For the following exercises, find (f x g)(x) and (g x f)(x) for each pair of functions.
f(x)=√x+2, g(x)=1/x
Answers
(f x g)(x) = √(1/x + 2)
(g x f)(x) = 1/(√(x + 2))
To find (f x g)(x), we need to evaluate the composition of functions f and g, which is denoted as f(g(x)).
Similarly, to find (g x f)(x), we need to evaluate the composition of functions g and f, which is denoted as g(f(x)).
Let's calculate (f x g)(x) and (g x f)(x) for the given pair of functions f(x) = √(x + 2) and g(x) = 1/x:
1. (f x g)(x):
We start by substituting g(x) into f(x) wherever we see an x in f(x):
(f x g)(x) = f(g(x)) = f(1/x)
Substitute 1/x into f(x):
(f x g)(x) = f(g(x)) = f(1/x) = √(1/x + 2)
2. (g x f)(x):
We start by substituting f(x) into g(x) wherever we see an x in g(x):
(g x f)(x) = g(f(x)) = g(√(x + 2))
Substitute √(x + 2) into g(x):
(g x f)(x) = g(f(x)) = g(√(x + 2)) = 1/(√(x + 2))
Therefore, we have:
(f x g)(x) = √(1/x + 2)
(g x f)(x) = 1/(√(x + 2))
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Related Questions
24,783 is invested, part at 15% and the rest 9%. If the interest earned from the amount invested at 15% exceeds the interest earned from the amount invested at 9% by $894.09, how much is invested at each rate?
Answers
If 24,783 is invested, part at 15% and the rest 9%. If the interest earned from the amount invested at 15% exceeds the interest earned from the amount invested at 9% by $894.09: 51,960 is invested at 15%, and 22,823 is invested at 9%.
How to find the amount invested?Let's x represent the amount invested at 15%
Let the amount invested at 9% = 24,783 - x.
Interest earned at 15% is 0.15 * x
Interest earned at 9% is 0.09 * (24,783 - x)
We can set up the equation: 0.15x = 0.09 * 24,783 - 0.09x + 894.09
Solving for x:
0.06x = 24,783 * 0.09 + 894.09
0.06x = 2223.47 + 894.09
0.06x = 3117.56
x = 51,960
So,
(24,783 - x)
24,783 - 51,960
= 22,823
Therefore 51,960 is invested at 15%, and 22,823 is invested at 9%.
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Write an expression to represent: 9 more than the quotient of 2 and x
Answers
Expression for given numerical is: 9+ (2/x)
Given that we have an word equation that is 9 more than the quotient of 2 and x
A quotient is a quantity produced by the division of two numbers.
Quotient of 2 and x is \(\frac{2}{x}\).
Nine(9) more than 2/x is = 9+ (2/x)
So we have an expression that is:
9+ (2/x)
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A convex lens with focal length f centimeters will project the image of an object on a
point behind the lens. If an object is placed a distance of p centimeters from the lens,
then the distance q centimeters of the image from the lens is related to p and f by the
lens equation: 1/p+1/q=1/f
A. If the focal length of the convex lens is supposed to be 5 cm, and if the image is
formed 7 cm from the lens, find the distance from the lens to the object, p. (It’s not necessary to simplify your answer.)
B. Find an expression that gives q as a function of p, assuming that the focal length is a constant of 5 centimeters.
C. Sketch a graph of q as a function of p (i.e., q(p)), assuming that the focal length is a
constant of 5 centimeters. Show any important features of the graph.
D. Find limq(p) as p approaches infinity and limq(p) as p approaches 5from the positive side. What do these limits represent physically? What must
happen to the distance of the image and the object?
Answers
Answer:
A. Using the lens equation, 1/p + 1/q = 1/f, and substituting f = 5 cm and q = 7 cm, we can solve for p:
1/p + 1/7 = 1/5
Multiplying both sides by 35p, we get:
35 + 5p = 7p
Simplifying and rearranging, we get:
2p = 35
Therefore, the distance from the lens to the object, p, is:
p = 35/2 cm
B. Solving the lens equation, 1/p + 1/q = 1/f, for q, we get:
1/q = 1/f - 1/p
Substituting f = 5 cm, we get:
1/q = 1/5 - 1/p
Multiplying both sides by 5qp, we get:
5p = qp - 5q
Simplifying and rearranging, we get:
q = 5p / (p - 5)
Therefore, the expression that gives q as a function of p is:
q = 5p / (p - 5)
C. Here is a sketch of the graph of q(p):
The graph is a hyperbola with vertical asymptote at p = 5 and horizontal asymptote at q = 5. The image distance q is positive for object distances p greater than 5, which corresponds to a real image. The image distance q is negative for object distances p less than 5, which corresponds to a virtual image.
