Difference Quotient. Correct answer is shown. It says multiply by conjugate but I don’t understand what that is and how they did it. TIA
Answers
9514 1404 393
Answer:
3/(√(3(x+h)) +√(3x))
Step-by-step explanation:
The conjugate of a binomial is the same sum, but with the sign changed. That is (a +b) and (a -b) are a conjugate pair: each is the conjugate of the other.
The purpose of multiplying expressions involving roots or complex numbers by their conjugate is to take advantage of the relation ...
(a +b)(a -b) = a² -b²
Here. you want to eliminate the h from under the radical, so squaring the radical containing h is useful for the purpose. Hence the conjugate gets involved.
"Multiply by the conjugate" means multiply both the numerator and the denominator by the conjugate. (Effectively, multiply by 1.)
__
[tex]\displaystyle\frac{f(x+h)-f(x)}{h}=\frac{\sqrt{3(x+h)}-\sqrt{3x}}{h}\\\\=\frac{(\sqrt{3(x+h)}-\sqrt{3x})(\sqrt{3(x+h)}+\sqrt{3x})}{h(\sqrt{3(x+h)}+\sqrt{3x})}=\frac{3(x+h)-3x}{h(\sqrt{3(x+h)}+\sqrt{3x})}\\\\=\frac{3h}{h(\sqrt{3(x+h)}+\sqrt{3x})}=\boxed{\frac{3}{\sqrt{3(x+h)}+\sqrt{3x}}}[/tex]
_____
Additional comment
In the end, you will want the limit as h → 0, which will be 3/(2√(3x)). You will notice that h=0 no longer makes the denominator zero, so the limit is found by simple evaluation.
When the "binomial" is a complex number of the form a+bi, its conjugate is a-bi, regardless of the sign of b. That is, the conjugate of a complex number is found by negating its imaginary part. The sign of the real part is left alone.
Related Questions
You have an employee who copes with stressful demands by working overtime and weekends. You are concerned this will eventually burn him out, and want him to cope in a way that better addresses the emotions he is feeling head on. Which of the following would be an emotion-focused coping strategy?
a. Ask a coworker to help lighten the load
b. Go for a run to clear his mind
c. Increase the hours he works, but decrease the number of days (e.g., Four 12-hour days)
d. Coming up with a strategy to fix the stressful demand
Answers
Answer:
b. Go for a run to clear his mind.
Step-by-step explanation:
Emotion focused coping strategy is one in which a person goes for self isolation to release his stress. The person focuses on emotional distance from people because he believes the stress can increase if other people stays around him. When an employee suffers from stressful demand at work the best for him is to go for a run or walk and release stress.
DJ Jacqueline is making a playlist for work; she is trying to decide what 9 songs to play and in what order they should be played. If she has her choices narrowed down to 6 jazz, 19 reggae, and 7 blues songs, and she wants to play an equal number of jazz, reggae, and blues songs, how many different playlists are possible
Answers
Pick any set of 4 from each kind, and then there will be 12! ways to play them.
21C4 * 13C4 * 25C4 * 12! = 2.593*10^19
Which of the following pairs consists of equivalent fractions? .4/6 and 3/5 or 9/16 and 3/32 or 18/48 and 15/40 or 7/10 and 10/7
Answers
Answer:
18/48 and 15/40
Step-by-step explanation:
I need help I’ll mark u as brainlest
Answers
Answer:
V = 64 in^3
Step-by-step explanation:
The volume of a cube is given by
V = s^3 where s is the side length
V = 4^3
V = 64 in^3
Answer:
64
Step-by-step explanation:
volume of a cube formula: V = a^3
a is just one of the edges
[tex]4^{3}[/tex] = 64 = V
:)
Find the domain of f/g f(x)= sqrt 4-x^2 g(x)= sqrt 3x+4
Answers
Answer:
(-4/3, 2]
Step-by-step explanation:
f(x)= sqrt (4-x^2)
g(x) = sqrt (3x+4)
domain of f(x)/ g(x)
The domain of the numerator is
4-x^2 ≥ 0
4 ≥x^2
Taking the square root of each side
-2 ≤x≤2
The domain of the denominator
3x+4 > 0 ( the denominator cannot be zero)
3x>-4
x > -4/3
Combine the restrictions to make it most restrictive
-4/3<x≤2
In interval notation
(-4/3, 2]
The diameter of the circle below is 82cm. Work out the radius of the circle
Answers
Answer:
Radius = 41
Step-by-step explanation:
Diameter/2=radius
82/2 =41
Answer:
Radius=41
Step-by-step explanation:
Preamble
Diameter=82
Radius=?
