Let 9x^2-1 = y^2
<span>=> 18xdx = 2ydy </span>
<span>=> ydy = 9xdx </span>
<span>lower limit = sqrt(9*2/9 - 1) = sqrt(1) = 1 </span>
<span>upper limit = sqrt(9*4/9 - 1) = sqrt(3) </span>
<span>Int. [sqrt(2)/3,2/3] 1/(x^5(sqrt(9x^2-1)) dx </span>
<span>= Int. [sqrt(2)/3,2/3] xdx/(x^6(sqrt(9x^2-1)) </span>
<span>= 81* Int. [1,sqrt(3)] ydy/((y^2+1)^3y) </span>
<span>=81* Int. [1,sqrt(3)] dy/(y^2+1)^3 </span>
<span>y=tanz </span>
<span>dy = sec^2z dz </span>
<span>=81*Int [pi/4,pi/3] cos^4(z) dz </span>
<span>=81/4*int [pi/4,pi/3] (1+cos(2z))^2 dz </span>
<span>=81/4* Int. [pi/4,pi/3] (1+2cos(2z)+cos^2(2z)) dz </span>
<span>=81/4*(pi/3-pi/4) + 81/4*(sin(2pi/3)-sin(pi/2)) + 81/8 * (pi/3-pi/4) </span>
<span>+ 81/32 *(sin(-pi/3)-sin(pi)) </span>
<span>=81(pi/48+pi/96+1/4*(sqrt(3)/2 - 1) - 1/32 * sqrt(3)/2) </span>
<span>=81/32*(pi+3sqrt(3)-8)</span>
Answer:
angle b = 79
Step-by-step explanation:
Angle b = 79 because they alternate exterior angles. Alternate exterior angles are equal when the lines are parallel.
The answer to the system of equations is x = 3, y = -2 and z = 5.
In order to find this you can use elimination to create two equations with only x and y. First we will add equation one with equation 2 multiplied by 2.
-x + 2y + 2z = 3
6x + 2y - 2z = 4
---------------------
5x + 4y = 7
Then we can add equation 2 with equation 3.
3x + y - z = 2
2x + y + z = 9
------------------
5x + 2y = 11
Now we can use these two equations together to solve for y. It will be easiest if we multiply the second one by -1.
5x + 4y = 7
-5x - 2y = -11
------------------
2y = -4
And then we can solve for y.
2y = -4
y = -2
With that answer we can go back to any equation with just y and x and solve for x.
5x + 4y = 7
5x + 4(-2) = 7
5x - 8 = 7
5x = 15
x = 3
Now we can use x and y in any equation to find z.
2x + y + z = 9
2(3) + (-2) + z = 9
6 - 2 + z = 9
4 + z = 9
z = 5
Answer:
Yes, (0,4) is a solution
Step-by-step explanation:
We have to plug in 0 in x and 4 in y IN BOTH THE INEQUALITIES.
IF BOTH ARE TRUE, then the system of inequalities is TRUE.
<u>Let's check:</u>
y ≤ -3x+4
4 ≤ -3(0)+4
4 ≤ 4
Is 4 less than OR equal to 4? Yes. THis is satisfied.
<u>Now, checking 2nd one:</u>
y > x^2 + 3x - 2
4 > (0)^2 + 3(0) - 2
4 > -2
Is 4 greater than -2? Yes, it is. So this is satisfied as well.
Hence, (0,4) is a solution to the system of inequalities shown.
Answer:
To determine if fractions are equivalent, you need to get a common denominator. When the denominators are the same, if the numerators are the same, the fractions are equivalent
Step-by-step explanation:
To determine if fractions are equivalent, you need to get a common denominator. When the denominators are the same, if the numerators are the same, the fractions are equivalent
