7. Blake made a rectangular table for his dining room. The sides of the table are 12 feet and 4 feet. What is the
1 answer:
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If you're just focusing on the boundary, it's the circle . Parameterize it by taking
and
, with
. Then
reduces to a univariate function
:
Then you can find any extrema on the boundary by checking the critical points of .
Answer:
15.
16. 10 ml of 20% saline and 40 ml of 10% saline
Step-by-step explanation:
A chemist takes x ml of 20% saline and y ml of 10% saline. In total, he takes
x + y ml that is 50 ml, so
There are ml of salt in x ml of 20% saline and
ml of salt in 10% saline. There are
ml of salt in 50 ml of 12% saline. Thus,
15. We get the system of two equations:
16. Solve this system. From the first equation:
Substitute it into the second equation:
Answer:
7.2
Step-by-step explanation:
To reach point D from point C, you need to add 4 to the x-value of point C and take away 6 from the y-value. These numbers are the sides of the hypothetical triangle.
The Pythagorean Theorem states that . If we plug the side lengths in for a and b, we get
. This can be simplified to
, or
. If we root both sides, we find that c is equal to
, which is slightly more than 7, at around 7.2.
Answer:
1/80 of the agency's employees have PhDs.
Step-by-step explanation:
Given that:
Total number of employees = 4000
Number of employees with bachelors degree = 1000
Fraction of employees with graduate degree = 1/4 of 1000 = 250
1/5 of the employees with graduate degrees have PhD.
Number of employees with PhDs = 1/5 of 250 = 50
Now,
Fraction of PhD employees to total employees =
Hence,
1/80 of the agency's employees have PhDs.