What is 28% of $48 when leaving a tip
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<h2>Hello!</h2>
The graph is attached.
To graph a parabola we need to know the following:
- If the parabola is open upwards or downwards
- They axis intercepts (if they exist)
- The vertex position (point)
We are given the function:
Where,
For this case, the coefficient of the quadratic term (a) is negative, it means that the parabola opens downwards.
Finding the axis interception points:
Making the function equal to 0, we can find the x-axis (t) intercepts, but since the equation is a function of the time, we will only consider the positive values, so:
Using the quadratic equation:
So, at t=4.0615 the height of the softball will be 0.
Since we will work only with positive values of "x", since we are working with a function of time:
Let's start from "t" equals to 0 to "t" equals to 4.0615.
So, evaluating we have:
Finally, we can conclude that:
- The softball reach its maximum height at t equals to 2. (68 feet)
- The softball hits the ground at t equals to 4.0615 (0 feet)
- At t equals to 0, the height of the softball is equal to 4 feet.
See the attached image for the graphic.
Have a nice day!
The term of the given quadratic sequence is found to be 3n² - n + 1 using the principle of mathematical induction.
Given,
In the question:
The quadratic sequence is :
3, 11, 25, 45, ...
To find the nth term of the quadratic sequence.
Now, According to the question;
The first term of the sequence is 3, the second term is 11, the third term is 25, and the fourth term is 45.
The difference between the first and second terms can be calculated as follows:
11-3 = 8
The difference between the second and third terms can be calculated as follows:
25-11 = 14
The difference between the third and fourth terms can be calculated as follows:
45-25 = 20
The sequence is expressed as follows:
3,3+8,11+11,25+20,...
The difference between consecutive terms expands by 6.
Use the principle of mathematical induction.
6
= 3n(n+1)
The sequence's nth term can be calculated as follows:
term = 3n(n+1) - 4n + 1
= 3n² - n + 1
Hence, the term of the given quadratic sequence is found to be 3n² - n + 1 using the principle of mathematical induction.
Learn more about Principle of mathematical induction at:
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Answer:
and
Step-by-step explanation:
Given:
Equation 1:
Simplifying the above equation by dividing both sides by 100
Equation 2:
Simplifying the above equation by dividing both sides by 400.
Now the system of equation is:
(1a)
(2a)
Solving by elimination
Multiplying equation (2a) with
(2b)
Adding equations (1a) and (2b) in order to eliminate
+
We get
∴
Plugging in equation (2a).
Adding both sides.
∴