Answer:
Step-by-step explanation:
a). Given a parametric equation, we are describing a set of coordinates based on the value of t. The variable t is called the parameter.
b) we have the following equations. x=t y=t^2, so in order for us to know where the object is at t=t' we must replace t with the specific value t'. Hence, when t=0 the object is at (0,0^2) = (0,0) (the origin). When t=6, the object is at (6,6^2) = (6,36).
c). To eliminate the parameter, we replace the parameter in one equation by using the second equation. Recall that we have that x=t. Then, by replacing in the second equation, we have the following
where 
Answer:
Part A:
( 1.8333, -0.08333)
Part B:
x = 2 or x = 5/3
Step-by-step explanation:
The quadratic equation
has been given.
Part A:
We are required to determine the vertex. The vertex is simply the turning point of the quadratic function. We shall differentiate the given quadratic function and set the result to 0 in order to obtain the co-ordinates of its vertex.
Setting the derivative to 0;
6x - 11 = 0
6x = 11
x = 11/6
The corresponding y value is determined by substituting x = 11/6 into the original equation;
y = 3(11/6)^2 - 11(11/6) + 10
y = -0.08333
The vertex is thus located at the point;
( 1.8333, -0.08333)
Find the attached
Part B:
We can use the quadratic formula to solve for x as follows;
The quadratic formula is given as,
From the quadratic equation given;
a = 3, b = -11, c = 10
We substitute these values into the above formula and simplify to determine the value of x;
Answer:
Step-by-step explanation:
Hello sorry I need points
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.
In this formula, the m represents the slope of the line and the b represents the y value where x is equal to zero. This value is otherwise known as the y-intercept