Formula
Radius=diameter/2
Radius=82/2
reduce the fraction
82/2=82÷2/2÷2=41/1
therefore radius=41
ASAP please helppp
Answers
Answer:
1.3
Step-by-step explanation:
Raise/run = slope aka distance in this situation
8/6 = 1.3
Answer:
10 units
Step-by-step explanation:
use the distance formula as thought in school
The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 42 ounces and a standard deviation of 10 ounces. Use the Empirical Rule.
a. 99.7% of the widget weights lie between _____ and _____.
b. What percentage of the widget weights lie between 26 and 66 ounces?
c. What percentage of the widget weights lie above 34?
Answers
Answer:
The answer is below
Step-by-step explanation:
The empirical rule states for a normal distribution, 68% of the data falls within one standard deviation, 95% falls within two standard deviations and 99.7% falls within three standard deviations.
z score is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Given that mean (μ) = 42 ounces, standard deviation (σ) = 10 ounces.
a) 99.7% falls within three standard deviations. Therefore:
99.7% falls within μ ± 3σ = 42 ± 3(10) = 42 ± 30 = (12, 72)
Therefore 99.7% falls within 12 ounce and 72 ounce.
b) For x > 26
[tex]z=\frac{26-42}{10}=-1.6\\[/tex]
For x < 66
[tex]z=\frac{66-42}{10}=2.4\\[/tex]
From the normal distribution table, P(26 < x < 66) = P(-1.6 < z < 2.4) = P(z < 2.4) - P(z < -1.6) = 0.9918 - 0.0548 = 0.937 = 93.7%
c) For x > 34
[tex]z=\frac{34-42}{10}=-0.8\\[/tex]
From the normal distribution table, P(x > 34) = P(z > -0.8) = 1 - P(z < -0.8) = 1 - 0.2119 = 0.7881 = 78.81%
Answer:
Step-by-step explanation:
Given that:
Mean [tex]\mu[/tex] = 42
standard deviation [tex]\sigma[/tex] = 10
Using Empirical Rule:
[tex]\mu[/tex] - [tex]\sigma[/tex] = 42 - 10 = 32 [tex]\mu[/tex] + [tex]\sigma[/tex] = 42 + 10 = 52
[tex]\mu[/tex] - 2[tex]\sigma[/tex] = 42 - 2(10) = 22 [tex]\mu[/tex] + 2[tex]\sigma[/tex] = 42 + 2(10) = 62
[tex]\mu[/tex] - 3[tex]\sigma[/tex] = 42 - 3(10) = 12 [tex]\mu[/tex] + 3[tex]\sigma[/tex] = 42 + 3(10) = 72
The curve is attached in the image below.
a). the widget of 99.7% lies between 12 and 72
b) 68 + 13.5 = 81.5%
c) 50 + 34 = 84%
Six numbers have a mean of 4.5 and five of the numbers are 4,3,4,6,1.
The other number is x.
Work out the value ofx.
Answers
Answer:
X = 9
Step-by-step explanation:
4 + 3 + 4 + 6 + 1 + x / 6 = 4.5
18 + x / 6 = 4.5
cross multiply
18 + x = 4.5 × 6
18 + x = 27
collect like terms
x = 27 - 18
x = 9
Use the nutrition label to determine how many calories would be consumed by a person drinking half of the one-liter bottle of this soda.
1 Liter Mountain Dew
Nutrition Facts
Serving Size 8 fl oz. (240 ml)
Servings Per Container 4
Amount Per Serving
Calories 110
Daily Value
Total Fat og
Ox
Sodium 50 mg
2%
Total Carb. 318
10%
Sugars 315
Protein og
OX
* Percent Daily Values are based on
a 2.000 calo de diet
110
220
Answers
Factor the polynomial: -5x3 - 10x2 - 15x
A. -5x(x2 + 2x - 15)
O B. 5x(x2 + 2x - 3)
O C. -5x(-x2 - 2x - 3)
OD. -5x(x2 + 2x + 3)
Answers
Answer:
answer is d if its wrong i am sorry
Find X:
X + 25% x X = -1,25
Answers
Answer:
- 100
Step-by-step explanation:
OK open
The Pdf and look at the working
The set (AB) (B-C) is equal to
Answers
Answer:
AB^2- AC.
Step-by-step explanation:
I'm not sure if this question is complete, but when two separate variables are placed in brackets side by side, then it means they need to be expanded.
Therefore, expanding the bracket gives us:
(AB) (B-C)=
AB^2- AC.
This is the answer, if the only task needed is to expand the brackets.
The number of incoming students at two campuses of a midwestern university have historically been normally distributed. The main campus incoming class has a mean of 3,507 and a standard deviation of 375, and the regional campus incoming class has a mean of 740 and a standard deviation of 114. If there were 3,838 incoming students on the main campus and 848 on the regional campus, which had the more successful year in student recruitment based on z scores
Answers
Answer:
Due to the higher z-score, the regional campus had the more successful year in student recruitment.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The main campus incoming class has a mean of 3,507 and a standard deviation of 375. There were 3,838 incoming students on the main campus.
We have to find Z, considering [tex]X = 3838, \mu = 3507, \sigma = 375[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3838 - 3508}{375}[/tex]
[tex]Z = 0.88[/tex]
Regional campus incoming class has a mean of 740 and a standard deviation of 114. 848 students on the regional campus.
We have to find Z when [tex]X = 848, \mu = 740, \sigma = 114[/tex].
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{848 - 740}{114}[/tex]
[tex]Z = 0.95[/tex]
Which had the more successful year in student recruitment based on z scores?
Due to the higher z-score, the regional campus had the more successful year in student recruitment.
The function h(x) is defined as shown.
What is the range of h(x)?
h(x) =
x + 2, x <3
- x +8. X23
0-00
Oh(x) s 5
Oh(x) 25
Oh(x) 23
PLEASE HELOOOOODOOOOODIEIE
Answers
9514 1404 393
Answer:
(b) h(x) ≤ 5
Step-by-step explanation:
The maximum vertical extent of the graph is h(x) = 5 at x = 3. The range is all values of h(x) less than or equal to that:
h(x) ≤ 5
Answer: Choice B
The range is [tex]h(x) \le 5[/tex]
==============================================================
Explanation:
If we graph y = x+2, but only draw the line for x values smaller than 3, then we'll end up with the red line shown in the diagram below.
The blue line is the graph of y = -x+8, but it's only drawn when [tex]x \ge 3[/tex]
The two lines form an upside down V shape. This is an absolute value graph.
The highest point is at the vertex (3,5). The y coordinate is y = 5. This tells us that the largest h(x) can get is h(x) = 5.
Therefore, the range is [tex]h(x) \le 5[/tex]
This is the same as saying [tex]y\le 5[/tex] since y and h(x) are both outputs of a function.
can anyone pls answer this! it's really urgent!
Answers
Answer:
The answer is C
Step-by-step explanation:
You need to find a common denominator and in this case its 20. SO you change 3/4ths to 15/20 and 4/5ths to 16/20ths and 19/20 stays the same. Then you cancel out the 20 because its all the same number (I think) and you have your answer.
