during a softball game kay hit a fly ball the function f(x) = -16t^2 + 64t + 4 describes the height of the softball in feet. make a table of values for the function and then graph it.
Answers
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:
[tex]f(t)=-16t^{2}+64t+4[/tex]
Where,
[tex]a=-16\\b=64\\c=4[/tex]
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:
[tex]f(t)=-16t^{2}+64t+4\\0=-16t^{2}+64t+4\\-16t^{2}+64t+4=0[/tex]
Using the quadratic equation:
[tex]\frac{-b+-\sqrt{b^{2}-4ac } }{2a}=\frac{-64+-\sqrt{64^{2}-4*-16*4} }{2*-16}\\\\\frac{-64+-\sqrt{64^{2}-4*-16*4} }{2*-16}=\frac{-64+-\sqrt{4096+256} }{-32}\\\\\frac{-64+-\sqrt{4096+256} }{-32}=\frac{-64+-(65.96) }{-32}\\\\t1=\frac{-64+(65.96) }{-32}=-0.06\\\\t2=\frac{-64-(65.96) }{-32}=4.0615[/tex]
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:
[tex]f(0)=-16(0)^{2}+64(0)+4=4\\\\f(1)=-16(1)^{2}+64(1)+4=52\\\\f(2)=-16(2)^{2}+64(2)+4=68\\\\f(3)=-16(3)^{2}+64(3)+4=52\\\\f(4.061)=-16(4.0615)^{2}+64(4.0615)+4=0.0034=0[/tex]
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!
Related Questions
What are these in function form
Answers
QUESTION 4.
The given function is [tex]f(x)=48x^2-32x[/tex].
The highest common factor is [tex]16x[/tex].
We factor to obtain;
[tex]f(x)=16x(3x-2)[/tex]
QUESTION 5
The given function is
[tex]g(x)=20x^2-8x[/tex]
The highest common factor is 4x.
We factor to obtain;
[tex]g(x)=4x(5x-2)[/tex]
QUESTION 6.
The given function is [tex]h(x)=42x^3-35x^2[/tex].
The highest common factor is 7x.
We factor to obtain;
[tex]h(x)=7x^2(6x-5)[/tex]
QUICKLY PLEASE! OFFERING 70 PTS AND WILL VOTE BRAINLIEST!
Complete the inequality statement. 14 ft ____ 4 1/2 yd.
Answers
ok if i am right their are 0.3333 yards in a foot so if their is 14 feet it would be 4.66667
so your answer would go to the 4 1/2
Answer:
14 ft > 4 1/2 yd.
Step-by-step explanation:
1 yard = 3 ft
so
4 1/2 yard = 4.5 x 3 = 13.5 ft so it's less then 14 ft or 14 ft is greater than 13.5 ft
answer
14 ft > 4 1/2 yd.
Is 8in, 15in, 17in a right triangle
Answers
[tex] {8}^{2} + {15}^{2} = 64 + 225 = 289 \\ {17}^{2} = 289 \\ \Rightarrow {8}^{2} + {15}^{2} = {17}^{2} \\ \Rightarrow A \: right \: triangle[/tex]
Answer:Yes
Step-by-step explanation:
a^2 + b^2 = c^2
C is the hypotenuse which is the longest side, b is the second longest and a is the shortest one
What is the distance from (-5,1) to (3,0)
Sqrt63, sqrt65 sqry67 sqrt69?
Answers
[tex] \sqrt{65} [/tex]
EXPLANATION
We were given the points,
(-5,1) and (3,0).
We use the distance formula to obtain;
[tex]d = \sqrt{ {(x_2-x_1)}^{2} + {(y_2-y_1)}^{2} } [/tex]
Let [tex](x_1,y_1)=(-5,1)[/tex]
and [tex](x_2,y_2)=(3,0)[/tex]
We substitute these values to get,
[tex]d = \sqrt{ {(3 - - 5)}^{2} + {(0 - 1)}^{2} } [/tex]
Simplify
[tex]d = \sqrt{ {(8)}^{2} + {( - 1)}^{2} } [/tex]
[tex]d = \sqrt{ 64 + 1} [/tex]
[tex]d = \sqrt{65} [/tex]
How do you calculate the area of a circle. Area of a circle is equal to the times
Answers
Answer:
Radius Squared
Step-by-step explanation:
Following answer is Pi
The area of a circle is π times the square of its radius.
