Please Help Me !!!! Its A Math Question!! The path of a ball being thrown off a building can be modeled by the equation y= -16t^2+64t+80
How long does it take to get to its maximum height?
What is its maximum height?
How long does it take to hit the ground?
What is an appropriate domain and range for this function?
What does the 80 in the equation represent?
Answers
Answer: Also can i have brainliest?
The ball will hit the ground 5 seconds after being thrown.
Step-by-step explanation:
The correct function is: h(t)= -16t^2+64t+80
You can rewrite the Quadratic function given in the exercise with making h(t)=0. Then this is:
0= -16t^2+64t+80
Now you can simplify the equation dividing both sides by -16. So you get:
0= t^2-4t-5
To find the solution of the Quadratic equation, you can factor it. In order to do this, it is necessary to find two numbers whose sum is -4 and whose product is -5. These number would be -5 and 1.
Therefore, you get this result:
0= (t-5) (t+1)
t1=5
t2=-1
Since the time cannot be negative, you can conclude that the ball will hit the ground 5 seconds after being thrown.
For the path of a ball being thrown maximum height is 144 units, time taken to reach maximum height is 2 units and time, it take to hit the ground is 5 units.
What is projectile motion?Projectile motion is the motion of the body, when it is thrown in the air taking the action of gravity on it.
The path of a ball being thrown off a building can be modeled by the equation
[tex]y= -16t^2+64t+80[/tex]
Time taken to reach maximum height-Comparing this equation, with standard form of quadratic equation, we get, a=-16, b=64 and c=80.
Thus, the maximum height time can be given as,
[tex]t=-\dfrac{b}{2a}\\t=-\dfrac{64}{2(-16)}\\t=2\rm sec[/tex]
Thus, the time taken to reach maximum height is 2 seconds.
The maximum height-Again by the equation,
[tex]y= -16t^2+64t+80[/tex]
As it reaches maximum height after the 2 seconds. Therefore,
[tex]y_{max}= -16(2)^2+64(2)+80\\y_{max}= 144\rm[/tex]
Time, it take to hit the ground-This can be find out with the following formula,
[tex]t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\t=\dfrac{-64\pm\sqrt{64^2-4(-16)(80)}}{2(-16)}\\t=\dfrac{-64\pm96}{-32}\\[/tex]
Taking negative sign,
[tex]t=\dfrac{-64-96}{-32}=5\\[/tex]
Taking positive sign,
[tex]t=\dfrac{-64+96}{-32}=-1\\[/tex]
Thus the time, it take to hit the ground is 5 units.
The 80 in the equation represent-80 is the constant coefficient of the equation, which represent the height in the feet.
Hence, for the path of a ball being thrown maximum height is 144 units, time taken to reach maximum height is 2 units and time, it take to hit the ground is 5 units.
Learn more about the projectile motion here;
https://brainly.com/question/24216590
Related Questions
Find the measure of x
Answers
Answer:
x=3.24
Step-by-step explanation:
cos(29)=x/3.7
x=3.7 cos(29)
x=3.24
Hope it helps!
help plssssssssssssssssss
Answers
Answer:
28.26 units³
Step-by-step explanation:
gi solved kopo yan
Find the volume of a sphere, whose diameter is 8 mm.(Take n = 3.14) (Round your answer to the nearest tenth).
Answers
[tex] \\ [/tex]
Diameter sphere = 8mm[tex]\small \pi = 3.14[/tex][tex] \\ [/tex]
To find:-Volume of sphere[tex] \\ [/tex]
Solution:To find volume of sphere first we have to convert Diameter into radius .
Diameter = 2 radius
So:-
⇢Diameter = 2 radius
[tex]\\[/tex]
⇢Radius = Diameter/2
[tex]\\[/tex]
⇢Radius = 8/2
[tex]\\[/tex]
⇢Radius = 2 × 2 × 2/2
[tex]\\[/tex]
⇢Radius = 2 × 2/1
[tex]\\[/tex]
⇢Radius = 4/1
[tex]\\[/tex]
⇢Radius = 4 mm.
[tex]\\[/tex]
Now Finally Let's find volume of sphere.
