A capacitor (C) which is connected with a resistor (R) is being charged by supplying the constant voltage (V) of (T+ 5)v. The thermal energy dissipated by the resistor over the time is given as E = ∫[infinity]-0 P(t) dt, where P(t) = (T+5/R e^-1/BC)^2 = R. Find the energy dissipated.
b. Evaluate: ∫7-0 Tx^2 e^-x dx
Answers
We integrate by parts once to get:
u = x^2, dv = e^-x dx, du = 2x dx, v = -e^-x ∫7-0 u dv= [-x^2 e^-x]7-0 + ∫7-0 2x e^-x dx
Applying integration by parts again gives:
u = x, dv = 2e^-x dx, du = dx, v = -2e^-x ∫7-0 x e^-x dx= [-x^2 e^-x]7-0 + 2[x e^-x]7-0 - 2∫7-0 e^-x dx= -49e^-7 + 14e^-0 + 2 = 14 - 49e^-7.
Therefore,
∫7-0 Tx^2 e^-x dx = 14 - 49e^-7.
The given thermal energy is given by:
E = ∫[infinity]-0 P(t) dt
= R∫[infinity]-0 (T+5/R e^-1/BC)^2 dt
Where
P(t)
= R
is the power in the circuit,
V
= T + 5
is the applied voltage, C is the capacitance, R is the resistance, and B is the time constant.Using the following identity:
(a + b)²
= a² + 2ab + b²,
we can expand the square to get:
E
= R(T+5)²/C² ∫[infinity]-0 e^-2t/BC dt
Use the substitution
u
= 2t/BC and du
= 2/BC dt
to get:E
= R(T+5)²/C² * BC/2 ∫[infinity]-0 e^-u du
= R(T+5)²/2C * [BC/e^∞ - BC/e^0]
= R(T+5)²/2Cb)
Evaluate: ∫7-0 Tx^2 e^-x dx
Firstly, we integrate by parts once to get:
u
= x^2, dv
= e^-x dx, du
= 2x dx, v
= -e^-x ∫7-0 u dv
= [-x^2 e^-x]7-0 + ∫7-0 2x e^-x dx
Applying integration by parts again gives:
u
= x, dv
= 2e^-x dx, du
= dx, v
= -2e^-x ∫7-0 x e^-x dx
= [-x^2 e^-x]7-0 + 2[x e^-x]7-0 - 2∫7-0 e^-x dx
= -49e^-7 + 14e^-0 + 2
= 14 - 49e^-7.
Therefore,
∫7-0 Tx^2 e^-x dx
= 14 - 49e^-7.
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Related Questions
The product of 2r- t and 5m + 3=
Answers
Answer: \(10rm+6r-5tm-3t\)
Step-by-step explanation:
\((2r-t)(5m+3)\\\\=10rm+6r-5tm-3t\)
Which equation shows a constant of proportionality
Answers
The equation that shows proportionality is in the form y = kx; Where k is the constant of proportionality.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Two variables are said to be proportional if an increase or decrease in one variable leads to a corresponding increase or decrease in the other variable.
The equation that shows proportionality is in the form:
y = kx
Where k is the constant of proportionality.
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I HAVE 5 MINUTES PLZ HELP!
(Multiple choice)
Answers
Answer:
i think its B or A
Step-by-step explanation:
what is a type ii error? rejecting a false null hypothesis accepting a false alternate hypothesis rejecting a false alternate hypothesis failing to reject a false null hypothesis
Answers
A type II error is a statistical term used to describe the failure to reject a false null hypothesis. It occurs when the null hypothesis is actually false but is not rejected because the statistical test failed to find significant evidence against it.
In other words, it happens when an alternative hypothesis is true, but we fail to reject the null hypothesis.
Types of errors in hypothesis testing
There are two types of errors in hypothesis testing:
Type I error: Rejecting a true null hypothesis
Type II error: Failing to reject a false null hypothesis.Type I error occurs when a true null hypothesis is rejected while Type II error occurs when a false null hypothesis is not rejected. These types of errors are inversely related, meaning that a decrease in one type of error causes an increase in the other.
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it is known that the trout in carter lake back in 1990 had an average weight of 5 pounds with a standard deviation of 1.4 pounds. it is wondered if the average has increased since 1990. assume the distribution is normal, and that the standard deviation has not changed. a new sample of 25 fish is taken, and the average was 5.672 the following hypothesis was done:
Answers
Null Hypothesis (H₀): The average weight of trout in Carter Lake has not increased since 1990.
Alternative Hypothesis (H₁): The average weight of trout in Carter Lake has increased since 1990.
Symbolically, this can be represented as:
H₀: μ = 5 (The population mean weight is equal to 5 pounds)
H₁: μ > 5 (The population mean weight is greater than 5 pounds)
In this case, since we are testing whether the average weight has increased, it is a one-tailed test with the alternative hypothesis being one-sided (greater than).
To further analyze the hypothesis, we can perform a statistical test, such as a one-sample t-test, using the given information from the new sample of 25 fish. This would involve calculating the test statistic and comparing it to a critical value or finding the corresponding p-value to make a decision regarding the hypothesis.
Please note that without additional information, such as the sample mean weight and the corresponding test statistics, it is not possible to draw any conclusions regarding the hypothesis or determine the significance of the observed increase in the average weight.
How does adding salt to water affect the boiling point?
Answers
When salt is added to water, the boiling point of water is increased. The boiling point elevation depends on the concentration of salt added. The addition of salt increases the boiling point of water.
The extent of the increase in boiling point is directly proportional to the amount of salt added. Boiling point is defined as the temperature at which the vapor pressure of a liquid is equal to the pressure exerted on it by the surrounding atmosphere.
In layman's terms, this means that a liquid boils when its vapor pressure equals atmospheric pressure. Boiling point of a liquid can be increased or decreased by the addition of solutes such as salt.When a solute such as salt is added to water, the boiling point of water increases due to the phenomenon of boiling point elevation.
This is because the solute particles in the water interfere with the formation of water vapor molecules at the surface of the liquid. As a result, more energy is required to boil the water, which means that the boiling point is elevated.
The amount of elevation is directly proportional to the concentration of salt added. In short, the addition of salt to water increases the boiling point of water.
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A group of people were asked how they travelled to work yesterday. Each person travelled using only one type of transport. The probabilities that a person picked from the group at random travelled to work by car, bus or bicycle are P( car )=47% P( bus )=0.13 P( bicycle )=(3)/(10) a
Answers
The probability that a person randomly selected from the group travelled to work by car is 52.2%, the probability that they travelled by bus is 14.4%, and the probability that they travelled by bicycle is 33.3%.
When a group of people was asked how they travelled to work yesterday, it was discovered that each person travelled using only one form of transport. Given the probabilities, P(car) = 47%, P(bus) = 0.13, and P(bicycle) = 3/10. We must calculate the probability that a randomly chosen person from the group travelled to work by car, bus, or bicycle. To do this, we first find the probability that a person travelled to work by any of the available modes of transport.
Then we can use conditional probabilities to determine the likelihood that a person travelled to work by car, bus, or bicycle. The probability that a person from the group travelled to work using any of the three modes of transport is:P(car) + P(bus) + P(bicycle) = 0.47 + 0.13 + 0.3 = 0.9Therefore, the probability that a person travelled to work using any of the three modes of transport is 0.9 or 90%.
The conditional probabilities are as follows:P(car|travelling to work) = P(car)/P(travelling to work) = 0.47/0.9 = 0.522 or 52.2%P(bus|travelling to work) = P(bus)/P(travelling to work) = 0.13/0.9 = 0.144 or 14.4%P(bicycle|travelling to work) = P(bicycle)/P(travelling to work) = 0.3/0.9 = 0.333 or 33.3%.
