Answer:
Maximum height = 16 yards
This occurs 20 yards from the quarterback.
Step-by-step explanation:
Given function: [tex]f(x)=-0.025x^2+x+6[/tex]
To find the maximum (turning point), differentiate the function:
[tex]f('x)=-0.05x+1[/tex]
Set the derivative to zero and solve for [tex]x[/tex]:
[tex]\implies f'(x)=0[/tex]
[tex]\implies -0.05x+1=0[/tex]
[tex]\implies 0.05x=1[/tex]
[tex]\implies x=20[/tex]
Substitute found value of [tex]x[/tex] into the function to find the maximum height:
[tex]f(20)=-0.025(20)^2+(20)+6=16[/tex]
Therefore, the maximum height is 16 yards.
This occurs 20 yards from the quarterback.
The maximum height of the football can be 16 yards and this occurs 20 yards from the quarterback. The concepts of differentiation are used to solve this problem.
Differentiation is a fundamental mathematical concept that is generally used to obtain the rate of change or slopes of a line.
It is given that the height of the football is modeled as the following function:
f(x) = -0.025x² + x + 6
where x is the ball's horizontal distance (in yards) from the quarterback.
To obtain the maximum height of the ball, the equation is needed to be differentiated and set equal to zero as follows:
[tex]\dfrac{d}{dx}f(x) = 0\\\dfrac{d}{dx}(-0.025x^2+x+6)=0\\-0.025\times2x +1 = 0\\-0.05x+1 = 0\\x = \dfrac{1}{0.05}\\x = 20[/tex]
Substitute this value of x in f(x) to find the maximum height,
f(20) = -0.025(20)² + 20 + 6
f(20) = -0.025 × 400 + 26
f(20) = -10 + 26
f(20) = 16
Therefore, the maximum height is 16 yards and this occurs 20 yards from the quarterback.
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The complete question is as follows:
A quarterback tosses a football to a receiver 40 yards downfield. The height of the football, f(x), in feet, can be modeled by f(x) = -0.025x²+x+6, where x is the ball's horizontal distance, in yards, from the quarterback. What is the ball's maximum height and how far from the quarterback does this occur?
Find the area of the circle.
Circle: r = 8.2 cm
Answer:
211.33cm²
Step-by-step explanation:
22/7×8.2²
=211.3257143
=211.33 to 3 d.p
The first user who answer is correct :)
As an estimation we are told £3 is €4.
Convert €44.80 to pounds.
Give your answer rounded to 2 DP.
Answer:
x= 59.73
HOPE IT HELPSSSS
These tables represent a quadratic function with a vertex at (0, 3). What is the average rate of change for the interval from x = 8 to x = 9?
Answer:
-17
Step-by-step explanation:
I think hopes help
HELP ME!!!! PLEASE (I have Points)
Answer:
yes pick .98 l
Step-by-step explanation: .
Solve for d.
d/9 = 27
d = 243
d = 3
d = 36
d = 18
Answer:
d=243
Step-by-step explanation:
[tex] \frac{d}{9} = 27[/tex]
Multiply both sides by 9
D= 243.
To test it:
[tex] \frac{243}{9} = 27[/tex]
Calculator verifys it.
Hope that helped ;)
There are 150 people ina golf club.a) there are 50%more men than women in the golf club. How many mena nd how many women are ther in the golf club.
The percentage computed shows that the number of women is 60 while men are 90.
How to calculate percentage?Let the number of women be represented by x.
Since there are are 50% more men than women in the golf club, the number of men will be:
= x + (50% × c)
= x + 0.5x
= 1.5x
Therefore, 1.5x + x = 150
2.5x = 150
x = 150/2.5
x = 60
Number of women = 60
Number of men = 1.5x = 1.5 × 60 = 90
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(32 divided by 4)+(3x4)
Answer:
20
Step-by-step explanation:
the answer is 20
ASAPPP HELP
PLEASE!!!!!!
Answer:
-36/7
Step-by-step explanation:
-4/7 x 9
-4 x 9/ 7
That’s how I got -36/7
Please help ! This homework is due tn :( Please answer number 3. If u know any other answers to any of the other questions let me know !
Rodney ordered their cards correctly
If you convert all of the values to decimals, you get
0.0345, 0.029, and -0.05, and you can see that they are in order from greatest to least
HELPPPP MEEE PLEASE QUICK 15 points
Answer:
hope this help uhh.. Have a good day.
help me ASAP...
no links
Answer:
2 , 3 , 1 , 4
Step-by-step explanation:
Best way to convert fractions to decimals without a calculator is to look at denominator.
divide 100 by the denominator.
take your answer and multiply the numerator by that number.
put a decimal in front of answer
example : [tex]\frac{7}{20}[/tex]
100 divided by 20 is 5
5 times 7 is 35
place a decimal in front of answer
.35
1. How many high fives will alan get in 30 seconds?
2. The maximum function is ......
The minimum function is .......
The amplitude of the function is .......
The Midline of the function is .......
The Period of the function is ......
3. Using the information given write a Trigonometric function for the situation below (Where x is time and f(x) represents the distance between Jose and Alan)
4. What makes trigonometric functions useful? (don't mention triangles) 5. Why are trigonometric functions periodic?
Answer:
1) [tex]Six[/tex]
Step-by-step explanation:
1) [tex]30\ seconds\div5\ seconds=6\ seconds[/tex] [tex]\left\{every\ 5\ seconds\ one\ time\right\}[/tex]
I am going to work on the other several tonight/tomorrow and will post when I get them done.
help me please, im stuck on this question
Answer:
4.95/1.1 = 4.5 approximately 5 bags
someone help me solve it step by step please
Urgent! Need HELP pls don't scam me and answer all questions
Answer:
450 in²119 ft³surface area of rectangular prism :
2 ( length * width + length * height + width * height )
2 ( 15 * 10 + 15 * 3 + 10 * 3 )
2 ( 225 )
450 in²
volume of triangular prism :
( base * height * length ) ÷ 2
( 7 * 4 * 8.5 ) ÷ 2
119 ft³
let n (AUB)=32n(B)=16and n(ANB)9 find n (A)
Answer:
32
Step-by-step explanation:
n(A∪B)=n(A)+n(B)−n(A∩B)−−−−−−−(1)
Given n(A)= ? we represent with x
n(B)= 16
n(A∪B) = 32
Substituting in equation 1 to get n(A)
32 = n(A) + 9 − 9
⇒n(A) = 32 − 0
n(A) = 32
to confirm this we put the values into the formula below
n(A∪B)=n(A)+n(B)−n(A∩B)−−−−−−−(1)
32 = 32 + 9 - 9
Answer:
n(A) = 25
Step-by-step explanation:
The relation between cardinality of two sets and that of their union and intersection is ...
n(A∪B) = n(A) +n(B) -n(A∩B)
32 = n(A) +16 -9 . . . . . use the given information
25 = n(A) . . . . . . . . . subtract 7
2.
Write an expression to show...
Six times the quotient of thirty-two and
eight, increased by seven
Answer:
[tex]6*\frac{32}{8}+7[/tex]
Step-by-step explanation:
The required expression, six times the quotient of thirty-two and
eight, increased by seven, is given as x = 6(32/8) + 7.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let the expression equal to x,
According to the question,
Six times the quotient of thirty-two = 6(32 /8)
Increased by seven = 6(32 /8) + 7
X = 6(32 /8) + 7
Thus, the required expression, six times the quotient of thirty-two and
eight, increased by seven, is given as x = 6(32/8) + 7.
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May you guys please help me on this one
Answer:
y maximum is at 1 for both the points (4,1) and (-4,1)
Step-by-step explanation:
If you answer my question, you will get points
What is the second smallest prime number
Answer:
3
Step-by-step explanation:
3 is the second smallest prime number.
The second smallest prime number is 3
What are prime numbers:
⇒ numbers that are divisible only by itself and '1'
⇒thus they are numbers that have exactly two factors, itself and one
The first prime number is 2, not 1, because 1 doesn't have two factors. Thus, the second prime number is 3.
Hope that helps!
make a number line and mark the points that represent the following values of x. x<1/3 and x>0?
PLEASE HELP
We can write the two given inequalities as:
0 < x < 1/3
And the graph of it can be seen below.
How to graph the inequalities?
Here we want to graph the inequalities:
x < 1/3
x > 0.
To do it, we can rewrite the inequality as:
0 < x < 1/3.
To graph this, we need to work with a number line. First, we will mark both of the ends of the inequality, that is x = 0 and x = 1/3, both will be graphed with open circles, which means that these points are not solutions. Then, we need to shade the region between these points.
The graph can be seen below.
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Why f([tex]\pi[/tex]) = 0 and f '([tex]\pi[/tex]) = 3
When [tex]\lim_{x \to \\\pi } \frac{f(x)}{x-\pi} = 3[/tex]
Answer:
application of L'Hopital's rule to the presumed indeterminate form yields this conclusion
Step-by-step explanation:
This is a reverse application of L'Hopital's rule for determining the limits involving indeterminate forms.
When the expression evaluated at the limit is 0/0, then L'Hopital's rule tells you the limit can be found from n'/d', where n and d are the numerator and denominator of the original expression, respectively.
We can see that x-π = 0 at x=π, so we assume that f(π) = 0 as well, and the expression n/d = f(x)/(x-π) evaluates to the indeterminate form 0/0.
The derivatives are ...
n' = f'(x)
d' = 1
Then we have the limit as ...
lim{x→π) = n'/d' = f'(π)/1 = 3 ⇒ f'(π) = 3
The conclusion f(π)=0 and f'(π)=3 follows from L'Hopital's Rule.
.pleaseeeee helppppp
Answer:
6
Step-by-step explanation: i just looked it up
Answer:
6gallons
Step-by-step explanation:
there are 48 pints in 6 gallons
Please give brainliest!!!! Thank you
NO LINKS!!!
A security camera in a neighborhood bank is mounted on a wall 9 feet above the floor. What angle of depression should be used if the camera is to be directed to a spot 6 feet above the floor and 12 feet from the wall?
======================================================
Explanation:
One way to draw out the diagram is shown below.
Focus on the right triangle.
tan(angle) = opposite/adjacent
tan(x) = 3/12
tan(x) = 0.25
x = arctan(0.25)
x = 14.03624
Side note: arctangent is the same as inverse tangent denoted as [tex]\tan^{-1}[/tex]
4) height = 18 in; radius = 12 in
=
=
Volume=
Answer:
the answer is 13yd
Step-by-step explanation:
you have to devide and have to mutlpy
What is the median of this data set? {29, 22, 23, 31, 29, 29, 22, 23} Enter your answer in the box.
Answer:
The median is 26
Step-by-step explanation:
A "median" is equivalent to, when the terms are arranged in the proper order, whichever term is in the "middle".
So- first, arrange the terms in ascending order.
[22, 22, 23, 23, 29, 29, 29, 31]
There are an even number- eight- terms in total, so we will take the average of the two "middle" terms.
(29+23)/2; 29 and 23 are the "middle" terms, and there are two of them.
(52)/2 = 26
Therefore, the median is 26.
I hope this helped! :)
Answer:
The answer is 26 hope this helps:DD
Step-by-step explanation:
Answer for: K12 5.03 Quiz: Median
What decimal place does the digit "2" occupy in the number 432,079?
hurry pleaseee i need help
Answer: Thousand
The 4 is in the hundred thousand
The 3 is in the ten thousand
The 2 is in the thousand
The 0 is in the hundred
The 7 is in the tens
The 9 is in the ones
fast help me please and thank you
Answer:
c
Step-by-step explanation:
-3-- or just + -3 * -1 since xy are not separated by anything so its multiplication
I need someone to find the answer this question involves mathematics and paper
no links that you
Answer:
[A] 3 1/2
Step-by-step explanation:
[tex]\mathrm{Given}[/tex]
[tex]4\frac{5}{8}-1\frac{1}{8}[/tex]
[tex]\mathrm{Subtract\;Whole\;numbers}[/tex]
[tex]4-1=3[/tex]
[tex]\mathrm{Combine\;fractions}[/tex]
[tex]\frac{5}{8}-\frac{1}{8}=\frac{4}{8}=\frac{1}{2}[/tex]
[tex]=3+\frac{1}{2}[/tex]
[tex]=3\frac{1}{2}[/tex]
Hence, the answer is [A] 3 1/2
~Lenvy~
Rewrite in simplest terms: -8(-2a+4a-8)-7a
Answer:
-23a + 64
Step-by-step explanation:
-8(-2a + 4a - 8) - 7a
First combine like terms
-8(2a - 8) - 7a
Then distribute
-16a + 64 -7a
Combine like terms
-23a + 64
Vocabulary Use a vocabulary word to complete the sentence.
An__________ fraction names the
same region, part of a set, or part of a segment.