Steps:
1. calculate the values of y at x=0,1,2. using y=5-x^2
2. calculate the areas of trapezoids (Bottom+Top)/2*height
3. add the areas.
1.
x=0, y=5-0^2=5
x=1, y=5-1^2=4
x=2, y=5-2^2=1
2.
Area of trapezoid 1 = (5+4)/2*1=4.5
Area of trapezoid 2 = (4+1)/2*1=2.5
Total area of both trapezoids = (4.5+2.5) = 7
Exact area by integration:
integral of (5-x^2)dx from 0 to 2
=[5x-x^3/3] from 0 to 2
=[5(2-0)-(2^3-0^3)/3]
=10-8/3
=22/3
=7 1/3, slight greater than the estimation by trapezoids.
That is called the dependent variable. It depends upon the value of the independent variable.
f(x)=y
So we can see by inspection that the dependent variable y value depends upon the input value of the independent variable x
Any questions please feel free to ask. Thanks
<u>Answer</u>
1st solution: a = 1
b = 3
2nd solution: a = 2
b = 6
<u>Explanation</u>
1st solution
<em> 1</em>
<em> 333</em>
<em> 333</em>
<em> 333</em>
<em> </em><em><u> +333</u></em>
<em> </em><em><u> 1333</u></em>
2nd solution
<em> 2</em>
<em> 666</em>
<em> 666</em>
<em> 666</em>
<em><u> + 666</u></em>
<em><u> 2666</u></em>
When multiplying the same number raised to different powers add the powers together.
3 + 2 + 5 = 10
Because you are also multiplying a value without a power you need to add 1 to the sum of the powers:
10 + 1 = 11
Answer: 6^11
Given:
6 girls
4 boys
Probability of 1 girl being chosen: 1/6
Probability of 1 boy being chosen: 1/4
Probability of another boy being chosen: 1/3
1/6 = 0.17 x 100% = 17%
1/4 = 0.25 x 100% = 25%
1/3 = 0.33 x 100% = 33%
17% + 25% + 33% = 75%
The probability that exactly one girl and two boys will receive awards is 75%.
