Let mZA = 40°. If ZB is a complement of A, and 2c is a supplement of 2B, what is m4B+m2c?
1 answer:
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<h3>Answer:</h3>
- 8 pieces
- 3/8 foot
a) Let n represent the number of 1 7/8 ft pieces. Then we have ...
... 16 1/2 ft = n × (1 7/8 ft)
We can find n by dividing this equation by 1 7/8.
... (16 1/2)/(1 7/8) = n = (132/8)/(15/8) = 132/15
... n = 8 12/15 = 8 4/5
The integer number of pieces that can be cut is 8 pieces.
b) The length of the left-over piece is 4/5 of the full length of a piece, so is ...
... (4/5) × (15/8 ft) = 12/8 ft
We want to divide this into 4 equal lengths, so each of those lengths will be 1/4 of the length of the left-over:
... (1/4) × (12/8 ft) = 3/8 ft
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<em>Comment on arithmetic with fractions</em>
This problem is easier if you <em>convert the mixed numbers to improper fractions</em>. This is done by expressing the integer as a number of fractional parts, then adding the fraction part of the mixed number:
... a + b/c = (a×c/c) + b/c = (ac +b)/c
Division with fractions is taught a couple of different ways. One way you can do it is to "invert and multiply". That is, you multiply the numerator fraction by the reciprocal of the denominator fraction:
... (a/b)/(c/d) = (a/b)×(d/c)
Another way you can do the division is to express each of the numerator and denominator fractions over the same denominator. Then the quotient is the ratio of numerators.
... (a/c)/(b/c) = a/b
This is the method we used here. Effectively, we converted 16 1/2 to 16 4/8 then to (16×8 +4)/8 = 132/8. Then the numerator and denominator fractions both had denominators of 8, so (132/8)/(15/8) = 132/15. This fraction can be reduced by removing a factor of 3 from numerator and denominator to give ...
... 132/15 = 44/5 = 8 4/5
Answer:
Part 1) The equation tells us that Terry started at an elevation of 2,600 ft
Part 2) The elevation is decreasing by 50 feet each second
Step-by-step explanation:
we have
where
E(t) is Terry's elevation in feet
t is the time in seconds
Part 1) Find the E intercept of the equation
The E-intercept is the value of E when the value of t is equal to zero
so
For t=0
substitute
therefore
The equation tells us that Terry started at an elevation of 2,600 ft
Part 2) Find the slope of the equation
we have
This is the equation of the line into slope intercept form
The slope m is equal to
The slope is negative, because is decreasing
therefore
The elevation is decreasing by 50 feet each second