The first sentence is not true in general. Consider the equation
. There are no solutions. Now consider
. There is only one solution,
.
But whatever. You're asked to demonstrate that
has two solutions (which is true; the right hand side must be a positive integer in order to have two solutions). This follows immediately from the definition of absolute value, which says
So suppose
. Then
Now suppose
. Then
So two solutions to
are
.
Answer:
Total number of animals in the group = 170
Step-by-step explanation:
Let the number of sheep = a
Number of dragons in the group = 75
Number of dragons opposite dragons = 37
Number of sheep opposite to the dragon = 1
Number of sheep left = a - 1
Number of sheep opposite to sheep =
Since. number of sheep opposite to sheep is 10 more than of dragons opposite dragons,
= 37 + 10
a - 1 = 94
a = 95
Then total number of animals in the group = Total number of sheep + Total number of dragons
= 95 + 75
= 170
Therefore, total number of animals in the group are 170.
The meaning of the horizontal asymptote for the given function is that;
The horizontal asymptote of y = 0 means that the person’s temperature will approach 98.6ºF as time elapses
We are told the increase in a person's body temperature above 98.6°F can be modeled by the function;
T(t) = 4t/(t² + 1)
Where;
t represents the time elapsed
Now, let us find a way to simplify the function so that t at the numerator is removed.
Thus, we will now have;
4t/(t² + 1) = 4/(t + (1/t))
To get the horizontal asymptote, we have to find the limit of the function as t approaches infinity.
Thus;
Lim t ➡ ∞ gives;
T(∞) = 4 × 1/(∞ + (1/∞))
T(∞) = 4 × 0
T(∞) = 0
This means that y = 0 is the horizontal asymptote of the function.
Thus, in conclusion The horizontal asymptote of y = 0 means that the person’s temperature will approach 98.6ºF as time elapses
Read more on horizontal asymptote at; brainly.com/question/8493280
Answer:
21 + 3a
Step-by-step explanation:
3 (7+a)
distribute 3 into parentheses:
21 + 3a
Answer:
Step-by-step explanation:
Given the equation 4x²+ 49y² = 196
a) Differentiating implicitly with respect to y, we have;
b) To solve the equation explicitly for y and differentiate to get dy/dx in terms of x,
First let is make y the subject of the formula from the equation;
If 4x²+ 49y² = 196
49y² = 196 - 4x²
Differentiating y with respect to x using the chain rule;
Let
c) From the solution of the implicit differentiation in (a)
Substituting into the equation to confirm the answer of (b) can be shown as follows
This shows that the answer in a and b are consistent.