Step-by-step explanation:
Enter a problem...
Calculus Examples
Popular Problems Calculus Find the Asymptotes f(x)=(2x^2)/(x^2-1)
f
(
x
)
=
2
x
2
x
2
−
1
Find where the expression
2
x
2
x
2
−
1
is undefined.
x
=
−
1
,
x
=
1
The vertical asymptotes occur at areas of infinite discontinuity.
x
=
−
1
,
1
Consider the rational function
R
(
x
)
=
a
x
n
b
x
m
where
n
is the degree of the numerator and
m
is the degree of the denominator.
1. If
n
<
m
, then the x-axis,
y
=
0
, is the horizontal asymptote.
2. If
n
=
m
, then the horizontal asymptote is the line
y
=
a
b
.
3. If
n
>
m
, then there is no horizontal asymptote (there is an oblique asymptote).
Find
n
and
m
.
n
=
2
m
=
2
Since
n
=
m
, the horizontal asymptote is the line
y
=
a
b
where
a
=
2
and
b
=
1
.
y
=
2
There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.
No Oblique Asymptotes
This is the set of all asymptotes.
Vertical Asymptotes:
x
=
−
1
,
1
Horizontal Asymptotes:
y
=
2
No Oblique Asymptotes
Triangle ABC is transformed to create triangle MNO and triangle PQR as described below.
• MNO represents the translation 2 units left and 2 units down of triangle ABC.
• PQR represents the dilation of triangle ABC by a scale factor of 2
Which of these is correct?
A - The transformation of ABC to PQR preserves both the side lengths and angle measures of the triangle
B - The transformation of ABC to PQR preserves the side lengths but not the angle measures of the angle
C - The transformation of ABC to MNO preserves both side lengths and angle measures of the triangle
D - The transformation of ABC to MNO preserves the angle measures but no the side lengths of the triangle.
Answer: the transformation of ABC to MNO preserves both side lengths and angle measures of the triangle.
Step-by-step explanation:
Answer:
B - The transformation of triangle ABC to triangle MNO preserves both the side lengths and angle measures of the triangle.
The 3 in 73.084 is _ times the 3 in 65.732.
10x
100x
1/10
Please pick one
what is equal to 12.9
(#1) 0.02+12+0.88
(#2) 0.06+12.03
(#3) 11.9+1
(#4) 6.2+3.4+2.3
(#5) 3.01+2.01+7.7
what are all that are equal to 12.9
Jamie is solving the equation; 4(x-3)=16. Her first step is; 4x - 12 = 16. Which step could be the next step?
Answer:
4x=4
Step-by-step explanation:
help me plz The formula K=59(F−32)+273.15 converts temperatures from Fahrenheit F to Kelvin K.
a. Solve the formula for F.
F=
Let's see what to do buddy...
Step-by-step explanation:
_________________________________
[tex]k = 59(f - 32) + 273.15[/tex]
Subtract the sides of the equation minus -273.15
[tex]k - 273.15 = 59(f - 32)[/tex]
Divided the sides of the equation by 59
[tex] \frac{k - 273.15}{59} = \frac{59}{59} (f - 32) \\ [/tex]
[tex] \frac{k - 273.15}{59} = f - 32 \\ [/tex]
Subtract the sides of the equation plus 32
[tex] \frac{k - 273.15}{59} + 32 = f \\ [/tex]
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
All lines that are parallel to AB
Answer:
BA
Step-by-step explanation:
Select the correct answer which rational number is negative
A.2
B-12/-18
C plus1/plus2
D plus3/-11
Answer: D
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
A farmer needs 5 men to clear his farm in 10days.How many men will he need to clear the bush in 2 days.
Answer:
13 men's.........
.........
.......
One single men is needed to clear the entire man.
What is linear function? What is a mathematical function, equation and expression? The linear function is given by → y = ax + bfunction : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that a farmer needs 5 men to clear his farm in 10 days.
Assume that the [x] men are needed to clear the bush in 2 days.
In 10 days, 5 men can clear the farm.
In 1 day, (5/10) men can clear the farm.
In 2 days -
{x} = (5/10 x 2) men
{x} = 1 men
Therefore, one single men is needed to clear the entire man.
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I’m confused !!!!!!!!!!
Answer:
Ok, so what you have to do is find the range of the number the way you find the range is by writing down the relation. (the relation is the set of the ordered pairs with x and y coordinates). Then you have to list the y-coordinates of the relation. The way to find the range of the relation, you simply have to write down all of the y-coordinates of each ordered pair. Also, make sure to remove any duplicate coordinates so that you only have one of each y-coordinate.
The way you find the ordered pair is by moving a certain amount of steps to the left or right on the x-axis and a certain amount of steps upwards or downwards on the y-axis.
Explanation:
I'm sorry for not giving you the actual range and the ordered pairs for each number but I have to have a graph so I can see and verify an actual answer. I hope that my explanations help you figure out what the answer is! Have a nice day! :)
Suppose you have a 6-face unfair dice with numbers 1,2,3,4,5,6 on each of its faces. If the probability distribution of throwing a number up is as follows:
1 with probability 1/12
2 with probability 1/12
3 with probability 1/12
4 with probability 1/12
5 with probability 1/12
6 with probability 1/2
Which of the following statement is correct?
a. The mathematical expectation of the dice throwing a number up is 3.5
b. The mathematical expectation of the dice throwing a number up is 6
c. The mathematical expectation of the dice throwing a number up is 4.25
d. This is not a proper probability distribution because all the probabilities do not sum up to one
Answer:
D is correct
Step-by-step explanation:
Here, we want to select which of the options is correct.
The correct option is the option D
Since the die is unfair, we expect that the probability of each of the numbers turning up
will not be equal.
However, we should also expect that if we add the chances of all the numbers occurring together, then the total probability should be equal to 1. But this does not work in this case;
In this case, adding all the probabilities together, we have;
1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/2
= 5(1/12) + 1/2 = 5/12 + 1/2 = 11/12
11/12 is not equal to 1 and thus the probability distribution cannot be correct
Brainliest is given to the correct answer!
A high school race track is composed of a rectangle and two semicircles.
a. If the length "l" of the rectangle is twice as long as the diameter of the semicircles, write a formula for "p," the distance around the track, in terms of the radius "r" of the semicircles.
b. Rewrite the formula from a so the radius of the semicircles is given in terms of the distance around the track. Show your work.
Answer:
a. [tex] p = 2\pi r + 8r [/tex]
b. [tex] r = \frac{p}{2\pi + 8} [/tex]
Step-by-step explanation:
a. Radius of semicircle (r) = r
Diameter of semicircle (d) = 2r
Length of rectangle (l) = 2*diameter of semicircle = 2*2r = 4r
Distance around the track (p) = circumference of circle + 2(l)
Note: the two semicircles of the track = 1 full circle
Circumference of full circle = πd = π*2r = 2πr
Distance around the track:
p = 2πr + 2(4r)
p = 2πr + 8r
b. Rewriting the formula to make radius, r, the subject of the formula in terms of distance around the track.
[tex] p = 2\pi r + 8r [/tex]
Factor out r
[tex] p = r(2\pi + 8) [/tex]
Divide both sides by (2π + 8)
[tex] \frac{p}{2\pi + 8} = \frac{r(2\pi + 8)}{2\pi + 8} [/tex]
[tex] \frac{p}{2\pi + 8} = r [/tex]
[tex] r = \frac{p}{2\pi + 8} [/tex]
Someone pls Help me out!!!
Answer:
Gasoline = 10.2 * 3.80= 38.76
Water= 3 * 3.98 = 11.94
Ice- 3 * 1.99 = 5.97
Oranges= 1 * 8.89 = 8.89
Step-by-step explanation:
What will be the price of gas if there is a 27% increase from $2.67 per gallon?
Answer:
The answer is $3.39
Step-by-step explanation:
the question states an increase in price. this means that we need to multiply the current prince ($2.67) by 127%.
drop the percent and put 127 over 100
[tex]\frac{127}{100}[/tex]
multiply
[tex]\frac{127}{100} *\frac{2.67}{1}\\\\ \frac{339.09}{100} \\\\3.39[/tex]
we are dealing with currency so rounding to the hundredths place will suffice.
hope this helps :)
a
Positive
b
Negative
c
Undefined
d
Zero
Answer:
B. Negative
Step-by-step explanation:
Because it is sliding down and if it was going up then it would be positive
[3] Find the Social Security tax of 6.2% on $36,511.98
$226,374
$2173.19
C
$2,263.74
$2558.03
Answer:
2263.74
Step-by-step explanation:
Find the equation for the line that passes through the points ( 1 , 1 ) and ( − 5 , 6 ) . Give your answer in point-slope form. You do not need to simplify.
Answer:
Step-by-step explanation:
The equation of the line is y - 1 = ( 5/6)(x - 1 ).
What is the equation of a line passing through two points?Suppose the given points are (x₁, y₁) and (x₂, y₂), then the equation of the straight line joining both two points is given by
[tex]\rm (y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]
Write an equation for the trend line.
(x₁, y₁) → (1,1)
(x₂, y₂) → (-5,6)
Then we have
y - 1 = [ 6 - 1 ]/[-5-1](x - 1)
y - 1 = ( 5 / -6 )(x - 1)
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If I read 12 books in 3 months, what was my rate of reading in months per book?
Answer:
Step-by-step explanation:
Take 3 divided by 3 which is 1, and 12 divided by 3 which is 4 so 4 is the answer.
Of three angles of a triangle, one is three times the smallest and the other is five times the smallest. Find the angles
Will mark brainliest
Answer:
20, 60, 100
Step-by-step explanation:
Since the angles in a triangle add up to 180 degrees, we can change the statement by saying x+3x+5x = 180 degrees. That would mean that 9x is equal to 180, and 180/9=20. 20 times 5 is 100, and 20 times 3 is 60.
Explain how compound interest is better than simple interest when it comes to saving money.
Answer:
When it comes to investing, compound interest is better since it allows funds to grow at a faster rate than they would in an account with a simple interest rate.
3/4 divided 3/8 what is the quotient of
Answer:2
Step-by-step explanation: Because the answer is 2 :)
f(x) = (x + 1)2 – 4 g(x) = –4 |x + 1| Which statement compares the ranges of the functions? The ranges of both f(x) and g(x) are limited to y ≥ –1. The ranges of both f(x) and g(x) are limited to y ≤ –1. Since the range of f(x) is limited to y ≤ 0 and the range of g(x) is limited to y ≥ –4, the ranges overlap for the values –4 ≤ y ≤ 0. Since the range of f(x) is limited to y ≥ –4 and the range of g(x) is limited to y ≤ 0, the ranges overlap for the values –4 ≤ y ≤ 0.
Answer:
Since the range of f(x) is limited to y ≥ –4 and the range of g(x) is limited to y ≤ 0, the ranges overlap for the values –4 ≤ y ≤ 0.
Step-by-step explanation:
From Function theory we get that range of a function is the set of values of [tex]y[/tex] so that exist a respective value of [tex]x[/tex], whose set is the domain of the function. Let be [tex]f(x) = (x+1)^{2}[/tex] and [tex]g(x) = -4\cdot |x+1|[/tex], the ranges of each function are, respectively:
f(x):
From Real Algebra we know that the square of every number is a non-negative number, which means that:
[tex](x+1)^{2} \geq 0[/tex]
[tex](x+1)^{2}-4 \geq -4[/tex] (Compatibility with addition)
[tex]f(x) \geq -4[/tex] (Definition/Result)
The range of [tex]f(x)[/tex] is: [tex]Ran \{f(x)\} = [-4, +\infty)[/tex]
g(x):
From Real Algebra we know that a absolute value leads to non-negative number, which means that:
[tex]|x+1|\geq 0[/tex]
[tex]-4\cdot |x+1| \leq 0[/tex] ([tex]a> b \longrightarrow a \cdot c < b\cdot c[/tex], if [tex]c < 0[/tex])
[tex]g(x) \leq 0[/tex] (Definition/Result)
The range of [tex]g(x)[/tex] is: [tex]Ran\{g(x)\} = (-\infty, 0][/tex]
If we compare each range, we came into the conclusion that:
[tex]-4 \leq y \leq 0[/tex].
