Not an expertise on infinite sums but the most straightforward explanation is that infinity isn't a number.
Let's see if there are anything we missed:
∞
Σ 2^n=1+2+4+8+16+...
n=0
We multiply (2-1) on both sides:
∞
(2-1) Σ 2^n=(2-1)1+2+4+8+16+...
n=0
And we expand;
∞
Σ 2^n=(2+4+8+16+32+...)-(1+2+4+8+16+...)
n=0
But now, imagine that the expression 1+2+4+8+16+... have the last term of 2^n, where n is infinity, then the expression of 2+4+8+16+32+... must have the last term of 2(2^n), then if we cancel out the term, we are still missing one more term to write:
∞
Σ 2^n=-1+2(2^n)
n=0
If n is infinity, then 2^n must also be infinity. So technically, this goes back to infinity.
Although we set a finite term for both expressions, the further we list the terms, they will sooner or later approach infinity.
Yep, this shows how weird the infinity sign is.
The graph is vertically stretched by a factor of 2 and translated 3 units right when it is transformed. Option A is correct.
<h3>What is transformation of a function?</h3>
Transformation of a function is shifting the function from its original place in the graph.
Types of transformation-
- Horizontal shift- Let the parent function is f(x). Thus by replacing parent function with f(x-b) shifts the graph b units right and by replacing parent function with f(x+b) shifts the graph b units left.
- Vertical shift- Let the parent function is f(x). Thus by replacing parent function with f(x)-c shifts the graph c units down and by replacing parent function with f(x)+c shifts the graph c units up.
The given function is,
This function is changed to the function,
Here the 3 units is substrate in the function. Thus, it is shiftet 3 units right. The number 2 is multiplied in the function which vertically stretched the graph by a factor of 2.
Thus, the graph is vertically stretched by a factor of 2 and translated 3 units right when it is transformed. Option A is correct.
Learn more about the transformation of a function here;
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Answer:209.84 - 20.00 = 189.84 / 2 = 94.92
94.92 + 20.00 = 114.92 Eva spent and Martha spent $94.92
Step-by-step explanation:
Answer:
There are 20 booths and (38 - 20), or 18, tables
Step-by-step explanation:
Represent the number of tables with t and the number of booths with b.
We need to find the values of t and b.
(6 people/table)(t) + (4 people/booth)b = 188 (units are "people")
t + b = 38 (units are "seating units")
Solving the second equation for t, we get 38 - b = t.
Substitute 38 - b for t in the first equation:
(6 people/table)(38 - b) + (4 people/booth)b = 188
Then solve for b: 6(38) - 6b + 4b = 188, or:
228 - 2b = 188, or 2b = 228 - 188, or 2b = 40. Thus, b = 20 (booths)
There are 20 booths and (38 - 20), or 18, tables.
Answer:
123 domestic stamps
89 foreign stamps
Step-by-step explanation:
