Answer:
78 dollars
Step-by-step explanation:
Function c is defined by the equation c(n) = 50 + 4n. It gives the monthly cost, in dollars, of visiting a gym as a function of the number of visits, n. Find the value of c(7).
Given:
c(n) = 50 + 4n
Where,
c = monthly cost of visiting a gym
n = number of visits
Find the value of c(7)
That is, when n = 7
c(n) = 50 + 4n
c(7) = 50 + 4(7)
= 50 + 28
= 78
c(7) = 78 dollars
As soon as I read this, the words "law of cosines" popped
into my head. I don't have a good intuitive feeling for the
law of cosines, but I went and looked it up (you probably
could have done that), and I found that it's exactly what
you need for this problem.
The "law of cosines" relates the lengths of the sides of any
triangle to the cosine of one of its angles ... just what we need,
since we know all the sides, and we want to find one of the angles.
To find angle-B, the law of cosines says
b² = a² + c² - 2 a c cosine(B)
B = angle-B
b = the side opposite angle-B = 1.4
a, c = the other 2 sides = 1 and 1.9
(1.4)² = (1)² + (1.9)² - (2 x 1 x 1.9) cos(B)
1.96 = (1) + (3.61) - (3.8) cos(B)
Add 3.8 cos(B) from each side:
1.96 + 3.8 cos(B) = 4.61
Subtract 1.96 from each side:
3.8 cos(B) = 2.65
Divide each side by 3.8 :
cos(B) = 0.69737 (rounded)
Whipping out the
trusty calculator:
B = the angle whose cosine is 0.69737
= 45.784° .
Now, for the first time, I'll take a deep breath, then hold it
while I look back at the question and see whether this is
anywhere near one of the choices ...
By gosh ! Choice 'B' is 45.8° ! yay !
I'll bet that's it !
Answer:
$93.33 per dose
Step-by-step explanation:
$1.4×10⁶/(7.5 kg) × (1 kg)/(1000 g) × (0.5 g)/(1 dose)
= (1.4×10⁶×0.5)/(7.5×10³) $/dose = 700/7.5 $/dose ≈ $93.33/dose
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Converting dollars per kilogram to dollars per dose involves units conversion from kilograms to doses. We have done it in two steps, first to grams, then to doses.
