I need assistance with this math assignment
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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The demand for an item is given as Q=2500-6P where P is the pric supply is Q=1750 +4P. How many units Q must be made for supply to equ
The quantity of items tha must be made for supply to equal demand is 2050 items
What is demand?Demand simply means a consumer's desire to buy goods and services without any hesitation and pay the price for it.
To calculate the unit of quantity Q that must be made for demand to be equal to supply, we equate the demand and supply equation.
From the question,
For Demand
Q = 2500-6P............... Equation 1From Supply,
Q = 1750+4P........... Equation 2When supply is equal to demand
2500-6P = 1750+4PSolve for P
10P = 2500-175010P = 750P = 750/10P = 75Substitute the values of P into equation 1
Q = 2500-6(75)Q = 2500-450Q = 2050Hence, the quantity of items tha must be made 2050 items.
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!!PLEASE HELP!!
The path of a baseball is modeled by the equation [tex]y=-0.25x^{2} +4x+3[/tex] where x represents the time (in seconds) and y represents the height of the baseball.
- Find and interpret the y-intercept. Find the maximum height of the baseball. Then sketch a graph of the path.
(please provide steps on how to solve if you can)
Answer:
The y-intercept is when $x=0$ so $y=32\frac{ft}{s}*0-\frac{1}{2}*9.8*0^2=0$, so the ball starts on the ground. The maximum height is when $v=0$, so $0=32\frac{ft}{s}-9.8t$ and solving for $t$ we get $t=\frac{32}{9.8}=3.265s$, and plugging this back in for $y$ we get $y=32\frac{ft}{s}*3.265s-\frac{1}{2}*9.8*3.265^2=156.205 ft$. So the ball will be at its maximum height of 156.205 ft at 3.265 seconds.
Step-by-step explanation:
The $y$-intercept is $-1$. The maximum height of the baseball is when $y=0$; that is when $x=\ln(4)$. Here is a sketch of the path.
From the $y$-intercept, we see that the baseball starts at height $y=-1$. It reaches a maximum height at $x=\ln(4)$; that is, $y=0$. From there, it falls and reaches the ground at $x=2\ln(4)$; that is, $y=-1$ again.
A company estimates that 0.5% of their products will fail after the original warranty period but within 2 years of the purchase, with a repair cost of $300. The company offers an extended two-year warranty.
If a consumer does not purchase the extended warranty, then the consumer will need to pay for any necessary repairs. What is the expected value of their repair costs?
The expected value of their repair costs is $41.50.
How to calculate the repair cost?Given the probability of failure as 0.5%, this can be illustrated as 0.005.
The cost of repair is given as $300.
The expected value of the company will be:
= Earnings - [(Cost × P(failure)]
= 43 - (300 × 0.005)
= 43 - 1.50
= 41.5
The value is $41.50.
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Complete question
company estimates that 0.5% of their products will fail after the original warranty period but within 2 years of the purchase, with a repair cost of $300. The company offers an extended two-year warranty.
If a consumer does not purchase the extended warranty, then the consumer will need to pay $43 for any necessary repairs. What is the expected value of their repair costs?
solve x^2-4x+3=0 using the quadratic formula
Answer:
1 and 3
Step-by-step explanation:
discriminant = 16 - 4 * 1 * 3 = 16 - 12 = 4
x1 = (4 + √4)/2 = (4+2)/2 = 6/2 = 3
x2 = (4 - √4)/2 = (4-2)/2 = 2/2 = 1
convert 62/80 to a decimal and to a percent
CAN SOMEONE HELP WITH THIS QUESTION?✨
The side x of the right triangle is 235.72 units.
How to find the sides of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sides of a right angle triangle can be found using trigonometric ratios or Pythagoras theorem depending on the sides and angles given.
Hence, let find the value of x in the combine right triangles.
