Answer:
a) The initial height of the rock is of 48 feet.
b) It takes 1 seconds for the rock to reach maximum height.
c) The rock's maximum height is 50 feet.
d) It takes 6 seconds for the rock to land on the ground.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, f(x_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]f(x_{v})[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
The height of the ball after t seconds, in feet, is given by:
[tex]h(t) = -2t^2 + 4t + 48[/tex]
Which is a quadratic equation with [tex]a = -2, b = 4, c = 48[/tex]
a) What is the initial height?
This is [tex]h(0) = 48[/tex]. So the initial height of the rock is of 48 feet.
b) How many seconds does it take to reach the maximum height?
This is the value of t at the vertex. So
[tex]t_{v} = -\frac{b}{2a} = -\frac{4}{2(-2)} = 1[/tex]
It takes 1 seconds for the rock to reach maximum height.
c) What is the rock's maximum height?
This is the height of the ball after 1 second. So
[tex]h(1) = -2(1)^2 + 4(1) + 48 = 50[/tex]
The rock's maximum height is 50 feet.
d) How many seconds does it take to for the rock to land on the ground?
This is t for which [tex]h(t) = 0[/tex], so we solve the quadratic equation.
[tex]\bigtriangleup = (4)^2-4(-2)(48) = 400[/tex]
[tex]t_{1} = \frac{-4 + \sqrt{400}}{2*(-2)} = -4[/tex]
[tex]t_{2} = \frac{-4 - \sqrt{400}}{2*(-2)} = 6[/tex]
Time is a positive measures, so it takes 6 seconds for the rock to land on the ground.
y = x^5 sin (2x) cos (4x)
find the derivative
The derivative of the equation will be y' = 5y/x + 2y cot (2x) - 4y tan (4x).
What is differential equation?An equation containing derivatives of a variable with respect to some other variable quantity is called differential equations.
The derivatives might be of any order, some terms might contain product of derivatives and the variable itself, or with derivatives themselves.
They can also be for multiple variables.
y = x⁵ sin(2x ) cos(4x)
The differentiation;
y' = d/dx (x⁵ sin (2x) × cos (4x) + x⁵ sin(2x) ). × d/dx (cos(4x) )
y' = 5x⁴ sin(2x) cos(4x)+2x⁵ cos(2x) cos(4x) -4x⁵ sin(2x) sin(4x)
From the given equation;
y' = 5y/x + 2x⁵ cos(2x) cos(4x) - 4x⁵ sin(2x) sin(4x)
y' = 5y/x + 2y cot (2x) - 4y tan (4x)
Learn more about derivatives ;
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What is 593832+872382828=
Plz answer /
Answer:
8,729,766,60
Step-by-step explanation:
593832+872382828= I'm 100% sure my answer is correct I worked it out on paper and calculated it after
Answer:
Step-by-step explanation:
872976660
converd improper fraction into mixed fraction 3/20
Answer:
Cannot be written as a mixed number
Step-by-step explanation:
Since 3/20 is a proper fraction, it cannot be written as a mixed number.
Areesh is trying to build a box fort. He has 8 feet of duct tape.
The instructions are to use 22.5 inches of the tape to secure the roof of the box fort. Then, the remaining
tape should be cut into 5 1/4 - inch sections to be used on the walls of the box fort. Areesh will use all of the
duct tape as instructed.
Determine the number of 5 1/4 - inch sections of tape Areesh can cut.
Answer:
14
Step-by-step explanation:
[tex]8 \times 12 = 96 [/tex]
[tex]96 - 22.5 = 73.5[/tex]
[tex]73.5 \div 5.25 = 14[/tex]
Step-by-step explanation:
Answer is 14 I hope you get it
18
Debbie, Kimi and Michael have
Ferraris.
Michael also has a Reliant Robin.
Jensen has a Mercedes and a Model
T.
Rubens also has a Mercedes.
Debbie also has a Bugatti Veyron.
Rubens has just bought a Toyota
Prius.
Who has the fewest cars?
(1 Point)
what is 2 4/7 + 9 5/6 =
Answer:
12 12/42
Step-by-step explanation:
Answer:
12 17/42
Step-by-step explanation:
18/7+59/6 LCD=42
108/42+413/42
521/42
12 17/42
I'm needing help with 4,5,6
Answer:
4. acute
5. obtuse
6. obtuse
Step-by-step explanation:
Joanna makes and sells candles online. She charges $7 per candle, and shipping is $5 per order. Select an expression that Joanna can use to find the total cost for any candle, n, order. 7 + n + 5 7 + n + 5 7n + 5 7n + 5 7 ÷ n + 5 7 ÷ n + 5 7n - 5
Answer: Total cost= 7n + 5
Step-by-step explanation:
7 is the M (money per every candle) and 5 is the B (additional fee for every order)
make a problem about simple interest
Answer:
Simple Interest (SI) = Amount (A) – Principal (P) = 6000 - 5400. = 600
Answer:
1. Robert deposits $ 3000 in State Bank of India for 3 year which earn him an interest of 8%.What is the amount he gets after 1 year, 2 years and 3 years?
Step-by-step explanation:
Solution:
In every $ 100, Robert gets $ 8.
(Since rate is 8% → 8 for every 100)
Therefore, for $ 1 he gets = $ 8/100
And for $ 2000 he gets = 3000 x 8/100
= $ 240
Simple Interest for 1 year = $ 240.
Simple Interest for 2 year = $ 240 x 2
= $ 480
Simple Interest for 3 year = $ 240 x 3
= $ 720
Therefore, Amount after 1 year = Principal (P) + Simple Interest (SI)
= 3000 + 240
= $ 3240
Amount after 2 years = Principal (P) + Simple Interest (SI)
= 3000 + 480
= $ 3480
Amount after 3 years = Principal (P) + Simple Interest (SI)
= 3000 + 720 = $ 3720
We observe from the above example that, the Interest cannot be calculated without Principal, Rate and Time.
Therefore, we can conclude that Simple Interest (S.I.) depends upon:
(i) Principal (P)
(ii) Rate (R)
(iii) Time (T)
And therefore, the formula for calculating the simple interest is
Simple Interest (SI) = {Principal (P) × Rate (R) × Time (T)}/100
Amount (A) = Principal (P) + Interest (I)
Principal (P) = Amount (A) – Interest (I)
Interest (I) = Amount (A) – Principal
Please help!!!
3 tacos cost 18 dollars. Complete the table to show the cost of 4, 5, and 6 tacos at the same rate.
Now I figured out the cost of each taco, but I need help completing the table.
Answer:
The rate is 6 for all of them
Step-by-step explanation:
The rate would be the price for one taco, so you divide the cost by the number of tacos you're getting.
Answers: Well 1 taco is 6$. 4 tacos is 24$. 5 tacos is 30$. 6 tacos is 36$.
Write a two-step inequality that could be represented by the number line.
Answer:
0
Step-by-step explanation:
solve t(3+4) if t= 7
Answer:
=49
Step-by-step explanation:
7(3+4) substitute 7 into t
7(7) add numbers in brackets bec of BODMAS
49
Given that € 1 = £0.72
a) How much is € 410 in £?
b) What is the £ to € exchange rate?
Answer:
a) 295.2
Step-by-step explanation:
a) cross multiplication method
€1=£0.72
€410=x
x=€410×£0.72
The NCAA basketball tournament begins with 64 teams, and after each round, half the teams are eliminated. The number of remaining teams t n) is an exponential function of the number n of rounds already played . Write the exponential function that represent the number of players after n rounds . How many players will be there after 4 rounds?
Answer:
64 (1/2) n
ssssssssssssssssssssssssssssssssssssssssssssss
32 is 200% of what number
Answer:
64
Step-by-step explanation:
Substitution 8th grade math homwork. 1 question
First person to get it answer gets reward
Answer: (5, 11)
Step-by-step explanation:
y = 2x + 1
x + y = 16
Substitute 2x + 1 for y in 'x + y = 16'
x + y = 16
x + (2x + 1) = 16
3x + 1 = 16
Subtract both sides by 1
3x = 15
Divide both sides by 3
x = 5
Now to find y
Since we know what x is, we can use one of the equations and substitute 5 for x. I'll use both to show that you get the same answer.
