Consider the straight line: y=1x+3. Calculate the area UNDER this line which is bounded by y=0, x=8 and x=15. (That is, the area from the horizontal axis (y=0) to the line, between the values of x=8 and x=15.) Give you answer to the nearest whole number, rounding up
Using Calculus:
Area = ∫(x+3) dx from 8 to 15
= [x^2/2 + 3x] from 8 to 15
= 225/2 + 45 - 64/2 - 24
= 203/2 or 101.5
of course we don't need Calculus to do this, since the shape is a simple trapezoid
at x=8, height = 11
at x = 15 , height = 18
distance between = 15-8 = 7
Area = (1/2)(11+18)(7) = 101.5
To calculate the area under the straight line bounded by y=0, x=8, and x=15, we need to find the region between the line and the x-axis. Since the line is a straight line with a positive slope, the area will form a triangle.
First, let's calculate the y-intercept of the line. In the equation y=1x+3, the y-intercept occurs when x=0. Plugging in x=0, we find that y=3.
Now, let's find the x-intercept of the line. Since it is a line with a slope of 1, the x-intercept will occur when y=0. Setting y=0 in the equation y=1x+3, we get 0=1x+3, which gives us x=-3.
Since the line intersects the x-axis at x=-3 and y=0 and the y-axis at x=0 and y=3, we have a triangle.
To calculate the area of a triangle, we use the formula: Area = (base * height) / 2.
In this case, the base is given by the difference between x=8 and x=15, which is 15 - 8 = 7.
The height is given by the y-coordinate at the x-intercept (x=-3), which is 0.
Now, let's substitute the values into the formula to calculate the area:
Area = (base * height) / 2
= (7 * 0) / 2
= 0
Therefore, the area under the straight line bounded by y=0, x=8, and x=15 is 0.
Note: Since the question asks for the answer rounded up to the nearest whole number, the final answer would be 0 (rounded up).