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What are the four conditions necessary for X to have a Binomial Distribution? Mark all that apply.
a. There are n set trials.
b. The trials must be independent.
c. Continue sampling until you get a success.
d. There can only be two outcomes, a success and a failure
e. You must have at least 10 successes and 10 failures
f. The population must be at least 10x larger than the sample. T
g. he probability of success, p, is constant from trial to trial
Answers
Options a, b, d, and g are the correct conditions for a Binomial Distribution.
The four conditions necessary for X to have a Binomial Distribution are:
a. There are n set trials: In a binomial distribution, the number of trials, denoted as "n," must be predetermined and fixed. Each trial is independent and represents a discrete event.
b. The trials must be independent: The outcomes of each trial must be independent of each other. This means that the outcome of one trial does not influence or affect the outcome of any other trial. The independence assumption ensures that the probability of success remains constant across all trials.
d. There can only be two outcomes, a success and a failure: In a binomial distribution, each trial can have only two possible outcomes. These outcomes are typically labeled as "success" and "failure," although they can represent any two mutually exclusive events. The probability of success is denoted as "p," and the probability of failure is denoted as "q," where q = 1 - p.
g. The probability of success, p, is constant from trial to trial: In a binomial distribution, the probability of success (p) remains constant throughout all trials. This means that the likelihood of the desired outcome occurring remains the same for each trial. The constant probability ensures consistency in the distribution.
The remaining options, c, e, and f, are not conditions necessary for a binomial distribution. Option c, "Continue sampling until you get a success," suggests a different type of distribution where the number of trials is not predetermined. Options e and f, "You must have at least 10 successes and 10 failures" and "The population must be at least 10x larger than the sample," are not specific conditions for a binomial distribution. The number of successes or failures and the size of the population relative to the sample size are not inherent requirements for a binomial distribution.
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Mitchell bought 3 postcards for $3.14. At this rate, how much would 12 postcards cost?
Answers
Answer:
12.56$
Step-by-step explanation:
12 / 3=4
4 × 3.14 = 12.56
please help asap!!
-
-
-
-
Answers
Answer:
a. y = 2x + 1
b. 20
Step-by-step explanation:
a. With each increasing figure, two more blocks are added on. Through this, we can determine the rule:
y = 2x + 1
y being the total number of blocks in a figure
x being the number of the figure.
_________
b. To figure out which figure number has 41 squares, we can set the equation we found equal to 41.
41 = 2x + 1
40 = 2x
20 = x
So figure 20 will have 41 squares.
Which statements are true about the graph of the function f(x) = x2 – 8x + 5? Select three options.
The function in vertex form is f(x) = (x – 4)2 – 11.
The vertex of the function is (–8, 5).
The axis of symmetry is x = 5.
The y-intercept of the function is (0, 5).
The function crosses the x-axis twice.
Answers
the y-intercept of the function is (0,5)
the function crosses the x-axis twice
The equation is f(x) = x² – 8x + 5. Then the y-intercept is at (0, 5) and the function crosses the x-axis twice. Then the correct options are A, D, and E.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The quadratic equation is given below.
f(x) = x² – 8x + 5
Convert the equation into vertex form, then the equation will be
f(x) = x² – 8x + 5
f(x) = x² – 8x + 16 – 16 + 5
f(x) = (x – 4)² – 16 + 5
f(x) = (x – 4)² – 11
The graph of the function is given below.
From the graph, the y-intercept is at (0, 5) and the function crosses the x-axis twice.
Then the correct options are A, D, and E.
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what is 6,588 divided by 4
Answers
Answer:
1647
Step-by-step explanation:
1647
4
6588
4
2 5
2 4
1 8
1 6
2 8
2 8
0
Find four numbers forming a geometric sequence such that the second term is 35 less than the first term and the third term is 560 more than the fourth term. Show your work.