Second equation:
x + y = 16
5 + y = 16
Subtract both sides by 5
y = 11
First equation:
y = 2x + 1
y = 2(5) + 1
y = 10 + 1
y = 11
The solution would be (5, 11)
Answer:
(5, 11) point form
x=5,y=11 equation form
Step-by-step explanation:
using suitable identity find 97 ×103
Answer:
9,991
Step-by-step explanation:
[tex]97 \times 103 \\ \\ = (100 - 3)(100 + 3) \\ \\ {(100)}^{2} - {(3)}^{2} \\ \\ = 10000 - 9 \\ \\ = 9,991[/tex]
A large store has a warehouse it uses for storage. Trucks back up to the loading dock where merchandise is unloaded, sorted, and stacked in the correct area of the warehouse. The large shelves in the storage area are 17 feet 8 inches apart so the forklift machines can operate between the shelves. Is that distance greater than or less than 216 inches?
Answer:
The distance is less than 216 inches.
Step-by-step explanation:
Each feet has 12 inches.
The large shelves in the storage area are 17 feet 8 inches apart
So, in inches, this distance is of:
17*12 + 8 = 212
This distance is less than 216 inches.
WILL MARK BRAINLIEST ONLY HAVE 10 MINUTES AND DOUBLE POINTS:
Jack scored 7,9,2,6,15,15 points 6 basketball games. Find the mean,median and mode scores for all the games
Answer:
mean = 9
mode = 15
median = 8
Step-by-step explanation:
10 lemons cost £1. 20 find the cost for 4
0.48p
Step-by-step explanation:
1.20÷10=0.12
0.12×4=0.48
put the wrong answer ignore this
please help im so lost
Does the expression (4r+6)
________
2
Also represent the number of females on the team this year? EXPLAIN.
Answer:
yes
Step-by-step explanation:
What is the distance between two points located at
(5,-5) and (-3,-5)?
Answer:the distance is 8
( this isn’t college math if anything it’s the ending and or beginning of 6th)
Step-by-step explanation:
Question 6
A cylinder has a radius of 4 cm and a height of 5 cm.
What is the volume of the cylinder when its radius is halved?
TT cm3
Step-by-step explanation:
3
[tex]3 \sqrt{xy { - }^{2} } [/tex]
A shade of green paint is made by mixing 2 cups of
yellow with 3.5 cups of blue.
Will a mixture that is 3 cups of yellow and 4.5 cups of
blue be more blue, more yellow, or the same shade of
green?
More blue
More yellow
Same shade
Explain your reasoning.
Answer:
7
Step-by-step explanation:
2×3.7=7 is easy and less money
The 2 line segments form a ___ that helps us find the ___
Answer:
is this on shapes or multiple answer?
Step-by-step explanation:
like i was thinking 2 segments as parallel
Find the x-intercept and y-intercept of the following
equation
2x + 5y = -6
Answer:
x = -3
y = -6/5
Step-by-step explanation:
To find the x-intercept(s), substitute in 0 for y and solve for x.
2x + 5(0) = -6
x = -3
Find the y-intercepts.
To find the y-intercept(s), substitute in 0 for x and solve for y.
2(0) + 5y = -6
y = -6/5
good luck, i hope this helps :)
The population of Yuba City, California is 61,360 people. What is 61,360 rounded to the nearest thousand? * 5 points
Answer: 61,000
Step-by-step explanation:
61,360 is nearest to 61,000 then too 62,000
Answer:
61,000
Step-by-step explanation:
if its under 5 rather it being 5 50 500 etc you put it to the smallest number in this case you look at the hundreds which is a 3.
Liliana and Marcus are playing a word game. Liliana spells a word incorrectly and loses 18 points. Then Marcus
spells a word correctly and has the opposite score. Which is the correct way to represent the opposite of
Liliana's score is equal to Marcus's score"?
0 -18-18
O-(-18) --18
-(18) --18
-(-18) - 18
Answer:
The answer is B or -(-18) = 18
Step-by-step explanation:
on Edg 2021
Answer:
D
Step-by-step explanation:
Cuz I did it on a test and I got it right.
Solve by using trial and error method. 3x = 16
Answer:
5.3...
..............
