Answer:
a) The stone takes approximately 6.704 second to reach the ground.
b) The stone takes approximately 6.704 second to reach the ground.
c) The stone hits the ground at a velocity of -215.695 meters per second.
Step-by-step explanation:
a) The stone experiments a free fall, which is a uniform accelerated motion due to gravity and in which effects from air friction and Earth's rotation are negliglble. Then, the vertical distance of the stone above the ground at any time [tex]t[/tex] is represented by the following model:
[tex]y = y_{o}+v_{o}\cdot t +\frac{1}{2}\cdot g\cdot t^{2}[/tex] (1)
Where:
[tex]y_{o}[/tex] - Initial height of the stone, measured in meters.
[tex]v_{o}[/tex] - Initial velocity of the stone, measured in meters per second.
[tex]t[/tex] - Time, measured in seconds.
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
If we know that [tex]y_{o} = 723\,ft[/tex], [tex]v_{o} = 0\,\frac{ft}{s}[/tex] and [tex]g = -32.174\,\frac{ft}{s^{2}}[/tex], then the distance of the stone above the ground at any time [tex]t[/tex] is represented by the following model:
[tex]y = 723 -16.087\cdot t^{2}[/tex] (2)
b) If we know that [tex]y = 0[/tex], then the time taken by the stone to reach the ground is:
[tex]723-16.087\cdot t^{2} = 0[/tex]
[tex]t = \sqrt{\frac{723}{16.087} }\,s[/tex]
[tex]t \approx 6.704\,s[/tex]
The stone takes approximately 6.704 second to reach the ground.
c) The function velocity is found by differentiating (2) once:
[tex]v = -32.174\cdot t[/tex] (3)
If we know that [tex]t \approx 6.704\,s[/tex], then the velocity when it hits the ground is:
[tex]v = -32.174\cdot (6.704)[/tex]
[tex]v = -215.695\,\frac{m}{s}[/tex]
The stone hits the ground at a velocity of -215.695 meters per second.
Mark paid $54.60 to fill his car's gas tank. The gas tank was empty and the cost of gasoline was $3.90 per gallon.
Kendra has an unlimited supply of unbreakable sticks of length 2, 4 and 6 inches. Using these sticks, how many non-congruent triangles can she make if each side is made with a whole stick
Answer:
Unlimited number of triangles.
Step-by-step explanation:
Unlimited number of triangles can be made because Kendra has unlimited supply of unbreakable sticks. If she has limited number of sticks suppose 90 sticks so she can be able to made 30 non-congruent triangles from these number of sticks so if the number is not known so we are unable to say about the number of triangles should be made from unlimited unbreakable sticks.
Which is the equation of a line that is perpendicular to the line
y
=
−
5
x
+
11
?
Answer:
y=1/5x
Step-by-step explanation:
hopefully that helped
What is the scientific notation of 0.00802
Answer:
8.02 × 10-³
Step-by-step explanation:
Find the values of a and b so that the linear system has the given solution.
Given Solution: (2, 1)
Equation 1: ax - by'= 4
Equation 2: bx - ay = 10
Answer:
The values are a=6, b=8
Step-by-step explanation:
System of Equations
We are given the system of equations:
ax - by = 4
bx - ay = 10
And it's known the solutions are: x=2, y=1.
Plugging in the solutions:
2a - b = 4 [1]
2b - a = 10 [2]
Now we have to solve the system above. Multiply [1] by 2:
4a - 2b = 8
Now we add with [2]:
3a = 18
a = 18/3 = 6
a = 6
From [2]:
2b - 6 = 10
2b = 16
b = 16/2 = 8
b = 8
The values are a=6, b=8
You bike 11.2 miles in 1.4 hours at a steady rate what equation represents to proportional relationship between the X ours your bike in the distance y in miles that you travel
Please don't just copy and paste or click an answer! PLEASE READ! I spend 14 minutes and I at least want you to read it!
11.2 * 1.4 = 15.68
Mark me brainliest if you can!
Give a common multiple of 8 and 10 between 1 and 100.
Answer:
40
Step-by-step explanation:
8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
10: 10, 20, 30, 40, 50, 60, 70, 80
Jeff modeled the number of minutes that he read each day during the first week of the summer. The recursive function, f(x), can be used to determine the number of minutes that he had read after a certain number of days, where x represents the number of days. f(1) = 28 f(x) = f(x - 1) + 8 Use the recursive function to find the number of minutes that Jeff read after 3 days of summer.
9514 1404 393
Answer:
44 minutes
Step-by-step explanation:
We are given f(1) = 28.
Using the recursive formula ...
f(2) = f(1) +8 = 28 +8 = 36
f(3) = f(2) +8 = 36 +8 = 44
Jeff read 44 minutes after 3 days of summer.
(a) Find the Total profit function P(q).
(b) Find the first and second derivatives for P(q).
(c) Find the optimum production quantity to maximize profit.
Answer:
answer is c Find the optimum production quantity maximize profit
to compound 50% solution in which proportion must 95% sol and 30% sol be mixed to make
500 ml
Answer:
4/9
Step-by-step explanation:
Let the amount of 95% sol = a ml and
the amount of 30% sol = b ml.
So, the total amount of the compound=a+b=500 ml
As the compound is 50% solution, so
95% of a + 30% of b= 50% of (a+b)
(95/100)a+(30/100)b=(50/100)(a+b) [from equation (i)]
95a + 30b = 50(a+b)
95(a/b)+30 = 50(a+b)/b [dividing both sides by b]
95(a/b)+30 = 50(a/b+1)
95(a/b)+30 = 50(a/b)+50
95(a/b)-50(a/b)=50-30
45(a/b)=20
a/b=20/45
a/b=4/9
Therefore, a:b=4:9
As a+b= 500 ml, so the amount of 95% sol = [tex]\frac {500}{13}\times 4=\frac{2000}{13}=153.85[/tex] ml
and the amount of 95% sol = [tex]\frac {500}{13}\times 9=\frac{4500}{13}=346.15[/tex] ml
Hence, the proportion of 95% sol and 30% sol to make a compound of 50% sol must be 4/9.
Create the f(x) function based on the table. Answer should be in function notation
Answer:
It will be
f(x)=x+4
Determine the quotient of 1 and 2 over 3 divided by 4 over 5 . (2 points)
1 and 1 over 3
1 and 8 over 15
2 and 1 over 12
2 and 5 over 6
Answer:
2 and 1 over 12
Step-by-step explanation:
[tex]1 \frac{2}{3} \div \frac{4}{5} \\ \\ = \frac{1 \times 3 + 2}{3} \div \frac{4}{5} \\ \\ = \frac{5}{3} \times \frac{5}{4} \\ \\ = \frac{25}{12} \\ \\ = 2 \frac{1}{12} \\ [/tex]
CAN SOMEBODY PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
x-intercept=-2
y-intercept=3
23) You are late for work. You have two options for getting to work. You may take the bus which takes on average 40 minutes with a standard deviation of 12 minutes. Or you can cycle which takes on average 50 minutes with a standard deviation of 2 minutes. Compare these two distributions.
You leave your house at 8.05 am and are supposed to start work at 9.00 am.
Which option would you choose if you will be fired if you are even a few minutes late?
Answer:
either of them because you wont be late because it only takes 52 minutes for both
Step-by-step explanation:
because
One of the objectives for this lesson is to find the length of a curve using the z score.
True
False
Answer:
true
Step-by-step explanation:
What's the right answer please
Answer:
2
Step-by-step explanation:
a>0 is maximum value of f
If you have 54/4 how does it equal 13.5
Answer:
I don't like mathematics
an amusement park sold 46 child tickets. The other 4 tickets it sold were adult tickets. What is the ratio of the number of adult tickets to the number of child tickets? Select all correct ratios
Answer:
2:46
1:23
Step-by-step explanation:
Using the quadratic formula to solve x2 + 20 = 2x, what are the values of x?
Answer:
X=1 = i√19 Put a vertical line through the second = sign
Step-by-step explanation:
when writing this .....put a line under all the + signs 0k and / is divided by 2
2 + √4-4(1)(20)
2 + √4-80 /2
x=2 +√76/2
x=2 +2i√19 the twos cancel out
1 +i√19
Put these fractions in order of size, smallest to largest.
7/10
2/3
4/5
11/15
Answer:
11/15 7/10 4/5 2/3
Step-by-step explanation:
the bigger the fraction the smaller the number
A minor league baseball team has a member’s club. It costs $30 to join and $3 per ticket. Non-members pay $6 per ticket. How many tickets will it take for the cost to be the same?
Answer:
2 tickets
Step-by-step explanation:
because if a no member ticket is 6 dollars than than two 3 dollar tickets will equal 6 dollars
Subtracting Fractions with Unlike Denominators
5/6 - 2/3 =
4/6
1/2 - 1/3 =
0/16
7/8 - 1/4 =
2/8
11/12 - 2/3 =
4/12
3/4 - 2/3 =
1/12
5/8 - 1/2 =
5/8 - 4/8 =
1 - 2/3 =
5/8 - 1/5 =
5/9 - 1/4 =
1/3 - 1/7 =
4/5 - 3/7
Answer:
5/6-2/3=1/6
Step-by-step explanation:
You make the denominators the same. Like 5/6 and 2/3 you can make the fractions have the same denominator.
5/6-2/3 is the same as the equation 5/6-4/6 but simplified.
Use the table below to answer the question.
Price Quantity Supplied of T-shirts Quantity Demanded of T-shirts
$5
0
300
$10
100
100
$25
300
50
$50
400
0
At the highest price of $50, producers supply _____ T-shirts and consumers demand _____T-shirts.
100, 100
0, 300
400, 0
Answer: 400,0
Step-by-step explanation:
I just took this on Ody
Find the equation of the tangent line to the function f(x) = 3x3 - x + 2 at a =0
Answer:
y=(9a^2-1)x-6a^3+2
Step-by-step explanation:
Pythagorean Theorem POSSIBLE POINTS : 13:33 Two joggers run 12 miles north and then 8 miles west. What is the shortest distance to reach their starting point? It irrational round to the nearest tenth of a mile.
Answer:
14.4 miles
Step-by-step explanation:
Given that :
Distance moved North = 12 miles
Distance moved West = 8 miles
Shortest distance to reach starting point :
Let shortest distance to reach starting point = d miles
Using the relation :
Longest side of a right angled triangle:
d = sqrt(8^2 + 12^2)
d = sqrt(64 + 144)
d = sqrt(208)
d = 14.422205
d = 14.4 miles (nearest tenth of a mile)
4x−2(x−4)=−3+4x+5 please I need help
Answer:
x=3
Step-by-step explanation:
4x−2(x−4)=−3+4x+5
4x+(−2)(x)+(−2)(−4)=−3+4x+5
4x+−2x+8=−3+4x+5
(4x+−2x)+(8)=(4x)+(−3+5)
2x+8=4x+2
2x+8−4x=4x+2−4x
−2x+8=2
−2x+8−8=2−8
−2x=−6
−2x /−2 = −6 /−2
x=3
Is 413.25 a whole number
Answer:
No
Step-by-step explanation:
Whole numbers do not have decimals
Please help me thank you I appreciate it
Answer:
73
Step-by-step explanation:
since it's a right angle it equals 90° and you already know there 17°. so you just subtract 90-17
Jeremy can do 22 push ups in 4 days. At this rate how many push-ups can he do in 6 days
Answer:
I think it's
Step-by-step explanation:
22=4
c=6
132,=4c
c=132/4
c=33
Answer:132 push ups
Step-by-step explanation:
Which of these is an example of driving at an average rate of 20 miles per hour?
driving 10 miles in 2 hours
O driving 25 miles in 5 hours
O driving 15 miles in 5 hours
driving 40 miles in 2 hours
Answer:
driving 40 miles in 2 hours