A box of Munchkins contains chocolate and glazed donut holes. If Jacob ate 2 chocolate
1 answer:
Answer:
24 munchkins.
Step-by-step explanation:
Let C be the number of chocolate and D be number of glazed donut holes in the original box.
We are told if Jacob ate 2 chocolate munchkins, then 1/11 of the remaining Munchkins would be chocolate. We can represent this information as:
We are also told if he instead added 4 glazed Munchkins to the original box, 1/7 of the Munchkins would be chocolate. We can represent this information as:
Upon substituting C's value from equation (2) in equation (1) we will get,
Let us have a common denominator on right side of equation.
Multiplying both sides of our equation by 7, we will get,
Multiplying both sides of our equation by 11, we will get,
Therefore, the total number of Munchkins in original box is 24.
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Answer:
Length of rectangular strip = 12
area of rectangular strip = 2*12 = 24
Area of square = x^2 = 12^2 = 144
Step-by-step explanation:
Area of square x^2
area of rectangle is given by length * width
Length of rectangular strip = x
width of rectangular strip = 2
area of rectangular strip = length * width = 2*x = 2x
Area of square piece of paper when rectangular strip is taken away from it
= Area of square - area of rectangular strip
=
It is given that Area of square piece of paper when rectangular strip is taken away from it is 120 square units.
Thus,
Thus,
either x+10 = 0 or x -12= 0
x = -10 or x = 12
but length cannot be negative hence neglecting x = -10
hence value of x is 12.
Hence,
Length of rectangular strip = 12
area of rectangular strip = 2*12 = 24
Area of square = x^2 = 12^2 = 144
Since g(6)=6, and both functions are continuous, we have:
![\lim_{x \to 6} [3f(x)+f(x)g(x)] = 45\\\\\lim_{x \to 6} [3f(x)+6f(x)] = 45\\\\lim_{x \to 6} [9f(x)] = 45\\\\9\cdot lim_{x \to 6} f(x) = 45\\\\lim_{x \to 6} f(x)=5](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%206%7D%20%5B3f%28x%29%2Bf%28x%29g%28x%29%5D%20%3D%2045%5C%5C%5C%5C%5Clim_%7Bx%20%5Cto%206%7D%20%5B3f%28x%29%2B6f%28x%29%5D%20%3D%2045%5C%5C%5C%5Clim_%7Bx%20%5Cto%206%7D%20%5B9f%28x%29%5D%20%3D%2045%5C%5C%5C%5C9%5Ccdot%20lim_%7Bx%20%5Cto%206%7D%20f%28x%29%20%3D%2045%5C%5C%5C%5Clim_%7Bx%20%5Cto%206%7D%20f%28x%29%3D5)
if a function is continuous at a point c, then
,
that is, in a c ∈ a continuous interval, f(c) and the limit of f as x approaches c are the same.
Thus, since
, f(6) = 5
Answer: 5
if a function is continuous at a point c, then
that is, in a c ∈ a continuous interval, f(c) and the limit of f as x approaches c are the same.
Thus, since
Answer: 5