Find the future value (FV) of the annuity due. (Round your answer to the nearest cent.) $175 monthly payment, 7% interest, 11 years
Answer:
The future value of the annuity due to the nearest cent is $2956.
Step-by-step explanation:
Consider the provided information:
It is provided that monthly payment is $175, interest is 7% and time is 11 years.
The formula for the future value of the annuity due is:
[tex]FV of Annuity Due = (1+r)\times P[\frac{(1+r)^{n}-1}{r}][/tex]
Now, substitute P = 175, r = 0.07 and t = 11 in above formula.
[tex]FV of Annuity Due = (1+0.07)\times 175[\frac{(1+0.07)^{11}-1}{0.07}][/tex]
[tex]FV of Annuity Due = (1.07)\times 175[\frac{1.10485}{0.07}][/tex]
[tex]FV of Annuity Due = 187.5(15.7835)[/tex]
[tex]FV of Annuity Due = 2955.4789[/tex]
Hence, the future value of the annuity due to the nearest cent is $2956.
if I've gained 35 pounds in 186 days, how many pounds per day?
Answer:
.188 pounds per day
Step-by-step explanation:
Given
35 pounds gained in 186 daysDivide the amount of pounds gained by the total number of days
35/186 = .188
Answer
Approximately .188 pounds per day.
Is the given function phi(x) = x^2 - x^-1 an explicit solution to the linear equation d^2y/dx^2 - 2/x^2 y = 0? Circle your answer. (a) yes (b) no
Answer:
Yes
Step-by-step explanation:
We are given that a function [tex]\phi(x)=x^2-x^{-1}[/tex]
We have to find that given function is an explicit solution to the linear equation
[tex]\frac{d^2y}{dx^2}-\frac{2}{x^2}y=0[/tex]
If given function is an explicit solution of given linear equation then it satisfied the given differential equation
Differentiate w.r.t x
Then we get [tex]\phi'(x)=2x+x^{-2}[/tex]
Again differentiate w.r.t x
Then we get
[tex]\phi''(x)=2-\frac{2}{x^3}[/tex]
Substitute all values in the given differential equation
[tex]2-\frac{2}{x^3}-\frac{2}{x^2}(x^2-x^{-1})[/tex]
=[tex]2-\frac{2}{x^3}-2+\frac{2}{x^3}=0[/tex]
Hence, given function is an explicit solution of given differential equation.
Therefore, answer is yes.
Find the range of the function f of x equals the integral from negative 6 to x of the square root of the quantity 36 minus t squared
[tex]f(x)=\displaystyle\int_{-6}^x\sqrt{36-t^2}\,\mathrm dt[/tex]
The integrand is defined for [tex]36-t^2\ge0[/tex], or [tex]-6\le t\le6[/tex], so the domain should be the same, [tex]-6\le x\le6[/tex].
When [tex]x=-6[/tex], the integral is 0.
The integrand is non-negative for all [tex]x[/tex] in the domain, which means the value of [tex]f(x)[/tex] increases monotonically over this domain. When [tex]x=6[/tex], the integral gives the area of the semicircle centered at the origin with radius 6, which is [tex]\dfrac\pi26^2=18\pi[/tex], so the range is [tex]\boxed{0\le f(x)\le 18\pi}[/tex].
The range of the function f(x) is the integral from -6 to x of the square root of the quantity 36 minus t squared is [0, 6*π] because the total area of the semicircle is the maximum value.
Explanation:The function f(x) is the integral from -6 to x of the square root of the quantity 36 minus t squared. This is a known geometrical shape, which is a semicircle with radius 6. To find the range of this function, we need to know the possible outcomes of this function. In general, for a semicircle of radius r, the values of the square root of the quantity r squared minus t squared will vary from 0 to r, both inclusive. So, if you consider the function from -6 to 6, the range would be [0, 6*π] because the total area of the semicircle is the maximum value.
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The slope of the _________________ is determined by the relative price of the two goods, which is calculated by taking the price of one good and dividing it by the price of the other good. Opportunity cost productive efficiency budget constraint production possibilities frontier
Answer:
The answer is - budget constraint
Step-by-step explanation:
The slope of the budget constraint is determined by the relative price of the two goods, which is calculated by taking the price of one good and dividing it by the price of the other good.
A budget constraint happens when a consumer demonstrates limited consumption patterns by a certain income.
WHAT IS THE PROBABILITY OF GETTING EITHER JACK OR A THREE WHEN DRAWING A SINGLE CARD FROM A DECK OF 52 CARDS? WHAT IS THE PROBABILITY THAT THE CARD IS EITHER A JACK OR A THREE?
Answer:
2/13
Step-by-step explanation:
there are 4 jacks and 4 threes in a standard poker deck.
4+4 is 8
8/52=2/13
The probability of drawing either a Jack or a three from a standard deck of 52 cards is 2/13, because there are 8 such cards in a deck and the total number of cards in the deck is 52.
The question asks for the probability of drawing either a Jack or a three from a standard deck of 52 cards. To solve this, we need to count how many Jacks and threes there are in a deck. Since each suit (hearts, diamonds, clubs, and spades) includes one Jack and one three, there are 4 Jacks and 4 threes in a standard deck. Therefore, there are 8 cards that satisfy the condition (either a Jack or a three).
Since the total number of cards in the deck is 52, the probability of drawing either a Jack or a three is calculated as the number of favorable outcomes (drawing a Jack or a three) divided by the total number of outcomes (drawing any card from the 52-card deck). Thus, the probability is:
Probability = (Number of Jacks + Number of threes) / Total number of cards = (4 + 4) / 52 = 8 / 52 = 2 / 13
Therefore, the probability of drawing either a Jack or a three from a standard deck of 52 cards is 2/13.
A person pulls horizontally with a force of 64 N on a 14-kg box. There is a force of friction between the box and the floor of 36 N. Find the acceleration of the box in m/s2 Show your work
The net force is what remains of the pull when we subtract the friction force:
[tex]F = 64-36 = 28N[/tex]
Now, use the law
[tex]F=ma[/tex]
and solve it for the acceleration
[tex]a = \dfrac{F}{m}[/tex]
to get the result:
[tex]a = \dfrac{28}{14}=2[/tex]
Answer:
2 m/s²
Step-by-step explanation:
F = applied force in the horizontal direction = 64 N
f = frictional force acting between the box and the floor = 36 N
m = mass of the box = 14 kg
a = acceleration of the box = ?
Force equation along the horizontal direction is given as
F - f = ma
Inserting the values
64 - 36 = 14 a
28 = 14 a
a = [tex]\frac{28}{14}[/tex]
a = 2 m/s²
The manufacturer of a certain engine treatment claims that if you add their product to your engine, it will be protected from excessive wear. An infomercial claims that a woman drove 33 hours without oil, thanks to the engine treatment. A magazine tested engines in which they added the treatment to the motor oil, ran the engines, drained the oil, and then determined the time until the engines seized. Determine the null and alternative hypotheses that the magazine will test.
Answer: [tex]H_0:\mu\geq33[/tex]
[tex]H_a:\mu<33[/tex]
Step-by-step explanation:
Let [tex]\mu[/tex] be the average number of hours a person drive without adding the product.
Given claim : An infomercial claims that a woman drove 33 hours without oil.
i.e. [tex]\mu\geq33[/tex]
It is known that the null hypothesis always contains equal sign and alternative hypothesis is just opposite of the null hypothesis.
Thus the null and alternative hypothesis for the given situation will be :-
[tex]H_0:\mu\geq33[/tex]
[tex]H_a:\mu<33[/tex]
A Game of Thrones fan predicts there is a 70% chance that her favorite character will survive the next season and a 75% chance that her second favorite character will die. There is also a 16% chance that both characters will die. What’s the probability that the second character will die given that the first character dies? What kind of probability is this called?
Final answer:
The probability that the second character will die given that the first character dies is 53.33%. This is known as conditional probability.
Explanation:
To find the probability that the second character will die given that the first character dies, we use the concept of conditional probability.
The formula for conditional probability is P(B|A) = P(A and B) / P(A), where P(B|A) is the probability of event B occurring given that event A has occurred, P(A and B) will be the probability of both events A and B occurring, and P(A) is the probability of event A occurring.
In this scenario, event A is the first character dying, and event B is the second character dying. The student has already stated there is a 70% chance that the first character will survive, which means there is a 30% (100% - 70%) chance that the first character will die.
They've also stated a 16% chance that both characters will die. Applying the formula gives us P(B|A) = P(A and B) / P(A) = 0.16 / 0.30 = 0.5333, or 53.33%.
Therefore, the probability that the second character will die given that the first character dies is 53.33%. This kind of probability is called conditional probability.
The recommended single dose for a particular drug is 100 mg. How many doses can be obtained from 20 grams of the drug?
A. 2,000 doses
B. 200 doses
C. 2 doses
D. 20 doses
Answer:
B. 200 doses
Step-by-step explanation:
Given,
1 dose is required for 100 mg,
Since, 1 mg = 0.001 g,
⇒ 100 mg = 0.1 g
⇒ 1 dost is required for 0.1 g,
Thus, the ratio of doses and quantity ( in gram ) is [tex]\frac{1}{0.1}=10[/tex]
Let x be the doses required for 20 grams,
So, the ratio of doses and quantity is [tex]\frac{x}{20}[/tex]
[tex]\implies \frac{x}{20}=10[/tex]
[tex]\implies x=200[/tex]
Hence, 200 doses can be obtained from 20 grams of the drug.
Option 'B' is correct.
To solve this question, we will follow these steps:
1. We need to ensure that we use the same units for both the drug amount and the dose. Since the drug amount is given in grams and the dose in milligrams, we will convert the drug amount from grams to milligrams.
2. We know that 1 gram is equivalent to 1000 milligrams.
3. Now, let's convert the drug amount from grams to milligrams:
We have 20 grams of the drug, so the conversion to milligrams is:
\(20 \text{ grams} \times \dfrac{1000 \text{ milligrams}}{1 \text{ gram}} = 20,000 \text{ milligrams}\)
4. Next, we will divide the total milligrams of the drug by the milligram dosage that is recommended per dose to find out how many doses we can get from the drug amount.
5. Given that each dose is 100 mg, we now divide the total drug amount in milligrams by the dose in milligrams:
\(20,000 \text{ milligrams} \div 100 \text{ milligrams per dose} = 200 \text{ doses}\)
Therefore, from 20 grams of the drug, we can obtain 200 doses.
The correct answer is:
B. 200 doses
We are given three coins: one has heads in both faces, the second has tails in both faces, and the third has a head in one face and a tail in the other. We choose a coin at random, toss it, and it comes head. What is the probability that the opposite face is tails?
Answer: 0.33
Step-by-step explanation:
Let,
E1 be the coin which has heads in both facesE2 be the coin which has tails in both facesE3 be the coin which has a head in one face and a tail in the other.In this question we are using the Bayes' theorem,
where,
P(E1) = P(E2) = P(E3) = [tex]\frac{1}{3}[/tex]
As there is an equal probability assign for choosing a coin.
Given that,
it comes up heads
so, let A be the event that heads occurs
then,
P(A/E1) = 1
P(A/E2) = 0
P(A/E3) = [tex]\frac{1}{2}[/tex]
Now, we have to calculate the probability that the opposite side of coin is tails.
that is,
P(E3/A) = ?
∴ P(E3/A) = [tex]\frac{P(E3)P(A/E3)}{P(E1)P(A/E1) + P(E2)P(A/E2) + P(E3)P(A/E3) }[/tex]
= [tex]\frac{(1/3)(1/2)}{(1/3)(1) + 0 + (1/2)(1/3)}[/tex]
= [tex]\frac{1}{6}[/tex] × [tex]\frac{6}{3}[/tex]
= [tex]\frac{1}{3}[/tex]
= 0.3333 ⇒ probability that the opposite face is tails.
Given a double-headed coin, a double-tailed coin, and a regular coin, the probability that the opposite face is tails after tossing a head is 33.33%, assuming we picked one coin randomly and tossed it to see a head.
The student is asking about a problem involving conditional probability, with the specific condition that one of the sides that came up is a head. We are given three coins: a double-headed coin, a double-tailed coin, and a regular coin. The aim is to calculate the probability that the opposite face is tails given that the tossed coin shows heads.
First, we need to consider the total number of heads that can come up when choosing any coin. This yields two heads from the double-headed coin, and one head from the regular coin, resulting in three possible heads. However, only the regular coin has a tail on the opposite side.
Consequently, the probability that the opposite face is tails given that a head has been tossed is 1 out of 3, or 33.33%.
You can afford monthly deposits of 140 into an account that pays 3.8% compounded monthly. How long will be untl you have $11.300 to buy a boat? Type the number of months: (Round to the next higher month it not exact Question He Check Answer Enter your answer in the answer box and then click Check Answer All parts showing
Answer:
72 months approx.
Step-by-step explanation:
Monthly deposit = m = $140
r = 3.8% or 0.038
Amount needed in the account = A = $11300
The formula will be :
[tex]11300=140(\frac{(1+0.038/12)-1}{0.038/12} )[/tex]
[tex]11300=140(\frac{(1+0.038/12)-1}{0.003166})[/tex]
[tex]11300=44219.83((1.003166)^{m}-1)[/tex]
[tex]0.2555=(1.003166)^{m}-1[/tex]
[tex]1.2555=(1.003166)^{m}[/tex]
m=log1.2555/log1.003166
m =71.98 ≈ 72
Hence, it will take 72 months approx.
List the different combinations of heads and tails that can occur when 3 ordinary coins are tossed. Use h for heads and t for tails. One combination is hht. List the other combinations, taking order into account (Use a comma to separate answers) More i () a Enter your answer in the answer box ere to search
[tex]HTT,HTH,HHH,TTT,THT,THH,TTH[/tex]
Express as the sum or difference of logarithms. log311y
The function log311y can be expressed as the sum of two logarithms, log3(11) + log3(y), according to the product rule of logarithms.
Explanation:The function log311y represents the logarithm base 3 of the product of the numbers 11 and y. Using the rules of logarithms, we can rewrite this expression as a sum of two logarithms.
According to the product rule of logarithms, the logarithm of a product is the sum of the logarithms of the component numbers. Applying this rule to our expression, log311y becomes:
log3(11) + log3(y)
This is the sum of the logarithm base 3 of 11 and the logarithm base 3 of y. In conclusion, the function log311y can be expressed as the sum of the separate logarithms: log3(11) + log3(y).
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The logarithm log3(11y) can be broken down into two simpler logarithms, log3(11) and log3(y), by using properties of logarithms. This is the sum of the two simpler logarithms.
Explanation:To express the logarithm log3(11y) as the sum or difference of logarithms, we will utilize the properties of logs:
The logarithm of a product is the sum of the logarithms of the numbers (log(xy) = log(x) + log(y)).The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number.The logarithm of a quotient is the difference of the logarithms of the numbers.Applying these properties to the given logarithm, we find:
log3(11y) = log3(11) + log3(y)
Thus, the original logarithm has been expressed as a sum of two simpler logarithms.
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Find the amount of time needed for the sinking fund to reach the given accumulated amount. (Round your answer to two decimal places.) $295 monthly at 5.2% to accumulate $25,000.
Answer:
8.82 years.
Step-by-step explanation:
Since, the monthly payment formula is,
[tex]P=\frac{PV(r)}{1-(1+r)^{-n}}[/tex]
Where, PV is the present value of the loan,
r is the rate per month,
n is number of months,
Here,
PV = $ 25,000,
Annual rate = 5.2 % = 0.052 ⇒ Monthly rate, r = [tex]\frac{0.052}{12}[/tex]
( 1 year = 12 months )
P = $ 295,
By substituting the values,
[tex]295=\frac{25000(\frac{0.052}{12})}{1-(1+\frac{0.052}{12})^{-n}}[/tex]
By the graphing calculator,
We get,
[tex]n = 105.84[/tex]
Hence, the time ( in years ) = [tex]\frac{105.84}{12}=8.82[/tex]
Graph the equation by plotting three
points. If all three are correct, the line
will appear.
-y = -x + 1
Answer:
(0, -1), (1, 0), (2, 1)
Step-by-step explanation:
I find this easier to do after multiplying the equation by -1:
y = x - 1
Pick any value for x, then subtract 1 from it to find the corresponding value of y.
point) Suppose that the trace of a 2 x 2 matrix A is tr(A)= -9 and the determinant is det(A) 18. Find the eigenvalues of A. The eigenvalues of A are (Enter your answers as a comma separated list.)
Answer with explanation:
Matrix A= (2 × 2) Matrix
Trace A= -9
Also,Determinant A= |A|=18
⇒Characteristics Polynomial is given by
Δ(A)=A² -A ×trace (A)+Determinant (A)
=A²+9 A+18
=(A+6)(A+3)
So, eigenvalues can be obtained by substituting :
Δ(A)=0
(A+6)(A+3)=0
A= -6 ∧ A= -3
Two Eigenvalues are = -6, -3
Find the derivative of the function at P 0 in the direction of A. f(x,y,z) = 3 e^x cos(yz), P0 (0, 0, 0), A = - i + 2 j + 3k
The derivative of [tex]f(x,y,z)[/tex] at a point [tex]p_0=(x_0,y_0,z_0)[/tex] in the direction of a vector [tex]\vec a=a_x\,\vec\imath+a_y\,\vec\jmath+a_z\,\vec k[/tex] is
[tex]\nabla f(x_0,y_0,z_0)\cdot\dfrac{\vec a}{\|\vec a\|}[/tex]
We have
[tex]f(x,y,z)=3e^x\cos(yz)\implies\nabla f(x,y,z)=3e^x\cos(yz)\,\vec\imath-3ze^x\sin(yz)\,\vec\jmath-3ye^x\sin(yz)\,\vec k[/tex]
and
[tex]\vec a=-\vec\imath+2\,\vec\jmath+3\,\vec k\implies\|\vec a\|=\sqrt{(-1)^2+2^2+3^2}=\sqrt{14}[/tex]
Then the derivative at [tex]p_0[/tex] in the direction of [tex]\vec a[/tex] is
[tex]3\,\vec\imath\cdot\dfrac{-\vec\imath+2\,\vec\jmath+3\,\vec k}{\sqrt{14}}=-\dfrac3{\sqrt{14}}[/tex]
Consider the sequence 1, 5, 12, 22, 35, 51, . . . (with a0 = 1). By looking at the differences between terms, express the sequence as a sequence of partial sums. Then find a closed formula for the sequence by computing the nth partial sum.
The given sequence can be expressed as a sequence of partial sums by finding the differences between terms and adding them to the previous term. The closed formula for the nth partial sum is Sn = n/2(3n - 1), where Sn represents the nth partial sum.
Explanation:To express the given sequence as a sequence of partial sums, we can find the differences between consecutive terms:
5 - 1 = 4
12 - 5 = 7
22 - 12 = 10
35 - 22 = 13
51 - 35 = 16
From these differences, we can observe that each term in the sequence is obtained by adding the difference to the previous term. Therefore, the sequence can be written as a sequence of partial sums:
1, 1+4, 1+4+7, 1+4+7+10, 1+4+7+10+13, ...
To find a closed formula for the nth partial sum, we can use the formula for the sum of an arithmetic series:
Sn = n/2(a1 + an), where Sn represents the nth partial sum, a1 is the first term, and an is the nth term.
For the given sequence, a1 = 1 and the difference between consecutive terms is 3, so the nth term can be represented as an = 1 + 3(n-1). Substituting these values into the formula, we get:
Sn = n/2(1 + 1 + 3(n-1)) = n/2(2 + 3(n-1)) = n/2(3n - 1).
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6. Let A and B be nxn matrices . Compute (A + B) (A + B). Explain all steps.
Answer:
(A+B)(A+B)=A.A+B.A+A.B+B.B
Step-by-step explanation:
Given that matrices A and B are nxn matrices
We need to find (A+B)(A+B)
For understanding the multiplication of matrices let'take A is mxn and B is pxq matrices,we can multiple only when n=p,so our Ab matrices will be mxq.
We know that that in matrices AB is not equal to BA.
Now find
(A+B)(A+B)=A.A+B.A+A.B+B.B
So from we can say that (A+B)(A+B) is not equal to A.A+2B.A+B.B because AB is not equal to BA in matrices.
So (A+B)(A+B)=A.A+B.A+A.B+B.B
. Break downs occur on a 20-years-old car with rate λ= 0.5 breakdowns/week. The owner of the car is planning to have a trip on his car for 2 weeks. What is the probability that there will be no breakdown on his car in the trip? [ The rate = ? per two weeks]
Answer: 0.3679
Step-by-step explanation:
The formula for Poisson distribution :-
[tex]P(x)=\dfrac{e^{-\lambda}\lambda^{x}}{x!}[/tex]
Let x be the number of breakdowns.
Given : The rate of breakdown per week : 0.5
Then , for 2 weeks period the number of breakdowns = [tex]\lambda=0.5\times2=1[/tex]
Then , the probability that there will be no breakdown on his car in the trip is given by :-
[tex]P(x)=\dfrac{e^{-1}1^{0}}{0!}=0.367879441171\approx0.3679[/tex]
Hence, the required probability : 0.3679
A company manufactures bicycles at a cost of $50 each. If the company's fixed costs are $700, express the company's costs as a linear function of x, the number of bicycles produced.
Answer:
[tex]y = 700 + 50x[/tex]
Step-by-step explanation:
Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.
If the company has a fixed cost (fixed being a keyword) of $700, then that cost will be a steady value before they even start to manufacture the bicycles. Afterwards they have to spend $50 on each bicycle they produce. Since we do not know the amount of bicycles that have been produced we can use the variable x to represent this.
[tex]y = 700 + 50x[/tex]
The equation above states that the company pays $700 plus $50 for every bike produced which comes out to a total of y.
Write the equation that passes through the given point and has the slope indicated: (1, -3); with slope (-3/5)
Answer:
y = -3/5x - 12/5
Step-by-step explanation:
The equation I'm going to give is going to be in slope-intercept form. If you need it in point-slope, I can do so in an edit or the comments.
Slope-intercept form is: y = mx + b where m is the slope, b is the y-intercept.
So let's plug in our given slope:
y = -3/5x + b
Using this, we now plug in our x- and y-coordinates from the given point to solve for b.
-3 = -3/5(1) + b
-3 = -3/5 + b
Add 3/5 to both sides to isolate variable b.
-3 + 3/5 = b
-15/5 + 3/5 = b
-12/5 = b
Plug this new info back into the original equation and your answer is
y = -3/5x - 12/5
When studying radioactive material, a nuclear engineer found that over 365 days, 1,000,000 radioactive atoms decayed to 973 comma 635 radioactive atoms, so 26 comma 365 atoms decayed during 365 days. a. Find the mean number of radioactive atoms that decayed in a day. b. Find the probability that on a given day, 51 radioactive atoms decayed.
Answer:
A. number of decayed atoms = 73.197
Step-by-step explanation:
In order to find the answer we need to use the radioactive decay equation:
[tex]N(t)=N0*e^{kt}[/tex] where:
N0=initial radioactive atoms
t=time
k=radioactive decay constant
In our case, when t=0 we have 1,000,000 atoms, so:
[tex]1,000,000=N0*e^{k*0}[/tex]
[tex]1,000,000=N0[/tex]
Now we need to find 'k'. Using the provied information that after 365 days we have 973,635 radioactive atoms, we have:
[tex]973,635=1,000,000*e^{k*365}[/tex]
[tex]ln(973,635/1,000,000)/365=k[/tex]
[tex] -0.0000732=k[/tex]
A. atoms decayed in a day:
[tex]N(t)=1,000,000*e^{-0.0000732t}[/tex]
[tex]N(1)=1,000,000*e^{-0.0000732*1}[/tex]
[tex]N(1)= 999,926.803[/tex]
Number of atoms decayed in a day = 1,000,000 - 999,926.803 = 73.197
B. Because 'k' represents the probability of decay, then the probability that on a given day 51 radioactive atoms decayed is k=0.0000732.
Answer all questions: 1) The electric field of an electromagnetic wave propagating in air is given by E(z,t) = 4cos(6 x 10^8 t - 2z) +3 sin(6 x 10 t -2z) (V/m). Find the associated magnetic field H(z,t)
The magnetic field H(z,t) of an electromagnetic wave is related to the electric field E(z,t) by a factor of the speed of light. Therefore, if E(z,t) = 4cos(6 x 10^8 t - 2z) +3 sin(6 x 10^8 t -2z), the associated magnetic field would be H(z,t) = (4/c) cos(6 x 10^8 t - 2z) +(3/c) sin(6 x 10^8 t -2z), where c is speed of light, approximately 3 x 10^8 m/s.
Explanation:The question is asking for the associated magnetic field H(z,t) of an Electromagnetic wave given the electric field E(z,t). A crucial fact to know for this question is that the electric and magnetic fields in an electromagnetic wave are perpendicular to each other and the direction of propagation. They also have a constant ratio of magnitudes in free space or air, which is the speed of light given by c = 1/√εOMO. Because of these relations, we know that we can find the magnetic field by simply dividing the given electric field by the speed of light in units that match the given Electric field.
So, if E(z,t) = 4cos(6 x 10^8 t - 2z) +3 sin(6 x 10^8 t -2z), then the associated magnetic field would be H(z,t) = (4/c) cos(6 x 10^8 t - 2z) +(3/c) sin(6 x 10^8 t -2z), where c is the speed of light, approximately 3 x 10^8 m/s.
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To find the associated magnetic field H(z, t), you can use Faraday's law of electromagnetic induction. This law states that the rate of change of magnetic flux through a surface is equal to the induced electromotive force (EMF) along the boundary of the surface. By following a step-by-step process, you can find the magnetic field B(z, t) using the given electric field E(z, t).
Explanation:The associated magnetic field H(z, t) can be found by using Faraday's law of electromagnetic induction. Faraday's law states that the rate of change of magnetic flux through a surface is equal to the electromotive force (EMF) along the boundary of the surface. In this case, the magnetic field is changing due to the time-dependent electric field, so we can use Faraday's law to find the magnetic field.
Start by finding the magnetic flux through a surface with an area A in the z-direction.The magnetic field B is perpendicular to the surface, so the magnetic flux is given by Φ = B * A.By Faraday's law, the rate of change of magnetic flux is equal to the induced EMF around the boundary of the surface. In this case, the induced EMF is caused by the changing electric field.From the given electric field E(z, t), we can differentiate it with respect to time to find the rate of change, which gives us the induced EMF.Equating the rate of change of magnetic flux to the induced EMF, we can solve for the magnetic field B(z, t).By following these steps, you can find the associated magnetic field H(z, t) using Faraday's law of electromagnetic induction.
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x + y + w = b
2x + 3y + z + 5w = 6
z + w = 4
2y + 2z + aw = 1
For what values a, b (constants) is the system:
(a) inconsistent?
(b) consistent w/ a unique sol'n?
(c) consistent w/ infinitely-many sol'ns?
Answer:
(a) a=6 and b≠[tex]\frac{11}{4}[/tex]
(b)a≠6
(c) a=6 and b=[tex]\frac{11}{4}[/tex]
Step-by-step explanation:
writing equation in agumented matrix form
[tex]\begin{bmatrix}1 &1 & 0 &1 &b\\ 2 &3 & 1 &5 &6\\ 0& 0 & 1 &1 &4\\ 0& 2 & 2&a &1\end{bmatrix}[/tex]
now [tex]R_{2} =R_{2}-2\times R_{1}[/tex]
[tex]\begin{bmatrix}1 &1& 0 &1 &b\\ 0 &1& 1 &3 &6-2b\\ 0& 0 & 1 &1 &4\\ 0& 2 & 2&a &1\end{bmatrix}[/tex]
now [tex]R_{4} =R_{4}-2\times R_{2}[/tex]
[tex]\begin{bmatrix}1 &1& 0 &1 &b\\ 0 &1& 1 &3 &6-2b\\ 0& 0 & 1 &1 &4\\ 0& 0 & 0 &a-6 &4b-11\end{bmatrix}[/tex]
a) now for inconsistent
rank of augamented matrix ≠ rank of matrix
for that a=6 and b≠[tex]\frac{11}{4}[/tex]
b) for consistent w/ a unique solution
rank of augamented matrix = rank of matrix
a≠6
c) consistent w/ infinitely-many sol'ns
rank of augamented matrix = rank of matrix < no. of variable
for that condition
a=6 and b=[tex]\frac{11}{4}
then rank become 3 which is less than variable which is 4.
Use set notation to write the members of the following set, or state that the set has no members
Odd numbers between 22 and 66 that are multiples of 5.
Answer:
Odd numbers that are multiple of 5 and are in between 22 and 66 are-
25, 35, 45, 55, 65
Let this set be represented by A
A= {25, 35, 45, 55, 65}
the above form represents the set in its roster form
The set notation for the odd numbers between 22 and 66 that are multiples of 5 is { x ∈ N | x is odd, 22 < x < 66, x ≡ 0 (mod 5) }.
Explanation:The set notation for the odd numbers between 22 and 66 that are multiples of 5 can be written as:
{ x ∈ N | x is odd, 22 < x < 66, x ≡ 0 (mod 5) }
Identify the set as a set of natural numbers, denoted as N.Define the condition for the set membership using a vertical bar |.List the conditions for the set, which include being odd, between 22 and 66, and a multiple of 5.Use the congruence notation x ≡ 0 (mod 5) to represent the requirement of being a multiple of 5.Learn more about Set notation here:https://brainly.com/question/32799768
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Write equations for the vertical and horizontal lines passing through the point . (7,5)
A horizontal line is a line where all of the [tex]y[/tex] values are the same. In this case, [tex]\boxed{y=5}[/tex], so that is the equation.
A vertical line is where all of the [tex]x[/tex] values are the same. Here, [tex]\boxed{x=7}[/tex], so that's the equation.
Answer:
see below
Step-by-step explanation:
A horizontal line has the same y value and has a constant y value
y=5
A vertical line has the same x value and has a constant x value
x=7
Solve the Method of variation of Parameters. y" - 3y' + 2y = 4e^3t
Answer:
CF+PI=[tex]c_1e^{2x}+c_2e^{x}[/tex]+[tex]2e^{3t}[/tex]
Step-by-step explanation:
we have given y"-3y'=2y=[tex]4e^{3t}[/tex]
this differential equation solution have two part that CF and PI
CALCULATION OF CF :
[tex]m^2-3m+2=0[/tex]
[tex]m^2-2m-m+2=0[/tex]
[tex](m-1)(m-2)=0[/tex]
m=1 and m=2
so CF=[tex]c_1e^{2x}+c_2e^{x}[/tex]
CALCULATION OF PI :
PI = [tex]\frac{4e^{3t}}{(m-1)(m-2)}[/tex]
at m= 3 in PI
[tex]PI=\frac{4e^{3t}}{2}=2e^{3t}[/tex]
so the complete solution is
CF+PI=[tex]c_1e^{2x}+c_2e^{x}[/tex]+[tex]2e^{3t}[/tex]
Assume that when adults with smartphones are randomly selected, 51% use them in meetings or classes. If 11 adult smartphone users are randomly selected, find the probability that fewer than 5 of them use their smartphones in meetings or classes.
Answer:
The probability is 0.2356.
Step-by-step explanation:
Let X is the event of using the smartphone in meetings or classes,
Given,
The probability of using the smartphone in meetings or classes, p = 51 % = 0.51,
So, the probability of not using smartphone in meetings or classes, q = 1 - p = 1 - 0.51 = 0.49,
Thus, the probability that fewer than 5 of them use their smartphones in meetings or classes.
P(X<5) = P(X=0) + P(X=1) + P(X=2) + P(X=3)+P(X=4)
Since, binomial distribution formula is,
[tex]P(x) = ^nC_r p^x q^{n-x}[/tex]
Where, [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Here, n = 11,
Hence, the probability that fewer than 5 of them use their smartphones in meetings or classes
[tex]=^{11}C_0 (0.5)^0 0.49^{11}+^{11}C_1 (0.5)^1 0.49^{10}+^{11}C_2 (0.5)^2 0.49^{9}+^{11}C_3 (0.5)^3 0.49^{8}+^{11}C_4 (0.5)^4 0.49^{7} [/tex]
[tex]=(0.5)^0 0.49^{11}+11(0.5)0.49^{10} + 55(0.5)^2 0.49^{9}+165 (0.5)^3 0.49^{8} +330(0.5)^4 0.49^{7} [/tex]
[tex]=0.235596671797[/tex]
[tex]\approx 0.2356[/tex]