Answers
Four numbers forming a geometric sequence such that the second term is 35 less than the first term and the third term is 560 more than the fourth term are -35/3, -140/3, - 560/3, -2240/3 and 7, -28, 112, - 448
Four numbers forming a geometric sequence can be calculate as follows
these terms: a₁, a₂, a₃, a₄
a₁ = a₂ + 35
a₃ = a₄ + 560
Use the formula for the n-term:
a₂ = a₁r
a₃ = a₁r²
a₄ = a₁r³
replace
a₁ = a₁r + 35 ⇒ a₁(1 - r) = 35
a₁r² = a₁r³ + 560 ⇒ a₁(1 - r)r² = 560
Subtracting from the first equation to the second:
r² = 560/35
r² = 16
r = √16
r = ± 4
Use the first equation to find the first term:
a₁( 1 ± 4) = 35
1. a₁ = 35/-3 = -35/3
2. a₁ = 35/5 = 7
We have two sequences:
r = 4
-35/3, -140/3, - 560/3, -2240/3
r = -4
7, -28, 112, - 448
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In the graph below, which value is the dependent variable: Total Cost or Days?
Days
Total cost
Answers
The dependent variable in the given graph is; Total Cost
How to identify the dependent variable?A dependent variable is defined as the variable that changes in an experiment.
Now, a dependent variable depends on other factors. For example, a test score could be classified as a dependent variable because it could change depending on several factors like how much the student studied, how much sleep the student got the night before taking the test, or even how hungry the student was when he took the test.
The domain of a function is simply defined as the set of all possible input values that we are allowed to plug into a particular function. Meanwhile the range of a function is defined as the set of all possible output values that the particular function assumes.
Now, in this question, we see that days is the domain because it is the set of all input values while total cost depends on the number of days and as such is the range and dependent variable.
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I need to find the value of x in this figure.
Please explain how to do so.
Answers
Answer: 2x^2
Step-by-step explanation:
(x+5)
x (2x - 9)
-----------------
X times 2x = 2x^2
Find an equation of the plane.
The plane through the origin and the points (2, –4, 6) and (5, 1, 3)
Answers
The equation of the plane through the origin and the points (2, –4, 6) and (5, 1, 3) is - 9x + 12y + 11 x = 0.
The general equation of a plane through (0, 0, 0) is a(x - 0) + b(y - 0) + c(z - 0) = 0
Since the plane passes though the origin, the equation of the plane is given by ( x, y, z ) = 0. Simplify it so that you write the equation of the plane in the form a x + b y + c z = 0
ax + by + cx = 0...(1)
It will pass through B(2, -4, 6) and C(5, 1, 3) if
a(2) + b(-4) + c(6) = 0
2a - 4b + 6c = 0
a - 2b + 3c = 0 ...(2)
a(5) + b(1) + c(3) = 0
5a + b + 3c = 0 ... (3)
Solving (2) and (3) by cross-multiplication, we have
\(& \frac{a}{-6-3}=\frac{b}{15-3}=\frac{c}{1+10} \\\)
\(& \Rightarrow \frac{a}{-9}=\frac{b}{12}=\frac{c}{11}=\lambda\) (say) }
\(& \Rightarrow\) a = - 9 \(\lambda\), b = 12 \(\lambda\) and c = 11 \(\lambda\)
Substituting the values of a, b and c in (1), we get
- 9 \(\lambda\) x + 12 \(\lambda\) y + 11 \(\lambda\) x = 0
- 9x + 12y + 11 x = 0
which is the required equation of the plane.
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4.if a man has six different sportshirts and four different pairs of slacks, how many different combinations can he wear?
Answers
The man can wear 15 different outfit combinations by mixing and matching his six different sport shirts and four different pairs of slacks.
Combination is a way of counting the number of different groups of items that can be selected from a larger set without regard to the order in which they are selected.
In this case, the man has six different sport shirts and four different pairs of slacks, and he wants to know how many different outfit combinations he can wear. We can use the formula for combinations to calculate the number of possibilities.
The formula for combinations is:
ⁿCₓ = n! / (x! * (n - x)!)
Where n is the total number of items, x is the number of items being selected, and the exclamation mark (!) represents the factorial of a number (i.e., the product of all positive integers up to that number).
Using this formula, we can calculate the number of different combinations the man can wear as follows:
Number of sport shirts (n) = 6
Number of slacks (x) = 4
Number of combinations = ⁶C₄ = 6! / (4! * (6 - 4)!)
= (6 * 5 * 4 * 3 * 2 * 1) / [(4 * 3 * 2 * 1) * (2 * 1)]
= 15
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Find the difference quotient of f; that is, find f(x+h)−f(x)/h ,h is not equal to 0, for the following function. Be sure to simplify. f(x)=x^2−6x+5
Answers
The difference quotient of \(f(x) = x^2 - 6x + 5\) is is 2x - 6 + h.
To find the difference quotient for the function \(f(x) = x^2 - 6x + 5\), we need to evaluate
(f(x + h) - f(x)) / h, where h is not equal to 0.
First, let's find f(x + h):
\(f(x + h) = (x + h)^2 - 6(x + h) + 5\)
\(= x^2 + 2hx + h^2 - 6x - 6h + 5\)
\(= x^2 - 6x + 5 + 2hx - 6h + h^2\)
Now, we can substitute the values of f(x + h) and f(x) into the difference quotient:
\((f(x + h) - f(x)) / h = ((x^2 - 6x + 5 + 2hx - 6h + h^2) - (x^2 - 6x + 5)) / h\)
= (2hx - 6h + h^2) / h
= 2x - 6 + h
Therefore, the difference quotient of \(f(x) = x^2 - 6x + 5\) is 2x - 6 + h.
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The given exponential function f(x)= (.67)* - 7 represents:
A. Exponential Growth
B. Exponential Decay
C. Neither
D. None of the above
Answers
Step by step explanation This is how I got the answer to your question and I gave you the solution I hope this helps you out
Ethan is a farmer. He spends 50 hours each week working on
the farm. In the summer, Ethan spends 4/11 of his time cleaning
and 2/9
of his time feeding the animals. How many hours does he
spend feeding the animals every week?
Answers
Ethan spends 11.1 hours feeding the animals every week
State whether True or False.
(a) All rectangles are squares
(b) All rhombuses are parallelograms
(c) All squares are rhombuses and also rectangles
(d) All squares are not parallelograms (e) All kites are rhombuses
(f) All rhombuses are kites (g) All parallelograms are trapeziums
(h) All squares are trapeziums
Answers
All rectangles are square is a false statement
The given statement is false statement.
What is a rectangle and square?
A rectangle is a quadrilateral with opposite sides parallel and equal and each angle is a right angle, where as a square is quadrilateral with opposite sides parallel and each side is equal. and every angle is a right angle.
We are given a statement All rectangle are squares.
As every side of a square is of equal length And only opposite sides are of equal length in rectangle
All rectangles are not square
Hence the statement is not true
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A baseball team plays the same opponent six times in a season. The set {0,1,2,3,4,5,6} describes the possible number of wins for the six games.
Set A contains the number of wins when exactly four games are won.
Set B contains the number of wins when at least four games are won.
Which of these statements are true? Choose all that are correct.
