Find r(t) given that r'(t) = 2ti + (1);- (cos(at))k, and r(1) = 2i + j - 3k.
Answers
To find r(t) given that r'(t) = 2ti + j - cos(at)k, and r(1) = 2i + j - 3k, we can integrate the components of r'(t) to obtain r(t).
Integrating the x-component, we have:
∫(2ti) dt = t^2 i + C1
Integrating the y-component, we have:
∫j dt = t j + C2
Integrating the z-component, we have:
∫(-cos(at)) dt = (1/a) sin(at) k + C3
Combining these results, we get:
r(t) = (t^2 i + C1) + (t j + C2) - (1/a) sin(at) k + C3
To determine the constants C1, C2, and C3, we can use the initial condition r(1) = 2i + j - 3k. Substituting t = 1 into the equation, we get:
2i + j - 3k = (1^2 i + C1) + (1 j + C2) - (1/a) sin(a) k + C3
From this equation, we can equate the coefficients of the unit vectors i, j, and k to find the values of the constants. This will give us the specific form of r(t) for the given conditions.
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Related Questions
Definition of a derivative (limit of the difference quotient)
Answers
The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:
f'(a) = lim (h → 0) [f(a + h) - f(a)] / h
What is derivative?
The derivative of a function in calculus measures the function's sensitivity to changes in its input variable. Specifically, at a particular point, it represents the function's rate of change with respect to its input variable at that moment.
The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:
f'(a) = lim (h → 0) [f(a + h) - f(a)] / h
This limit represents the instantaneous rate of change or slope of the function at the point x = a. The difference quotient is the change in the function value divided by the change in the input variable (or the distance between two points on the graph of the function).
The derivative is a fundamental concept in calculus, and it has many applications in various fields of science, engineering, and economics. It allows us to calculate important quantities such as velocity, acceleration, and marginal cost, and it is used to optimize functions and solve many real-world problems.
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t−7≤12
asap please hjvgjuiohkbjknl m kl;m
Answers
Answer:
t is less than or equal to 19
Step-by-step explanation:
t-7<12
+7
t is less than or equal to 19
What is 4 divided 2/3
Answers
Answer:
the answer for that equation is 6
Answer:
Step-by-step explanation:
4÷2/3=4/1÷2/3=4/1×3/2=12/2=6
I hope it'll help you much
Thank you for asking
Please answer correctly !!!!! Will mark brainliest !!!!!!!!!!!!!
Answers
Answer:
10 and 8
Step-by-step explanation:
For exercises 4-6, use the imaginary unit to write an equivalent expression for
the radicals.
Just number 4 and 6
Answers
6) 2(11i)
I’m pretty sure these are correct
if 12% of a number is 75, find 4% of that number
Answers
Answer:
25.60
Step-by-step explanation:
first divide 12%of a number with 75 Ans will be 6.25 then multiply with 4 Ans will be 25.60
Answer: 25
Step-by-step explanation:
12 divided by 4 = 3
75 divided by 3 = 25
25 = 4%
when would you a subtract in an expression
Answers
Answer:
You would need to subtract when:
Step-by-step explanation:
If there is a negative number like 4 -5
If there is a parentheses,
A subtraction sign.
Hope this helps you.
State the coordinates of the point.
Answers
The ratio of cats to dogs is
4:5. If there are 20 dogs,
how many cats are there?
29
Answers
Answer:
16
Step-by-step explanation:
Since the common ratio between cats and dogs is 4:5. We want to know cat and dogs in the ratio X:20. Thus, we can set up the equation as 4/5=X/50. Cross multiplication gets us 80=5X Solving for we get that 80/5 =X....16 =X Now, we know that the number of cats there are is 16
A bakery has 40 different flavored muffins
Answers
Answer:
nice
Step-by-step explanation:
Company XYZ closed at $100.76 per share with a P/E ratio of 1525 Answer the following questions. a. How much were earnings per share? b. Does the stock seem overpriced , underpriced, or about right given that the historical P/E ratio is 12-14? a. How much were earnings per share? $ Round to the nearest cent as needed. b. Based on the fact that the Company XYZ stock historically trades at an average P/E ratio of 12-14, does the stock price seem overpriced, underpriced, or about right?
Answers
The earnings per share can be calculated as $0.066 per share (rounded to the nearest cent).
a. The earnings per share for Company XYZ can be calculated by dividing the closing price by the P/E ratio. In this case, the closing price is $100.76 and the P/E ratio is 1525. Therefore, the earnings per share can be calculated as $0.066 per share (rounded to the nearest cent).
b. Based on the historical P/E ratio range of 12-14, the stock price of Company XYZ seems overpriced. The P/E ratio indicates the price investors are willing to pay for each dollar of earnings generated by the company. A higher P/E ratio suggests that investors have higher expectations for future earnings growth. In this case, the P/E ratio of 1525 is significantly higher than the historical range of 12-14, indicating that the stock is being valued at a much higher premium relative to its earnings. This suggests that the stock price may be inflated and not in line with the company's historical valuation metrics, indicating an overpriced condition.
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Umm what do I do here?
Answers
Answer:
X is equal to 1.2
Step-by-step explanation:
6/5 equals 1.2
i don't have to sound rude but can i have brainliest please i need 4 more :')
sierra read for 220 minutes 1 week. Chen read for 1/2 hour a day for 7 days which explanation is correct
Answers
The correct answer is option D: Chen read for less time because an hour a day for 7 days is equal to 210 minutes.
To determine the correct answer, we need to use the unitary method. This method involves converting the units of measurement into a common unit and then comparing them.
In this case, we need to convert hours into minutes to compare the reading time of Sierra and Chen.
An hour is equal to 60 minutes. Therefore, 1 hour a day for 7 days is equal to
=> 60 minutes * 7 days = 420 minutes.
However, we need to divide this number by 2 because Chen only read for half an hour a day. Hence, Chen read for 210 minutes
=> (420 minutes / 2).
Now that we have both the reading times in minutes, we can compare them. Sierra read for 220 minutes while Chen read for 210 minutes. As 220 > 210, it is clear that Sierra read for more time.
In conclusion, option D is the correct answer as Chen read for less time because an hour a day for 7 days is equal to 210 minutes. The unitary method is useful in comparing measurements with different units and it provides us with accurate results.
Complete Question:
Sierra read for 220 minutes in 1week. Chen read for an hour a day for 7 days. Which explanation is correct?
A. Sierra read for more time because 220 is greater than
B. Sierra read for less time because minutes are less than hours.
C. They read for the same amount of time because 1 week is equal to 7 days.
D. Chen read for less time because an hour a day for 7 days is equal to 210 minutes.
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The ratio table below shows the number of miles Shondra drove in a car for certain amounts of time during a road trip. Driving Distance Hours Driven Miles Driven 1 60 2 120 3 180 4 ? If Shondra traveled the same number of miles each hour, how many miles did she travel in 4 hours?
Answers
Answer:
Step-by-step explanation:
u take 2(64)-600-94 then u get 120
Answer:
240
Step-by-step explanation:
i had a stroke reading the one above me but i took the test:)
the mode of the numbers 2,3,6,2,2 is?
Answers
Answer: 2
Step-by-step explanation:
The mode is the most frequent number that appears. The number 2 appears the most so 2 would be the mode for this problem.
What is the slope of the line represented by the equation 2y = 5x + 4? A. 2. 5 B. 2 5 C. 2 D. 5
Answers
Answer:
A i think
Step-by-step explanation:
Pleasee pleaseee help me so I can not get in trouble because my grades
Answers
Answer:
she has 40 times as many
Step-by-step explanation:
Answer: 20
Step-by-step explanation:
80/4= 20
Look at attachment below please help
100 POINTS AND BRAINLYIEST
Answers
Answer:
x = 28 unitsy = 14 unitsStep-by-step explanation:
Given is 30 x 60 x 90 right triangle
The side ratios of this triangle is
y : 14√3 : x = 1 : √3 : 2Find the value of x and y using this ratio
y = 14√3/√3 = 14x = 2y = 2*14 = 28Let's find
sin60=14√3/x√3/2=14√3/xx=14×2x=28unitsAnd
tan60=14√3/y√3=14√3/yy=14unitsWhat is 100% of 80?
o A. 8
ов. 80
Ос. 800
D. 8,000
Answers
Answer:Its B or in other words its 80
Step-by-step explanation:
please brainliest
It takes Ryan 1 5 of an hour to bike from home to school. His biking speed is 10 mph.
How far apart are his school and his house?
Answers
Answer:
2
Step-by-step explanation:
1/5*10
Let Z be a standard normal random variable: i.e., Z ~ N(0,1). (1) Find the pdf of U = Z2 from its distribution. (2) Given that f(1/2) = VT Show that U follows a gamma distribution with parameter a = 1 = 1/2. (3) Show that I (1/2) = V1. Note that I (1) = Soe ex-1/2dx. Hint: Make the change of variables y = V2x and then relate the resulting expression to the normal distribution.
Answers
1)The pdf of U is f(u) = (1/(2√u)) exp(-u/2) for u > 0 and f(u) = 0 otherwise.
2)U follows a gamma-distribution with parameter a = 3/2 or a = 1/2.
3)x = (y²/2) and dx = y dy using exponential distribution
We can rewrite the integral as:
I(1/2) = ∫₀^∞ y exp(-y²) dy
= 1/2 ∫₀^∞ exp(-u/2) du
This is the same as the integral for f(u) when u = 1/2.
Therefore, we have:
I(1/2) = V1
(1) For U = Z², we can use the method of transformations.
Let g(z) be the transformation function such that
U = g(Z)
= Z².
Then, the inverse function of g is given by h(u) = ±√u.
Thus, we can apply the transformation theorem as follows:
f(u) = |h'(u)| g(h(u)) f(u)
= |1/(2√u)| exp(-u/2) for u > 0 f(u) = 0 otherwise
Therefore, the pdf of U is given by:
f(u) = (1/(2√u)) exp(-u/2) for u > 0 and f(u) = 0 otherwise.
(2) We are given that f(1/2) = VT, where V is a constant.
We can substitute u = 1/2 in the pdf of U and equate it to VT.
Then, we get:VT = (1/(2√(1/2))) exp(-1/4)VT
= √2 exp(-1/4)
This gives us the value of V.
Now, we can use the pdf of the gamma distribution to find the parameter a such that the gamma distribution matches the pdf of U.
The pdf of the gamma distribution is given by:
f(u) = (u^(a-1) exp(-u)/Γ(a)) for u > 0 where Γ(a) is the gamma function.
We can use the following relation between the gamma and the factorial function to simplify the expression for the gamma function:
Γ(a) = (a-1)!
Thus, we can rewrite the pdf of the gamma distribution as:
f(u) = (u^(a-1) exp(-u)/(a-1)!) for u > 0
We can now equate the pdf of U to the pdf of the gamma distribution and solve for a.
Then, we get:
(1/(2√u)) exp(-u/2) = (u^(a-1) exp(-u)/(a-1)!) for u > 0 a = 3/2
Therefore, U follows a gamma distribution with parameter
a = 3/2 or equivalently,
a = 1/2.
(3) We need to show that I(1/2) = V1.
Here, I(1) = ∫₀^∞ exp(-x) dx is the integral of the exponential distribution with rate parameter 1 and V is a constant.
We can use the change of variables y = √(2x) to simplify the expression for I(1/2) as follows:
I(1/2) = ∫₀^∞ exp(-√(2x)) dx
Now, we can substitute y²/2 = x to obtain:
x = (y²/2) and
dx = y dy
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Which equations define y as a linear function of x ?
Select all that apply.
A
y = 2x
B
y= 5x + 3
1
y === 9
D
y = 22
E
y = 4x2 + 2.c
TI
y = 2(4x – 2) + 16
Answers
Answer:
gkgk
Step-by-step explanation:
find a volume of a cube whose base radius is 5 cm and height 28 cm
Answers
Answer:
The volume of the cube is 21952.
Step-by-step explanation:
V = L x W x H
because a cube's sides are all the same, the length, width, and height are also the same. So we use the formula:
V= S^3
(S standing for side)
we know the height is 28 and as all sides measure the same we use the equation:
V= 28^3
28^3 = 21952
So, V= 21952
MC) Determine the surface area of the cylinder. (Use π = 3.14) net of a cylinder where radius of base is labeled 5 inches and a rectangle with a height labeled 4 inches
Pls help it’s for 20 point pls
Answers
The surface area of the cylinder is 314.6 square inches.
The surface area of a cylinder is given by the formula:
S.A. = 2πrh + 2πr²
Where r is the radius of the circular base of the cylinder and h is the height of the cylinder.
If we know the radius and height of a cylinder, we can easily calculate its surface area.
