A ball is thrown upward from a height of 15 feet with an initial velocity of 64 feet per second. Use indefinite integrals to write the position function of the ball at time t.
Answer:
The equation of the position at time t will be:
[tex]y(t)=-\frac{1}{2}9.81t^{2}+64t+15[/tex]
Step-by-step explanation:
We can start by saying that the acceleration here is g = -9.81 m/s². The minus sign is because the gravity acceleration is a vector downward (negative value), and the ball is going upward (positive value).
And we know that acceleration can be written as a second derivative:
[tex]g=\frac{d^{2}y}{dt^{2}}=y''[/tex] (1)
Now, we can take the integral in each side:
[tex]\int gdt=\int y''dt[/tex]
[tex]\int y''dt=\int -9.81dt[/tex] (2)
Solving the integral in each side we have:
[tex]y'(t)=-9.81t+C[/tex] (3)
Where y'(t) is the velocity at t time (v = dy/dt = y' ) and c is a constant value.
Now, the initial conditions are:
initial height y(0) = 15 feet
initial velocity y'(0) = v(0) = 64 feet/s
Using this condition we can find C. Let's evaluate equation (3) at t = 0.
[tex]y'(0)=-9.81(0)+C[/tex]
[tex]C=64\: feet/s[/tex]
So we have:
[tex]y'(t)=-9.81t+64[/tex] (4)
Now, we need to take the integral of equation (4) to get the position function:
[tex]\int y'(t)dt=\int (-9.81t+64)dt[/tex]
Solving this new integral we have:
[tex]y(t)=-\frac{1}{2}9.81t^{2}+64t+D[/tex] (5)
Using the same method above, we can find D evaluating (5) at t = 0, we have:
[tex]y(0)=-\frac{1}{2}9.81(0)^{2}+64(0)+D[/tex]
[tex]D=y(0)[/tex]
[tex]D=15\: feet[/tex]
Finally, the equation of the position at time t will be:
[tex]y(t)=-\frac{1}{2}9.81t^{2}+64t+15[/tex]
I hope it helps you!
how do i find the surface area and volume of this shape?
Answer:
3,761.46 m³
Step-by-step explanation:
Volume of a cone = 1/3πr²h
π = 3.14
radius, r = diameter/2
= 25/2 = 12.5 m
Height, h = 23m
Volume of a cone = 1/3πr²h
= 1/3 * 3.14 * 12.5² * 23
= 1/3 * 3.14 * 156.25 * 23
= 11,284.375 / 3
= 3761.4583333333
Approximately,
Volume of the cone = 3,761.46 m³
Find x. PQR = MNR ...............
Answer:
x = 55
Step-by-step explanation:
<QRP = <NRM because of vertical angles
To find <NRM:
x + 35 + 90 = 180
x + 125 = 180
x = 55
<NRM = 55
<QRP or x = 55
g(x)=-3x-8
g( )=10
what does x equal?
Answer: X = 24/G
G = 24/x
Step-by-step explanation:
Laurence is saving money for a set of speakers. He has $230 dollars in his savings right now. He just got a part-time job at Kroger and can increase his savings account by 20.6% each week. Write an equation to represent the amount of money
in his account, y after x weeks.
if your not good with percentages, i suggest you should go...
25% of ______ is 15
70% of 30 is ______
What % is 15 of 50?
15% of ______ is 6
40% of 30 is _____
LAST ONE!!!
What % is 40 of 50?
BONUS! (I'm good at these so its oppional)
3 / 1 1/6 =
19. y = 3x? - 12x
Find the discrimanite of each equation.Then,determine the number of solution
need help with this step by step please and thank you
Answer: y=−9x
x= y/9
Step-by-step explanation:
Find the value of x. Show your work of a piece of paper
Answer:
3
Step-by-step explanation:
x/1= 9/3
solve to get 3
Answer:
X = 3
Step-by-step explanation:
1. Find the difference between 1 and 3. The larger triangle is being multiplied by 3
2. To find x you must divide 9 by 3 since the bigger triangle is 3 times bigger then the smaller one. X then equals 3
Hope that helps
Let me know if it is confusing
2. Felix visited a math website that featured
a random number generator. He used the
generator to create a list of five random
integers. felix found the correct sum of the five integers. what is the correct sum?
name another pair of lines that appear to be perpendicular
Answer:
parallel lines
Step-by-step explanation:
im pretty sure this is it hope this helps
can SOMEBODY HELP ME WITH THIS LESSON I NEED HELP ASAP !!
Answer:
what's your question? I'm here to help if I can.
On a quiz show, the contestant who gets the answer correct in the shortest amount of time wins. The host asks for the solution to 49+83+51. Contestant number one quickly found the sum of 49 and 51 to be 100, then added 83 to get 183. Which property did the contestant use?
Answer:
The contestant used commutive property!
Step-by-step explanation:
The commutative property of addition simply means that it does not matter in which order we add numbers together. Subtraction is not commutative. This means that the order of the numbers in the subtraction matters.
Please mark me brainliest!
8) The volume of a cuboid 12cm long 9 sm broad and 6 cm high is
a) 648 cm
b) 648 m
c) 648 cm
d) 648 m
Answer:
648 cm³
Step-by-step explanation:
For Cuboid
l = 12cm
b = 9cm
h = 6cm
Now, The volume of a cube is
l × b × h
12 × 9 × 6 cm
108 × 6 cm
648 cm³
Thus, The volume of a cuboid 12cm long 9 sm broad and 6 cm high is 648 cm³
-TheUnknownScientist
This box plot shows the heights (in feet) of a sample of pine trees.
Pine tree heights
A pine tree that is 8 feet tall is added to the sample. How will this outlier
affect the shape of the box plot?
When a pine tree that is 8 feet tall is added to the sample, A. The new box plot will be negatively skewed.
What is negative skewness?Negative skewness occurs when the tail of the left side of the box plot is longer than the tail on the right side.
Negative skewness highlights the risk of left tail events or negative outliers known as “black swan events.”
Thus, when a pine tree that is 8 feet tall is added to the sample, A. The new box plot will be negatively skewed.
Learn more about negative skewness at https://brainly.com/question/20378699
#SPJ1
Answer:
A
hope this helps
Use the image to solve
what can you conclude from the box-and-whisker plot?
Answer:
that it is a cat :')
Step-by-step explanation:
remember, whisker = cat
The fractuon 3/5 is found between which pair of fractions on a number line?
Answer: It's kinda simple, 2/5 and 4/5
Just add 1 to the numerator of the original fraction, and there's where you get 4/5. Then subtract 1 from the original fraction, and that's where you get 2/5!
A health club charges a $75 membership fee. Weasley has $300 to spend on a health club membership. Write an inequality to model the number of months that Weasley can afford to be a member of the health club. What is the maximum number of months that he can use the health club?
Answer:
4 months
Step-by-step explanation:
we take $300 ÷$75 which is per month
then we get 4 , which is our months
10 points! Brain person too!
The stem-and-leaf plot shows mandy’s math test scores. What is the median of her test score?
A- 88
B- 87
C- 85
D- 84
Answer: C
Step-by-step explanation:
All the numbers are 78, 80, 83, 84, 84, 86, 89, 91, 95, 100. That’s because for each row, you take the number in the first column, and create each score by putting one of the numbers in the second column next to the first number. The median is the number in the middle if you were to put them out in order. I already listed the numbers in order, and the middle numbers are 84 and 86, so the find the middle of those, you add them together and divide by 2. You get 85, a.k.a. option C.
which property is BEST to use when combining 3/5 + 1/4 + 2/5? A) distributive property B) identity property of addition C) additive inverse property D) commutative property of addition
Answer:
D Community property of addition
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
Find the slope of each line.
Answer:
C) 1
Step-by-step explanation:
Slope = change in y over change in x
In the graph shown as y goes up 1 x goes up 1
so slope = 1/1 or 1
The slope equation is y=mx+b.
b is where the line crosses on the y axis, also known as the y-intercept.
m is the slope, which you are trying to find.
y and x are the points on the graph.
The slope is 3/3, which can be turned into 1, so the answer is c.
Erick no es mas alto que andres, oscar es mas bajo que carlos y este no es mas alto que erick. se puede deducir que:
a. Andrés es más alto que Erick
b. Carlos es más alto que Andrés
c. Oscar es más alto que Carlos
d. Oscar es el más bajo de todos
e. Ninguna de las anteriores
Answer:
es la b) Oscar es más bajos que todos
Step-by-step explanation:
espero y te ayude
Simple Composite figures question. Find the area of the shape.
