Answer:
30 pencils
Step-by-step explanation:
Given :
Number of pencils shared = 40
Sharing ratio = 2 : 6
Nimah's share = (2 / sum of ratio) * number of pencils
Nimah's share = (2 / 8) * 40
Nimah's share = 80 / 8
Nimah's share = 10 pencils
Jack's share = total number - Nimah's share
Jack's share = 40 - 10
Jack's share = 30
The answer is:
The inverse of a function is another function, , with the following property:
In other words, the inverse of a function does exactly "the opposite" of what the original function does, and so if you compute them both in sequence you return to the starting point.
Think for example to a function that doubles the input, , and one that halves it: . Their composition is clearly the identity function , since you consider "twice the half of something", or "half the double of something".
In general, to invert a function , you have to solve the expression for , writing an expression like . If you manage to do so, then is the inverse of .
In your case, you have
Multiply both sides by to get
Square both sides to get
Finally, subtract 3 from both sides to get
Since the name of the variables doesn't really have a meaning, you can say that the inverse function is
As for the domain of the inverse function, remember what we said ad the beginning: if the original function goes from set A (domain) to set B (codomain), then the inverse function goes from set B (domain) to set A (codomain). This means that the inverse function is defined on an element in B if and only if that element belongs to the range of the original function, i.e. the set of the elements of the codomain such that there exists . So, we need the range of .
We know that the range of is . When you transform it to you simply translate the graph horizontally, so the range doesn't change. But when you multiply the function times you affect both extrema of the range, turning it into , which you can simply write as
Answer:
<h2>B.
r = 4cosθ</h2>
Step-by-step explanation:
Given the expression in rectangular coordinate as x²+y²−4x=0, in order to write the given expression in polar coordinates, we need to write the value of x and y as a function of (r, θ).
x = rcosθ and y = rsinθ.
Substituting the value of x and y in their polar form into the given expression we have;
x²+y²−4x=0
( rcosθ)²+( rsinθ)²-4( rcosθ) = 0
Expand the expressions in parenthesis
r²cos²θ+r²sin²θ-4rcosθ = 0
r²(cos²θ+sin²θ)-4rcosθ = 0
From trigonometry identity, cos²θ+sin²θ =1
The resulting equation becomes;
r²(1)-4rcosθ = 0
r²-4rcosθ = 0
Add 4rcosθ to both sides of the equation
r²-4rcosθ+4rcosθ = 0+4rcosθ
r² = 4rcosθ
Dividing both sides by r
r²/r = 4rcosθ/r
r = 4cosθ
<em>Hence the correct equation in polar coordinates is r = 4cosθ</em>
Answer:
31792.5 cu
A cylindrical tank has a radius of 15 feet and a height of 45 feet. Volume of cylinder = pi *r^2*h , volume =3.14*15^2*45 , volume = 31792.5 cu.
so the answer is B
Answer:
$1200
Step-by-step explanation:
Every month, Kiersten receives a subscription fee of $10 from each of the subscribers to her website.
Last month she had 100 subscribers. This month, 30 new subscribers joined and 10 members canceled their subscription. The amount of subscribers she has now is:
100 + 30 - 10 = 120
This means that this month, Kiersten will earn:
10 * 120 = $1200