D. Taking the limit of q as p approaches infinity, we get:
lim q(p) = 5
This represents the horizontal asymptote of the graph. As the object distance becomes very large, the image distance approaches the focal length of the lens, which is 5 cm.
Taking the limit of q as p approaches 5 from the positive side, we get:
lim q(p) = -infinity
This represents the vertical asymptote of the graph. As the object distance approaches the focal length of the lens, the image distance becomes infinitely large, indicating that the lens is no longer able to form a real image.
In order for the lens to form a real image, the object distance p must be greater than the focal length f. When the object distance is less than the focal length, the lens forms a virtual image.
Which graph accurately represents the inequality 2x +4> 10?
Answers
Answer:
E.
Step-by-step explanation:
2x+4>10
Subtract 4 from both sides
2x>6
Divide both sides by 2
x>3
So, E represents this inequality as x is greater than 3 and it does not include 3 in it which is represented by an empty bubble.
Answer:
E
Step-by-step explanation:
the bakery sold 60 cheesecakes yesterday. 4/5 of the cheesecakes were vanilla. How many vanilla cheesecakes were sold?
Answers
Answer:
60 x 4/5 = 240/5 = 48
48 vanilla cheesecakes
The measure of one small angles of a right triangle is 45 less than twice the measure of the other small angle. Find the measure of both angles
Answers
Answer:
x + x - 45 = 90
2x - 45 = 90
2x = 135
x = 67.5, so x - 45 = 22.5
The other two angles measure 22.5° and 67.5°.
A zip wire runs between two posts, 25m apart. The zip wire is at an angle of 10 degrees to the horizontal. Calculate the length of the zip wire.
∘
to the horizontal. Calculate the length of the zip wire
Answers
The length of the zip wire, with a 10-degree angle to the horizontal and a distance of 25 meters between the posts, is approximately 25.35 meters.
To calculate the length of the zip wire, we can use trigonometry. Let's consider the triangle formed by the zip wire, where the horizontal distance between the two posts is 25 meters and the angle between the zip wire and the horizontal is 10 degrees.
Using trigonometric functions, we can determine the length of the zip wire. In this case, we'll use the sine function because we have the opposite side (the vertical distance) and we want to find the hypotenuse (the length of the zip wire).
The formula for sine is:
sin(angle) = opposite / hypotenuse
Rearranging the formula, we have:
hypotenuse = opposite / sin(angle)
In this case, the opposite side is the vertical distance, which is h.
So, the formula becomes:
hypotenuse = h / sin(angle)
To find h, we can use the formula for the length of the zip wire:
h = 25 * tan(angle)
Substituting this into the previous formula, we get:
hypotenuse = (25 * tan(angle)) / sin(angle)
Calculating the value, we have:
hypotenuse = (25 * tan(10°)) / sin(10°)
Using a calculator, we find:
tan(10°) ≈ 0.1763
sin(10°) ≈ 0.1736
Substituting these values, we can calculate the length of the zip wire:
hypotenuse ≈ (25 * 0.1763) / 0.1736 ≈ 25.35 meters
Therefore, the length of the zip wire is approximately 25.35 meters.
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I need help with C please.
Answers
9514 1404 393
Answer:
║w║ = 6
Step-by-step explanation:
(c) The magnitude of w is computed the same way the magnitudes of the other vectors are computed. It is the root of the sum of the squares of the components.
║w║= ║<-6, 0>║ = √((-6)² +0²) = √36
║w║= 6
An animal population is modeled by the function A(t) that satisfies the differential equation dA dt equals the product of A divided by 1125 and the quantity 450 minus A . What is the animal population when the population is increasing most rapidly?
45 animals 225 animals 40 animals 180 animals
Answers
Answer:
225 animals
Step-by-step explanation:
From the given information:
\(\dfrac{dA}{dt} = ( \dfrac{A}{1125}) (450 - A)\)
\(\dfrac{dA}{dt} = \dfrac{450A - A^2}{1125}\)
For a population increasing most rapidly; we have:
\((\dfrac{dA}{dt} \implies max = A')\)
Thus; for \(\dfrac{d}{dA} ( \dfrac{dA}{dt}) \implies \dfrac{450-2A}{1125}\)
\(\dfrac{dA'}{dA} \implies 0 \\ \\ \\ A = 225\)
Suppose we have a random sample of size n = 5 from a continuous uniform distribution on the interval [0, 1]. Find the probability that the third largest observation in the
sample is less than 0.7.
Answers
The probability that the third largest observation in the sample is less than 0.7 is 0.2401 = 24.01%.
How do we calculate?The sample size n = 5,
Therefore the order statistics will be represented as X₁, X₂, X₃, X₄, and X₅.
Probability that X₃ is less than 0.7:
Since X₃ is the third largest observation = (X₁ and X₂) < 0.7.
The probability that X₃ is less than 0.7 is (0.7)² = 0.49.
The Probability that X₁ and X₂ < or equal to 0.7 is found as:.
The probability that both X₁ and X₂ are less than or equal to 0.7 is (0.7)² = 0.49 because in a continuous uniform distribution, the probability of any single observation being less than 0.7 is 0.7 - 0 = 0.7.
We then get the product of both cases:
Probability = 0.49 * 0.49 = 0.2401
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Sebastian purchases two pieces of equipment for $109,000. Appraisals of the equipment indicate that the fair market value of the first piece of equipment is $76,300 and that the second piece of equipment is $119,900. What is Sebastians basis in these two assets?
Answers
Sebastian's basis in the two assets are: $42,389 and $66,611
How to calculate the total assets?The computation of the Sebastian's basis in these two assets is shown below:
= Market value of the first piece of equipment ÷ Total market value of two pieces of equipment × purchase value of two pieces of equipment
= ($76300 ÷ $(76300 + 119900)) × $109,000
= $42,389
= Market value of the second piece of equipment ÷ Total market value of two pieces of equipment × purchase value of two pieces of equipment
= ($119,900 ÷ $(76300 + 119900)) × $109,000
= $66,611
The Total market value of two pieces of equipment
= $(76300 + 119900)
= $196,200
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what type of music did 1/5 of the girls choose as their ? 25% hip -pop 15%R&B 5% rock 35% pop 20% country
Answers
Answer:
Step-by-step explanation:
probably country (20%) because 1/5 is 20%.
I don't understand how to solve the proportion.2x/x+3 = 25/x
Answers
Given the following proportion:
\(\frac{2x}{x+3}=\frac{25}{x}\)You can solve it by following the steps shown below:
1. You can multiply both sides of the equation by:
\(x+3\)Then:
\(\begin{gathered} (x+3)(\frac{2x}{x+3})=(\frac{25}{x})(x+3) \\ \\ 2x=\frac{25(x+3)}{x} \\ \\ 2x=\frac{25x+75}{x} \end{gathered}\)2. Now you can multiply both sides of the equation by "x":
\(\begin{gathered} (x)(2x)=(\frac{25x+75}{x})(x) \\ \\ 2x^2=25x+75_{} \end{gathered}\)3. Rewrite the Quadratic Equation in the form:
\(ax^2+bx+c=0\)Then:
\(2x^2-25x-75_{}=0\)4. You can identify that:
\(\begin{gathered} a=2 \\ b=-25 \\ c=-75 \end{gathered}\)5. Then, you can use the Quadratic Formula to find the solutions:
\(x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\)Substituting values and evaluating, you get:
\(\begin{gathered} x=\frac{-(-25)\pm\sqrt[]{(-25)^2-4(2)(-75)}}{(2)(2)} \\ \\ x=\frac{25\pm35}{4} \\ \\ x_1=\frac{25+35}{4}=15 \\ \\ x_2=\frac{25-35}{4}=\frac{-10}{4}=-\frac{5}{2} \end{gathered}\)Therefore, the answer is:
\(\begin{gathered} x_1=15 \\ \\ x_2=-\frac{5}{2} \end{gathered}\)please help me awarding brainliest!
Answers
Answer:
a
Step-by-step explanation:
because the rest aren't true
Answer:
A. because the rest are not true
HELP ME QUICK FIND THE AREA ILL MARK BRAINLY
Answers
Answer:
6 square centimeters
Step-by-step explanation:
Answer:
6
you need to multiply base and height, i forget the actual terms, hope this helps
Which graph displays points that correspond to the x and y values in the table?
Answers
hm this is weird, i thought i answered the question. or maybe they're two different questions? line graph because i said so. i know im so helpful
the perimeter of a triangle is 32 feet. One side of the triangle is 11 feet longer than the second side. The third side is 9 feet longer than the second side. Find the length of each side.
Answers
Answer:
One side - 15 feet
Second side - 4 feet
Third side - 13 feet
Step-by-step explanation:
Let's call the sides A B and C, respectively.
We know that:
A = B + 11
C = B + 9
and that
A + B + C = 32
Please note that we have 3 equations and 3 unknowns. We can solve this, we'll use substitution.
A + B + C = (B + 11) + B + (B + 9) = 32
3B + 20 = 32
3B = 12
B = 4
The sides have lengths of 4+11 = 15, 4 and 4+9 = 13. This is in fact a proper triangle (because the shorter sides add up to more than the longer side).
Find the volume of the prism
Answers
= 1/2 x 2.5 x 3.4 x 4.8
= 2.5 x 1.7 x 4.8
= 20.4 mm^3
You are considering the services of three different employment agencies, all of which can get you a job that starts at $2,000 a month. Agency A charges 50 percent of the first month's gross salary. Agency B charges 10 percent of your monthly salary for the first six months. Agency C charges a $100 up-front fee and a flat fee of $500 when you are placed. Compare the three choices. Which of these offers the least expensive overall fee?
Answers
Answer:
Agency C offers the least expensive overall fee
Step-by-step explanation:
Alone from gross salary, you would make 24000 a year.
Agency A
24000 - ( 2000 x 0.5)
= 23,000
$1000 fee
Agency B
24000 - ( 2000 x 0.1 ) x 6
= 24000 - 200 x 6
= 24000 - 1200
= 22,800
$1200 fee
Agency C
24000 - (500 + 100)
= 24000 - 600
= 23,400
$600 fee
The organizer of a conference is selecting workshops to include. She will select from 4 workshops about genetics and 7 workshops about ethics. In how many ways can she select 6 workshops if 2 or fewer must be about genetics?
Answers
List all the subsets of the given set.
{e, n, t}
Answers
The subsets of the set {e, n, t} are given as follows:
{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.
How to obtain the number of subsets in a set?Considering a set with n elements, the number of subsets in the set is the nth power of 2, that is:
\(2^n\)
The set for this problem is given as follows:
{e, n, t}
The cardinality is given as follows:
n = 3.
Hence the number of subsets is given as follows:
2³ = 8.
The subsets are given as follows:
{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.
In which {} is the empty set.
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In a certain video game, there is a mini-game where the main character can choose from a selection of twenty
presents. The presents are wrapped, so the character does not know what is in them. If 7 presents contain money, 3
presents contain gems, 6 presents contain ore, and 4 presents contain fish, what is the probability that the main
character does not choose a present that contains a gem?
Your answer should be an exact decimal value.
The probability of randomly selecting a present that does not contain a gem is
Answers
Answer:
There are a total of 20 presents, and 3 of them contain gems. Therefore, there are 20 - 3 = 17 presents that do not contain gems.
The probability of randomly selecting a present that does not contain a gem is 17/20 = 0.85 or 85%.
hope it helps you...
Find the value of x.
Answers
Answer:
x=65°
Step-by-step explanation:
Solution Given:
let the point having angle 115° be e.
and point having side containing a and c be f.
we have
∡bec+115°= 180° being linear pair
∡bec=180°-115°=65°
again
∡bec= ∡afc=65° being corresponding angle
again
∡afc=x°=65° being corresponding angle
what is the simplified form of 4 log3x+6 log3y-7 log3z
Answers
Answer:
A
Step-by-step explanation:
Using the properties of logarithms, we can simplify the expression:
4 log3x + 6 log3y - 7 log3z = log3x^4 + log3y^6 - log3z^7
Now, we can use another property of logarithms, which states that:
loga (mn) = loga m + loga n
Using this property, we can combine the logarithms with addition or subtraction:
log3x^4 + log3y^6 - log3z^7 = log3(x^4 * y^6 / z^7)
Therefore, the simplified form of 4 log3x + 6 log3y - 7 log3z is log3(x^4 * y^6 / z^7).
if x was 4, what is the value of 4x + 3
Answers
Answer:
19
Step-by-step explanation:
4(4)+3
16+3=19
Answer:
19
Step-by-step explanation:
4x+3
4(4)+3
16+3
19
hope it helps
graph the system below2x-3y=-183x+y=-5
Answers
ANSWER:
STEP-BY-STEP EXPLANATION:
We have the following system of equations:
\(\begin{gathered} 2x-3y=-18 \\ \\ 3x+y=-5 \end{gathered}\)To graph, we calculate the intercepts in each equation to then draw the straight line corresponding to each equation, like this:
\(\begin{gathered} \text{ For }2x-3y=-18 \\ \\ \text{The x-intercept} \\ \\ \:2x-3\cdot 0=-18 \\ \\ x=-9\rightarrow(-9,0) \\ \\ \text{The y -intercept} \\ \\ 2\cdot0-3y=-18 \\ \\ y=6\rightarrow(0,6) \\ \\ \\ \text{For }3x+y=-5 \\ \\ \text{The x-intercept} \\ \\ 3x+0=-5 \\ \\ x=-\frac{5}{3}\rightarrow\left(-\frac{3}{5},0\right) \\ \\ \text{The y- intercept} \\ \\ \:3\cdot 0+y=-5\: \\ \\ y=-5\rightarrow(0,-5) \end{gathered}\)Now we graph:
Please help I’m stuck and keep getting the wrong answer
Answers
The time spent higher than 26 meters above the ground is 0.42 minutes. Answer: 0.42
A Ferris wheel is 30 meters in diameter and boarded from a platform that is 4 meters above the ground.
The six o'clock position on the Ferris wheel is level with the loading platform.
The wheel completes 1 full revolution in 2 minutes.
We have to find how many minutes of the ride are spent higher than 26 meters above the ground.
So, let's start with some given data,Consider the height of a person at the six o'clock position = 4 meters
So, the height of a person at the highest point = 4 + 15 = 19 meters (since the diameter is 30 meters, the radius will be 15 meters)
Also, the height of a person at the lowest point = 4 - 15 = -11 meters
Therefore, the Ferris wheel completes one cycle from the lowest point to the highest point and back to the lowest point.
So, the total distance travelled will be = 19 + 11 = 30 meters.
Also, we are given that the wheel completes 1 full revolution in 2 minutes.
We need to calculate the time spent higher than 26 meters above the ground.
So, the angle between the 6 o'clock position and 2 o'clock position will be equal to the angle between the 6 o'clock position and the highest point.
This angle can be calculated as follows:
Angle = Distance travelled by the Ferris wheel / Circumference of the Ferris wheel * 360 degrees
Angle = 30 / (pi * 30) * 360 degrees
Angle = 360 degrees / pi
= 114.59 degrees
So, the total angle between the 6 o'clock position and the highest point is 114.59 degrees.
Now, we need to find out how much time is spent at an angle greater than 114.59 degrees.
This can be calculated as follows:
Time = (Angle greater than 114.59 degrees / Total angle of the Ferris wheel) * Total time taken
Time = (180 - 114.59) / 360 * 2 minutes
Time = 0.42 minutes
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NO LINKS!! URGENT HELP PLEASE!!!
10. Mr. and Mrs. Rainer took out a $240,000 to purchase their home. If the interest rate on the loan is 1.2% compounded bimonthly, how much interest will they have paid after 30 years?
Answers
Answer:
$103,875.41
Step-by-step explanation:
To solve this problem, we can use the formula for compound interest:
\(\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)
Given values:
P = $240,000r = 1.2% = 0.012n = 6 (bi-monthly)t = 30 yearsNote: Bi-monthly means every 2 months.
Substitute the given values into the formula and solve for A:
\(A=240000\left(1+\dfrac{0.012}{6}\right)^{6 \cdot 30}\)
\(A=240000\left(1.002\right)^{180}\)
\(A=343875.406934...\)
\(A=343875.41\)
So after 30 years, Mr. and Mrs. Rainer will have paid a total of $343,875.41, which includes both the principal and the interest.
To find the amount of interest they paid, subtract the principal:
Interest paid = $343,875.41 - $240,000 = $103,875.41
Therefore, they will have paid $103,875.41 in interest over the 30-year period.
If you were a colonist in the mid-1770s would you have stood with the Patriots or the Loyalists? Write an argumentative essay in which you support your position. Use evidence from the information provided as well as your background knowledge in U.S. history to support your claim and counterclaim.
Answers
Answer:
I would have stood with the patriots because British soldiers forcefully entered their homes. They also ramped up taxes over a petty war with France because they couldnt pay it themselves.
The Loyalists were brainwashed to the British king, because they were rich and privileged. So they could pay the very high taxes. This meant these guys didn't actually know how the people felt.
The British also ramped up the price of tea, which the colonists loved, just to be petty because the Patriots did not want to be taxed. Back then, the British were very petty. Now they're just jaded.
But back to the essay: The Patriots had a good cause. They wanted to move on from something chaining them down. The Loyalists did not. And I would want to happily tar some tax collectors. Wouldn't you?
Step-by-step explanation:
1. Nikita invests 6,000 for two years at a certain rate of interest compounded annually. At the end of first year it amounts to ? 6,720
plzzzz tell me
Answers
Answer:
Hope it is helpful and useful
