CALCULUS: Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = cos(t) - sin(t) and v(0) = 3.
A. v(t) = sin(t) + cos(t) + 3
B. v(t) = sin(t) + cos(t) + 2
C. v(t) = sin(t) - cos(t) + 3
D. v(t) = sin(t) - cos(t) + 4
I picked A., which was marked wrong, although I truly believe that is the answer because I got sin(t) - (-cos(t)) + 3. Please tell me whether you believe this is right or am I doing something wrong. I really want to learn/master this concept. Thanks is advance.
Answers
Answer:
B. v(t) = sin(t) + cos(t) + 2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
Function NotationCalculus
Antiderivatives - Integrals
Integration Constant C
Solving Integration Equations
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Step-by-step explanation:
*Note: Remember that the velocity function is the integral of the acceleration function/acceleration is the derivative of velocity.
[tex]\displaystyle v'(t) = a(t)\\v(t) = \int {a(t)} \, dt[/tex]
Step 1: Define
a(t) = cos(t) - sin(t)
v(0) = 3
Step 2: Integrate
Set up integral: [tex]\displaystyle v(t) = \int {cos(t) - sin(t)} \, dt[/tex][integral] Rewrite [Integration Property - Subtraction]: [tex]\displaystyle v(t) = \int {cos(t)} \, dt - \int {sin(t)} \, dt[/tex][Integral] Trig integration: [tex]\displaystyle v(t) = sin(t) - [-cos(t)] + C[/tex][Velocity Integration] Simplify: [tex]\displaystyle v(t) = sin(t) + cos(t) + C[/tex]Step 3: Find Function
We need to solve for the entire function, meaning we need to find constant C.
Substitute in given point [Velocity Integration]: [tex]\displaystyle v(0) = sin(0) + cos(0) + C[/tex][Velocity Integration] Substitute: [tex]\displaystyle 3 = sin(0) + cos(0) + C[/tex][Velocity Integration] Evaluate trig: [tex]\displaystyle 3 = 0 + 1 + C[/tex][Velocity Integration] Add: [tex]\displaystyle 3 = 1 + C[/tex][Velocity Integration] Isolate C [Subtraction Property of Equality]: [tex]\displaystyle 2 = C[/tex][Velocity Integration] Rewrite: [tex]\displaystyle C = 2[/tex][Velocity Function] Substitute in C [Velocity Integration]: [tex]\displaystyle v(t) = sin(t) + cos(t) + 2[/tex]Topic: Calculus
Unit: Basic Integration
Book: College Calculus 10e
Related Questions
Jennifer has 12 nickels and dimes. The value of her coins is $1
Answers
Answer:
4 dimes, 12 nickels
Step-by-step explanation:
nickels are worth 5 cents,
12x5=60
$1 is worth 100 cents
100-60 is 40
dimes are worth 10 cents
40 / 10 is 4
so 4 dimes
The number of dimes = 8 dimes
The number of nickels = 4 nickels
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of nickels be = x
Let the number of dimes be = y
Now , the total number of coins = 12
So , the equation will be
x + y = 12 be equation (1)
Now , the total value of coins = $ 1
The value of 1 dime = $ 0.10
The value of 1 nickel = $ 0.05
So , the equation will be 0.05x + 0.10y = 1 be equation (2)
Multiply equation (2) by 100 , we get
5x + 10y = 100 be equation (3)
Multiply equation (1) by 5 , we get
5x + 5y = 60 be equation (4)
Subtracting equation (4) from equation (3) , we get
5y = 40
Divide by 5 on both sides of the equation , we get
y = 8
Therefore , the value of y = 8
Substitute the value of y in equation (1) , we get
x + y = 12
x + 8 = 12
Subtracting 8 on both sides of the equation , we get
x = 4
Therefore , the value of x is 4 and value of y is 8
Hence , The number of dimes = 8 dimes
The number of nickels = 4 nickels
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At Garcia's Bike Rentals, it costs $45 to rent a bike for 8 hours. How many hours of bike use does a customer get per dollar?
Answers
Answer:
5
Step-by-step explanation:
Answer:
$0.09/minute
Step-by-step explanation:
$45/8 hours is $5.63 per hour
There is 60 minutes in an hour.
