Answers
a) The maximum height of the ball is 100 feet.
b) The velocity of the ball on its way up is +16 feet per second.
c) The velocity of the ball on its way down is - 16 feet per second.
How to analyze quadratic equations to find the main features of a free fall
A free fall is an uniformly accelerated motion experimented by a particle due to the effects of gravity. The position of the ball (s) in time (t), in seconds, is described by a quadratic equation.
a) First, we find the maximum height reached by the ball:
s(t) = 80 · t - 16 · t²
16 · t² - 80 · t + s(t) = 0
Then, by using the discriminant:
(- 80)² - 4 · 16 · s(t) = 0
64 · s(t) = (- 80)²
s(t) = 100 ft
b) Second, find the function velocity by derivatives:
v(t) = 80 - 32 · t
Third, find the time related to the position s(t) = 96 ft:
s(t) = 80 · t - 16 · t²
100 = 80 · t - 16 · t²
16 · t² - 80 · t + 96 = 0
Then, by quadratic equation:
t = 3 s or t = 2 s.
Fourth, evaluate the function velocity:
v(2) = 80 - 32 · 2
v(2) = 16
v(3) = 80 - 32 · 3
v(3) = - 16
The velocity of the ball when s(t) = 96 ft on its way up is 16 feet per second.
c) The velocity of the ball when s(t) = 96 ft on its way down is - 16 feet per second.
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Related Questions
This is what I need help with
Answers
Answer:no picture
Step-by-step explanation:
Question 7 of 10
Here is a table of values for y = f(x).
X
-2 -1 0 1 2 3
f(x) 5 6
7
Mark the statements that are true.
4
8 9 10 11
5 6
12 13
A. The range for f(x) is all real numbers.
B. f(5) = -2
C. The domain for f(x) is the set (-2,-1, 0, 1, 2, 3, 4, 5, 6).
D. f(-1) = 6
Answers
Option (C) is the correct one and the only true statement is
The domain of the function f(x) is { -2, -1, 0, 1, 2, 3, 4, 5, 6 }.
Given, a table of values for y = f(x)
x -2 -1 0 1 2 3 4 5 6
y 7 8 9 10 11 5 6 12 13
We have to find the correct statements,
as the range of the function f(x) is { 4, 8, 9, 10, 11, 5, 6, 12, 13 }
the image of 5 in the function is 6 i.e. f(5) = 6.
The domain of the function f(x) is { -2, -1, 0, 1, 2, 3, 4, 5, 6 }
the image of -1 in the function is 8 i.e. f(-1) = 8.
Hence, only the option (C) is the correct one and the only true statement is
The domain of the function f(x) is { -2, -1, 0, 1, 2, 3, 4, 5, 6 }.
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QUESTION 1: In the clip, Danny Nguyen is all-in with A 7 against an opponent with A K+. The flop is
5 K 5. After this, the next two cards must both be sevens for Nguyen to win. Compute the probability
of this happening. NOTE: There are three sevens left in the deck and it is no longer a 52 card deck
because the cards shown are removed. Show all calculations in determining your answer
Answers
The probability is 0.00332.
From the given question,
Danny Nguyen has A 7 and opponent has A K+.
The flop is : 5 K 5
As there are two players playing the remaining cards in the deck will be (52 - 2 - 2 - 3 -1(burn)) = 44
For Nguyen to win he needs two of the three 7's left in the deck for turn and river.
For turn we have to select a 7 from the three 7's and for river we have to select a 7 of the remaining two 7's.
So the probability is
P = [tex]\frac{\binom{3}{1}}{\binom{43}{1}}*\frac{\binom{2}{1}}{\binom{41}{1}}[/tex]
P = 0.00332
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What are numbers that have 2,3,4,5,6 as their factors? (under 200)
Answers
Answer:
120, 60, 180
Step-by-step explanation:
Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared.
d²-3d
Answers
The trinomial and binomial form of the incomplete algebraic expression is [tex]d^{2}[/tex] -3d + 9/4 and [tex](d-\frac{3}{2}) ^{2}[/tex]
What is a perfect square expression?A perfect square is a quadratic expression that factors into two identical binomials.
For example, if you multiply these two identical binomials factors:
(x + 2)(x + 2)
to complete the square in the expression [tex]d^{2}[/tex] -3d, we square the half of the coefficient of d which is -3/2
so the expression becomes,
[tex]d^{2}[/tex] -3d + [tex](\frac{-3}{2}) ^{2}[/tex] = [tex]d^{2}[/tex] -3d +[tex]\frac{9}{4}[/tex]
The Binomial form of the expression [tex]d^{2}[/tex] -3d + [tex](\frac{-3}{2}) ^{2}[/tex]
can be written by take [tex]d^{2}[/tex] term and the constant and putting them in a bracket and squaring
which becomes
[tex](d - \frac{3}{2} )^{2}[/tex]
In conclusion, the trinomial form of the expression is [tex]d^{2}[/tex] -3d +[tex]\frac{9}{4}[/tex] while the Binomial form of the expression is [tex](d - \frac{3}{2} )^{2}[/tex]
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Determine the perimeter of the right triangle shown.
