for the implicit integration I got:
the vertical tangent would at points at which y' goes to infinity.
that happen when the right-hand side has singularities, that is, the denominator is 0:
so the two points y above have a vertical tangent.
Answer:
Yes
Step-by-step explanation:
xy=yx because either way, you would end with the same product. For example, if x was 3 and y was 2, you would have (3)(2)=(2)(3), giving you 6=6 which is, in fact, a true statement.
A two digit number has a tens digit and a ones digit.
Let's say x = tens digit and y = ones digit
"The sum of the digits is 5"
x + y = 5
The next phrase is "the number multiplied by 3 is 42" but we need to represent the number using the digits. So they need to be multiplied first by their place value and added together. [Example: 34 = 3(10) + 4(1)]
The number is: 10x + y
3(10x + y) = 42
The system of equations: (two equations for two unknowns)
x + y = 5
30x + 3y = 42
Then you can use substitution or elimination to combine and solve.
I'll use elimination, multiply the entire top equation by -3 and add the equations together. y will cancel out
-3x - 3y = -15
30x + 3y = 42
------------------
27x + 0 = 27
x = 1
then plug x = 1 into either equation to find y
1 + y = 5
y = 4
remember the x and y represent digits so the number xy is 14
The range of a function is the set of possible values that can be obtained from the dependent variable. The range of the function is: 
Given that:
Let the number of months be t. So, the function C(t) is calculated as follows:
The range is calculated as follows:
The smallest possible value of t is 0 i.e. when no monthly subscription is done.
So, we have:
And the highest is 
i.e. for a large value of t
So, we have:
Hence, the range of the function is:
Read more about range of functions at:
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