So you do $5.63/60 minutes and it's about $0.09
So it's 9 cents per minute
hope this helps :)
Helppppppp meeeeeee pleaseeeeee asappp
Answers
Answer:
C
Step-by-step explanation:
open circle, arrow pointing left
(Look at attached imagine)
Answers
Answer:
C. [tex]r=\sqrt[3]{\frac{3V}{4\pi}}[/tex]
Step-by-step explanation:
Are the two expressions in the equation 2b + 5 + 1b = 3b + 5 equal or equivalent? How do you know
Answers
The blizzard company sent a survey to their world of warcraft subscribers and asked if they were expected about the up coming expansion. From the survey, 16 people of the 20 people surveyed said they were excited. A) the probability that 2 people were excited without replacement is
Answers
Answer:
0.6316
Step-by-step explanation:
The computation of the probability that 2 people were excited without replacement is shown below:
There is a total of 20 people
out of which 16 are excited and the remaining 4 would be non-excited
Now the probability would be
[tex]= \frac{^{16}C_2}{^{20}C_2}[/tex]
= 0.6316
Please help ten points
Answers
B=55 degrees
C=25 degrees
what is the sum of 7 and t/2
Answers
Answer:
14/2+t/2 so ( 14+t)/2 is the answer
(7)(2)+(t)(1) /(2) (1)
=(14+t)/(3)
JJack, Jill, and Bill each carried a 48-fluid ounce bucket full of water down the hill. By the time they reached the bottom, Jack's bucket was only 3/4 full, Jill's was 2/3 full, and Bill's was 1/6 full. How much water did they spill altogether on their way down the hill?
Answers
Answer:
Jill lost 1/3
Bill lost 1/6
and Jack lost 1/4
Make a common denominator - let's use 12
Jill lost 4/12
Bill lost 2/12
Jack lost 3/12
Add them together = 9/12
reduce by dividing by 3.
total of 3/4 spilt
48 divided into 4 parts then multiplied by 3 of those parts
48 / 4 * 3 = 36
Step-by-step explanation:
A sum amount to $2400 at 15% simple interest per annum after 4 years. Find the sum
Answers
Answer:
1500
Step-by-step explanation:
We can required to find the sum which also means the value
Future value= value × [ 1 + rate×time]
2400= value × [1 + 15/100×4]
2400= value × [1 + 0.15×4]
2400= value × [1+0.6]
2400= value × 1.6
Value= 2400/1.6
= 1500
A point P os equi distant from R(-2,4) and S(6,-4) and its x co ordinate is twice its Y co ordinate find co ordinates of P
Answers
Answer: [tex]P(-4,-2)[/tex]
Step-by-step explanation: Distance between two points is calculated as
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
Equidistant means the same distance, i.e., the distance between points P and R is equal to the distance between points P and S.
Suppose P's y-coordinate is a. If its x-coordinate is double, then
(x,y) = (2a,a)
Thus
[tex]\sqrt{(2a+2)^{2}+(a-4)^{2}} =\sqrt{(2a-6)^{2}+(a+4)^{2}}[/tex]
Solving
[tex]4a^{2}+8a+4+a^{2}-8a+16=4a^{2}-24a+36+a^{2}+8a+16[/tex]
[tex]5a^{2}+20=5a^{2}-16a+52[/tex]
[tex]-16a=32[/tex]
[tex]a=-2[/tex]
y-coordinate is [tex]-2[/tex], then x-ccordinate is
2a = 2(-2) = [tex]-4[/tex]
Coordinates of point P equidistant for R and S is [tex](-4,-2)[/tex].
Solve for X: X+8=3(x-7)-5
Answers
Answer:
x = 17
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightDistributive Property
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
x + 8 = 3(x - 7) - 5
Step 2: Solve for x
Distribute 3: x + 8 = 3x - 21 - 5Combine like terms: x + 8 = 3x - 26[Subtraction Property of Equality] Subtract x on both sides: 8 = 2x - 26[Addition Property of Equality] Add 26 on both sides: 34 = 2x[Division Property of Equality] Divide 2 on both sides: 17 = xRewrite/Rearrange: x = 17Answer:
17
Step-by-step explanation:
X+8=3(x-7)-5
x+8=3x-21-5
x+8=3x-26
8=2x-26
34=2x
Megan is planning to make dinner for a group of friends. She wants to make each person a personal pizza. It takes Megan 3 minutes to prepare a personal pizza with toppings. The function P(f) = 3f represents the time it takes to prepare the pizzas, where f is the number of friends attending her dinner party.
The function C(f) = 30 represents the time to cook the pizzas since it will take Megan 30 minutes regardless of how many friends attend..
Which expression represents how long it will take Megan to prepare and cook the pizzas
A. P(f) + C(f)
B. P(f) – C(f)
C. P(f) ∙ C(f)
Answers
Answer:
The answer is A
Step-by-step explanation:
You are adding the time it takes to make a pizza so it isn't B or C
What is the height of the boat in the scale model?
What length is the real boat?
Answers
Answer:
15
Step-by-step explanation:
a) The height of the real boat is 15 feet and the scale model is 3 inches
b) The scale model is 9 inches , and the real height is H = 45 feet
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion be represented as A
Now , the value of A is
The proportion of scale model of the boat to the real boat is 1 : 5
Now ,
a)
The height of the real boat is 15 feet and the scale model is k inches
From the proportion , we get
1 / 5 = k / 15
Multiply by 15 on both sides , we get
k = 3 inches
b)
The scale model is 9 inches , and the real height is H
From the proportion , we get
5 / 1 = H / 9
Multiply by 9 on both sides , we get
H = 45 feet
Hence , the proportion is solved
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6 + 4y = Y-6
hurry please giving 15 points
Answers
Answer:
y= -4
Step-by-step explanation:
Using technology, determine the monthly payment on a 35 month loan of $28,000 at 8.1% compounded monthly. Round your answer to the nearest cent.