We know:-
[tex]\\[/tex]
[tex]\star\boxed{\rm Volume~of~sphere=\frac{4}{3}\pi r^3}[/tex]
so:-
[tex]\\\\[/tex]
[tex]\dashrightarrow \sf Volume~of~sphere=\frac{4}{3}\times 3.14 \times 4^3\\[/tex]
[tex]\\\\[/tex]
[tex]\dashrightarrow \sf Volume~of~sphere=\dfrac{4}{3}\times \dfrac{314}{100} \times 4^3\\[/tex]
[tex]\\\\[/tex]
[tex]\dashrightarrow \sf Volume~of~sphere=\dfrac{4}{3}\times \dfrac{314}{100} \times 4\times 4\times 4\\[/tex]
[tex]\\\\[/tex]
[tex]\dashrightarrow \sf Volume~of~sphere=\dfrac{4}{3}\times \dfrac{314}{100} \times 64\\[/tex]
[tex]\\\\[/tex]
[tex]\dashrightarrow \sf Volume~of~sphere=1.33\times \dfrac{314}{100} \times 64\\[/tex]
[tex]\\\\[/tex]
[tex]\dashrightarrow \sf Volume~of~sphere= \dfrac{1.33\times314 \times 64}{100}\\[/tex]
[tex]\\\\[/tex]
[tex]\dashrightarrow \sf Volume~of~sphere= \dfrac{26,727.68}{100}\\[/tex]
[tex]\\\\[/tex]
[tex]\dashrightarrow \sf Volume~of~sphere=26,7.28 (approx)\\[/tex]
[tex]\\\\[/tex]
[tex] \therefore \underline{ \textbf{ \textsf{Volume~of~sphere = \red{26,7.28(approx)}}}}[/tex]
(6,5) and (3, 7.5)
slope:
Answers
Step-by-step explanation:
Slope formula:
[tex] \frac{y2}{x2} - \frac{y1}{x1} = m[/tex]
m = slope
Substitute the points into the formula format:
[tex] \frac{7.5}{3} - \frac{5}{6} = m[/tex]
Solve:
[tex] \frac{ 7.5}{3} - \frac{5}{6} = \frac{2.5}{ - 3} [/tex]
[tex] \frac{ 2.5}{ - 3} = - \frac{5}{6} [/tex]
The slope equals -5/6.
How to Calculate discount rate
Answers
Answer:
[tex]\frac{i\times d}{100}[/tex]
Step-by-step explanation:
To calculate the discount, we multiply the initial amount (i) to the discount (d) and then divide that answer by 100. After we find that answer we then subtract it from the initial price.
For example:
A computer costs $695 and it has a 7% discount. Calculate the total costs of the computer after the 7% discount.
[tex]\frac{695\times7}{100} =695\times7=4865\div100=48.65[/tex]
[tex]695-48.65=646.35[/tex]
[tex]c=646.35[/tex]
The computer (after a 7% discount) costs "$646.35 dollars."
Hope this helps.
In-n-Out sells their cheeseburger for 4.50 but they charge .50 for extra patties. Carls Jr. sells a cheeseburger for 4.25 and will charge .75 cents for an extra patty. When will the burgers cost the same amount? How many extra patties do they have to order? Solve using tables.
Answers
Answer:
just add 0.75 on the bottom
Step-by-step explanation:
The answer need help fast please
Answers
Answer:
D.) Equation (4)
Step-by-step explanation:
1. y= (2)+6 =8
2. y=2(2)+4 =8
3. y= 3(2)+2 =8
4. y=5(2)-4 =6
x y
−1 −10
3 14
y= ?x + (?)
Answers
Answer:
12. 5
11.
10
10
15. 7
14. 11
2
=
16
16
18. 3
+
11
17
3
4
co
loo
8
Step-by-step explanation:
12. 5
11.
10
10
15. 7
14. 11
2
=
16
16
How do you do this problem and show work
Answers
Answer
the answer is 16 but i cant tell if there is anything after that is there?
