Answer:
.
Step-by-step explanation:
Differentiate each function to find an expression for its gradient (slope of the tangent line) with respect to 
. Make use of the power rule to find the following:
.
.
The question states that the graphs of 
and 
touch at 
, such that 
. Therefore:
.
On the other hand, since the graph of and coincide at , 
(otherwise, the two graphs would not even touch at that point.) Therefore:
.
Solve this system of two equations for 
and 
:
.
Therefore, 
whereas 
.
Substitute these two values back into the expression for and :
.
.
Evaluate either expression at to find the 
-coordinate of the intersection. For example, 
. Similarly, 
.
Therefore, the intersection of these two graphs would be at .
3279 is greater than 3273
Answer:
There are N students in the class.
We know that ONLY ONE of the inequalities is true:
N < 10
N > 10
N < 22
N > 22
We want only one of these four inequalities to be true.
Remember that if we have:
x > y
y is not a solution, because:
y > y is false.
Then:
If we take N = 10, then:
N < 22
Is the only true option.
While if we take N = 22
N > 10
is the only true option.
So there are two possible values of N.
Answer:
-7/10
Explanation:
Given the expression
We can rewrite the expression as:
The number line showing the location of the two numbers is attached below. Therefore:
