The coordinate of point Y such that the ratio of CY to YE is 1:1 on the number line is: -1.
<h3>How to Determine the Coordinate of a Point on a Number Line?</h3>
The number line gives us a good view of how real numbers are ordered. On a number line, any point can be located depending on their coordinates.
Given the number line on the diagram above, we are told that the ratio of CY to YE is 1 : 1. This ratio implies that the distance from point C to Y is the same as the distance from Y to E. Therefore, CY or YE is half of CE.
C has a coordinate of -4.
E has a coordinate of 2.
Distance from point C to point E = |-4 - 2| = 6 units
Half of 6 units is 3 units.
3 units from point C would be -1
Also, 3 units away from point E towards point C would be -1.
Therefore, the coordinate of point Y such that the ratio of CY to YE is 1:1 on the number line is: -1.
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Answer:
General Formulas and Concepts:
<u>Algebra II</u>
- Natural logarithms ln and Euler's number e
- Logarithmic Property [Exponential]:
<u>Calculus</u>
Limits
- Right-Side Limit:
- Left-Side Limit:
Limit Rule [Variable Direct Substitution]:
L’Hopital’s Rule:
Differentiation
- Derivatives
- Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Step-by-step explanation:
We are given the following limit:
Substituting in <em>x</em> = 0 using the limit rule, we have an indeterminate form:
We need to rewrite this indeterminate form to another form to use L'Hopital's Rule. Let's set our limit as a function:
Take the ln of both sides:
Rewrite the limit by including the ln in the inside:
Rewrite the limit once more using logarithmic properties:
Rewrite the limit again:
Substitute in <em>x</em> = 0 again using the limit rule, we have an indeterminate form in which we can use L'Hopital's Rule:
Apply L'Hopital's Rule:
Simplify:
Redefine the limit:
Substitute in <em>x</em> = 0 once more using the limit rule:
Evaluating it, we have:
Substitute in the limit value:
e both sides:
Simplify:
And we have our final answer.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Answer:
D
Step-by-step explanation:
To find the inverse, all we have to do is switch the x and f(x) so instead of f(x) = 5x + 6, it becomes:
x = 5f(x) + 6
x - 6 = 5f(x)
f⁻¹(x) = (x - 6) / 5
<h3>
===> Exercise 1</h3>
(3x² - 7x + 14) + (5x² + 4x - 6)
Match 3x² and 5x² to get 8x².
Combine −7x and 4x to get −3x.
Subtract 6 from 14 to get 8.
Therefore, the expression (3x² - 7x + 14) + (5x² + 4x - 6), is equivalent to the expression "B".
<h3>
===> Exercise 2</h3>
(2x² - 5x -3) + (-10x² + 2x + 7)
Combine 2x² and -10x² to get −8x².
Combine −5x and 2x to get −3x.
Add −3 and 7 to get 4.
Therefore, the expression (2x² - 5x -3) + (-10x² + 2x + 7), is equivalent to the expression "A".
<h3>
===> Exercise 3</h3>
(12x² - 2x - 13) + (-4x² + 5x +9)
Combine 12x² and -4x² to get 8x².
Combine −2x and 5x to get 3x.
Add −13 and 9 to get −4.
Therefore, the expression (12x² - 2x - 13) + (-4x² + 5x +9), is equivalent to the expression "C".
I don't know how to solve this but im pretty sure the table is needed so you should atleast take a picture or just type it out