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2 years ago

Which of the following equations has exactly one solution?

Mathematics

1 answer:

shusha [124]2 years ago

6 0

Answer:

Step-by-step explanation:

5a+4=9a+3-4a

5a-9a+4a=3-4

a=-1

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Solve the given initial-value problem. the de is of the form dy dx = f(ax + by + c), which is given in (5) of section 2.5. dy dx

shutvik [7]

$\dfrac{\mathrm dy}{\mathrm dx}=\cos(x+y)$

Let $v=x+y$ , so that $\dfrac{\mathrm dv}{\mathrm dx}-1=\dfrac{\mathrm dy}{\mathrm dx}$ :

$\dfrac{\mathrm dv}{\mathrm dx}=\cos v+1$

Now the ODE is separable, and we have

$\dfrac{\mathrm dv}{1+\cos v}=\mathrm dx$

Integrating both sides gives

$\displaystyle\int\frac{\mathrm dv}{1+\cos v}=\int\mathrm dx$

For the integral on the left, rewrite the integrand as

$\dfrac1{1+\cos v}\cdot\dfrac{1-\cos v}{1-\cos v}=\dfrac{1-\cos v}{1-\cos^2v}=\csc^2v-\csc v\cot v$

Then

$\displaystyle\int\frac{\mathrm dv}{1+\cos v}=-\cot v+\csc v+C$

and so

$\csc v-\cot v=x+C$

$\csc(x+y)-\cot(x+y)=x+C$

Given that $y(0)=\dfrac\pi2$ , we find

$\csc\left(0+\dfrac\pi2\right)-\cot\left(0+\dfrac\pi2\right)=0+C\implies C=1$

so that the particular solution to this IVP is

$\csc(x+y)-\cot(x+y)=x+1$

5 0

3 years ago

Hamburger sells 3 pounds for six dollars if Samantha 510 pounds of hamburger how much will she pay

Lina20 [59]

I believe you meant to say that if Samantha bought 510 pounds of hamburger, how much will she pay?

Now from the information we already have, we know that 3 pounds of hamburger will cost 6 dollars.

The next thing we need to know is how much one pound of hamburger will cost. This will help us calculate how much the rest will cost.

we now form an equation to assist us.
3 = 6
1= x

(where x represents the unknown price of one pound of hamburger)

Now we must cross-multiply:

3 * x = 6 x 1

3x = 6

x = 6/3

x = 2

therefore one pound of hamburger costs 2 dollars.

Now, If one pound costs 2 dollars, how about 510 pounds?

We simply multiply: 510 x 2 = 1,020

Therefore Samantha will pay 1, 020 dollars for 510 pounds of hamburger.

5 0

3 years ago

Factor completely and find the roots of the following . X^2-6x+8=0

LiRa [457]

Answer:

x =2, x = 4

Step-by-step explanation:

x^2 - 6x + 8 = 0

(x - 2)(x - 4) = 0

x - 2 = 0; x = 2

x - 4 = 0; x = 4

5 0

3 years ago

3/4 + 2/3 = 1 5/12 eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

satela [25.4K]

3/4+2/3= 17/12

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Five minutes on the clock

Nuetrik [128]

Answer:

15/32 cm²

Step-by-step explanation:

Area of rectangle = l × b

=> 3/4 × 5/8

=> 15/32

Therefore,

Area of rectangle is 15/32 cm²

4 0

2 years ago

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