Therefore,
tan 28 = opposite / adjacent
tan 28 = 105 / l
cross multiply
l = 105 / tan 28
l = 105 / 0.53170943166
l = 197.479781832
l = 197.50
tan 70 = 105 / a
a = 105 / tan 70
a = 38.2168804325
a = 38.22
Therefore,
x = 197.50 + 38.22
x = 235.72 units
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Need help with question
The composite functions and their domains are listed as follows:
a) (f ∘ g)(x) = sin(2x/(x + 5)), domain is all real values except x = -5.
b) (g ∘ f)(x) = sin(2x)/(sin(2x) + 5), domain is all real values except x = -5 and the values of x for which sin(2x) + 5 = 0.
c) (f ∘ f)(x) = sin(sin(2x)), domain is all real values.
d) (g ∘ g)(x) = x/(6x + 5), domain is all real values except x = -5 and x = -5/6.
How to obtain the composite functions and their domains?
The composite functions are found applying the inner function as the input to the outer function, according to the rule presented as follows:
(f ∘ g)(x) = f(g(x)).
The domain is the set of values that respect all the input constraints of the inner function, of the outer function, and of the composite function.
For this problem, the functions are given as follows:
f(x) = sin(2x).g(x) = x/(x + 5).For item a, the inner function g is applied as the input to the outer function f, hence:
f(g(x)) = sin(2x/(x + 5))
The sine has no constrains, the fraction cannot have a denominator zero, hence the domain is composed by all real values except x = -5.
The other composite functions are listed as follows:
g(f(x)) = sin(2x)/(sin(2x) + 5), domain is all real values except x = -5(constraint of g(x)) and the values of x for which sin(2x) + 5 = 0.f(f(x)) = sin(sin(2x)), the domain is all real values, as the sine has no restriction.[tex]g(g(x)) = \frac{\frac{x}{x + 5}}{\frac{x}{x + 5} + 5} = \frac{x}{6x + 5}[/tex]
Domain is all real values except:
x = -5 -> constraint of g(x).x = -5/6 -> constrain of the composite function.More can be learned about composite functions at https://brainly.com/question/10687170
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H
3/21
(5,4)
Type here to search
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(5,2)
[12]
Triangle RST has vertices R(1, 1), S(1, 4), and T(3, 1).
Graph the figure and its rotated image after a
counterclockwise rotation of 180° about the origin.
What are the coordinates of T'?
6
(-3,-1)
6048 4787 3
(-3,-2)
721 PM
11/10/2012
The coordinates of T' are, T'(-3, -1).
What is rotation?
A rotation is a transformation in which each point of a preimage is turned through a predetermined angle and direction around a fixed point. The center of rotation is the fixed point. The term for the amount of rotation is the angle of rotation, and it is expressed in degrees. Measure the specified angle in the anticlockwise direction using a protractor.
Given: Triangle RST has vertices R(1, 1), S(1, 4), and T(3, 1).
We have to find the coordinates of T' after counterclockwise rotation of 180°.
Since, The rule for a rotation by 180° about the origin is (x, y) → (−x, −y).
So, the coordinates R(1, 1), S(1, 4) and T(3, 1) changes to R'(-1, -1), S'(-1, -4) and T'(-3, -1).
Therefore, the coordinates of T' are T'(-3, -1).
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When planning a cruise, you have a choice of 3 destinations: Cozumel (C), Jamaica (J), or Grand Caymans (G); a choice of 2 types of rooms: balcony (B) or inside view (I); and a choice of 4 types of excursions: water sports (W), horseback riding (H), parasailing (P), or zip-lining (Z). If you are choosing only one of each, list the sample space in regard to the vacations (combinations of destinations, rooms, and excursions) you could pick from.
The sample space in regard to the vacations is 24
Choice of 3 destinations: Cozumel (C), Jamaica (J), or Grand Caymans (G) =
3C1
A choice of 2 types of rooms: balcony (B) or inside view = 2C1
And a choice of 4 types of excursions: water sports (W), horseback riding (H), parasailing (P), or zip-lining (Z) = 4C1
Choosing only one of each, the sample space in regard to the vacations
Sample space = choice of destination x choice of room x choice of water sports
= 3C1 x 2C1 X 4C1
= 3 x 2 x 4 = 24
Therefore, the sample space in regard to the vacations is 24
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need help???????????????????
