Hi there!
We can evaluate using the power rule and trig rules:
Therefore:
![\int\limits^{12}_{2} {x-sin(x)} \, dx = [\frac{1}{2}x^{2}+cos(x)]_{2}^{12}](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B12%7D_%7B2%7D%20%7Bx-sin%28x%29%7D%20%5C%2C%20dx%20%3D%20%5B%5Cfrac%7B1%7D%7B2%7Dx%5E%7B2%7D%2Bcos%28x%29%5D_%7B2%7D%5E%7B12%7D)
Evaluate:
Start by seeing where the lines go. They cross (intersect) at (1, -1). We can use this to check later.
Now for slope: green is -4/2 = -2
pink is 4/2 = 2
Now we can create the equations
Let's make green = g(x) and pink = p(x)
if we use y = mx + b, then the green has a y-intercept (b) of +1
So g(x) = -2x + 1
pink has a y-intercept of -3, so p(x) = 2x - 3
Now let's plug n play: put our solutions x into each equation and confirm that it makes the y = -1
g(x) = -2x + 1 = -2(1) + 1 = -2+1 = -1
p(x) = 2x - 3 = 2(1) - 3 = 2-3 = -1
✔ YES THEY ARE CONFIRMED
Answer:
<u>The most simplified form is 15√10</u>
Step-by-step explanation:
1. Let's simplify the expression:
20√270 ÷ 4√3
20√9 * 30/ 4√3 (√270 = √9 * 30)
60 √30/ 4√3
(60 √3 * √10) / 4√3 (√30 = √3 * √10)
60/4 √10 ( We cancel √3 in the numerator and in the denominator)
15√10
<u>The most simplified form is 15√10</u>
Answer:
897 liters
Step-by-step explanation:
The motor oil is composed of 8 liters of natural oil and 5 liters of synthetic oil. This means there is a ratio of 8/5. We have 552 liters of natural oil to y liters of synthetic. This is the ratio 552/y. Create a proportion that compares the two ratios.
Solve by cross multiplying.
8y = 5(552)
8y = 2,760
y= 345
345 liters of synthetic oil.
Together 552+345= 897 liters of motor oil.
Yesssssss ittttt isssssss
