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2 years ago

Simplify the expression IabI if a>0 and b>0

Mathematics

1 answer:

Brums [2.3K]2 years ago

7 0

Answer:

Step-by-step explanation:

The "ab" inside absolute value has to go out positive, such as |-2|=2

Since both the a and b values are positive, the value of |ab| should be "ab"

For example:

a=2

b=3

|ab| = |2*3| = |6| = 6

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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

2 years ago

(9-2x)+(6x+4) find the sum

aliya0001 [1]

Answer:

4x+13

Step-by-step explanation:

combine like terms -2x and 6x to get 4 then combine 9 and 4 to get 13

8 0

3 years ago

A stray dog ate 4 of your muffins. That was 2/9 of all of them! How many are left?

oksano4ka [1.4K]

Answer:

14muffins are left. please give brainliest

Step-by-step explanation:

so first we need to figure out how many there are in total so if 4 muffins is 2/9 so every 2 muffins is 1/9 so we need 9x2 wich is 18 so there are 18 muffins in total but the stray dog ate 4 of them so 18-4 is 14 so the answer is 14muffins are left.

8 0

2 years ago

What is the value of X ?

SashulF [63]

Answer:

Step-by-step explanation:

x^2 + 48^2 = 50^2

x^2 + 2304 = 2500

x^2 = 196

x = 14

answer is a

7 0

2 years ago

Find the unknown number 5/12+()=1/2

xenn [34]

Hello from MrBillDoesMath!

Answer: 1/12

Discussion:

We solve 5/12 + x = 1/2 for x. Begin by subtracting 5/12 from each side

5/12 - 5/12 + x = 1/2 - 5/12

0 +x = 6/12 - 5/12 (as 1/2 = 6/12)

So x = 1/12

Regards, MrB

8 0

2 years ago