Step-by-step explanation:
it is totally simple : you need to put the x-value into every place of the x-variable, and then we calculate.
and then the same for the next x-value. and the next. ...
-2
-2×-2 + 9 = 4 + 9 = 13
0
-2×0 + 9 = 0 + 9 = 9
2
-2×2 + 9 = -4 + 9 = 5
4
-2×4 + 9 = -8 + 9 = 1
In 6 years, a father wants to accumulate $110000 to pay for his daughter's college expenses. If he can get 8% interest, compounded quarterly, how much must he invest now to achieve his goal?
The amount that hw must invest to achieve the goal when it will be compounded annualy is $68750
Given Information:
Principal Amount (P) = to be calculated
Rate of Interest (r) = 8 %
Time Period (t) = 6
Amount Received (A) = $110000
Number of times the interest is compounded quarterly (n) = 4
The Formula for the amount received when the principal (P) is compounded is given by,
[tex]A = P( 1 + \frac{r}{100n} )^{nt}[/tex]
Now, putting the values, we get:
[tex]110000 =P( 1 + \frac{8}{100*4} )^{4*6}[/tex]
P = $68750
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Darren and Clara live in a tall building. Clara lives 12 floors above Darren. One day Darren went up to visit Clara and he took the stairs up from his apartment to Clara’s. Half-way up he was on the 8th floor. On what floor does Clara live? Show your work.
If Clara lives 12 floors above Darren, Clara lives on the 16 floor while Darren lives on the 4 floors.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
Given that Darren and Clara reside in a towering structure, this is expected. Twelve stories above Darren, Clara resides. One day, Darren climbed the stairs from his apartment to Clara's and went to see her. He was halfway up, on the eighth floor.
Suppose Darren and Clara live on x and y number of floor respectively.
If Clara lives 12 floors above Darren.
x-y=12
If in halfway he is on the 8th floor the total number of floors in the building will be 16.
As a result, we can say that Clara lives on the 16 floors while Darren lives on the 4 floor.
Thus, if Clara lives 12 floors above Darren, Clara lives on the 16 floors while Darren lives on the 4 floors.
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Simplify
15x²y³-10x²y² +5xy² divided by 5xy
Answer:
y(3xy-2x+1)
Step-by-step explanation:
I'm pretty sure it'd be y(3xy-2x+1).
Answer:
3xy²-2xy +y
Step-by-step explanation:
15x²y³-10x²y² +5xy² = 5xy(3xy²-2xy +y)
then
5xy(3xy²-2xy +y) / 5xy = 3xy²-2xy +y
Your classmate is starting a new fitness program. He is planning to ride his bicycle 60 minutes every day. He burns 8 calories per minute bicycling at 11 mph and 12.75 calories per minute bicycling at 15 mph. How long should he bicycle at each speed to burn 575 calories?
The distance it should take my classmate to ride the bicycle at each speed to burn 575 calories would be = 13.2m for first speed and 11.3m for the second speed.
What is a fitness program?A fitness program is defined as the program that is adequately organised for the purpose of maintaining proper healthy calories.
The period he plans to ride the bicycle for a day = 60minutes.
For the first speed,
8 cal/ min = 11mph
To convert to hour,
8 × 60 =480
He burns 480cal per hour in 11mph speed
If 480cal = 11 mph
575 cal = X
make X the subject of formula;
X = 575×11/480
X = 6325/480
X = 13.2 m
For the second speed;
12.75 cal/ min = 15mph
To convert to hour,
12.75 × 60 =765cal
He burns 765cal per hour in 11mph speed.
If 765cal = 15mph
575 cal = y
make y the subject of formula;
y = 575 × 15/765
y = 8625/765
y = 11.3 m
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A species of bacteria has a population of 80 at noon. It double every 8 hours. The function that models the growth of the population, P, at any hour, t, is
P(t) = 80(28) 8 a. Why is the exponent ?
b. Why is the base 2?
c. Why is the multiplier 80?
d. Determine the population at noon the next day.
e. Determine the time at which the population first exceeds 60 Thousand.