Answers
Answer:
27
Step-by-step explanation:
I looked at the graph and added 6+6=12 so the bottom is 12 and for the height i added 1+8=9 and then i added another 12 because the bottom is also 12 and divided that by 2 which is 6 so i got 27.
this may not be right but i am hoping that is it!
Have A Great Day!!!
Please help with the following question.
Answers
The probabilities, using the Poisson distribution, are given as follows:
a) Two earthquakes in a year: 0.0446 = 4.46%.
b) No earthquakes in two consecutive months: 0.3679 = 36.79%.
c) No earthquakes in two consecutive months, given that there were no earthquakes in the previous month: 0.3679 = 36.79%.
What is the Poisson distribution?The Poisson distribution is used when we only have the mean in a given interval and the mass function is given as follows:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are listed as follows:
x is the number of successes.e = 2.71828 is the Euler number.[tex]\mu[/tex] is the mean in the given interval or range of values of the input parameter.For one year, the mean number of earthquakes is given as follows:
[tex]\mu = 6[/tex]
The probability of exactly two earthquakes in a year is obtained as follows:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 2) = \frac{e^{-6}6^{2}}{(2)!} = 0.0446[/tex]
For two months, the mean is given as follows:
[tex]\mu = 2 \times 6 \times \frac{1}{12} = 1[/tex]
For items b and c, the probabilities are the same, P(X = 0), as the events are independent, hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-1}1^{0}}{(0)!} = 0.3679[/tex]
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Which transformation always preserves distance and angle measures?
Answers
Step-by-step explanation:
Rigid motion
Rigid motion – A transformation that preserves distance and angle measure (the shapes are congruent, angles are congruent).
Dwayne wants to redecorate his bedroom and decides to purchase new furniture. The following graph could be used to represent the value of the new bedroom furniture, f(x), after x years.
A graph of an exponential function which decreases through the points 0 comma 1200 and 2 comma 675.
Which of the following statements is/are true based on the graph and the context of the problem?
The y-intercept (0, 1200) represents the initial cost of the bedroom furniture.
The function is negative on its entire domain.
The domain is x ≥ 0 to represent the number of years after the bedroom furniture was purchased.
Answers
The y-intercept (0, 1200) represents the initial cost of the bedroom furniture option (A) is correct.
What is an exponential function?It is defined as a function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a×
where a is a constant and a>1
The exponential function is of the form:
y = ab×
Plug x = 0 and y = 1200
1200 = a
Plug x = 2, y = 675, and a = 1200
675 = 1200(b)²
b = 0.75
y = 1200(0.75)×
y = 1200
Thus, the y-intercept (0, 1200) represents the initial cost of the bedroom furniture option (A) is correct.
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The overhead reach distances of adult females are normally distributed with a mean of 202.5 cm and a standard deviation of 8.6 cm.
a. Find the probability that an individual distance is greater than 211.80 cm.
b. Find the probability that the mean for 20 randomly selected distances is greater than 200.30 cm.
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
a. The probability is
(Round to four decimal places as needed.)
Answers
Answer: I am not sure if you're accustomed to using a z-score and table of probabilities or technology, so I will answer using both!
a) Since you're choosing one person from the population, you will use the mean and standard deviation from the population. z= (210.9-197.5)/8.6 = 1.56 Using a table of normal probabilities,
P(x>210.9)= 1-P(z<1.56)= 1- 0.9406=0.0594
Using technology: normalcdf(210.9, 1E99, 197.5, 8.6)=0.0596
b) Since you're calculating the population for a sample to occur, you need to get a mean of the sampling distribution and standard deviation of the sampling distribution.
Meanpop=Meansampling dist.=197.5
St. Devsampling dist.= Stdpopulation/√n = 8.6/√15 = 2.22
Using technology, P(X>196.20)= normalcdf( 196.20, 1E99, 197.5, 2.22) = 0.7209
c) You only have to worry about the sample size in a sampling distribution if you either do not know the shape of the distribution of the population or if the distribution of the population is not normally distributed. Since this population is normally distributed (as stated in the given information), then your sample size does not have to be greater than 30.
Hope this helps! I can solve part b using a z-score if you need me to.
