The distances of the person from the first three images as seen from the left hand mirror are 10.0 ft, 30.0 ft and 40.0 ft respectively.
From the question
The person is 5.00 ft from the mirror on the left wall
But the focal length of plane mirror is infinity which means both the image and object are equidistant from mirror
Therefore, the distance of first image on left wall of the mirror is
D1 = 5.00 + 5.00
= 10.0 ft
where D1 is first distance.
So the image is 10.0 ft away from object.
From the second image,
The right side of the mirror forms the image of object at distance of 10.0 ft from the mirror on the right wall.
The person second distance is
d2 = (2 * 10.0) +10.0
d2 = 30.0 ft
where d2 is second distance.
And the third image is acquired by the addition of the image presented by the left mirror and the image presented by the right mirror.
d3 = (2 × 5.00) + 30.0
d3 = 40.0 ft
Therefore, the distances of the person from the first three images are 10.0 ft, 30.0 ft and 40.0 ft respectively.
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If matrix M is of dimension 5 x 3, and matrix N is of dimension 5 x 5 then the dimension of NM is
A₂ₓ₃ matrix and B₃ₓ₄ matrix, The dimension of the matrix AB obtained by multiplying A and B will be AB₂ₓ₄.
What are matrices?Matrices represent data in the form of rows and columns in an array form.
Suppose we have two matrices and their multiplication is possible only when the no. of columns in the first matrix is equal to the no. of rows in the second matrix.
Let A₂ₓ₃ matrix and B₃ₓ₄ matrix, Then the dimension of the matrix AB obtained by multiplying A and B will be AB₂ₓ₄.
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.
For the following, find the length of AB:
(Use \large \pi=3.14 when necessary and round your final answer to the hundredths.)
Arc AB =
In the given diagram, the length of arc AB is 10.05.
Calculating the length of an arc ABFrom the question, we are to determine the length of arc AB.
From the formula for calculating the length of an arc, we have that
Length of an arc = θ/360° × 2πr
Where θ is the angle subtended by arc at the center of the circle
and r is the radius of the circle
In the given diagram,
Angle subtended by the arc = 48°
Radius, r = 12
Therefore,
The length of the arc = 48/360 × 2×3.14×12
Length of the arc = 2/15 × 1884/25
Length of the arc = 10.05
Hence, the length of AB is 10.05
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A bank put $50 into a savings account when you opened the account. 12 weeks later, you have a total of $275. a. If y is the total amount of money in the savings account and x represents the number of weeks, write an equation in the form of y=mx+b that describes the situation. Be sure to show or explain how you got your answer.
Answer:
In this problem, we are looking for an equation in the form of y = mx + b that describes the situation where a bank puts $50 into a savings account when it is opened and 12 weeks later, the account has a total of $275.
To find the equation, we need to find the slope (m) and the y-intercept (b). The y-intercept is the point at which the line crosses the y-axis, which in this case is the initial amount of money in the account ($50). The slope is the rate at which the amount of money in the account is changing over time.
To find the slope, we can use the following formula:
slope = (y2 - y1) / (x2 - x1)
In this case, y2 is the total amount of money in the account after 12 weeks ($275), y1 is the initial amount of money in the account ($50), x2 is the number of weeks after the account is opened (12 weeks), and x1 is the number of weeks before the account is opened (0 weeks).
Plugging these values into the formula, we get:
slope = (275 - 50) / (12 - 0) = 225 / 12 = 18.75
Now that we have the slope, we can plug it into the equation y = mx + b, along with the y-intercept (b = 50), to get the final equation:
y = 18.75x + 50
This equation represents the situation described in the problem, where the bank puts $50 into a savings account when it is opened and 12 weeks later, the account has a total of $275.
Need help on this! (Many points!)
Answer:
[tex]\frac{-8}{9}[/tex]
Step-by-step explanation:
Substitute in 7 for x
[tex]\frac{7^{2}-5(7) -6 }{7^{2}-6(7) - 16 }[/tex]
[tex]\frac{49-35-6}{49-42-16}[/tex]
[tex]\frac{-8}{9}[/tex]
simplify 1+1
[tex] \frac{1}{(1 - { \sqrt{ 5} )}^{2 } } + \frac{1}{(1 + \sqrt{ {5)}^{2} } } [/tex]
simplify
The value of the surd when simplified is 1/6
How to simplify the surd?We should recall that surd is the square root of all irrational numbers, simplification involves making it more simpler.
The given question is [tex]\frac{1}{(1-\sqrt{5 })^{2} } + \frac{1}{(1+\sqrt{5} )^{2} }[/tex]
We shall be simplifying the expression in parts
From difference of two squares
(1)/[(1-√5)(1+√5) = 1+5 = 1/6
The second part is 1/[(1+√5)(1+√5) = 1/(1+√10+5)
= 1/(6+√10)
Joining the two parts to get
1/6 + 1/(6+√10
Simplifying the fractions
(√10+1)/(6+√10)
= 1/6
Therefore the value of the expression is 1/6
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At the time of her grandson's birth, a grandmother deposits 14000 in an account that pays 9.5% compounded monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period?
The value of the account at the child's twenty-first birthday is 102125.44
How to determine the value of the account at the child's twenty-first birthday?We can use the compound interest formula to determine the value of the account (A) on the child's twenty-first birthday:
A = P (1 + r/n)^(nt)
Where:
P is the initial amount of money deposited in the account
r is the interest rate
n is the number of times the interest is compounded per year
t is the number of years
Given: P = 14000, r = 9.5% = 0.095, t = 21, n = 12 (i.e. 12 months per year)
Substitututing into A = P (1 + r/n)^(nt):
A = 14000 (1 + 0.095/12)^(12×21)
A = 14000 (1 + 0.095/12)^(252)
A = 102125.44
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A library is holding a special five-day event honoring successful local writers. One writer will be invited to be a guest speaker for each night from Monday through Friday, and no writer will be asked to participate twice. The writers have each written books in only one of four different genres—science fiction, mystery, historical fiction, and non-fiction. A, J, and X are all science fiction writers. B and Y are both mystery writers. C and Z are both historical fiction writers. L is a non-fiction writer. The following conditions apply without exception:
At least one writer from each genre will be invited to speak on at least one night.
No two authors from the same genre will be invited to speak on the following night.
If C is invited to speak, then X is invited to speak on the following night.
If Y is invited to speak, then neither C nor A are invited to speak.
If X and J are both invited to speak, then neither will speak on either the first or last night.
If L and B are both invited to speak, then neither will speak on either the first or last night.
If L is invited to speak on Friday, then on what days MUST a science fiction writer be invited? Possible Answers:Monday and Wednesday
Monday and Tuesday
Tuesday and Thursday
Only Wednesday
Monday and Thursday
As per the concept of probability, If L is invited to speak on Friday, then the science fiction writer be invited on Monday and Wednesday
Probability:
In statistics, probability refers the possible and favorable outcome of the particular event.
Given,
Here we need to find if L is invited to speak on Friday, then on what days MUST a science fiction writer be invited.
Here we know that the writers of the same genre may not speak on consecutive nights.
And here we have the only five slots to fill, two of the three science fiction writers must speak on Monday and Friday
So, If both X and J are invited, then at least one will be forced to speak on Monday or Friday, which is not allowed.
Then, modification of the rules is actually just a bit of a red herring, since all of the answer choices except for the one regarding science fiction writers is true regardless.
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What does the statement below mean?
Range: {-7 < y < 12}
The statement -7 < y < 12 meant y is greater than -7 and less than 12.
How to interpret inequality?{-7 < y < 12}
This is a compound inequality.
A compound inequality is a type of inequality which combones two or more simple inequality.
-7 < y < 12
This can be broken down into two parts;
-7 < y (minus 7 less than y)y < 12 (y is less than 12This can also be written together as y is greater than -7 and less than 12.
This means y is between the values that are greater than -7 but less than 12
So,
y could be -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Therefore, y can be said to be within the range of values between -6 and 11
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Solve by using substitution. Express your answer as an ordered pair.
{4x+y=1
y=x−4
Answer:
The correct answer is (1, -3).
Step-by-step explanation:
To solve this question, we should use substitution. This means we can substitute the value given for y (as indicated by the second equation) into the first equation. This is shown below:
4x + y = 1
4x + (x - 4) = 1
We simplify the left side of the equation and then solve for x.
5x - 4 = 1
5x = 5
x = 1
We must also solve for y. To do this, we can plug in x = 1 into either of the given equations.
y = x - 4
y = 1 - 4
y = -3
Therefore, x = 1 and y = -3. The question asks us to express the answer as an ordered pair (x,y), so the answer is (1, -3).
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Find m<2
(Please help my test ends 12:50 west coast)
Answer:
40
Step-by-step explanation:
40
Your classmate is starting a new fitness program. He is planning to ride his bicycle for 45 minutes every day. He burns 6 calories per minute bicycling at 11 mph and 9.25 calories per minute bicycling at 15 mph. How long should he bicycle at each speed to burn 400 calories?
He will spend 5 minutes bicycling at 11mph and 40 minutes bicycling at 15mph.
How to calculate the time taken?From the information, the person is planning to ride his bicycle for 45 minutes every day. He burns 6 calories per minute bicycling at 11 mph and 9.25 calories per minute bicycling at 15 mph
This will be illustrated as:
x + y = 45 ..... i
6x + 9.25y = 400 ..... ii
From equation i, x = 45 - y ..... iii
x = number of minutes cycling at 11mph
y = number of minutes cycling at 15mph
Put equation iii into ii
6x + 9.25y = 400
6(45 - y) + 9.25y = 400
270 - 6y + 9.25y = 400
3.25y = 130
Divide
y = 40
Since x + y = 45.
x = 45 - 50
x = 5
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write the following python function: asquare(k) takes k as a parameter and returns a list containing squares of first k integers. asquare(5) will return the list [1, 4, 9, 16, 25] print that list
The python function is, [1, 4, 9, 16, 25] [1, 4].
What is square of a number?
It is easy to determine a number's square. To determine the given number's square, we must multiply it by itself. A number raised to the power of 2 is always used to represent the square term.
For instance, the square of 6 is equal to 6 times 6, or 6 x 6 = 6^2 = 36.
A "Square Number" is the product of multiplying an integer or number (not a fraction) by itself.
For instance, 3 x 3 = 3^2, or 3 multiplied by 3 equals 3 squared. In essence, a square number is the result of multiplying an integer or number by itself exponentially.
Hence, the python function is, [1, 4, 9, 16, 25] [1, 4].
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Find the derivative using the Fundamental Theorem of Calculus, part 1, which states that if f(x) is continuous over an interval [a, b], and the function F(X) is defined by F(X) - F'(x) = f(x) over [a, b]. [*re) or, then del tot Additional Materials eBook 4.
then Find the derivative using the Fundamental Theorem of Calculus, part 1, which states that if f(x) is continuous over an interval (a, b), and the function F(x) is defined by F(X) - F'(x) = f(x) over [a, b]. de la intu In(u) du 6.
Evaluate the definite integral using the Fundamental Theorem of Calculus, part 2, which states that iffis continuous over the interval [a, b] and F(x) is any antiderivative of f(x), then Giºrno dx = F(b) – Fla). [x?- ») 3x) dx Х
On solving the question, by the help of, Fundamental Theorem of Calculus, we got answer [tex]3xe^x[/tex]
What is fundamental Theorem of Calculus?A theorem that connects the ideas of differentiating a function from integrating a function is known as the fundamental theorem of calculus. The two processes are inverses of one another, with the exception of a constant number that is dependent on the starting point for computing area.
When asked to compute the derivative of an integral, utilize the calculus fundamental theorem rather than evaluating the integral.
FTOC informs us that:
[tex]\frac{d}{dx} [\int\limits^{3x}_t {3lnt} \, dxt] = 3xe^x[/tex]
(That is, the integral's derivative returns the original function to us.)
We are required to locate:
h'(x) where h(x)= [tex]\int\limits^{3x}_t {3lnt} \, dxt= 3xe^x[/tex]
what we want
[tex]h'(x) = \frac{d}{dx} [\int\limits^{ex}_t {3lnt} \, dxt] = 3xe^x.............................A[/tex]
(Note that the first integral's upper limits are not in the proper format for the FTOC to be applied immediately.) The chain rule and a replacement can be used to alter the definite integral. Let:
[tex]u = e^x = \frac{du}{dx} = e^x[/tex]
Using the chain rule and substituting into the integral [A], we obtain:
[tex]\frac{d}{dx} [\int\limits^{ex}_t {3lnt} \, dxt] =[/tex][tex]\frac{d}{dx} [\int\limits^{u}_t {3lnt} \, dxt] = 3xe^x[/tex]
= [tex]e^x \frac{d}{du} [\int\limits^{ex}_t {3lnt} \, dxt] = 3xe^x[/tex]
now we got answer - [tex]3xe^x[/tex]
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customers is equally likely to report a food allergy, what is the probability that at least one customer will report a food allergy?
The probability that at least one client will have a food allergy is 0.6323 and the percentage of customers who will have a food allergy is 0.08.
What is probability?
The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not.
As given in the question,
The percentage of customers who will have a food allergy is 0.08
At Ying Ying's bakery,
121 people place orders on a single day.
We can utilize the binomial distribution if we believe that each of the 12 clients has an equal probability of reporting a food allergy.
Formula for Binomial probability distribution:
P(X=x)=ⁿCₓ pˣ (1-p)ⁿ⁻ˣ
Here, P(x) = probability of getting success in x trials, n= sample size ,p = represents the probability that each event will succeed.
As given, we have
n = 12
p=0.08
Let x is the client will have a food allergy.
Following that, the probability that at least one client will have a food allergy will be:
P(x≥1) = 1 - P(x<1)
= 1 - P(x=0)
= 1 - ¹²C₀(0.08)⁰(1 - 0.08)¹²⁻⁰
= 1 - (1)(0.12)¹²
= 1 - 0.3677
= 0.6323
Hence , the probability that at least one client will have a food allergy will be 0.6323 when the percentage of customers who will have a food allergy is 0.08.
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Complete Question
When a customer places an order at Ying Ying's bakery, there is an 8\%8%8, percent probability that the customer will report a food allergy. One day, 121212 customers place orders at Ying Ying's bakery.
Assuming that each of the 121212 customers is equally likely to report a food allergy, what is the probability that at least one customer will report a food allergy?
What is the solution set of the quadratic inequality x^2-5<0?
The solution set of the quadratic inequality x² - 5 < 0 is - √5 < x < √5
How to determine the solution set?From the question, we have the following parameters that can be used in our computation:
The quadratic inequality is:
x^2-5<0
Express properly
x² - 5 < 0
Add 5 to both sides of the inequality
x² < 5
Take the square root of both sides
x < ±√5
Expand the inequality expression
- √5 < x < √5
Hence, the solution is - √5 < x < √5
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YodelAir operates a charter jet service out of an airport in a secluded mountain ski resort. The chief safety officer for YodelAir uses a normal distribution with a
mean of 629 m and a standard deviation of 120 m to model the takeoff distance of the company's X15 jets in wintry weather.
Use this table or the ALEKS calculator to find the percentage of takeoff distances between 467 m and 611 m according to the model. For your intermediate
computations, use four or more decimal places. Give your final answer to two decimal places (for example 98.23%).
By "standard deviation", 30.62% the percentage of takeoff distances .
How to interpret a standard deviation?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.
Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
X ~ N ( µ = 628 , σ = 80 )
P ( 464 < X < 592 ) = ?
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 464 - 628 ) / 80
Z = -2.05
Z = ( 592 - 628 ) / 80
Z = -0.45
P ( -2.05 < Z < -0.45 )
P ( 464 < X < 592 ) = P ( Z < -0.45 ) - P ( Z < -2.05 )
P ( 464 < X < 592 ) = 0.3264 - 0.0202
P ( 464 < X < 592 ) = 0.3062
= 30.62%
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() Type the missing digits:
6,4 18,6 ? 8
-?,?85,835
2,9 3 2,863
Answer:
6418698
-3485835
2932863
Step-by-step explanation:
The Fitzhugh-Nagumo model for the electrical impulse in a neuron states that, in the absence of relaxation effects, the electrical potential in a neuron v(t) obeys the differential equation dv dt = −v[v2 − (1 + a)v + a] where a is a positive constant such that 0 < a < 1. (a) For what values of v is v unchanging (that is, dv/dt = 0)? (Enter your answers as a comma-separated list.) v = (b) For what values of v is v increasing? (Enter your answer using interval notation.) (c) For what values of v is v decreasing? (Enter your answer using interval notation.)
The values of v for the electric impulse model in the Fitzhugh-Nagumo model are 0, 1, and a.
What is electric impulse?The strength of the field is shown by the distance between the lines; the closer they are to one another, the stronger the field.
In this scenario, the field weakens as we travel away from the charge because the distance between the lines widens (it actually obeys an inverse square law,
The electric field, which is pointed away from the core charge, is indicated by the direction of the lines.
This is due to the fact that a positive test charge would be repelled away from the electric field if it were placed there because the direction of the electric field corresponds to the direction of the force that a positive test charge would experience when immersed in the electric field.
Hence, The values of v for the electric impulse model in the Fitzhugh-Nagumo model are 0, 1, and a.
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Find the measure of the arc or central angle indicated.
The central angle of the given arc LKJ is; 211°
How to find the length of an arc of a circle?
We want to find the length of the arc LKJ. The central angle for this arc length is; 115° + 96° = 211°
The formula for length of arc is;
L = θ/360 * 2πr
where;
θ is central angle
r is radius
We are not given the radius and as such, we can only find the central angle which is 211°
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Three long wires (wire 1 wire 2 and wire 3 ) hang vertically. The distance between wire 1 and wire 2 is 23.0 cm On the left, wire 1 carries an upward current of 1.50 A. To the right, wire 2 carries a downward current of 3.60 A. Wire 3 is to be located such that when it carries a certain current, each wire experiences no net force. (a) Is this situation possible? Is it possible in more than one way? Describe (b) the position of wire 3 and the magnitude and direction of the current in wire 3.
Based on the combination technique,
1. The position of wire 3
2. The magnitude and direction of current in wire 3
Combination method:
In statistics, the mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter is know a combination method.
Given,
Here we have the three long wires hang vertically. The distance between wire 1 and wire 2 is 23.0 cm On the left, wire 1 carries an upward current of 1.50 A. To the right, wire 2 carries a downward current of 3.60 A. Wire 3 is to be located such that when it carries a certain current, each wire experiences no net force.
And now we need to find the position of wire 3 and the magnitude and direction of the current in wire 3.
As per the given question, we know that the
=> Current in wire 1, i1 =1.2A upward
=> Current in wire 2, i2=5A downward
And the distance between wire 1 and 2 is calculated is
=> 20cm = 0.2m
Here the current is calculated as
=> F/l = μo•i1•i3/2πx
So,
=> F/l=6×10⁻⁶N/m
=> 6×10⁻⁶ = μo•i1•i3/2πx
=> 6×10⁻⁶ =4π×10⁻⁷×1.2×i3/(2π×0.0632)
When we do Cross multiply,
=> 6×10⁻⁶×2π0.0632=4π×10⁻⁷×1.2×i3
=> 2.383×10⁻⁶=4π×10⁻⁷×1.2×i3
=> i3= (2.383×10⁻⁶)/(4π×10⁻⁷×1.2)
Therefore, i3= 1.58A and it's direction is downward.
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Your sorority is preselling tickets for an end of year formal. You will save 22% off the door price by prepaying
$56.40 per ticket now.
How much will you pay if you wait to purchase tickets at the door?
Answer:
$68.81
Step-by-step explanation:
22% of 56.40 can be found by multiplying
.22 and 56.4, which equals 12.408
therefore, if you add 12.408, or 12.41, to 56.40 you will get 68.81
write an equation in slope-intercept form that would have infinitely many solutions in a system of equations with 5x-2y=8
Answer:
y = 2.5x - 4--------------------------
The linear functions will have same or equivalent equations in order to have infinitely many solutions.
Convert the given to slope-intercept form, y = mx + b, to make it equivalent:
5x - 2y = 82y = 5x - 8y = 2.5x - 4Callie took out a loan for $7000 to purchase a car. The loan must be repaod at the end of six years in one payment with interest of 5%. The total amount Callie has to pay back at the end of the loan is
A.$7350
B.$9100
C.$7900
D.$9700
The correct value of answer is B. $9100.The interest on the loan is 5% of the principal. So, the interest amount is:= $350
To calculate the total amount Callie has to pay back at the end of the loan, we need to add the principal amount (the original loan amount) and the interest accrued over the six-year period.
The interest can be calculated using the formula: Interest = Principal * Rate * TimeHere, the principal amount is $7000, the interest rate is 5% (or 0.05 as a decimal), and the time is 6 years.
Interest = $7000 * 0.05 * 6 = $2100
Adding the interest to the principal, the total amount Callie has to pay back is:
Total amount = Principal + Interest = $7000 + $2100 = $9100
Therefore, the correct answer is B. $9100.
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a 10-cmcm-long spring is attached to the ceiling. when a 2.0 kgkg mass is hung from it, the spring stretches to a length of 15 cmcm.
When a mass of 3 kg is hanged to it, the string will stretch 7.5 cm.
Given,
The length of the spring attached to the ceiling = 10 cm
The quantity of the mass hanged in the spring = 2 kg
The amount of stretching happened in the spring = 15 cm
We have to find the stretching of string when a mass of 3 kg is hanged to it;
Here,
Given that the force applied to the spring by the 2.0 kg is equal to the mass's weight:
F = mg = 2 kg × 9.8 m/s² = 19.6 N
Additionally, the stretching of:
Δx = 15 cm - 10 cm = 5 cm
So, applying Hooke's law:
F = kΔx
To determine the spring constant, k;
k = F/Δx = 19.6/5 = 3.92 N/ cm
The spring is now coupled to a new mass of m = 3.0 kg; the force this mass exerts on the spring equals
F = mg = 3 kg × 9.8 m/s² = 29.4 N
Thus, we may apply Hooke's law once more to determine the new stretching:
Δx = F/k = 29.4/3.92 = 7.5 cm
Therefore,
The string will be stretched 7.5 cm when a mass of 3 kg is hanged to it.
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Albert has a credit card with an APR of 20.7% and the following daily balances for this billing period: Days 1-3: $50 Days 4-10: $100 Days 11-25: $175 Days 26-30: $225 1. What is Albert’s daily rate? Round to the nearest ten thousandth.
Albert daily rate is 3.79%
How to determine Albert daily rate?We know that rate is the quantity or amount or the degree of a quantity measured with another quantity.
Albert's credit card APT = 20.7%
Daily balances are
Days 1-3 = (20.7*50)/100 = 10.35
Days 4-10 = (20.7*100)/100 =20.70
Days 11-25 = (20.7*175)/100 = 36.225
Days 26-30 = (20.7*225)/100 =46.575
Number of days in the month = 30 days
Total balance = $113.80
Daily rate = [tex]\frac{Total amount }{number of days}[/tex]
daily rate = [tex]\frac{113.80}{30}[/tex]
Dividing the figures we have 3.79
Therefore the daily rate is 3.79%
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Find Θ in radians:
(Use \large \pi=3.14 when necessary and round your final answer to the tenths.)
Θ =
Angle θ in radians is 12/5 or 2.4 radians.
Define Arc Length
Arc length is more accurately described as the length along the perimeter of any circle or curve (arc). The arc length is the measurement of any distance along the curved path that forms the arc. Arc refers to a segment of a curve or the circumference of a circle. Each of them is shaped like a curve. An arc's length is more than the distance in a straight line between its endpoints (a chord).
Given,
radius = 5 cm
length of arc = 12 cm
We know that,
θ = length of arc / radius
Now, plug in the values
θ = 12 / 5 or 2.4 radians
Hence,angle θ in radians is 12/5 or 2.4 radians.
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Answer: 2.4
Step-by-step explanation:
radius = 5 cm
length of arc = 12 cm
θ = length of arc / radius
θ = 12 / 5 or 2.4 radians
2.4 radians
Use the Alternating Series Estimation Theorem to estimate the range of values of x for which the given approximation is accurate to within the stated error.sin x = x − x 36 ( | error | < 0.01)
The Alternating Series Estimation Theorem to estimate the range of values of x for which the given approximation is ( -0.0654 , 0.0654 ) .
Given :
Use the Alternating Series Estimation Theorem to estimate the range of values of x for which the given approximation is accurate to within the stated error.sin x = x − x^3 / 6 ( | error | < 0.01 )
The next nonzero term in the Taylor series for sine is x^5 / 120 .
x^5 / 120 < .00000001
-0.00000001 < x^5 / 120 < .00000001
-0.0000012 < x^5 < .0000012
( -0.0000012 )^1/5 < x < ( .0000012 )^1/5
we have ( .0000012 )^1/5 ≈ .0654
= ( -0.0654 , 0.0654 )
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When finding f(g(x)) what do you need to know about the domains and ranges
of f(x) and g(x)? Explain
All x-values that are within the scope of both f and g make up the domain of the (f g)(x).
How can the domain of f/g)(x be determined?All x-values that are within the scope of both f and g make up the domain of the (f g)(x). In this case, f has a domain of "x | x 0" and g has a domain of "all real numbers," thus (f g)(x) also has a domain of "x | x 0" since these values of x fall within both f and g's domains.Utilizing graphs is another method for determining the domain and range of functions. The collection of possible input values is referred to as the domain, and the domain of a graph is made up of all the input values displayed on the x-axis. The collection of potential output values that make up the range is represented by the y-axis.To learn more about Domain refer to:
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Choose one point on the graph of the proportional relationship and explain what this point means in terms of the situation
A point on the graph is (30, 4) and the meaning is that the cost of 30 units of electricity is £4
How to interpret the point on the graph of the proportional relationshipFrom the question, we have the graph that can be used in our computation:
From the graph, we have the following ordered pairs
(0, 0) and (30, 4)
Rewrite the above points properly
So, we have the following ordered pairs
(x, y) = (0, 0) and (30, 4)
The gradient of the line is then calculated using the following slope equation
gradient = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (0, 0) and (30, 4)
Substitute the known values in the above equation
So, we have the following equation
gradient = (4 - 0)/(30 - 0)
Evaluate
gradient = 4/30
So, the gradient of the line is 4/30
As a general rule:
Generally, slope or gradient means rate
This means that the gradient of this line represent the rate
i.e. the amount for each unit is 4/30
So, we can conclude that the point (30, 4) on the graph means that the cost of 30 units is £4
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Complete question
An electricity company charges the same fixed amount for each unit of electricity used. David uses this graph to work out the total cost of the electricity he has used.
See attachment for graph
What is the horizontal shift for the absolute value function f(x)=3 |x+6| +9
Answer:
Left shift, 6 units
Step-by-step explanation:
In the equation:
f(x)=3 |x+6| +9
the " +6 " in close to the x represents the horizontal shift. X always tells us about horizontal or right/left moves. So an adjustment to the x is a horizontal adjustment.
But Caution! It is the opposite of what you might think. A PLUS6 is a LEFT shift. (While a MINUS6 would be a right shift, not the case here).
The parent function is:
f(x) = |x|
So our equation:
f(x)=3 |x+6| +9
has two changes made to it. LEFT6 because of the
" +6 " by the x. And the +9 tacked onto the end of the equation is a vertical shift UP9.
