(a) The integral is equal to the area of the triangle; it has height 20 and base 10, so the area is 20*10/2 = 100.
(b) The integral is equal to the area of the semicircle with radius 10. It's also under the horizontal axis, so the area is negative. The semicircle has area 
, so the integral is -50π.
(c) First compute
which is the area of the triangle on the right. It has height and base 5, so its area is 25/2.
Then split up the desired integral as
and plug in the integral values you know:
When you are looking for this, the best way to do this is to divide 28 by 7. This will give you 4.
The other way to do this is to list the factors of 28, which are 1,2,4,7,14,28, and you will then be able to see which two are paired.
In this case, x is 4.
Hope I have been able to help you
Answer:
it's A because all of those numbers are less than 14
Step-by-step explanation:
The units of the first number are "dollars." The second number has no apparent units, so we'll consider it a "pure number". This means the product will have the units of "dollars."
The two numbers together have 2+1=3 digits to the right of the decimal point(s). This means the final product will have 3 digits to the right of the decimal point. Since one of the factors is "dollars," it seems likely the result will need to be rounded to cents (2 decimal places). We'll provide the answer both ways (with 3 and with 2 decimal places.)
With these preliminaries out of the way, we have the problem of multiplying
... 79 × 37
There are numerous methods taught for finding this product. In the end, they all amount to multiplying every digit in one number by every digit in the other number and adding the results with appropriate place values. Several methods use 2-dimensional tables or arrays in their process. Here, we will use text on a line.
... 79 × 37 = (70 +9) × (30 +7)
... = 70×30 + 9×30 + 70×7 + 9×7
... = 2100 + 270 +490 + 63
... = 2100 +760 +63
... = 2860 +63
... = 2923
Putting the decimal point 3 places from the right, and adding the dollar sign gives our product:
... $0.79 × 3.7 = $2.923 ≈ $2.92
Answer:
100 liters of 10% solution is used and 20 liters of 40% solution is used
Step-by-step explanation:
Let "X" amount of 10% solution is used. Then the amount of 40% solution used is equal to 120-X
Now
10% of X + 40% of (120-X) = 15% of 120
On solving the above equation, we get
liters
Amount of 40% solution used = 120 -X = 120-100 = 20 liters
100 liters of 10% solution is used and 20 liters of 40% solution is used