Answer:123
Step-by-step explanation:
31231231232131
In AGHI, h = 300 inches, ZG=30° and H=29°. Find the
length of i, to the nearest inch.
The length of i will be 531.3 inch when h is 300 inch and ∠G is 30° and ∠H is 29°.
What is angle?When two straight lines or rays intersect at a shared terminal, an angle is generated. An angle's vertex is the common point of contact. The difference in direction between two lines or surfaces is defined as an angle. Angles are expressed in degrees. From a same point, the two hands draw separate sets of lines. Angle refers to these groups of lines that originate from a common point. Every minute, the two hands create various angles. In real life, one example of an angle is a clock.
Here,
∠I=180-(30+29)
=180-59
∠I=121°
h/sin H=i/sin I
300/sin 29=i/sin 121
i=300*sin 121/sin 29
i=531.3 inch
When h is 300 inches, G is 30 degrees, and H is 29 degrees, the length of I is 531.3 inches.
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Express the angle in radian measure.
-22½°
a. -π/8
b. -π/4
c. -π/16
the answer is a, -π/8
The lifetime of a certain type of battery is known to be normally distributed with standard deviation =σ17 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 95% confidence interval for the mean lifetime for this type of battery.
The point estimate for the lifetime of a certain type of battery is 120.1 hours.
How to illustrate the information?Let X represent the battery's lifetime. X has a normal distribution with a standard deviation of 20 hours. The sample size is 50, and the average lifetime is 120.1 hours.
Calculating the mean of a sample drawn from the population yields a point estimate of the population's mean. The mean is calculated as the sum of all sample values divided by the number of values.
A single value estimate of a parameter is referred to as a point estimate. A sample mean, for example, is a point estimate of the population mean. An interval estimate provides a range of values within which the parameter is expected to fall. The population mean point estimate is sample mean and this is 120.1 hours.
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Complete question
The lifetime of a certain type of battery is known to be normally distributed with standard deviation =σ17 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 95% confidence interval for the mean lifetime for this type of battery. What is the point estimated?
Question 9 of 10
Mark all the statements that are true.
A. This graph is not a function because the value x = 3 is assigned to
more than one y-value.
B. The equation of this line is x = 3.
C. This graph is a function whose range is the set (3).
D. This graph is a function because the value of x is the same for
every value of y.
E. This graph is a function whose domain is the set (3).
True statement are:
A. This graph is not a function because the value x = 3 is assigned to
more than one y-value.
D. This graph is a function because the value of x is the same for
every value of y.
Given,
In the question:
To see the graph :
Mark all the statement that are true.
Now, According to the question:
From the graph,
Equations are expressions of two mathematical expressions t such as two numbers, functions. An equality between quantities and operations, usually with an equal sign "=".
Functions is a correspondences between two sets that are not empty each element in the set of input values can corresponds to a element in a set of output values that is unique.
Hence, True statement are:
A. This graph is not a function because the value x = 3 is assigned to
more than one y-value.
D. This graph is a function because the value of x is the same for
every value of y.
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What is h in the parallelogram?
The value of h in the parallelogram is 4 feet
The area of the parallelogram = b × h
Where b is the base of the parallelogram
h is the height of the parallelogram
One side of the parallelogram = 6 feet
The second side of the parallelogram = 8 feet
If the base of the parallelogram is 6 feet
The area = 6 × h
If the base of the parallelogram is 8 feet
Then the area of the parallelogram = 8 × 3
= 24 square feet
In both cases the area will be equal, then the equation will be
6h = 24
h = 24 / 6
h = 4 feet
Hence, the value of h in the parallelogram is 4 feet
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92. Which key word would help you decide which operation to use to solve the following: If Kay has 5 pencils, but gives 1 to Mary, how many would she have left? (a) has (c) pencils (b) give (d) left
Answer:
Step-by-step explanation:
the correct answer is A.
because if Kay has 5 pencils and it is given to Merry 1, it means that Kay still has 4 pencils.
Using a calculator, work out the value of
(7.6 x 10^-4) × (8.2 × 10^11)
Give your answer in standard form.
At a particular restaurant, each pizza roll has 65 calories and each chicken wing has 50 calories. A combination meal with pizza rolls and chicken wings is shown to have 1015 total calories and 5 more pizza rolls than chicken wings. Determine the number of pizza rolls in the combination meal and the number of chicken wings in the combination meal
Rewrite
barrel
hour
о
as a unit rate.
O A. 2 barrels/hour
OB. barrel/hour
OC. 6 barrels/hour
D. barrel/hour
Please I need it asap
Unit rate of (1 /5 barrel) / (1/2hour) is equals to (2/5) barrels /hour.
What is unit rate?
"Unit rate is defined as the representation of the ratio of the two different units with value of the denominator equals to 1."
According to the question,
Given,
1/5 barrel/1/2 barrel
⇒ (1/2) hour = (1/5) barrel
⇒ 1 hour = (2/5) barallel
⇒ (2/5) barrel per one hour.
Therefore,
Unit rate of given value is rewritten as
2/5 barrel/hour
hence option b is correct.
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Your question is incomplete. Please find the missing content below.
Rewrite 1/5 barrel 1/2 hour as a unit rate.
A. 2 1/2 barrel/hour
B. 2/5 barrel/hour
C. 10 barrels/hour
D. 1/10 barre./hour
This is due tomorrow, please help!
Mr. Phone stayed in a hotel room for 2 nights that cost $210. The hotel room tax rate is 12% what is the total cost for the hotel room?
Answer:
$235.20
Step-by-step explanation:
the tax :
[tex] \frac{12}{100} \times 210 = 25.20[/tex]
total cost :
$210 + $25.20 = $235.20
The length of the longer side of a rectangle is 2 in. less than twice the length of
the shorter side. The area of the rectangle is 60 in2. What is the difference
between the lengths of the longer and shorter sides?
Solve the following equation below. Show each step and check your work.
72y - 126 = 522 + 144
Answer: y = 11
Step-by-step explanation:
Our problem: 72y - 126 = 522 + 144
1. Simplify 552 + 144 to 666
72y - 126 = 666
2. Add 126 to both sides
72y = 666 + 126
3. Simplify 666 + 126 to 792
72y = 792
4. Divide both sides by 72
y = [tex]\frac{792}{72}[/tex]
5. Simplify [tex]\frac{792}{72}[/tex] to 11
y = 11
Arrange the following numbers in increasing order (smallest first, biggest last):
A = 2*1/2*4*1/6
B = 12*128
C = 1*8*1/5^2
D = 4*(-1)/2*(-1)*8*(-1)
E = 3*2^(1/2)*4*1/4
The numbers arranged in increasing order are D < C < A < E < B.
We are given a set of five numbers. The numbers are represented by the variables A, B, C, D, and E. The numbers need to be calculated. The numbers are solved below.
A = 2*1/2*4*1/6 = 2/3 = 0.667
B = 12*128 = 1,536
C = 1*8*1/5² = 8/25 = 0.32
D = 4*(-1)/2*(-1)*8*(-1) = -16
E = 3*√2*4*1/4 = 3√2 = 4.24
We need to arrange the numbers in increasing order. Ascending order refers to the arrangement of numbers in increasing order, from least to greatest. The numbers in ascending order are given below :
-16 < 0.32 < 0.667 < 4.24 < 1,536
The increasing order of the corresponding variables is : D < C < A < E < B.
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factorise 6x^2+11x+4
Answer:
(2x+1)(3x+4)
Step-by-step explanation:
6x² + 11x + 4
multiply the first and last term
i.e (6x²)(4) = 24x²
find two terms that multiplies to give 24x² and when added would give 11x
¶ 8x and 3x
Therefore; 6x² + 11x + 4
6x² + 8x + 3x + 4
2x(3x + 4) + 1(3x + 4)
Answer; (2x + 1)(3x + 4)