Thus, correct answer is: Since the range of f(x) is limited to y ≥ –4 and the range of g(x) is limited to y ≤ 0, the ranges overlap for the values –4 ≤ y ≤ 0.
Answer:
Its D
Step-by-step explanation:
Got it right on EDGE
1. The students put together 12 jigsaw puzzles. Each puzzle had 345 pieces. How many puzzle pieces did they put together in all?
Answer:
4140 pieces
Step-by-step explanation:
This is true because we would have to multiply the number of jigsaw puzzles and how many pieces each on of them had to see how many pieces they put together in all.
To set up the equation we would do 345 times 12,
if you calculate it, the answer would be 4140.
Hopes this helps, and good luck!! :)
PLEASE HELP I AM BEING TIMED!!! WILL MARK BRAINLIEST FOR CORRECT ANSWER!!! 100 PTS!!!
The sum and product of two linear functions are shown.
Which statements can be used to describe the original functions f(x) and g(x)? Select two options.
A. When added, the sum of the y-intercepts must be 1.
B. When multiplied, the product of the y-intercepts must be –15.
C. Either f(x) or g(x) has a positive rate of change and the other has a negative rate of change.
D. f(x) could have a rate of change equal to 1 and g(x) could have a rate of change of 2.
E. f(x) could have a rate of change equal to 2 and g(x) could have a rate of change of –6.
Answer:
A and DStep-by-step explanation:
Let the functions be
f(x)= ax + bg(x) = cx + dTheir sum
j(x) = (a+c)x + b+dTheir product
k(x)= (ax + b)(cx + d)The answer optionsA. When added, the sum of the y-intercepts must be 1.
Correct. We see point (0,1) of j(x) on the graph. b+d = 1B. When multiplied, the product of the y-intercepts must be –15.
Incorrect. -15 is the vertex of k(x). The vertex of ax^2 + bx + c is -b/2a. So it has no relation to constants of the functions f(x) and g(x)C. Either f(x) or g(x) has a positive rate of change and the other has a negative rate of change.
Incorrect. It refers to the value of ac. If one of a or c has opposite sign it makes k(x) to open down but it is not as per graph.D. f(x) could have a rate of change equal to 1 and g(x) could have a rate of change of 2.
Correct. As per above statement, both linear equations could be positive as their sum and product is positive from the graphs of j(x) and k(x)E. f(x) could have a rate of change equal to 2 and g(x) could have a rate of change of –6.
Incorrect. It should result in decreasing function of j(x) with slope of -4 but it is increasing as per graph.How do I Invert 6/7? Can you please help me!
Answer:
0. 857142i hope this helps
Hot tub has a capacity of 1458 liters. Mrs smith put 487 liters 750 millimeters of water in the tub.
How much water needs to be added to fill the hot tub completely?
The equation is x + 487.75 = 1458. Then the value of the variable 'x' will be 970.25 liters.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The capacity of the hot tub is 1458 liters. Mrs. Smith filled the tub with 487 liters and 750 millimeters of water.
Let x be the amount of water that needs to be filled in the tub. Then the equation is given as,
x + 487.75 = 1458
Simplify the equation, then the value of the variable 'x' will be
x = 1458 - 487.75
x = 970.25 liters
The equation is x + 487.75 = 1458. Then the value of the variable 'x' will be 970.25 liters.
