Answer: B
Step-by-step explanation: A=πr2
The formula for calculating the area of a circle is A = πr2 where pi (π) equals 3.14 and the radius (r) is half the diameter.
You must times 5 by 5 because of exponents and then times it by pie
5 times 5 = 25
25 times pie is 78.5
1.
"The spending limit on John’s credit card is given by the function f(x)=15,000+1.5x"
means that if the monthly income of John is $ 5,000 ,he can spend at most
f(5,000)=15,000+1.5*5,000=15,000+ 7,500=22, 500 (dollars)
Or for example
if Johns monthly income is $8,000, then he can spend at most
f(8,000)=15,000+1.5*8,000=15,000+ 12,000=27,000 (dollars)
2.
Now, assume that the maximum amount that John can spend is y.
Then, y=15,000+1.5x
we can express x, the monthly income, in terms of y by isolating x:
y=15,000+1.5x
1.5x = y-15,000
X=y-15,000/1.5
thus, in functional notation, x, the monthly income, is a function , say g, of variable y, the max amount:
X=g(y) y-15000/1.5
since we generally use the letter x for the variable of a function, we write g again as:
G (x) x-15000/1.5
tells us that if the maximum amount that John can spend is 50,000 $, then his monthly income is 23,333 $.
3.
If John's limit is $60,000, his monthly income is
G(600,000)=60,000-15,000/ 1.5=45,000/1.5 =30,000
dollars.
Answer: $ 30,000
Remark: g is called the inverse function of f, since it undoes what f does.
instead of g(x), we could use the notation
Answer:
B.
Step-by-step explanation:
Represent the unknows with n and d.
Then n+d = 44 (# of coins)
and
$0.05n + $0.10d = $3.10 (value of coins)
Solving the first equation for n, we get n = 44-d. Subst. 44-d for n in the 2nd equation:
0.05(44-d) + 0.10d = 3.10
Then 2.20 - 0.05d + 0.10d = 3.10, or
2.20 + 0.05d = 3.10, or 0.05d = 0.90. Solving for d,
0.90
d = -------- = 18
0.05
There are 18 dimes and 44-18 nickels. How many nickels is that? ;)
