Answer:
Step-by-step explanation:
2. area of a triangle is 1/2 b h
1/2 (5 * 2) = 5 yd squared
area of the circle is pi r squared
you only need 1/2 of this area
find all these areas and add them together.
6. this is just a square sitting on a rectangle.
36 x 36 for the square
36 x 60 for the rectangle
add these together.
8. this a 1/2 circle and a triangle.
area of a circle is pi r squared
r is 7 in this problem
the area of a triangle is 1/2 b h
height is 7x2 here or 14
add the two together.
5/12*6 =5/12*6/1 crosscancle you get 5/2 the you get 2 1/2
(a) The differential equation is separable, so we separate the variables and integrate:
When x = 0, we have y = 2, so we solve for the constant C :
Then the particular solution to the DE is
We can go on to solve explicitly for y in terms of x :
(b) The curves y = x² and y = 2x - x² intersect for
and the bounded region is the set
The area of this region is
Hello! So, this question is in the form of ax² - bx - c. First thingd first, let's multiply a and c together. c = -8 and a = 5. -8 * 5 is -40. Now, let's find two factors that have a product of 40, but a sum of 18. If you list the factors, you see that 2 and 20 have a product of 40, but 2 - 20 is -18. The factors we will use are -2 and 20.
How to factor it:
For this question, you can use something called a box method and factor it by finding a factor of each column and row. Just make 4 boxes and put 5x² on the top left and -40 on the bottom left box. Put 2x on the top right box and -20x on the bottom left box. Now, factor out for each row and column. The factors should be 5x + 2 for the top part and x - 4 for the side. It should look like (5x + 2)(x - 4). Let's check it. Solve it by using the FOIL method and you get 5x² - 20x + 2x - 8. Combine like terms and you get 5x² - 18x - 8. There. The answer is B: (5x + 2)(x - 4)
Note: The box method may be challenging at first, but it can be really helpful on problems like these.