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On a Ferris wheel, Sarah observes that it takes 45 seconds for her chair to complete a full revolution. Her chair is 30 feet from the axle of the Ferris wheel. To the nearest hundredth, Sarah's angular velocity is radians per minute?
Answer: 4.71
Step-by-step explanation:
Answer:
8.38
Step-by-step explanation:
That's what other ppl got on the same question
The J.R. Ryland Computer Company is considering a plant expansion to enable the company to begin production of a new computer product. The company’s president must determine whether to make the expansion a medium- or large-scale project. Demand for the new product is uncertain, which for planning purposes may be low demand, medium demand, or high demand. The probability estimates for demand are 0.20, 0.20, and 0.60, respectively. Letting x and y indicate the annual profit in thousands of dollars, the firm’s planners developed the following profit forecasts for the medium- and large-scale expansion projects.
Medium-Scale Large-Scale
Expansion Profit Expansion Profit
x f(x) y f(y)
Low 50 0.2 0 0.2
Demand Medium 150 0.5 100 0.5
High 200 0.3 300 0.3
a. Compute the expected value for the profit associated with the two expansion alternatives.
Which decision is preferred for the objective of maximizing the expected profit?
b. Compute the variance for the profit associated with the two expansion alternatives.
Which decision is preferred for the objective of minimizing the risk or uncertainty?
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
Medium-Scale Large-Scale
Expansion Profit Expansion Profit
x f(x) y f(y)
Low 50 0.2 0 0.2
Demand Medium 150 0.5 100 0.5
High 200 0.3 300 0.3
a. Compute the expected value for the profit associated with the two expansion alternatives.
Which decision is preferred for the objective of maximizing the expected profit?
Expected value for medium scale expansion profit :
Expected value (E) = Σ(X) * f(x)
Σ[(50 * 0.2) + (150 * 0.5) + (200 * 0.3)]
= 145
Expected value for Large scale expansion profit :
Expected value (E) = Σ(X) * f(x)
Σ[(0 * 0.2) + (100 * 0.5) + (300 * 0.3)]
= 140
Medium scale expansion profit is preferred as it has the highest expected value.
b. Compute the variance for the profit associated with the two expansion alternatives.
Which decision is preferred for the objective of minimizing the risk or uncertainty?
Variance (V) = Σ(X - E)² * f(x):
Variance for medium scale expansion profit :
V = [((50-145)^2 * 0.2) + ((150-145)^2 * 0.5) + ((200-145)^2 * 0.3) = 2725
Variance for Large scale expansion profit :
V = [((0-140)^2 * 0.2) + ((100-140)^2 * 0.5) + ((300-140)^2 * 0.3) = 12400
Smaller variance is required to minimize risk, Hence, choose the medium scale expansion profit.
Universal Claims Processors processes insurance claims for large national insurance companies. Most claim processing is done by a large pool of computer operators, some of whom are permanent and some of whom are temporary. A permanent operator can process 16 claims per day, whereas a temporary operator can process 12 per day, and on average the company processes at least 450 claims each day. The company has 40 computer workstations. A permanent operator generates about 0.5 claim with errors each day, whereas a temporary operator averages about 1.4 defective claims per day. The company wants to limit claims with errors to 25 per day. A permanent operator is paid $64 per day, and a temporary operator is paid $42 per day. The company wants to determine the number of permanent and temporary operators to hire in order to minimize costs.
Required:
a. Solve the linear programming model using graphical method.
b. Interpret the slack/surplus variables that you obtain based on the optimal values of decision variables in (a).
c. Are there any binding constraints in the model? Explain.
What is the equation in standard form of the line shown
on the graph?
The equation of the line in standard form is
vbx +
N +
2
-2
2
4
-2
-4
Answer:
Step-by-step explanation:
.
Answer: 3x-4y=12
Step-by-step explanation:
what is the value of (2^4) ^3 divided by 2^6
Answer:64
Step-by-step explanation:
2*2*2*2=4*4=16. 16*16*16=4,096. 2*2*2*2*2*2=4*4*4=64. 4,096/64=64.