Sum of two angles that are supplementary = 180°
Let the smaller angle be = x
Using this let us find the measures of the smaller angle and bigger angle .
∴ The measure of the two angles are = 21° and 159° .
5 years ago, my grandfather was five times as old as I was. Three years from now, my grandfather will be three times as old as I
2 answers:
<u>Answer:</u>
13 years
<u>Step-by-step explanation:</u>
5 years ago, let the grandchild's age to be x so the grandfather's age will be 5x.
3 years from now, the grandchild's age will be x+8 (x+3+5) and the grandfather's age will be 5x+8 (5x+3+8).
So we can establish an equation:
Therefore, the present age of the grandchild is x+5 = 8+5 = 13 years and the present age of the grandfather is 5x+5 = 5(8)+5 = 45.
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Answer:
Step-by-step explanation:
We want to calculate the right-endpoint approximation (the right Riemann sum) for the function:
On the interval [-1, 1] using five equal rectangles.
Find the width of each rectangle:
List the <em>x-</em>coordinates starting with -1 and ending with 1 with increments of 2/5:
-1, -3/5, -1/5, 1/5, 3/5, 1.
Since we are find the right-hand approximation, we use the five coordinates on the right.
Evaluate the function for each value. This is shown in the table below.
Each area of each rectangle is its area (the <em>y-</em>value) times its width, which is a constant 2/5. Hence, the approximation for the area under the curve of the function <em>f(x)</em> over the interval [-1, 1] using five equal rectangles is:
