A football is thrown into the air from an initial height of 4 feet with an upward velocity of 46 ft/sec. The function h = -16t² + 46t + 4 gives the height after t sec.
whats the vertex?
axis of symmetry?
solutions?
2 other points?
and i know the balls max height is 37.06
Answers
Answer:
Vertex = (1.4375, 37.0625)
Axis of symmetry: t = 1.4375
x-intercept: (2.9595, 0)
y-intercept: (0, 4)
another point: (2, 32)
Step-by-step explanation:
Given function: [tex]h(t)=-16t^2+46t+4[/tex]
(where h is the height in feet and t is the time in seconds)
The vertex is the turning point of the parabola.
To find the x-value of the turning point, differentiate the function:
[tex]\implies h'(t)=-32t+46[/tex]
Set it to zero:
[tex]\implies h'(t)=0[/tex]
[tex]\implies -32t+46=0[/tex]
Solve for t:
[tex]\implies 32t=46[/tex]
[tex]\implies t=\dfrac{23}{16}[/tex]
Input found value of t into the function to find the y-value of the vertex:
[tex]\implies h(\frac{23}{16})=-16(\frac{23}{16})^2+46(\frac{23}{16})+4=\dfrac{593}{16}[/tex]
Therefore, the vertex is [tex]\left(\dfrac{23}{16},\dfrac{593}{16}\right)[/tex] or (1.4375, 37.0625) in decimal form.
The axis of symmetry is the x-value of the vertex.
[tex]\implies \textsf{Axis\:of\:Symmetry}:t=\dfrac{23}{16}=1.4375[/tex]
To find the x-intercepts, use the quadratic formula.
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\implies t=\dfrac{-46 \pm \sqrt{46^2-4(-16)(4)} }{2(-16)}[/tex]
[tex]\implies t=\dfrac{-46 \pm \sqrt{2372}}{-32}[/tex]
[tex]\implies t=\dfrac{23 \pm \sqrt{593}}{16}[/tex]
As time is positive,
[tex]\implies t=\dfrac{23 + \sqrt{593}}{16}=2.959474458...\:\sf s\quad only[/tex]
The y-intercept is when t = 0:
[tex]h(0)=-16(0)^2+46(0)+4=4[/tex]
So the curve intercepts the y-axis at (0, 4)
Because of the modelling of the function, there will be a restricted domain: 0 ≤ t ≤ 2.9595
Therefore, to find another point, input a value in the domain into the function and solve:
[tex]t=2 \implies h(2)=-16(2)^2+46(2)+4=32[/tex]
⇒ (2, 32)
Related Questions
Which is the value of `3/4 + 1/2 - 1/3`?
A
`2/3`
B
`7/12`
C
`11/12`
D
`3/3`
Answers
Hey there!
3/4 + 1/2 - 1/3
= 5/4 - 1/3
≈ 15/12 - 4/12
≈ 15 - 4 / 12 - 0
= 11/12
Therefore, your answer is: 11/12
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Nick wanted to determine the length of one blade of a windmill. He stood at a point on the ground 440 feet from the windmill's base. Using surveyor's tools, Nick measured the angle between the ground and the highest point reached by the top blade and found it was 38.8°. He measured the angle between the ground and the lowest point of the top blade and found it was 30°. Determine and state a blade's length, x, to the nearest foot.
Answers
Using the slope concept, it is found that rhe blade's length is of 90 feet.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem, the horizontal change is of 440 feet.
At the highest point, the angle is of 38º, hence:
[tex]\tan{38^\circ} = \frac{h_1}{440}[/tex]
[tex]h_1 = 440\tan{38^\circ}[/tex]
[tex]h_1 = 344[/tex]
At the lowetst point, the angle is of 30, hence:
[tex]\tan{30^\circ} = \frac{h_2}{440}[/tex]
[tex]h_2 = 440\tan{30^\circ}[/tex]
[tex]h_2 = 254[/tex]
Hence, the difference is:
[tex]h_2 - h_1 = 344 - 254 = 90[/tex]
The blade's length is of 90 feet.
More can be learned about the slope concept at https://brainly.com/question/18090623
Skylar made 25% of her free throws over the season. If she shot 200 free throws, how many did she make?
Answers
Answer:
50 Free Throws
Step-by-step explanation:
Answer: 50 Free Throws
25% = 0.25
0.25*200=50
skylar sucks at basketball
what are the formula to find the vertex of hexagon
Answers
Answer:
the answer is 6
Step-by-step explanation:
there are 6 side you times the 6 with the area of an equilateral triangle so the area of hexagon = 6
PLEASE HELP I WILL GIVE YOU BRAINLEY CROWN
The volume of a rectangular prism is 162 cm
If the height is doubled, what is the new volume?
Answers
Answer:
1296 cm³
Step-by-step explanation:
Given
Volume of original rectangular, V = 162 cm³V = lwhSolving
Here it is mentioned the height is doubledTherefore, h is now 2hSubstitute in the volume formulaV = lw(2h)³V = 8 x lwhV = 8 x 162V = 1296 cm³Answer:
1296 cm³
Original Rectangle:
height : H
volume : 162 cm³
New Rectangle:
height : 2H
volume : x (let it be x)
Solve:
[tex]\rightarrow \sf (\dfrac{H}{2H})^3 = \dfrac{162}{x}[/tex]
[tex]\rightarrow \sf (\dfrac{1}{2})^3 = \dfrac{162}{x}[/tex]
[tex]\rightarrow \sf x = 1296[/tex]
Find a real life example of an inequality and explain why it represents an inequality
Answers
Answer:
Roads have speed limits
Step-by-step explanation:
Roads have speed limits. This is an inequality because it doesn't reflect an exact number, but rather a restriction on what is permissible or possible.
× 10^-3 is 2,000 times greater than 1. 9 × 10-6. It is also times greater than 9. 5 × 10^-4
Answers
Answer:
1.9 × 10^-6.
Step-by-step explanation:
Jesse planted several marigold seeds in his garden and, several weeks later, measured and recorded the height (in centimeters) of each plant. The data is organized in the frequency table shown. Of those planted, how many marigolds are less than 4 cm or more than 10 cm long?
A.) 1
B.) 5
C.) 2
D.) 3
Answers
Answer:
D. 3
Step-by-step explanation:
Look at how many are less than 4cm (1) and how many are more than 10 (2) and add them together (1+2=3)
5/6-1/8 Solve by finding a common denominator
A)30/48
B)34/48
C)38/48
D)42/48
Answers
Answer:
B) 34/48
Step-by-step explanation:
The easiest common denominator to find is the product of the denominators you have.
__
The difference is ...
[tex]\dfrac{5}{6}-\dfrac{1}{8}=\dfrac{5}{6}\cdot\dfrac{8}{8}-\dfrac{1}{8}\cdot\dfrac{6}{6}\\\\=\dfrac{40-6}{48}=\boxed{\dfrac{34}{48}}[/tex]
__
Additional comment
The difference numerator and denominator have a common factor of 2, so can be reduced to 17/24. The denominator 24 could have been used as the common denominator from the start.
5/6 -1/8 = 20/24 -3/24 = 17/24 . . . . reduced result
__
Using the least common denominator does not always result in a reduced sum or difference. If some other denominator is used (as here), then you can be assured that the result will need to be reduced to get to lowest terms.
pls help me thank you
Answers
Answer:
A no. is correct one
Step-by-step explanation:
Hope it will help you. and please mark me brilliant
Answer:
A
Step-by-step explanation:
12x+6x=90deg
90deg+90deg=180deg
A bag with 12 marbles has 5 red marbles, 3 yellow marbles, and 4 blue marbles. A marble is chosen from the bag at random. What is the probability that it is red?
Write your answer as a fraction in the simplest form.
Answers
5 red marbles + 3 yellow marbles + 4 blue marbles = 12 total marbles.
And there are 5 RED marbles in the special bag . . .
So the probability of a red marble would be 5/12. The reason why is because there are 5 TOTAL RED marbles and there are 12 TOTAL marbles.
Hope this helps!
Hello, i am currently having a hard time in school for a while if anybody can help me out it would be greatly appreciated
Answers
Answer:
36 m
Step-by-step explanation:
PT = x
This is True because of similar sides [tex]\frac{8}{x} = \frac{7}{14}[/tex]
solve for x to get PT and you get 16
Then to find the perimeter you would do P = PR + PR + PT = 6m + 14m + 16m = 36m
Answer:
36 m
Step-by-step explanation:
Line QS = (1/2) Line PT
8 m = (1/2) Line PT
Line PT = 16 m
Perimeter = 3 + 3 + 7 + 7 + 16
P = 36 m
I hope this helps!
A graphics company charges $50 per hour to create a logo plus $250 for the ownership rights of the logo. a private contractor charges $75 per hour to develop a logo plus a $100 supply fee. which equation can be solved to determine x, the number of hours after which the costs would be the same? 50x 250 = 75x 100 50 250x = 75 100x 50x 100 = 75x 250 50 100x = 75 250x
Answers
The equation that can be solved to determine x, the number of hours after which the costs would be the same is; 50x + 250 = 75x + 100
How to create Linear Equations?
The general formula for the slope intercept form of an equation is;
y = mx + c
We are told that;
Charge per hour = $50
Ownership rights = $250
Thus, for the first company, total cost is;
y = 50x + 250
For the second company;
Total cost is;
y = 75x + 100
Thus, at same cost, we have;
50x + 250 = 75x + 100
Read more about Linear Equations at; https://brainly.com/question/1884491
Answer:
50x + 250 = 75x + 100
Step-by-step explanation:
I did the test
The local store has 7 containers with 14 apples in each container. If they sell 23 apples, how many apples will they have left?
Answers
Answer: 75 apples they have left
Step-by-step explanation:
7 (14) = 98 apples total
98 - 23 = 75
Annual sales for a fast food restaurant are 650000 and are increasing at a rate of 4% per year. Use an exponential function to find the annual sales after 5 years. What is the equation
Answers
Principal as 650000
Rate = 4% or 0.04%
Time = 5 years
We are adding because as it is exponentially growth
650000(1+0.04)^5
= 790824.39
PLEASE HELP!!!! Find the volume. Round to the nearest tenth, if necessary.
Answers
Answer:
[tex]63cm {}^{3} [/tex]
Step-by-step explanation:
the shape above is a cuboid and volume of a cuboid
= length x breath x height
=length=3cm
breath= 7cm
height= 3cm
volume= (3x7x3)cm =63 cm^3
What is the volume of the solid figure?
Enter your answer in the box.
Solid is made up of 3 cuboids. First cuboid has length as 4 ft, height as 9 ft and width as 3 ft. Remaining 2 cuboids are placed on the right and left side of the 1st cuboid whose length as 1 ft, height as 1 ft and width as 3 ft.
Answers
Answer:
Volume of the solid = 2[1 x 1 x 3] + (4 x 3 x 9) = 114 ft³
Ans: 114 ft³
Step-by-step explanation:
Consider the function f(x) = x2 + 8x +1. Which equation shows function f written in vertex form?
f() = (x + 8)2 +1
f(x) = (x – 4)²+1
f(x) = (x – 8)² – 17
f()= (x +4)2 - 15
Answers
Answer:
4th option
Step-by-step explanation:
f(x) = x² + 8x + 1
using the method of completing the square
add/subtract ( half the coefficient of the x- term )² to x² + 8x
f(x) = x² + 2(4)x + 16 - 16 + 1
= (x + 4)² - 15 ← in vertex form
You roll a 6-sided die.
What is P(5)?
Write your answer as a fraction or whole number.
Submit
Work it out
Not feeling radunt? Th
Answers
Answer:
6*5=30= 30/100
Step-by-step explanation:
we will multiply 6* by 5 and after that we will do it fraction by doing that 30/100
Miguel practiced more than 5 hours for his first soccer game. which inequality represents p, the amount of time Miguel practiced?
Answers
Answer:
P>5hours
Step-by-step explanation:
practice time is > five hours
How many bars would the team need to purchase from each company in order for the total cost to be equal? 6 8 30 40
Answers
Answer:
It's 40
Step-by-step explanation: Fortunately for you I risked my test for you and ended up getting the correct answer of course^0^
Answer:
40
Step-by-step explanation:
Find the mean absolute deviation of the data set: 1,3,7,11,13
Answers
Please help me I am stuck on this problem!!!!
Answers
Step-by-step explanation:
From less value to large value
30 32 33 33 35
Median is the center number = 33
Mean is (30+32+33+33+35)/5 = 32.6
The same value
What is the constant of proportionality?
Answers
Answer: y= 2x
Explanation: The constant of proportionality is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same rate. The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other.
what's the ans?
[tex]\bf 6(x+4)+1=x+5[/tex]
Answers
Answer:
x = -4
Step-by-step explanation:
6 (x + 4) + 1 = x + 5
6x + 24 + 1 = x + 5 (distributive property)
6x + 25 = x + 5
6x + 25 - x = 5
5x + 25 = 5
5x = 5 - 25
5x = -20
x = -20/5
x = -4
Hope it helps ⚜
Answer: x = -4
Step-by-step explanation:
[tex]6\left(x+4\right)+1=x+5[/tex]
[tex]$$Expand the parentheses[/tex]
[tex]6x+25=x+5[/tex]
[tex]\mathrm{Subtract\:}25\mathrm{\:from\:both\:sides}[/tex]
[tex]6x+25-25=x+5-25[/tex]
[tex]$$Simplify[/tex]
[tex]6x=x-20[/tex]
[tex]\mathrm{Subtract\:}x\mathrm{\:from\:both\:sides}[/tex]
[tex]6x-x=x-20-x[/tex]
[tex]$$Simplify[/tex]
[tex]5x=-20[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}5[/tex]
[tex]\frac{5x}{5}=\frac{-20}{5}[/tex]
[tex]$$Simplify[/tex]
[tex]x=-4[/tex]
Which expression is equivalent to side "8"?
2
d
8
3
45
1.
e
5
nv2
n3
O O OO
5
n
2n
Answers
Answer:
n
Step-by-step explanation:
Let d = n.
As both d and 8 are opposed by the same angle (45°) in the right triangle, they are equalTherefore, n = 8What is the completely factored form of x4 8x2 – 9? (x 1)(x – 1)(x 3)(x 3) (x 1) (x minus 1) (x squared 9) (x2 – 1)(x 3)(x – 3) (x 1)(x 1)(x 3)(x 3)
Answers
The complete factor of the polynomial expression is (x² + 9)(x – 1)(x + 1), then the correct option is B.
What is a factorization?It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.
The expression is given as
x⁴ + 8x² – 9
Then by the factorization, we have
x⁴ + 8x² – 9
x⁴ + 9x² – x² – 9
x²(x² + 9) – 1(x² + 9)
(x² + 9)(x² – 1)
(x² + 9)(x – 1)(x + 1)
More about the factorization link is given below.
https://brainly.com/question/6810544
Answer:b
Step-by-step explanation:
on edg 2022
The diagram shows a solid shape.
The shape is a hemisphere on top of a cylinder,
Volume of a sphere = 4/3pir^3
Pressure = force/area
The solid shape is placed on a table. The solid exerts a force of 4 Newtons on a table. The pressure on the table is 100 N/m. The height of the cylinder is 45 cm. Work out the total volume of the solid shape.
Please can someone help explain it.
Answers
Based on given information about pressure from table and geometry of the solid shape, the total volume of the solid shape is approximately 21073.745 cubic centimeters. [tex]\blacksquare[/tex]
How to determine the volume of the solid shape under pressureIn this question we must apply the concepts of pressure (P), in newtons per square meter, cross section area (A), in square meters, and volume (V), in cubic meters, to determine that Let assume that the bottom experiments an uniform pressure due to a reaction force (F), in newtons, from the table, whose formula is described below:
P = F/A = 4 · F /(π · D²) (1)
If we know that F = 4 N and P = 100 N/m², then the diameter of the cylinder is:
[tex]D = 2\cdot \sqrt{\frac{F}{\pi\cdot P} }[/tex]
D ≈ 0.226 m²
And the volume of the solid shape is: (H = 0.45 m)
V = 0.25π · D² · H + (π/12) · D³
V = 0.25π · (0.226 m)² · (0.45 m) + (π/12) · (0.226 m)³
V ≈ 0.021 m³ (21073.745 cm³)
Based on given information about pressure from table and geometry of the solid shape, the total volume of the solid shape is approximately 21073.745 cubic centimeters. [tex]\blacksquare[/tex]
To learn more on pressure, we kindly invite to check this verified question: https://brainly.com/question/356585
in the figure below line x is parallel to line yz find the measure of angle a and the measure of angle b
Answers
Answer:
∠a = 35° ∠b = 65°
Step-by-step explanation:
a = 35 ° ( alternate interior angles )
( the line x is parallel to line yz hence we can consider XY as a transversal)
∠b + 35° + 80° = 180 ° ( angle sum property of triangle)
∠b+ 115° = 180°
∠b= 180 - 115
∠b = 65°
SALE
60% OFF!
The original price of a swing set is $940. How much will Carmen pay if she buys it
during the sale?
Answers
Answer:
Carmen will pay $376.
Step-by-step explanation:
Multiply $940 by 40% because 100% - 60% = 40%:
(40%)(940) = 0.4 * 940 = $376