Step-by-step explanation:
Answer:
1/x^8
Step-by-step explanation:
x^3*x^2 = x^5
x*x*x*x*x*x*x = x^7
x^5 / x^7 = 1/x^2
(1 / x^2)^4 = 1^4 / x^2*4 = 1/x^8
ANSWER PLS FREE BRAINLIEST
Answers
Answer:
[tex]x = \frac{-1}{4}[/tex]
Step-by-step explanation:
[tex]\frac{2}{x} = -8[/tex]
[tex]2 = -8x[/tex]
[tex]x = \frac{-2}{8}[/tex]
[tex]x = \frac{-1}{4}[/tex]
Answer:
[tex]\sf x=-\cfrac{1}{4}[/tex]
Step-by-step explanation:
[tex]\sf \cfrac{2}{x}=-8[/tex]
[tex]\sf \cfrac{2}{x}x=-8x[/tex]
[tex]\sf 2=-8x[/tex]
[tex]\sf \cfrac{-8x}{-8}=\cfrac{2}{-8}[/tex]
[tex]\sf x=-\cfrac{1}{4}[/tex]
Joel borrowed 518,000 for 6 years at simple interest to purchase a vehicle. If Joel repaid a
total of $20,953.80, at what rate did he borrow the money?
Answers
Answer:
2.735%
Step-by-step explanation:
The amount due on principal P after t years at rate r is ...
A = P(1 +rt)
Filling in the given values, we can solve for r:
20,953.80 = 18000(1 +6r)
20953.80/18000 -1 = 6r = 0.1641
r = 0.1641/6 = 0.02735 = 2.735%
Joel's interest rate was 2.735%.
100 points for user sweet Jennifer Whenever we observe a distant planet, star or galaxy, we are seeing it as it was hours, centuries or even millennia ago. This is because light travels at a finite speed (the speed of light) and given the large distances in the Universe, we do not see objects as they are now, but as they were when the light was emitted.
Answers
The soccer team is selling bags of popcorn for $3 each and cups of lemonade for $2 each. To make a profit, they must collect a total of more than $120. Solutions can be represented by coordinates (p,c), where p represents the number of bags of popcorn sold and c represents the number of cups of lemonade sold. Is the coordinate (10,45) a solution to the inequality? Explain your reasoning or show your work.
Answers
3x + 2y ≥ 120
you are asking me to confirm whether the below statement is true
10 * 3 + 45 *2 ≥ 120 ?
30 + 90 = 120
120 ≥ 120
its not greater but its equal which means it is a possible solution
Which of these is a service industry?
A. a textile plant
B. an oil refinery
C. an aircraft manufacturer
D. a dry-cleaning store
I think its either c or b but more but not so sure.... help......
Answers
Its D i hope that helped
What is the measure of angle Y in this figure
Y=____ degrees
Answers
Answer:
163
Step-by-step explanation:
What's great about these problems is that when there is a line that is divided by another line, causing 2 angles, the 2 angles must equal 180 degrees. That means the 163-degree angle + either the x or the z angle would equal 180 degrees. The second best part about this is that if it is separated how yours is, with 2 lines, opposite angles are equal. That means that angle x and angle z are equal, as well as the 163 angle is equal to the y angle. Hope this helps with more than just this problem!
The quotient of 10 and a
Answers
Answer:
The answer I believe is 10? Sorry if i am wrong
Step-by-step explanation:
in algebra, if there is a variable without a coefficient, then it just means 1. So a = 1, and 10 ÷ 1 = 10
Emily has some marbles. After Mrs. Kim gave her another 21 marbles, the number of marbles became four times the number of marbles at first. How many marbles does Emily have now?
Answers
Answer:
Emily has 84 marbles now
Step-by-step explanation:
21×4
=84
If 3a+5=12, what is the value of 6a+14?
Answers
Answer:For example, choice A is incorrect because if the value of 10x + 3 were 4, then it would follow that x = 0.1, and the value of 5x + 6 would be 6.5, not 10.
Step-by-step explanation:
The answer is
283a + 5 = 12
subtract 5 from both sides
3a = 7
divide by 3 on both sides to isolate "a"
a = 7/3
Substitute 7/3 for "a" in the second equation
6(7/3) + 14
6 multiplied by 7/3 = 42/3 = 14
14 + 14 = 28
A bag contains 7 yellow marbles and 35 red marbles. If a representative sample contains 2 yellow marbles, then how many red marbles would you expect it to contain? Explain.
Answers
30 maybe, not to sure, sorry if its wrong
im stumped on this question. someone help me plss
Answers
Answer:
One of the answers could be linear
Step-by-step explanation:A linear graph is always a straight line, and this looks to demonstrate that. Sorry if this is incorrect, just my understanding.