9514 1404 393
Answer:
453.9 m²
Step-by-step explanation:
It considerably simplifies the area calculation to assume the figure decomposes to a parallelogram and an equilateral triangle.
The area of the parallelogram is ...
A = bh
A = (17 m)(6 m) = 102 m²
The area of the equilateral triangle—using the given altitude—is ...
A = 1/2bh
A = 1/2(17 m)(14.7 m) = 124.95 m²
The area of the whole figure is double the sum of these areas, so is ...
A = 2(102 m² +124.95 m²) = 453.9 m²
The area of the shape is 453.9 m².
__
Additional comment
Unless we make some assumptions about the location of the concave exterior angle at the left and right, we cannot compute the area of the figure. At least, we must assume the 10 m segments are parallel. If that is the only assumption, and other dimensions are taken at face value, the area of the figure computes to about 453.4 m². As you can see from the attachments, the altitude of 14.7 is not quite enough to make the triangle equilateral. That prevents the quadrilateral from being a parallelogram.
Further dividing the quadrilateral along its short diagonal, various lengths and angles can be found using the law of sines and the law of cosines. Then the figure area can be found as the sum of triangle areas: two triangles in the quadrilateral, and the one with altitude 14.7. This alternate approach is shown in the second attachment.
does anyone wanna do my iready IM GIVING 77 POINTS OR MORE. i have 240 points in total sooooo yeah i can give a lot. its 8th grade iready.
Answer:
YAY
Step-by-step explanation:
HELP, thanks, If a triangle has a side length of 8 inches, and another side length of 5 inches, which of the
following choices for the third side length will make a triangle?
a. 7 inches
b. 2 inches
c. 13 inches
d. 15 inches
Answer:
a. 7
Step-by-step explanation:
So a triangle a two sides that will always sum up to be greater than the third side.
Meaning:
a + b > c
a + c > b
b + c > a
So here, we're given a and b:
8 + 5 > c
8 + c > 5
5 + c > 8
Plug in the values:
13 > 7
15 > 5
12 > 8
These are all true, so it's probably 7.
13 > 2
10 > 5
7 > 8 This one is not true, so not 2.
13 > 13 This is not true, so not 13.
If not 13, we can't go any higher and so it can't be 15.
2. Find the length of AD if the length of AB is
14 units, the length of BC is 5 units, and the
length of CD is 8 units
Step-by-step explanation:
can you please show the picture too
Please answer correctly !!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!
Answer:
MN = 4 units
m<MLN = 42 degrees
Step-by-step explanation:
For this problem, we need to know the definition of congruence. Two shapes are said to be congruent if the angles and sides have the exact same measurements.
We are given that these two triangles are congruent, so we know they are the same. XYZ ~= NML
Since we know this, we simply rotate the triangles to be the same to know the measurements.
We know that XY = MN = 4 units.
We know that m<YZX = m<MLN = 42 degrees.
So, these are the solutions.
Cheers.
 ?!!!!!!!!!!!!!!!!!!!!!!!
The graph shows that the distance a dog runs is proportional to the time the dog is running. You want to use only one plotted point to find the unit rate. Which of the three plotted points could you choose? Select all that apply.
hence (1,7.5) or (5,37.5) points
Which statement(s) most directly apply to communism?
I. There is little or no private ownership.
II. Businesses are operated for the benefit of the people as a whole.
III. Individuals who take risks can gain great profits.
a.
I and II
b.
II only
c.
II and III
d.
I and III
Please select the best answer from the choices provided
A
B
C
D
Answer:
A
Step-by-step explanation:
In the beginning, there was little or no private ownership. Cucumbers are a pretty interesting example. We had an exchange student who said all the cucumbers were raised on one collective the size of 10 sections. He didn't know how many people were on that farm but it employed many people. The farm was located near a very large city so transportation was not a problem. The state owned the farm.
The second one is a result of the first one. Collectives are not meant to benefit the individual. They benefit everyone.
Three is a characteristic of free enterprise.
A: I and II
Answer:
a.
I and II
Step-by-step explanation: