To ease your problem, consider "L" as you x-axis
Then the coordinate become:
A(- 4 , 3) and B(1 , 2) [you notice that just the y's changed]
This is a reflection problem.
Reflect point B across the river line "L" to get B', symmetric of B about L.
The coordinates of B'(1 , -1) [remember L is our new x-axis]
JOIN A to B' . AB' intersect L, say in H
We have to find the shortest way such that AH + HB = shortest.
But HB = HB' (symmetry about L) , then I can write instead of
AH + HB →→ AH + HB'. This is the shortest since the shortest distance between 2 points is the straight line and H is the point requiered
Answer:
1/6 for the cube and 1/2 for the coin
it would be 4/6 or 2/3 both are the same
Step-by-step explanation: sorry if im wrong btw
If the limit of f(x) as x approaches 8 is 3, can you conclude anything about f(8)? The answer is No. We cannot. See the explanation below.
<h3>What is the justification for the above position?</h3>
Again, 'No,' is the response to this question. The justification for this is that the value of a function does not depend on the function's limit at a given moment.
This is particularly clear when we consider a question with a gap. A rational function with a hole is an excellent example that will help you answer this question.
The limit of a function at a position where there is a hole in the function will exist, but the value of the function will not.
<h3>What is limit in Math?</h3>
A limit is the result that a function (or sequence) approaches when the input (or index) near some value in mathematics.
Limits are used to set continuity, derivatives, and integrals in calculus and mathematical analysis.
Learn more about limits:
brainly.com/question/23935467
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<span>Scientific NotationDate: 09/16/97 at 00:42:42
From: Aubin
Subject: Scientific notation
How do you do this problem? I don't understand how you're supposed to
get the answer:
5x10 to the 3rd power = 5,000
5x10 to the -3rd power = -5,000
Is this correct?
<span>Date: 11/03/97 at 09:56:46
From: Doctor Pipe
Subject: Re: Scientific notation
Aubin,
The first part of what you wrote is correct; 5x10 to the 3rd power =
5,000. The second part is not correct.
Writing a negative exponent, such as 10^-3 (read that as ten to the
minus third power) is the same as writing 1/(10^3) (read that as one
over ten to the third power). Notice that the exponent is negative
when writing 10^-3 and positive when writing 1/(10^3) - yet the two
numbers are equal.
Remember that any number to the zeroeth power, say 10^0, is equal
to 1. 10^0 = 1; 5^0 = 1; 275^0 = 1.
Remember also that when multiplying two numbers written as
base^exponent, if the base in both numbers is equal then we add
together the exponents: 10^5 x 10^6
= 10^(5+6)
= 10^11.
If we have a number 10^5, what number do we multiply it by to get 1?
Well, 10^5 x 10^(-5)
= 10^(5 + (-5))
= 10^0
= 1.
So if 10^5 x 10^(-5) = 1
then 10^(-5) = 1 / 10^5
So, since 10^3 = 1,000 then 10^(-3) = 1/(10^3) = 1/1,000 = 0.001 .
It follows from this that:
5x10 to the -3rd power = 5 x 10^(-3) = 5 x 0.001 = 0.005 .
The reason for this can be seen by examining what numbers to the right
of the decimal point represent. You know what numbers to the left of
the decimal point represent: the units digit represents the numeral
times 10^0 (any number to the 0th power is 1), the tens digit
represents the numeral times 10^1, the hundreds digit represents the
numeral times 10^2, and so on.
Well, to the right of the decimal point, the tenths digit represents
the numeral times 10^-1, the hundredths digit represents the numeral
times 10^-2, the thousandths digit represents the numeral times 10^-3,
and so on.
It's important to understand exponents because exponents allow us to
extend the range of numbers that we can work with by allowing us to
easily write and work with very large and very small numbers. It's so
much easier to write:
10^23
then to write:
100,000,000,000,000,000,000,000
Or to write:
10^(-23)
instead of:
0.00000000000000000000001</span></span>