What is a circle?A circle is a locus of a point in a plane such that its distance from a fixed point always remains constant. This fixed point is called the centre of the circle while the distance between the centre and the moving point is called the radius of the circle.
The area of a circle is given by [tex]A=\pi r^{2}[/tex]
Where [tex]\pi[/tex] is an irrational number with a value of 3.14159...... and r is the radius of the circle.
So, the area of a circle is π times the square of its radius.
Hence, the area of a circle is π times the square of its radius.
To get more about circle visit:
https://brainly.com/question/24375372
How far will a freight train travel in 3 hours at an average speed of 48 miles per hour?
Answers
Answer:
48 X 3= 144 miles
Step-by-step explanation:
Answer:
144 miles
Step-by-step explanation:
First, let's use the distance formula which is distance = rate*time.
We know the rate is 48 miles and the time is 3 hours so if you were to plug it in to the formula you'd get distance = 48*3.
When you multiply 48 by 3 you get 144 which will be the distance.
what is 3097.48 rounded to the nearest whole?
Answers
3097 is the value you get when rounded off to nearest whole number
Can I get help pleass
Answers
f(5) is basically another way of saying x = 5, so we can plug 5 as x into the equation.
3(5) + 2
The answer is D. 17
Answer:
f(5) is basically another way of saying x = 5, so we can plug 5 as x into the equation.
3(5) + 2
The answer is D. 17
Step-by-step explanation:
If f(x)=2x to the second power what is f(x) when x=3
Answers
➷ Just substitute 3 in:
2(3)^2 = 18
It would be 18
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
36
Step-by-step explanation:
2*3
6^2
6*6 = 36
A jogger runs 4 miles on Monday, 5 miles on Tuesday, 3 miles on Wednesday, and 5 miles on Thursday. He doesn’t run on Friday. How many miles did he run in all
Answers
[tex]\huge\boxed{\text{$17$ miles}}[/tex]
This is a fairly simple problem. Just add all of the miles together:
[tex]\begin{array}{c}4+5+3+5\\9+8\\\boxed{17}\end{array}[/tex]
Answer:
17 miles in all.
Step-by-step explanation:
4+5+3+5=17
A number of students go on a coach trip. The cost of hiring the coach is £180. The school pays 80% of this cost. The students pay the rest of the cost. Each students pays £1.50. Work out the number of students on the coach trip.
Answers
Answer:
24
Step-by-step explanation:
the school will pay: 180 × (80÷100)
= 144
the remaining amount is: 180 - 144
= 36
if each student is paying 1.50 then no. of students is equal to: 36÷1.5
= 24
Can someone please help me with these two questions
Answers
I can't read number 15, but number 16 is C
Which answer represents the domain of the logarithmic function given below? F(x) = log8x
a. x 0
b. x < 0
c. x > 0
d. All real number
ASAP !!!!
Answers
Answer:
C. [tex]x>0[/tex]
Step-by-step explanation:
Given: [tex]f(x)=log(8x)[/tex]
To find the domain of a logarithmic function, we need to take the argument, 8x, and set it greater to zero. This is because an argument of a logarithmic function cannot be zero or negative.
[tex]8x>0[/tex]
[tex]x>0[/tex]
So since x is greater than zero, we have just found out our domain:
Interval Notation: (0, ∞)
Set Notation: {[tex]x|x>0[/tex]}
The domain of the logarithmic function is,
⇒ x > 0
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that:
The function is,
⇒ F (x) = log₈ x
Now, To find the domain of a logarithmic function, we need to take the term, 8x, and set it greater to zero.
This is because an argument of a logarithmic function cannot be zero or negative.