Step-by-step explanation:
) 3 1+ − 2 2− + 2 1−
Answers
help me please I am in need of this answer too
Answers
When corresponding angles are congruent, the lines are parallel
Congruent AnglesCongruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other. The type of angles does not make any difference in the congruence of angles, which means they can be acute, obtuse, exterior, or interior angles. The angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.
Examples of the corresponding angle are any angles which are formed on the opposite side of the transversal. Now, it should be noted that the transversal can intersect either two parallel line or two non-parallel lines. Thus, corresponding angles can be of two types:
Corresponding angles formed by parallel lines and transversals
Corresponding angles formed by non-parallel lines and transversals
Looking at the image, angle I is congruent to each other. Angle II is congruent with each other as well as angle III.
When corresponding angles are congruent, the lines connecting them must be parallel. This is the only valid or correct options in the task.
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0.721x10 to the second power
Answers
Answer:
72.1
Step-by-step explanation:
It is 10 to the power of 2 because the exponent is 2. The result is a number bigger than the origin or base number because the exponent is positive. We move the decimal two times to the right to arrive at our conclusion:
0.721--> 72.1
therefore, your answer will be 72.1
Make the subject of
X
16
=
р
Answers
Answer: x= p16
Step-by-step explanation:
Bike Cost $800 $600 $400 $200 $0 Bike City Comparing Costs Fast BMX Bike World Bike Store Awesome Bikes How much more is the cost at Fast BMX than Bike World?
Answers
Using the mathematical operation of subtraction, the cost at Fast BMX is $200 more than the cost at Bike World.
How is the difference computed?The difference in the cost of bikes can be computed using the mathematical operation of subtraction.
Subtraction operations involve deducting the subtrahend from the minuend to get the result known as the difference.
Bike Stores Prices
Bike City $300
Fast BMX $500
Bike World $300
Awesome Bikes $400
Difference between Fast BMX and Bike World
= $200 ($500 - $300)
Thus, the cost of bikes is higher at Fast BMX than at Bike World by $200.
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Complete the statement. The drawing is not to scale.
Answers
Answer:
The second option so 54 degrees.
Step-by-step explanation:
The line drawn on angle d in both spots indicates it's congruent so if one side is a number the other side is that same number so in this case, it's 54 degrees.
What is the value of the expression m - when m = 3?
1/15
13/15
23/15
Answers
The value of the expression when m = 3 is 13/15. So option(2) is correct.
The equation is defined in its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, x + 3 = 4 is an equation, in which x + 3 and 4 are two expressions separated by an 'equal' sign.
Given the expression as shown below:
2/5 m - 1/3
If m is equal to 3, then the expression will be;
2/5(3) - 1/3
6/5 - 1/3
Find the LCM
6/5 - 1/3 = 3(6)-5/15
6/5 - 1/3 = 18-5/15
6/5 - 1/3 = 13/15
Therefore the value of the expression if m = 3 is 13/15
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5–3 3/5 ÷ (–3– –3 3/4)
Answers
Answer:
[tex]0.2[/tex]
Step-by-step explanation:
... .. ... .. .
400 passengers go on a coach trip.
Each coach takes 50 passengers.
Each passenger pays £23
The table shows the costs for the
coach company.
Each coach travels 200 miles.
Work out the total profit the company makes from this trip.
Answers
The total profit that the company would make on the trip can be found to be £7,320
How to find the total profit made?The revenue that the company makes would be:
= Number of passengers x Amount that each passenger pays
= 400 x 23
= £9, 200
Each coach takes 50 passengers so the number of coaches needed are:
= 400 passengers / 50 passengers per coach
= 8 coaches
The total cost to the company for the trip is:
= (Number of coaches x Driver cost per coach) + (Number of coaches x Fuel per mile x Distance traveled for each coach)
= ( 8 x 95) + ( 8 x 70p x 200)
= 760 + 112, 000 p
= 760 + 112, 000/ 100 pence per pound
= £ 1,880
The total profit is:
= Revenue - total cost
= 9, 200 - 1, 880
= £7,320
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. √-100 rewrite each expression using I
Answers
Answer:
?????
Step-by-step explanation:
6. A garbage truck collects trash from
68 trash cans. Another truck collects
trash from 39 fewer trash cans. How
many trash cans do the trucks collect
trash from in all?
trash cans
Answers
Write an equation for the quadratic graphed below:
x-intercepts: (-3,0) and (1,0); y-intercept: (0,-3)
Answers
Answer:
y = (x + 3)(x - 1) or y = x² + 2x - 3Step-by-step explanation:
Quadratic equation:
y = a(x - p)(x - q), where a - constant, p and q - x-intercepts.Substitute p and q:
y = a(x - (-3))(x - 1)y = a(x + 3)(x - 1)Find the value of a, using the y-intercept:
- 3 = a(0 + 3)(0 - 1)- 3 = a*3*(-1)-3 = - 3aa = 1The equation is:
y = (x + 3)(x - 1)or
y = x² + 2x - 3can you help meeeeeeeeeeeeeeeeeeee pleaseeeeeeee!!!
Answers
Answer:
[tex]f(x) = 2(x-9)^{2} + 3[/tex]
Step-by-step explanation:
In vertex form, (h, k) represents the vertex.
With the given vertex of (9, 3), h = 9 and k = 3. You can substitute those values into the equation.
In vertex form, a represents vertical stretch or compression.
In this case, since the parent function, x^2 is multiplied by 2, a = 2. You can substitute this into the equation.
You end up with [tex]f(x) = 2(x-9)^{2} + 3[/tex]
The siding of a house is 2250 square feet. The siding needs two coats of paint.
1 quart costs 18 dollars and covers 80 square feet;
1 gallon, costs 29 dollars, covers 320 square feet.
A. What is the minimum cost of the paint needed to complete the job?
B. How much paint is left over when you spend the minimum amount?
Answers
Answer: Minimum cost = $264
Paint left over = 7/8 qt
Step-by-step explanation:
6 gal covers 1920 sf (6 gal x 320 sf/gal)
6 gal x $29/gal = $174
2250 sf - 1920 sf = 330 sf
Need 4.125 qt to cover 330 sf, but you can't buy a partial quart
5 qt x $18/qt = $90
Total cost = $174 + $90 = $264
You have 7/8 qt left over
two buses leave a station at the same time and travel in opposite directions. One bus travels 15 km/h faster than the other. If the two buses are 1004 kilometers apart after 4 hours, what is the rate of each bus?
Answers
The speed of slower bus is 118 km/hr and speed of faster bus is 133 km/hr
What is speed?Speed is a scalar quantity that refers to "how fast an object is moving".
Given that, two buses leave a station at the same time and travel in opposite directions, one bus travels 15 km/h faster than the other, the two buses are 1004 kilometres apart after 4 hours,
Speed = distance/ time
Let the speed of the slower bus be v and the faster bus be (v+15)
According to the question,
vt + (v+15)t = 1004
vt + vt + 15t = 1004
t = 4
4v + 4v + 60 = 1004
8v = 944
v = 118
Hence, The speed of slower bus is 118 km/hr and speed of faster bus is 133 km/hr
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A car travels 210 kilometres in 3 hours 30 minutes
Calculate the average speed, in km/h, of the car.
Answers
Answer:
70 km/hr
Step-by-step explanation:
The sum of twelve times a number and eleven is 251. Find the number.
Answers
Answer:
x = 20
Step-by-step explanation:
12x + 11 = 251
12x + 11 - 11 = 251 - 11
12x = 240
12x /12 = 240/12
x=20
What is the image of (3,3)(3,3) after a dilation by a scale factor of 1/3
centered at the origin?
Answers
The image of (3, 3) after dilation by a scale factor of 1/3 centered at the origin will have coordinate (1, 1)
What is dilation?Dilation refers to the transformation that increases or reduces the image formed after the transformation
When the scale factor is greater that 1 the transformation will lead to magnification when the scale factor is less than 1 the image formed is compressed.
The transformation rule fir dilation is (x, y) → (kx, ky)
where k is the scale factor = 1/3
(3, 3) → (1/3 * 3, 1/3 * 3) → (1, 1)
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A coach can take 40 passengers.how many passenger can be carried by 18 coaches
Answers
C:P
1:40
18:x
Solve the equation without using a calculator
[tex]\displaystyle\\3^\frac{x+2}{3x-4}-2\cdot3^\frac{5x-10}{3x-4}=7[/tex]
Answers
Answer:
x = 2=========================
Rewrite(5x - 10)/(3x - 4) = (6x - 8 - x - 2)/(3x - 4) = 2 - (x + 2)/(3x - 4)Substitute[tex]3^{(x + 2)/(3x - 4)} = t[/tex]New equationt - 2·9/t = 7t - 18/t = 7t² - 7t - 18 = 0t² - 9t + 2t - 18 = 0t(t - 9) + 2(t - 9) = 0(t - 9)(t + 2) = 0t - 9 = 0 and t + 2 = 0t = 9 and t = - 2 (excluded as the power of 3 can't be negative)Substitute back[tex]3^{(x + 2)/(3x - 4)} = 9[/tex][tex]3^{(x + 2)/(3x - 4)} = 3^2[/tex][tex](x + 2)/(3x - 4) = 2[/tex][tex]x + 2 = 6x - 8[/tex][tex]6x - x = 2 + 8[/tex][tex]5x = 10[/tex][tex]x = 2[/tex]