To solve for the surface area of the cylinder whose radius is 5 inches, we use the formula and substitute the values. The net of a cylinder whose radius of the base is labeled 5 inches and a rectangle with a height labeled 4 inches is given below:
Given the radius, r = 5 inches, height of cylinder, h = 4 inches.
Substituting the values in the formula:
S.A. = 2πrh + 2πr²
= 2 × 3.14 × 5 × 4 + 2 × 3.14 × 5²
= 157.6 + 157
= 314.6 square inches
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If
x
=
4
and
y
=
6
, evaluate the following expression:
20
+
3
(
3
y
−
4
x
)
Answers
20+3(3y-4x)
if x=4 y=6
20+3((3×6)-(4×4))=20+3(18-16)=20+3×2=20+6=26
answer: 26.
To find the sum of 4/10 and 3/100 how must 4/10 be expressed before adding it to 3/100
Answers
Answer:
It should be expressed as 40/100.
Step-by-step explanation:
The denominators should be equal
PLEASE HELP MEH 2I will do anything :(
Answers
Answer:
C = 125
Step-by-step explanation:
Since a straight line is 180 degrees. We can conclude that:
10x + 15 + 5x = 180
And that:
C = 10x + 15
First we need to find the value of x to find C. So,
10x + 15 + 5x = 180
15x + 15 = 180
- 15 -15
15x = 165
15x/15 = 165/15
x = 11
So now, we need to substitute the values of x into C and solve it.
C = 10(11) + 15
= 110 + 15
= 125
find the volume v v of the described solid s s. a right circular cone with height 3 h 3h and base radius 3 r 3r.
Answers
The answer to your question is that the volume of the solid s, which is a right circular cone with height 3h and base radius 3r, can be calculated using the formula V = (1/3)πr^2h.
a cone can be thought of as a pyramid with a circular base. The volume of a pyramid is given by the formula V = (1/3)Bh, where B is the area of the base and h is the height. In the case of a right circular cone, the base is a circle with radius r, so the area of the base is πr^2.
Substituting B = πr^2 and h = 3h into the formula for the volume of a pyramid gives:
V = (1/3)πr^2(3h) = πr^2h
So the volume of the right circular cone with height 3h and base radius 3r is (1/3)π(3r)^2(3h) = 9πr^2h.
the volume of a cone can also be derived using calculus. By slicing the cone into thin disks, we can approximate its volume as the sum of the volumes of these disks. As the thickness of the disks approaches zero, this approximation becomes more accurate and we obtain the exact volume of the cone.
Integrating the area of a disk over the height of the cone gives:
V = ∫0^3πr^2(y/3)dy
where y is the height above the base of the cone and r = (3/y)r is the radius of the disk at that height. Evaluating this integral gives the same result as the formula derived earlier:
V = (1/3)π(3r)^2(3h) = 9πr^2h.
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The diameter of a circular pizza is 24 in. How much pizza is eaten (in square inches) if half of it is consumed? (Pie and л... hmmmm...interesting...)
Answers
Using the formula of area of a circle, about 226.08in² has been eaten
How much pizza is eaten?The diameter of the pizza is given as 24 inches. To calculate the area of the entire pizza, we need to use the formula for the area of a circle:
Area = π * r²
where π is approximately 3.14 and r is the radius of the circle.
Given that the diameter is 24 inches, the radius (r) would be half of the diameter, which is 12 inches.
Let's calculate the area of the entire pizza first:
Area = 3.14 * 12²
Area = 3.14 * 144
Area ≈ 452.16 square inches
Now, if half of the pizza is consumed, we need to calculate the area of half of the pizza. To do that, we divide the area of the entire pizza by 2:
Area of half of the pizza = 452.16 / 2
Area of half of the pizza ≈ 226.08 square inches
Therefore, if half of the pizza is consumed, approximately 226.08 square inches of pizza would be eaten.
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Under her cell phone plan, Meena pays a flat cost of $38 per month and $3 per gigabyte. She wants to keep her bill under $55 per month. Which inequality can be used to determine xx, the maximum number of gigabytes Meena can use while staying within her budget?
Answers
The.maximum number of gigabytes Meena can use while staying within her budget is 5 gigabytes
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal.
They are denoted by the symbols ≥ < > ≤.
Let the maximum gigabytes be x.
The inequality to illustrate the information will be:
38 + 3x < 55
Collect like terms
3x < 55 - 38
3x < 17
Divide
x < 17/3
x < 5 2/3
The maximum gigabytes is 5.
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