Hence, We get;
8x > 0
x > 0
Thus, The domain of the logarithmic function is,
⇒ x > 0
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ7
PLS HELP ASAP. IM TIMED
Answers
Answer:
Choice 3
Step-by-step explanation:
Using V = πr^2 h
Choice 1. π2^2x6 = 75.4
Choice 2. π2.5^2x5 = 98.17
Choice 3. π3^2x4 = 113.1
Choice 4. π3.2^2x3 = 96.51
slope intercept equation for (0,-4) and (4,1)
Answers
Answer:
y = (5/4)x - 4
Step-by-step explanation:
As we move from (0, -4) to (4, 1), x increases by 4 and y increases by 5.
Thus, the slope of the line segment connecting these two points is
m = rise / run = 5/4.
Subbing these knowns into the point-slope formula for the equation of a straight line, we get:
y - 1 = (5/4)(x - 4), or
y = (5/4)x - 5 + 1, or
y = (5/4)x - 4
Let's check this out. Determine whether or not (0, -4) satisfies the equation:
-4 = (5/4)(0) - 4
Yes, this is true; the equation is correct.
Simplify the expression given below x^2+x-2/x^3-x^2+2x-2
Answers
Answer:
The simplest form is [tex]\frac{x+2}{x^2+2}[/tex]
Explanation:
The given is: [tex]\frac{x^2 + x-2}{x^3-x^2+2x+2}[/tex]
1- For the numerator:
[tex]x^2+x-2[/tex] can be factorized to give (x-1)(x+2)
2- For the denominator:
[tex]x^3-x^2+2x-2[/tex]
We will factor this using grouping
Take [tex]x^2[/tex] as a common factor from the first two terms and [tex]2[/tex] as a common factor from the last two terms
This will give us:
[tex]x^3-x^2+2x-2[/tex] [tex]=x^2(x-1) + 2(x-1)[/tex]
Now, take (x-1) as a common factor:
[tex]x^3-x^2+2x-2[/tex] = (x-1)(x²+2)
3- Finally, getting the simplest form:
[tex]\frac{x^2+x-2}{x^3-x^2+2x-2}=\frac{(x-1)(x+2)}{(x-1)(x^2+2)}=\frac{x+2}{x^2+2}[/tex]
Hope this helps :)
The solution is [tex]\frac{x+2}{x^2+2}[/tex]
Step-by-step explanation:See the image attached
The attic shown is a triangular prism. Insulation will be placed inside the walls, not including the floor. Find the surface area that will be covered with insulation
Answers
Answer:
[tex]1,125\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the triangular prism that will be covered with insulation is equal to the area of the two triangular faces plus the two lateral rectangular faces
so
[tex]SA=2[\frac{1}{2}(15)(15)]+2[(30)(15)]= 1,125\ ft^{2}[/tex]
Colin and Brian were playing darts. Colin scored 141. Brian scored 154 more than Colin. What was their combined score
Answers
Given:
Brian scored 154 more than Colin
Colin’s score=141
Let Brian’s score be x
x= Colin’s score+ 154
x= 141 + 154
x=295
Brian’s score=x=295
Combined score= Brian’s +Colin’s
Combined score= 436
They have a combined score of 436 points
Data;
Colin's score = 141Brain = 154 + 141 EquationLet's write an equation showing Brain's score
[tex]x = 141+ 154\\x = 295[/tex]
Brain's score is equal to 295 points.
The sum of their combined score would be
Collin + Brain
[tex]141+295=436[/tex]
They have a combined score of 436 points.
Learn more on word problem here;
https://brainly.com/question/13818690
plz help!! 2 questions 15 points
Answers
Question 1: Both are solutions.
Question 2: (4, 0)
Here ya go. This highlights the solution for you along with the work. Let me know if you have questions.
Define a variable and write an expression for the phrase.
6 minus a number
6n
6/n
n/6
6 – n
Answers
Answer:
6-n
Step-by-step explanation:
it is subtracting a number from 6
I hope this helps!
6-n because n is equivalent to a number
Which number equals (3)^-3
A)-27
B)-9
C)-1/27
D)1/27
Answers
3 to a negative 3 would be 1/3^3 and then simplify to 1/27 so your answer is D
I hope I helped♥️♥️
The vertex form of the equation of
a parabola is y = 2(x +4^2 - 7.What is the standard form of the equation?