Please select the best answer from the choices provided
A. $900.90
B. $875.02
C. $1,102.94
D. $1,012.10
Answers
Answer: a
Step-by-step explanation:
Took test
At a sale, dresses were sold for $192 each. This price was 96% of the dress's original price. How much did a dress originally cost?
Answers
Answer:
$199.68
Step-by-step explanation:
You would have to find 4% of 192.
That is 7.68.
192+7.68=199.68.
How do you write 75% as a unreduced fraction
Answers
Answer:75/100
Step-by-step explanation:
75%=75/100
Answer:
75/100
Step-by-step explanation:
reduced fractions of this include but are not limited too: 3/4 6/8 12/16 24/32 48/64
Write a story to match the equation: x + 2 1/2 = 10
Lin likes to bake batches of muffins and share them with friends and family. She needs 10 cups of flour for her next batch, but only has 2 1/2 cups left. How much more flour does she need?
Answers
Answer:
She needs 15/2 cups of flour.
Step-by-step explanation:
x+2 1/2=10
2 1/2=5/2
x+5/2=10
x=10-5/2
x=20/2-5/2=15/2
A vending machine sells chips for $0.50 and candy bars for $1.00. If Jim spent $5.50 on snacks in the machine over the course of a week, how many candy bars did he buy? G. 2 H. 3 J. 4 K. Cannot be determined from the given information
Answers
Answer:
can't be determined
Step-by-step explanation:
we would need to know the total number of bars/chips he brought
Suppose f(x)=x^2 +1. Find the graph of 4 f(x).
Graph 1
Graph 2
Answers
Answer:
Graph 1.
Step-by-step explanation:
The graph of f(x) will be compressed by a factor 4 and the vertex will be 4 units up from the origin.
Solve for x
Solve for x
Answers
Answer:
x=19
Step-by-step explanation:
20/36=30/(x+5+30)
20(x+35)=30(36)
20x+700=1080
20x=380
x=19
Select all the statements that are true about rhombuses. Group of answer choices
Opposite angles are congruent.
Diagonals are congruent.
Diagonals bisect each angle.
Diagonals are perpendicular.
Opposite sides are parallel.
Answers
Step-by-step explanation:
By method of elimination;
- Opposite angles are congruent
Congruent means Equal
This is correct.
- Diagonals are congruent
This is incorrect.
- Diagonals bisect each angle.
This is correct.
- Diagonals are perpendicular.
This is correct.
- Opposite sides are parallel.
This is correct.
Answer:
- Opposite angles are congruent
- Diagonals bisect each angle.
- Diagonals are perpendicular.
- Opposite sides are parallel
Which of the following answers would have
no solution?
X=3
5=3
2=2
Answers
Answer:
no entiendo me explican que significa por fa
plz solve it
all the 3 sub questions
chapter quadrilaterals
9 cbse
Answers
Answer:
I edited answer
hope it helped
The sum of my number and two and two thirds is seven. What is my number?
7 is in one box. Below it are 2 boxes. N is in one. 2 and 2-thirds is in the other.
Check all that apply.
The variable, n, represents the unknown number.
The unknown number and 2Two-thirds equals 7
4One-third+2Two-thirds= 7
9Two-thirds- 2Two-thirds= 7
n = 4One-third
Answers
Answer:
1,2,3,5
Step-by-step explanation:
Answer:
abce
Step-by-step explanation:
HELP MEEEEE PLEASEEE
Answers
Answer:
i do not know but you need to answer you text messages
Step-by-step explanation:
1.) 87.743
2.)123.789
3.) 3256.1254
4.) 102356.78
5.) 78.56
Round to whole number..
Answers
Answer:
1.)88
2.)124
3.)3256
4.)102357
5.)79
Step-by-step explanation:
what would be the reminder of 20,000 divided by 24 ?
Answers
Answer:
I think 2500..not sure tho
Step-by-step explanation:
Which table and graph represent the equation y = 3X?
—————————
a.table B and graph A
b.table B and Graph B
c.table A and graph B
d.table A and graph A
Answers
Answer:
d. table A and graph A
Step-by-step explanation:
y=3x
y = 3X is represented by graph B .
y = 3X is represented by table A .
Hence option C is correct .
Given, Equation : y = 3X
Now, to get the values of y substitute x.
Firstly table A:
y = 3X
x = 1 : y = 3
x = 2 : y = 6
x = 3 : y = 9
Thus table A represents the equation .
Next graph B :
Starting point of graph B is origin.
Coordinates of origin : (0,0)
Equation of graph B : y = 3X
Thus graph B represents the equation .
Therefore option C is correct .
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