Answer:
$42.84
Step-by-step explanation:
P = 85 * 6 = 510
Formula:
I = Prt
Given:
P = 510
r = 2.1% or 0.021
t = 4
Work:
I = Prt
I = 510(0.021)(4)
I = 42.84
evaluate the line integral c f · dr, where c is given by the vector function r(t). f(x, y, z) = sin(x) i cos(y) j xz k r(t) = t4 i − t3 j t k, 0 ≤ t ≤ 1
The value of the line integral ∫c f · dr is -cos(1) i - sin(1) j + 1/6 k.
Evaluate the integral?
To evaluate the line integral ∫c f · dr, we need to substitute the given values of f(x, y, z) and r(t) into the integral expression.
[tex]f(x, y, z) = sin(x) i cos(y) j\ x(z) k[/tex]
[tex]r(t) = t^4 i - t^3 j + t k[/tex] , 0 ≤ t ≤ 1
The line integral becomes:
[tex]\int c f * dr = \int c (sin(x) i cos(y) j x(z) k) * (dx i + dy j + dz k)[/tex]
Substituting [tex]x = t^4,\ y = -t^3, and\ z = t:[/tex]
[tex]\int c f * dr = \int c (sin(t^4) i cos(-t^3) j (t^4)(t) k) * (4t^3 dt i - 3t^2 dt j + dt k)[/tex]
Simplifying the expression:
[tex]\int c f * dr = \int c (4t^3 sin(t^4) dt i - 3t^2 cos(t^3) dt j + t^5 dt k)[/tex]
Integrating each component separately:
[tex]\int c f * dr = (\int 0^1 4t^3 sin(t^4) dt) i - (\int 0^1 3t^2 cos(t^3) dt) j + (\int 0^1 t^5 dt) k[/tex]
Evaluating each integral:
[tex]\int c f * dr = [-(cos(t^4))][/tex] evaluated from 0 to [tex]1 i - [sin(t^3)][/tex] evaluated from 0 to [tex]1 j + [t^6/6][/tex] evaluated from 0 to 1 k
Simplifying the expression:
[tex]\int c f * dr = -cos(1) i - sin(1) j + 1/6 k[/tex]
Therefore, the value of the line integral [tex]\int c f * dr\[/tex] is [tex]-cos(1) i - sin(1) j + 1/6 k.[/tex]
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Look at this graph.
What type of function is shown above?
O A.
exponential
OB. absolute value
OC. polynomial
2021 Frimenti
Answer:
It's exponential
Step-by-step explanation:
Question 5 Use the rules of differentiation to find the derivative of the function y (6x + 1)5 + 30x(6x + 1)ª (6x + 1)² (36x + 1) 1 X 6 No correct answer provided. = X x(6x + 1)5.
The derivative of the function y = x(6x + 1)⁵ is: dy/dx = (6x + 1)⁵ + 30x(6x + 1)⁴
To find the derivative of the given function, we can apply the rules of differentiation. Using the product rule, we differentiate each term separately and then add them together.
For the first term x, the derivative is simply 1.
For the second term (6x + 1)⁵, we apply the chain rule. The derivative of (6x + 1)⁵ with respect to x is 5(6x + 1)⁴ multiplied by the derivative of the inner function 6x + 1, which is 6.
Multiplying these derivatives together, we get (6x + 1)⁵ * 6 = 6(6x + 1)⁵.
For the third term x(6x + 1)⁴, we again apply the product rule. The derivative of x is 1, and the derivative of (6x + 1)⁴ is 4(6x + 1)³ multiplied by the derivative of the inner function 6x + 1, which is 6.
Multiplying these derivatives together, we get x * 4(6x + 1)³ * 6 = 24x(6x + 1)³.
Finally, we add the derivatives of each term to get the derivative of the entire function: dy/dx = (6x + 1)⁵ + 30x(6x + 1)⁴.
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Complete question:
Use the rules of differentiation to find the derivative of the function y= x(6x + 1)⁵
(6x + 1)⁵ + 30x(6x + 1)⁴
(6x + 1)⁴ (36x + 1)
x-1/6
No correct answer provided.
Which of the following points lie on the graph of y=x^2-2x+6
Answer:
Did this help?
