As x tends to infinity the function [tex]f(x) = \frac{2x}{1-x^{2} }[/tex] approaches zero.
Given function is:
[tex]f(x) = \frac{2x}{1-x^{2} }[/tex]
What is a function?A function f(x) is a rule which relates two variables where x and y are independent and dependent variables.
Divide the numerator and denominator of the given function by x.
[tex]f(x) = \frac{2}{\frac{1}{x} -x}[/tex]
[tex]\lim_{x \to \infty} f(x) \\\\\lim_{x \to \infty} \frac{2}{\frac{1}{x} -x}[/tex]
As we know that as x approaches the infinity 1/x approaches 0.
So, [tex]\\\\\lim_{x \to \infty} \frac{2}{\frac{1}{x} -x} = \lim_{x \to \infty} \frac{2}{-x}[/tex]
[tex]\lim_{x \to \infty} \frac{-2}{x} =0[/tex]
Therefore, as x tends to infinity the function [tex]f(x) = \frac{2x}{1-x^{2} }[/tex] approaches zero.
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You randomly draw a marble out of a bag containing 4 green marbles, 6 blue marbles, 8 yellow marbles, and 2 red marbles. Find the probability of drawing a marble that is not yellow.
Answer:
The probability is [tex] \frac{3}{5} [/tex]Step-by-step explanation:
Green marbles = 4
Blue marbles = 6
Yellow marbles = 8
Red marbles = 2
[tex]4 + 6 + 8 + 2 = 20 \: marbles[/tex]
The probability of drawing marble not yellow:
[tex]4 + 6 + 2 = 12 \\ \frac{12}{20} = \frac{3}{5} [/tex]
Brainliest please.
The perimeter of the original rectangle is 16 feet. A small rectangle has a length of 6. 2 feet and width of 1. 8 feet. A larger rectangle has a length of 12. 4 feet and width of blank. Not drawn to scale What is the perimeter of the enlarged rectangle? Round to the nearest tenth if necessary. 22. 3 feet 31 feet 32 feet 42. 7 feet.
The perimeter of the enlarged rectangle is 32 ft and the width of the larger rectangle is 3.6 ft.
What is perimeter of plane?The measure of the boundary of a plane or shape is called its perimeter. The perimeter of a plane or shape is the sum of all the sides.
A small rectangle has a length of 6.2 feet and width of 1.8 feet. The parameter of this triangle is,
[tex]P_s=6.2+1.8\\P_s=8\rm\; ft[/tex]
The small rectangle has a length of 6.2 and the larger rectangle has a length of 12.4 feet. Thus the scale factor of enlargement is,
[tex]r=\dfrac{12.4}{6.2}\\r=2[/tex]
The perimeter of the original rectangle is 16 feet and scale factor is 2. Thus, the perimeter of the enlarged rectangle is,
[tex]P_l=2\times16\\P_l=32\rm\; ft[/tex]
The small rectangle has width of 1.8 feet and scale factor is 2. Thus, the width of the larger rectangle is,
[tex]w_l=1.8\times2\\w_1=3.6\rm\; ft[/tex]
Hence, the perimeter of the enlarged rectangle is 32 ft and the width of the larger rectangle is 3.6 ft.
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If the figures below are similar, find the scale factors
HELP PLEASE
Answer: 3:2 and 2:3
Step-by-step explanation:
Scale factor is image/preimage.
So from A to B, the image is B and the preimage is A, so the scale factor is 6/4 = 3/2.
Similarly, from B to A, the scale factor is 4/6=2/3
HELP: What is another name for Angle 1?
Answer:
it could be many answers but my guess is acute
Answer:
(3) We can also name an angle by placing any number or symbol at the vertex in the INTERIOR of the angle. So, angles can also be called angle 1 or angle 2 or angle 4, etc. Sides AB and AC of the given angle are actually rays.
Step-by-step explanation:
Write a sentence to represent the solution set in the context of the problem.
___________________________________________________________
920 = 560 + 60(x) He has to make at least 6 sales to get $920
Answer:
6 sales
Step-by-step explanation:
(I MADE THIS QUESTION I DIDINT KNOW IF YOU NEEDED IT)
Jake wants to but the new computer(it costs $920). Jake has $560 saved in his bank. Jake also gets $60 whenever he makes a sale at his job. How many sale(s) at his job does Jake need to make? Answer -- Jake needs to make 6 sales of $60 to buy the new computer.
MATH -----
$6 x $60 = $360
$360 + $560 = $920
Leah likes getting her hair done at Hair Forever because they offer free drinks in the waiting room. The cups for hot drinks are cylindrical with a height of 9 centimeters and a radius of 3.8 centimeters. What is the volume of each hot-drink cup?
Use ≈3.14 and round your answer to the nearest whole number.
For cold drinks, there are cone-shaped paper cups. They have the same volume as the hot-drink cups and a radius of 5.1 centimeters. What is the height of each paper cup?
Use 3.14 and round your answer to the nearest whole number
The height of each paper cup to the nearest whole number is 15cm
The volume of a cylinder and coneThe formula for calculating the volume of a cylinder is expressed as:
V = πr²h
r is the radius
h is the height
Given that h = 9cm and r = 3.8cm
V = 3.14 * (3.8)² * 9
V = 408cm³
For the cone
V = 1/3πr²h
408 = 1/3 (3.14 * (5.1)² * h)
1224 = 81.6714h
h = 1224/81.6714
h= 15cm
Hence the height of each paper cup to the nearest whole number is 15cm
Learn more on volume of solid shapes here: https://brainly.com/question/1355179
the surface area?
A - 216
B - 336
C - 438
Answer:
B
Step-by-step explanation:
Leslie earned $12 Friday, $20 Saturday, and $56 Sunday selling bracelets. If she sold each bracelet for the same amount of money what is the most she could charge for each bracelet?
Answer:
$4
Step-by-step explanation:
12÷4=3
20÷4=5
56÷4=14
please help! pleaseeeeee
Answer:
D-27 cm
Step-by-step explanation:
we are given that the top is 8cm
one side is 3..the 2 sides are the same length so total of 6
the bottom is 5, we know the top is 8 so 8-5 =3
the 2 breaks are 1 each
so we do
8 + 5+ 6+ 2+3 =24
Find the area of the rectangle.
l=10 in, w=7.5 in
Answer:
It should be 75 inches
Step-by-step explanation:
Find the area of the trapezoid.
95 cm
133 cm
Answer: A=a+b
2h=95
2·13.5=675
Step-by-step explanation:
Answer:
D 57.5
Step-by-step explanation:
9.5 + 13.5 = 23
23 x 5 = 115
115 divided by 2 is 57.5
Consider the function defined by f(x) lnx/x^4 for x > 0 and its graph y = f(x).
The graph of f has a horizontal tangent at point P. Find the coordinates of P.
Answer:
[tex]\sqrt[4]{e};\frac1{4e}[/tex]
Step-by-step explanation:
The first derivative of [tex]f(x)[/tex] will give, for each x, the slope of the tangent at that specific x. Let's calculate the derivative, applying the quotient rule.
[tex]D(\frac AB) = \frac{A'B-AB'}{B^2}\\f'(x)= \frac1{x^8}[(\frac1x)x^4-(lnx)(4x^3)]=\frac1{x^8}[x^3(1-4lnx)]=\frac{1-4lnx}{x^5}[/tex]
Now, to find the point with an horizontal tangent (called "stationary points"), we set the first derivative equal to 0. Considering that we're working with [tex]x > 0[/tex] we deal only with the numerator.
[tex]1-4lnx = 0 \rightarrow lnx= \frac14\\x=e^\frac14 =\sqrt[4]{e}[/tex]
At this point we Replace the value we found in the equation to find it's y coordinate
[tex]f(\sqrt[4]e) = \frac{ln\sqrt[4]e}{\sqrt[4]e^4}= \frac{\frac14}{e} = \frac1{4e}[/tex]
Use the equation from the previous problem to predict the price of bzg stock on day 30.
Answer:
925.798
Step-by-step explanation:
1.65(x) x 18.703 = 925.798
The prism below is made of cubes which measure of 1/2 a foot on one side. What is the volume?
The diagram shows a parallelogram.
The dotted line forms a right angle with side xy.
Use given information to find m Angle p.
Check the picture below.
Simplify.
Cubed root of -128x^6y^5
Answer
-640x^6y
Step-by-step explanation:
2x+4=8
Find x and show work.
Answer:
X is 2 2+2= 4 plus 4 = 8
Step-by-step explanation:
Hoped this helped
Answer:
x = 2
explanation:
2x + 4 = 8
subtract 4 from both sides
2x + 4 -4 = 8 -4
2x = 4
divide both sides by 2
2x/2 = 4/2
x = 2
Recheck:
2x + 4 = 8
2(2) + 4 = 8
8 = 8
Hence proved the solution is correct.
5. For all real values of x such that -1 < x < 0, which of the following
expressions has the greatest value? *
Answer:
x<0
Step-by-step explanation:
-1<0 is greater
hope this helps your question
State if each is a right triangle?
Answer:
yes
Step-by-step explanation:
because the hypotenus is the longest of all the other sizes
last question and ty please help me answer
Step-by-step explanation:
1. 6 ounce = 1.56 $
So, 1 onuce = 1.56/6 =
2. 14 ounce = 3.36 $
So, 1 ounce = 3.36/14 =
3. 20 ounce = 5.60 $
So, 1 ounce = 5.60/20 =
Anyone know the answer?
Answer:
Positive
Step-by-step explanation:
Negative over a negative cancel out and become positive.
Use the triangle to find each of the six trigonometric functions of _. Show all work
Answer:
you need to find that missing side... so (A squared) x (B squared) = (C squared)
A squared = 5
B squared is missing
C squared = 6
A=25
C=36
36-25= B squared....... B= (square root of 11)
now you need to plug in the numbers for the 6 trig equations...
sin0 = 5/6
cos0 = (square root of 11)/6
tan0 = 5/(square root of 11) which actually equals 5(square root of 11)/11
csc0 = 6/5
sec0= 6/ (square root of 11) which actually equals 6(square root of 11)/11
cot0 = (square root of 11/5
Step-by-step explanation:
Angela had 8 computer games.
She got 3 more for her birthday. But then she gave
away 4 computer games.
4
How many computer games did Angela have then?
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
we're given that Angela formerly had 8 computer games.
★ She got 3 more video games on her birthday.
★ Then she gave away 4 video games.
_____________________________
To calculate - number of computer games she's finally left with._____________________________
[tex]\huge\red{ Solution -}[/tex]
[tex]8 + 3 - 4 \\ \dashrightarrow \: 11 - 4 \\ \dashrightarrow \: 7[/tex]
hope helpful :D
Which equation can be used to find x, the length of the hypotenuse of the right triangle? a triangle has side lengths 63, 16, x. 16 63 = x 16 squared 63 = x (16 63) squared = x squared 16 squared 63 squared = x squared
The Pythagoras is the sum of the square of two sides equal to the square of the longest side. The equation is x² = 16² + 63² then the correct option is D.
What is a right-angle triangle?It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.
The dimensions of the triangle are 16, 63, and x.
Where x is the hypotenuse.
By the Pythagoras theorem, we have
x² = 16² + 63²
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
Answer:
D. 16 squared + 63 squared = x ^2 is the answer.
Step-by-step explanation:
Jess makes and sells cube-shaped jewelry boxes. She designs the jewelry boxes in different sizes and with different patterns. Jess wants to include the volume of each box on her price list.
s = length (in.) of one side of the jewelry box
Options:
s
6s
s^2
s^3
(It’s middle school I-Ready)
Answer:
Step-by-step explanation:
s to the 3rd power so S3
I hope this works
Answer:Part two is (s+2)3
Step-by-step explanation:
I got it right I hope it helps
can you help me with this
Answer:
The answer is b. 979,000
Step-by-step explanation:
If you move the decimal right five time from 9.79 you would get 979,000
What is the distance between the points (3, 4.1) and (3, 1.2)?( i will give brainly points)
Answer:
2.9
Step-by-step explanation:
subtract the distances:
4.1-1.2
2.9
Kaylib’s eye-level height is 48 ft above sea level, and addison’s eye-level height is 85 and one-third ft above sea level. how much farther can addison see to the horizon? use the formula d = startroot startfraction 3 h over 2 endfraction endroot, with d being the distance they can see in miles and h being their eye-level height in feet. startroot 2 endroot mi 2 startroot 2 endroot mi 14 startroot 2 endroot mi 28 startroot 2 endroot mi
The addison see to the horizon at 2 root 2mi.
We have given that,Kaylib’s eye-level height is 48 ft above sea level, and addison’s eye-level height is 85 and one-third ft above sea level.
We have to find the how much farther can addison see to the horizon
Which equation we get from the given condition?[tex]d=\sqrt{\frac{3h}{2} }[/tex]
Where, we have
d- the distance they can see in thousands
h- their eye-level height in feet
For Kaylib
[tex]d=\sqrt{\frac{3\times 48}{2} }\\\\d=\sqrt{{3(24)} }\\\\\\d=\sqrt{72}\\\\d=\sqrt{36\times 2}\\\\\\d=6\sqrt{2}....(1)[/tex]
For Addison h=85(1/3)
[tex]d=\sqrt{\frac{3\times 85\frac{1}{3} }{2} }\\d\sqrt{\frac{256}{2} } \\d=\sqrt{128} \\d=8\sqrt{2} .....(2)[/tex]
Subtracting both distances we get
[tex]8\sqrt{2}-6\sqrt{2} =2\sqrt{2}[/tex]
Therefore, the addison see to the horizon at 2 root 2mi.
To learn more about the eye level visit:
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Answer:
2 root 2mi.
Step-by-step explanation:
Edge2020
I need this ASAP PLS
(will give brainliest)!
Answer:
The answer is A since it does the same movements twice. Think of it like flipping a coin, then actually taking the coin and flipping it back over regardless of what it lands on.
Step-by-step explanation:
Hope this helps have a good rest of your day
Please help me!!!
it would be greatly appreciated
Answer:
11.72
Step-by-step explanation:
6.76 + 4.96 = 11.72