How many kilograms is a rice packet that weighs 750 g?
(Please answer quick!)
Answers
Answer:
0.750 kg
Step-by-step explanation:
Hi there ,
As you know 1 kg = 1000g
So when we convert g to kg then we divide the given value of grams by 1000.
So in this case we have 750 grams, changing it we have :
[tex]\frac{750}{1000}[/tex]
Since there are 3 zeroes in 1000 we move the decimal point by 3 places to the left leaving the answer as : 0.750 kg or [tex]\frac{750}{1000}[/tex] kg
Please mark me as brainliest if you found the above answer helpful
Which decimal is less than 2.87? 2.859 C. 2.971 b. 2.8711 d. 2.88 Please select the best answer from the choices provided
Answers
Answer:
Step-by-step explanation:
2.859 is less than the rest
Answer:
2.859 is ur answer.
..............
JADA, DIEGO, AND ELENA EACH USE THE SAME SPINNER THAT HAS FOUR (NOT NECESSARILY EQUAL SIZED) SECTIONS MARKED A, B, C, AND D.
JADA SAYS, "THE PROBABILITY OF SPINNING B IS 0.3 BECAUSE I SPUN 10 TIMES, AND IT LANDED ON B 3 TIMES."
DIEGO SAYS, "THE PROBABILITY OF SPINNING B IS 20% BECAUSE I SPUN 5 TIMES, AND IT LANDED ON B ONCE."
ELENA SAYS, "THE PROBABILITY OF SPINNING B IS 2/7 BECAUSE I SPUN 7 TIMES, AND IT LANDED ON B TWICE."
Based on their methods, which probability do you think is most accurate? Explain your reasoning.
Answers
Of the following transformations, which of the following is not one that maintains congruence?
a. A dilation with a scale factor of 0.5
b. A reflection over the x-axis
c. A translation 1 unit left
d. A dilation with a scale factor of 1
Answers
Answer:
A because its not the one that maintains congruence
Step-by-step explanation:
^^^^^
Find the value of x.
Step by Step
Answers
Answer:
sorryi dont know
Step-by-step explanation:
Complete the function operation.
For the function [tex]\frac{32}{x+3}[/tex], find [tex](g^{-1} * g)(5)[/tex]
Answers
Answer:
5
Step-by-step explanation:
[tex]g(x)=\frac{32}{x+3}\\\\\implies g^{-1}(x)=\frac{32}{x}-3\\\\g^{-1}o \ g=[g(g^{-1}(x))]=\frac{32}{\frac{32}{x}-3+3}=x\\\\\implies (g^{-1}o \ g)(5)=5[/tex]
In the table to the right, the P(0) is blank so we can assume P(O) = 0 What does a probability equal to zero mean?
Answers
Answer:
It means there is no chance this will happen or in other words a 0% chance
Step-by-step explanation:
Bella needs 15 quarters of paint for one wall in her cellar she has 2 1/4 gallons left over from painting the other walls she has another 5 quarts that her neighbor gave her is that enough paint
Answers
0.0455 quarters of paints is not enough to paint the wall. she needs 15 quarters.
She needs 15 quarters of paint for one wall .
She has 2 1 / 4 gallons left over from painting the other walls and she also has another 5 quarts that her neighbour gave her.
Therefore,
Conversion of measurement units4 quarts = 1 gallon
5 quarts = 5 / 4 gallons
Then,
total gallon = 9 / 4 + 5 / 4 = 14 / 4 = 7 / 2 gallons
Therefore,
1 gallons = 0.01301053418982 quarters
7 / 2 gallons = ?
cross multiply
number of quarters = 3.5 × 0.01301053418982
number of quarters = 0.0455 quarters
Therefore, 0.0455 quarters of paints is not enough to paint the wall. she needs 15 quarters.
learn more on algebra here; https://brainly.com/question/821377
(4k3 +3k3) - (5k3 + 2k4)
Answers
Answer:
-2k
Step-by-step explanation:
Answer: You combine like terms
2k^3-2k^4
A plane has traveled 26 miles on a course heading 48º east of north. How far north (x) has the plane traveled at this point, to the nearest tenth of a mile?
Answers
Answer:
17.39
Step-by-step explanation:
48+a = 90
x= 42
sin 42 = x / 26
x = 17.39