Step-by-step explanation:
Find the Laplace transform of the following functions.(8 pts/each x 8 = 64 pts) a. a(t) = 28(t) + 3+ 4u(t) b. b(t) = 5 – 5e-2t(1 + 2t)
a. the Laplace transform of a(t) is (28/s^2) + (3/s) + (4/s). b. the Laplace transform of b(t) is 5/s - 10/(s + 2) - 10/(s^3 + 2s^2).
a. To find the Laplace transform of a(t) = 28t + 3 + 4u(t), where u(t) is the unit step function, we can apply the linearity property and the transform of elementary functions.
Applying the linearity property, we can split the transform into three parts:
L{28t} + L{3} + L{4u(t)}
Using the transform of t (L{t} = 1/s^2), we get:
28/s^2 + 3/s + 4/s
Simplifying, we can combine the terms:
(28/s^2) + (3/s) + (4/s)
Therefore, the Laplace transform of a(t) is:
(28/s^2) + (3/s) + (4/s).
b. To find the Laplace transform of b(t) = 5 - 5e^(-2t)(1 + 2t), we can again apply the linearity property and the transform of elementary functions.
Applying the linearity property, we can split the transform into two parts:
L{5} - L{5e^(-2t)(1 + 2t)}
The transform of 5 is simply 5/s.
For the second part, we need to use the transform of e^(-at) and t.
The transform of e^(-at) is 1/(s + a), and the transform of t is 1/s^2.
Using these formulas, we get:
-5/(s + 2)(1 + 2/s^2)
Simplifying and combining terms, we have:
5/s - 10/(s + 2) - 10/(s^3 + 2s^2)
Therefore, the Laplace transform of b(t) is:
5/s - 10/(s + 2) - 10/(s^3 + 2s^2).
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40
in.
in?
What is the area of this trapezoid?
b2 = 5 in.
h = 4 in.
2 in.
3 in.
b = 10 in.
state four reasons why choice should be made in satisfaction human wants
Expert Answer Please! If The Area Of A 60 Sector In A Circle Is 75.4,Find The Diameter Of The Circle.
Answer:
multiply 75.4 by 60 =4,524
A null and alternative hypothesis are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Hoi 3.1 Ha 3.1 What type of test is being conducted in this problem?
A. Two-tailed test
B. Left-tailed test
C. Right-tailed test
The given null and alternative hypotheses, Hoi 3.1 and Ha 3.1, indicate that the hypothesis test is a two-tailed test.
In hypothesis testing, the null hypothesis (Hoi) represents the claim or assumption that is being tested, while the alternative hypothesis (Ha) represents the opposing claim or the hypothesis that the researcher is trying to support. The directionality of the test is determined by the alternative hypothesis.
In this case, the null hypothesis is stated as Hoi 3.1, and the alternative hypothesis is stated as Ha 3.1. Without knowing the specific details of the hypotheses, it can be determined that the test is two-tailed based on the notation used. The presence of two distinct hypotheses (Hoi and Ha) indicates that the test considers both directions of the distribution.
A two-tailed test is used when the alternative hypothesis does not specify a particular direction of the effect or relationship being tested. It is designed to determine whether the observed results are significantly different from the null hypothesis in either the positive or negative direction.
Therefore, the correct answer is A. Two-tailed test.
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Which of the following equations? (picture included)
Answer:
B
Step-by-step explanation:
PLEASE HELP ME!!!! I WILL MARK!!!
Answer:
6(x - 3 ) = 6x - 18
2(3x - 3) = 6x - 6
Step-by-step explanation:
4th grade math lolll
Answer:
2/5x7
Step-by-step explanation:
What is the GCF of each polynomial?
1) -10x^7 + 25x^4 - 25x^2
2) 9v^5 - 24v^4 - 21v^2
Can someone help me find and answer an equation to the following math question : Natalie earns 5% commission on all electronics she sells.On Monday she sold a television for $1130 and a DR that cost $325. What was the total she earned in commission?
Answer:
She will make a total commission of $1130+$325=$1445
Then 5% of $1445= $1445×5%=$72,75
Solve the stimultanious equations
Answer:
x = -1 /2= -0.5 y = 15 /10= 1.5
PLEASE HELP ASAP! 10 POINTS ‼️
Answer:
The correct answer would be D, it is a logarithmic function.
Step-by-step explanation:
y=Ax^2 + Bx + C is the solution of the DEQ: y'=87x. Determine A,B. A 'C' is the constant of integration.
The exact value of A in the general solution is 87/2 and B is 0
How to determine the value of A and B in the general solutionFrom the question, we have the following parameters that can be used in our computation:
y = Ax² + Bx + C
The differential equation is given as
y' = 87x
When y = Ax² + Bx + C is differentiated, we have
y' = 2Ax + B
So, we have
87x = 2Ax + B
By comparing both sides of the equation, we have
2Ax = 87x
B = 0
So, we have
2A = 87
B = 0
Divide both sides of 2A = 87 by 2
A = 87/2
B = 0
Hence, the value of A in the general solution is 87/2 and B is 0
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hi i need help again
(I need help on number 9) ty
Answer:
You did not take the picture correctly, try taking it again
Step-by-step explanation:
I can’t seeeee
Find each x-value at which f is discontinuous and for each x-value, determine whether f is continuous from the right, or from the left, or neither. f (x) = x + 3 if x < 0 3x^2 if 0 lessthanorequalto x lessthanorequalto 1 3 - x if x > 1 x = 3 (smaller value) continuous from the right continuous from the left neither x = 0 (larger value) continuous from the right continuous from the left neither
The function f(x) is discontinuous at x = 0 and x = 1.To determine the points of discontinuity, we need to look at the different intervals defined by the function.
At x = 0, the function has different definitions for the left and right sides of the point. For x < 0, f(x) = x + 3, and for x ≥ 0 and x ≤ 1, f(x) = 3x^2. Therefore, at x = 0, f(x) is discontinuous. It is continuous from the left (approaching from x < 0) and from the right (approaching from x > 0).
At x = 1, the function has different definitions for the left and right sides of the point. For x ≤ 1, f(x) = 3x^2, and for x > 1, f(x) = 3 - x. Therefore, at x = 1, f(x) is discontinuous. It is continuous from the left (approaching from x ≤ 1) and from the right (approaching from x > 1).
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prove each statement using a proof by exhaustion. (a) for every integer n such that 0 ≤ n < 3, (n 1)2 > n3.
b.for every integer n such that 0 ≤ n < 4, 2^(n+2) > 3^n
a) the inequality holds true for all values of n within the given range, we can conclude that for every integer n such that 0 ≤ n < 3, (n+1)² > n³
b) the inequality holds true for all values of n within the given range, we can conclude that for every integer n such that 0 ≤ n < 4, 2⁽ⁿ⁺²⁾ > 3ⁿ.
(a) To prove the statement for every integer n such that 0 ≤ n < 3, (n+1)² > n³ using proof by exhaustion, we will evaluate the inequality for each value of n within the given range.
For n = 0:
(0+1)² > 0³
(1)² > 0
1 > 0 - This is true.
For n = 1:
(1+1)² > 1³
(2)² > 1
4 > 1 - This is true.
For n = 2:
(2+1)² > 2³
(3)² > 8
9 > 8 - This is true.
Since the inequality holds true for all values of n within the given range, we can conclude that for every integer n such that 0 ≤ n < 3, (n+1)² > n³
(b) To prove the statement for every integer n such that 0 ≤ n < 4, 2⁽ⁿ⁺²⁾ > 3ⁿ using proof by exhaustion, we will evaluate the inequality for each value of n within the given range.
For n = 0:
2⁽⁰⁺²⁾ > 3⁰
2² > 1
4 > 1 - This is true.
For n = 1:
2⁽¹⁺²⁾ > 3¹
2³ > 3
8 > 3 - This is true.
For n = 2:
2⁽²⁺²⁾ > 3²
2⁴ > 9
16 > 9 - This is true.
For n = 3:
2⁽³⁺²⁾ > 3³
2⁵ > 27
32 > 27 - This is true.
Since the inequality holds true for all values of n within the given range, we can conclude that for every integer n such that 0 ≤ n < 4, 2⁽ⁿ⁺²⁾ > 3ⁿ.
