Convert the following liquid measures.
2 answers:
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Answer:
Step-by-step explanation:
Answer:
29% of the drive
Step-by-step explanation:
The plot of the problem is:
Transmitter at origin (0,0)
City to the north at (0,70)
City to the east at (74,0)
The path from city to city is a line with slope:
m = (-70)/74 = -35/37
and y-intercept at y = 70, so the equation is y = (-35/37)*x + 70.
The transmitter reach the area enclosed by the next circle:
x^2 + y^2 = 53^2
See the picture attached
The intersection is gotten from the picture or solving:
x^2 + [(-35/37)*x + 70]^2 = 53^2
the points approximately are: (24.1, 47.2) and (45.8, 26.7)
From Pythagorean theorem the total distance of the trip is:
d1 = √(70^2 + 74^2) ≈ 101.9 miles
And the distance when the signal is picked up is:
d2 =√ [(45.8 - 24.1)^2 + (47.2 - 26.7)^2] ≈ 29.9 miles
You will pick up a signal from the transmitter in (d2/d1)*100 = 29% of the drive.
Answer: 9 and 3/7
Step-by-step explanation: To multiply a mixed number by a mixed number, we first want to write each mixed number as an improper fraction.
We can write a mixed number as an improper fraction by multiplying the denominator by the whole number and adding the numerator.
We can change to the improper fraction 30/7.
We can also change to the improper fraction 11/5.
Now, we are simply multiplying fractions. To multiply fractions, we multiply across the numerators and multiply across the denominators. When we multiply these fractions, we will end up with the fraction 330/35. Since 330/35 is not in lowest terms, we need to divide both the numerator and denominator by the greatest common factor of 330 and 35 which is 5 and we will get the improper fraction 66/7.
Notice however that 66/7 can be changed into a mixed number by dividing the denominator which is 7 into the numerator which is 66.
66 divided by 7 equals 9 with a remainder of 3 so we can write 66/7 as the mixed number 9 and 3/7.
Therefore, 4 and 2/7 × 2 and 1/5 = 9 and 3/7