,

$\boxed{y=2x+\dfrac6{1+e^{6x}}-3}$

5 0

3 years ago

How much do subtract from 37/6 to make 6

choli [55]

37÷6
=6.1666666667
- 0.1666666667
=6

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3 years ago

The 5th graders decided to have a bake sale to raise money for graduation! They had 332 people volunteer to bake. Each volunteer

m_a_m_a [10]

Answer:

249 brownies in each bag.

Step-by-step explanation:

I know this because 332x15=4,980

And 4,980 divided by 20 equals 249

Hope this helps :)

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IRISSAK [1]

Convert to base 10
2×3² + 0×3¹ + 1×3^0 = 18 + 0 +1 = 19 base 10
so convert 19 to base 8
19 base 10 = 23 base 8
D is your answer

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HACTEHA [7]

Answer:

1st option (Vertical).......

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