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Choose the compound inequality that can be used to solve the original inequality |3x – 5| > 10.
Step-by-step explanation:
Nsjssjsjsjshsnmsksjnsnsns
The price of fuel may increase due to demand and decrease due to overproduction. Marco is studying the change in the price of two types of fuel. A and B. over time.
The price in dollars of fuel A after x months is represented by the function below.
10 = 2.961.04)
Part A: is the price of the increasing or decreasing and by what percentage per month? Justify your answer. (5 points)
Part 8: The table below shows the price 9m) in dollars of fuels afer m months
64
m (number of months) 1
3
sim) (price in dollars) 3.04 3.22 3.41 3.61
Which ope of fuel recorded a greater percentage change in pace over the previous month? Justity your answer. (5 points)
Answer:
A. Increasing by 4%.
Step-by-step explanation:
Answer:
A) The price of product A is increasing by 3% per year.
(B) The product A recorded a greater percentage change in price over the previous year.
Step-by-step explanation:
(A)
The function representing the price, in dollars, of product A after x years is:
FA(x)=0.69*(1.03)x
The function FA(x)can be written as:
FA(x)=0.69*1+(0.03)x
The function FA(x) is similar to the exponential growth function, y=a(1+r)x .
Here r is the growth rate.
Thus, it can be said that the price of product A is increasing by 3% per year.
(B)
Consider the data of product B for the year 3 and 4.
The price of product B for year 3 and 4 are 10,303.01 and 10,406.04.
Compute the percent price change from year 3 to 4 as follows:
10406.04-10303.01/10303.01*100
which is 0.999%
~1%
The price of product B is increasing by 1% per year.
Thus, the product A recorded a greater percentage change in price over the previous year.
What is A= bh in math?
Step-by-step explanation:
In math the area of the parallelogram equal the base times the high
A= bhWhere.....
A stand for (Area)
b stand for (Base)
h stand for (High)
Like shown in the photo above
I hope that is useful for you :)
write an equation, waths the equation for thise graph.
Answer:
y = -2x + 3
Step-by-step explanation:
If you do rise/run, you recognize that the slope of the line is -6/3, which = -2. You can also see that the y-intercept of the line is at 3.
The equation of a line is represented by y=mx+b, with m being the slope and b being the y-intercept value.
Just plug in -2 as m and 3 as b in y=mx + b, and you will get your answer.
You spin the spinner shown below once. The spinner has 444 equal sectors colored pink, purple, blue, and green.
What is \text{P(green})P(green)start text, P, left parenthesis, g, r, e, e, n, end text, right parenthesis?
If necessary, round your answer to 222 decimal plac
hola'
your answer is going to be 2.22 or 0.002 i think .
Answer:
0.75
Step-by-step explanation:
There are 3 favorable outcomes (pink, green, or blue).
There are 4 possible outcomes since there are 4 equal sectors.
P(not purple)=3/4 =0.75
Only one correct answer
Answer:
19
Step-by-step explanation:
ngl its kinda easy 5(2)+3(3) = 10+9 = 19
Answer:19
Step-by-step explanation:5x2=10+3x3=9 so 10+9=19
James has a bank account with $500 that collects 3% interest annually. How much will be in James account after 24 months if no transaction are made?
Answer:
$360
Step-by-step explanation:
Find 3% of 500 = 15
Multiply 15 by 24 = 360
The starting salary of a starting teacher is $40,000, which will increase by 2% each year.
Which of the following is the function that models the teacher salary scenario?
The answer choices are in the picture.
Answer:
The first choice is the correct one.
Step-by-step explanation:
The first choice is the correct one. It starts with the base salary and then is multiplied by (1 + 0.02)^t, which is the correct formula for compounding once per year.
1) Evaluate the following expressions.show your work
a) 7(m - 8) for m = -4
Answer:
-84
Step-by-step explanation:
Since m=-4, we can plug -4 into the expression and use PEMDAS
7(m - 8)
7((-4)-8)
7(-12)
-84
What do a rectangle and a rhombus have in common? Select all that apply.
Their angle measures add to 360°.
They have four right angles.
They have four congruent sides.
The opposite sides are parallel.
The opposite sides are parallel.
Their angle measures add to 360°