In order to figure this out you need to use
Descartes Rule. I attached a picture showing Descartes Rule. If the signs changes for when x is positive then the number of times it changes are the possible positive solution. If the sign changes when x is negative then the number of times it changes are the possible negative solutions. With that said the answer is A. View the picture I have attached for the possible + - and imaginary solutions.
Answer = A) One possible positive solution.
5/8 I believe. You can divide both by 9
Answer: 11. Is A
Step-by-step explanation:
Answer:
There are a total of 23 cars with air conditioning and automatic transmission but not power steering
Step-by-step explanation:
Let A be the cars that have Air conditioning, B the cars that have Automatic transmission and C the cars that have pwoer Steering. Lets denote |D| the cardinality of a set D.
Remember that for 2 sets E and F, we have that
Also,
|E| = |E ∩F| + |E∩F^c|
We now alredy the following:
|A| = 89
|B| = 99
|C| = 74
|(A \cup B \cup C)^c| = 24
|A \ (B U C)| = 24 (This is A minus B and C, in other words, cars that only have Air conditioning).
|B \ (AUC)| = 65
|C \ (AUB)| = 26
We want to know |(A∩B) \ C|. Lets calculate it by taking the information given and deducting more things
For example:
99 = |B| = |B ∩ C| + |B∩C^c| = 11 + |B∩C^c|
Therefore, |B∩C^c| = 99-11 = 88
And |A ∩ B ∩ C^c| = |B∩C^c| - |B∩C^c∩A^c| = |B∩C^c| - |B \ (AUC)| = 88-65 = 23.
This means that the amount of cars that have both transmission and air conditioning but now power steering is 23.
Answer:
Time = 3secs
Max height = 56m
Step-by-step explanation:
Given the height reached by the rocket modeled by the equation;
h(x) = -5(x - 3)² + 56 where;
x is in seconds
The rocket velocity at its maximum height is zero.
Hence dh/dx = 0
dh/dx = 2(-5)(x-3)
dh/dx = -10(x-3)
Since dh/dx = 0
0 = -10(x-3)
0 = -10x + 30
10x = 30
x = 3secs
<em>Hence it takes 3 secs to reach the maximum height.</em>
Get the maximum height reached by the rocket. Substitute x = 3 into the equation given;
Recall that:
h(x) = -5(x - 3)² + 56
If x = 3
h(3) = -5(3 - 3)² + 56
h(3) = 0 + 56
h(3) = 56
<em>Hence the maximum height that the rocket reaches is 56m</em>