The union of set A and B is an empty set
The complement of the union of set A and B is {0,1,2,3} set A
The complement of set B is {0,1,2,3}
The intersection of set A and set B is an empty set
The complement of set B is {1,2,3}
Answers
- The complement of set B is {0,1,2,3}
- The complement of set B is {1,2,3}
Please help me :))))
Answers
Answer:
12617.13
Step-by-step explanation:
250(1+0.103)^40= 12617.13
hope it help
Answer:
12617.13
Step-by-step explanation:
Increase £120 by 25%
Answers
120 + 30 = £150
answer correctly plz
Answers
Answer:
1/3
Step-by-step explanation:
Use the Up/to left or right rule to help you
Find a start point (or the one the gave you (3,2)) and then follow the line to the next point that crosses exactly over where to points cross (where poth x and y would be whole numbers) count how many times the point moved up, then how many time it moved left. Put the first over the second in fraction form and there is your slope.
Answer:
m = 1/3
Step-by-step explanation:
Given two points (x₁, y₁) and (x₂, y₂), the slope m is:
\(m=\frac{y_2-y_1}{x_2-x_1}\)
We are given the points:
(x₁, y₁) = (3, 2)
(x₂, y₂) = (6, 3)
Plug in the points:
\(m= \frac{3-2}{6-3}\)
\(m = \frac{1}{3}\)
if x=5, y=-3, and z=-7 z=-7, evaluate 3x^2-9y/yz
Answers
Kevin is a server at an all-you-wish-to eat sushi restaurant. At one table, the customers ordered 3 child meals and 2 adult meals, which cost $80 in total. At another table, the customers ordered 5 child meals and 3 adult meals, which cost $125 in total. How much does each child meal and adult meal cost?
Answers
Answer:
Read below for full answer :)
Step-by-step explanation:
We can conclude that the total cost of all meals was $205.
There were a total of 8 kids meals and 5 adult meals.
You'd have to divide 205 by 8, and you'd get 25.625.
Then, divide 205 by 5, and you'd get 41.
For example, we could say that each childrens meal was $15 ($120 total in kid's meals), and each adult was $17 ($85 total in adult meals).
When you total $85 and $120, it then given you a sum of $205.
There are many ways to complete this equation, but i feel that this is the easiest way.
Hope this helps! :)
h graphed below is all real numbers, and all of its extreme values occur when -3 < x < 3. Use the graph to answer the following questions y= h(x) Identify all of the values of for which h' (c) 0_ If there is more than one value, enter the values as a comma-separated list_ If there are none, enter DNE: values: Identify all of the values of C for which h' (c) does not exist: If there is more than one value, enter the values as a comma-separated list: If there are none;, enter DNE values:
Answers
Answer: C= -2.5,1
Step-by-step explanation:
h'(x) exist where function is continuous and having smooth turning (no pointed corner)
And having h'(x)=0 where there is maxima minima or point of contra-flexure, it means slope becomes 0.
By observing the graph we can see that at x=-2.5 there is point of contra-flexure.
As curve is changing from concave down to concave up.
By observing the graph we can see that at x=1 there is point of maxima.
h'(c)=0 for following values of c
Estimate the percentage of engineers that are chemical engineers using the following data
-Total number of engineers listed in this figure is approximately 1,326,800.
-chemical engineers: 27,860
Show work and type formulas Speed=distance=
Time
Answers
Based on the number of people who are engineers and those who are chemical engineers, the percentage who are chemical engineers is 2.01%
How to find the percentage?To find the percentage of something out of the total number, the formula is:
= Number of selected variables / Total number of variables x 100%
The selected variable here is chemical engineers so the percentage of chemical engineers out of the total number of engineers is:
= Number of chemical engineers / Total number of engineers x 100%
= 27,860 / 1,326,800 x 100%
= 2.01%
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Mary has completed 8 problems of her 20 question test. How much of the test has she completed in fraction form (simplity!)
O 8/20
O 4/10
O 1/2
0 2/5
Answers
Answer:
2/5
Step-by-step explanation:
She completed 8 out of 20 so we divide 8 by 20
8/20 can be simplified if we divide both the numerator and denominator by 4
which equals 2/5
Answer:
2/5
Step-by-step explanation:
8 divided by 20 gives you .4 which is 2/5