Answer:
The intersection is 
.
The Problem:
What is the intersection point of 
and 
?
Step-by-step explanation:
To find the intersection of and , we will need to find when they have a common point; when their 
and 
are the same.
Let's start with setting the 's equal to find those 's for which the 's are the same.
By power rule:
Since 
implies 
:
Squaring both sides to get rid of the fraction exponent:
This is a quadratic equation.
Subtract 
on both sides:
Comparing this to 
we see the following:
Let's plug them into the quadratic formula:
So we have the solutions to the quadratic equation are:
or 
.
The second solution definitely gives at least one of the logarithm equation problems.
Example: 
has problems when 
and so the second solution is a problem.
So the where the equations intersect is at .
Let's find the -coordinate.
You may use either equation.
I choose .
The intersection is .
Answer:
The length of the sloping section of the ramp is 20.12 m
Step-by-step explanation:
Given;
the total height of the bank, h = 2.8 m
The slope of the ramp must be 8° to the horizontal, i.e, θ = 8°
Let the length of the sloping section = L
let the horizontal distance between the height of the bank and sloping section = b
Thus, h, L and b forms three sides of a right angled-triangle, with L as the hypotenuse side, h (height of the triangle) as the opposite side and b (base of the triangle) as the adjacent side.
We determine L by applying the following formula;
Sinθ = opposite / hypotenuse
Sin θ = h / L
L = h / Sin θ
L = 2.8 / Sin 8
L = 2.8 / 0.13917
L = 20.12 m
Therefore, the length of the sloping section of the ramp is 20.12 m
The answer is B.
X = -11 :-)
Answer:
35
Step-by-step explanation:
40=1/2(115-x)
80=115-x
-35=-x
x=35
Use PEMDAS, the answer that I got is 19.