Answers
Answer:
The standard form of the equation is y = 2x^2 + 16x + 25
Step-by-step explanation:
To find the standard form, first square the parenthesis.
y = 2(x + 4)^2 - 7
y = 2(x^2 + -8x + 16) - 7
Now distribute the 2
y = 2(x^2 + 8x + 16) - 7
y = 2x^2 + 16x + 32 - 7
Now combine like terms
y = 2x^2 + 16x + 32 - 7
y = 2x^2 + 16x + 25
Answer:
y = 2x^2 + 16x + 25
I need help, please
Answers
Answer:
Top- 23 square cm
Bottom- 172.5 square m
Step-by-step explanation:
Let me know if you need an explanation
A sticker is in the shape of a trapezoid the height is 3 centimeters and the base are 2.5 centimeters and 5.5 centimeters what is the area of the sticker
Answers
An 8-car Ferris wheel is shaped like a regular octagon. Does the Ferris wheel have rotational symmetry?
Answers
Answer:
yes
Step-by-step explanation:
plz give me brainliestttt
the price c of a used car plus 8% sales tax
Answers
Answer:
1.08c or c + 0.08c
Step-by-step explanation:
The price of any used car plus 8% tax can be found by writing an expression. You can write an expression using a variable c where c is the price of the car. You will pay the 100% the whole price of the car and add on 8% of the price as tax. This means you pay 100 + 8 = 108% of the price c. This is 1.08c. Or you can also write it as c + 0.08c.
Triangle ABC
is similar to
triangle DEF
. The length of
AC
¯
¯
¯
¯
¯
is 12 cm. The length of
BC
¯
¯
¯
¯
¯
is 18 cm. The length of
DF
¯
¯
¯
¯
¯
is 10 cm.
What is the length of
EF
¯
¯
¯
¯
¯
?
Answers
Answer:
15 cm
Step-by-step explanation:
Similar triangles are triangles which have the same shape but not the same size. This means their angle measures are equal but their side lengths are not instead they are proportional. To solve, we will set up a proportion and solve.
A proportion is two equal ratios set equal to each other. We form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). Out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:
[tex]\frac{BC}{EF} =\frac{AC}{DF}[/tex].
[tex]\frac{18}{x}=\frac{12}{10}[/tex]
To solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.
[tex]\frac{18}{x}=\frac{12}{10}\\ 18*10 = x*12 \\ 180 = 12x \\ 15 = x[/tex]
Daleton has 7 bills, all tens and twenties, that total $100 in value. How many of each bill does he have?
Answers
Answer:
two $20 and five $10
He has three $20 and four $10. Hope this helps!
Ella completed the division problem below.
Answers
Answer:
B. She multiplied the dividend by 100 instead of 10.
Step-by-step explanation:
Ella had to divide[tex]1.848[/tex] by [tex]0.6[/tex]. To make it easier to divide, she thought of multiplying both the dividend and the divisor by 10.
Ella multiplied the divisor by 10 but mistakenly she multiplied the dividend by 100 instead of 10.
So her division problem changed totally.
Therefore, the correct answer option is B. She multiplied the dividend by 100 instead of 10.
Easy Question! The first answer gets brainliest!
Solve for x: 2 over 3 (x − 4) = 2x.
2
−2
−8
−4
Answers
Step-by-step explanation:
1 1/3x=-8/3
Answer:
x=−2 is the answer
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
2/3(x - 4) = 2x
(2/3) (x) + (2/3) (-4) = 2x Distributed
2x/3 + -8/3 = 2x
Step 2: Subtract 2x from both sides.
2x/3 + -8/3 = 2x
(2x/3) (-2x/1) + -8/3 =0
-4x/3 + -8/3 = 0
Step 3: Add 8/3 to both sides.
-4x/3 = 8/3
Step 4: Multiply both sides by 3/(-4).
(3/-4) (-4x/3) = ( 3/-4) (8/3)
X= -2 because 3 x 8= 24 and -4 x 3 = -12
24 Divided by -12 give -2
Hopes this helps!