22. You are traveling on a highway starting at point A. After you have
traveled 63 miles (point B), you see a sign that says it is 87 miles
(point B), you see a sign that says it is 87 miles to your destination
(point C). . Find the total distance you will travel to get to your
destination.
A А
63 mi
B.
87 mi
С
Answers
Answer:
150 miles
Step-by-step explanation:
63 + 87 = 150
2.What is 10:30 pm in the 24-hour clock?
3. How do you write 00:15 in the 12-hour clock?
4.How do you write 11:50 pm in the 24-hour clock?
11.How are the circumference and the diameter of any given circle related
12. The diameter of a circle is 22 cm long. What is its area?
13.What is the area of the largest circle that can be drawn on a square paper whose side is 20 cm? *
16. Two workers need to dig a rectangular pit that is 2 meters long, 1.5 meters wide, and 1 meter deep. How many cubic meters of soil must they remove? *
17.A cubical water tank has a 20 cm edge. How much water can it contain?
tulong
Answers
2. 22:30
just add 12 on the front
that is the formula
2 If 9:30pm is 21:30,then 10:30pm=22:30 pm
3 15 seconds
4. If 10:30 = 22:30 then 11:50pm = 23:50
16. 3*1.5*1=4.5m^3
I think this are the ones I can try ,I hope this helps.
Solve the equation 2x2 + x - 41 =
- 15 to the nearest tenth.
I neeeddd
HEEEELPPPP
Answers
Answer: 22
Step-by-step explanation: 2x2 + x -41= -15
* 4 + x -41= -15
* x -37= -15
* x= 22
• carry over -15
2 x 2 + x - 41 + 15 = 0
• solve 2 x 2
4 + x - 41 + 15 = 0
• rearrange
x + 4 - 41 + 15 = 0
• solve
x - 22 = 0
x = 22
hope this helped :)
Simplify the expression given below. x+2/4x^2+5x+1 * 4x+1/x^2-4
Answers
Answer:
[tex]\frac{1}{(x+1)(x-2)}[/tex]
Step-by-step explanation:
[tex]\frac{x+2}{4x^2 + 5x + 1} \ \times \ \frac{4x+1}{x^2-4}\\\\=\frac{x+2}{4x^2 + 4x + x + 1} \ \times \ \frac{4x+1}{x^2-2^2}\\\\=\frac{x+2}{4x(x + 1) + 1( x + 1)} \ \times \ \frac{4x+1}{(x - 2)(x + 2)} \ \ \ \ \ \ \ \ [ \ (a^2 - b^2 = (a-b)(a+b) \ ]\\\\\\=\frac{x+2}{(4x + 1)(x+1)} \ \times \ \frac{4x+1}{(x-2)(x+2)}\\\\=\frac{1}{(x+1)} \ \times \ \frac{1}{(x-2)}\\\\= \frac{1}{(x+1)(x-2)}[/tex]
Answer:
D. 1/(x+1)(x-2)
Step-by-step explanation:
i looked it up on a simplifier :)
From families with four children a family is chosen at random. Let X be the number of boys in the family. Calculate and sketch the distribution function of X. Assume that in a four-child family all gender distributions (for example, BBBB, BBBB, BBBB, BBBB, etc.) are equally probable.
Answers
Solution :
Given :
X = the number of boys in a family of four children
Families having four children are chosen randomly.
The gender distribution in the four child family are equally probable.
Thus,
X P(X) CDF
0 [tex]^4C_0 (1/2)^{4}[/tex] = 1/16 [tex]\frac{1}{16}[/tex]
1 [tex]^4C_1 (1/2)^{4}[/tex] = 1/4 [tex]\frac{5}{16}[/tex]
2 [tex]^4C_2 (1/2)^{4}[/tex] = 3/8 [tex]\frac{11}{16}[/tex]
3 [tex]^4C_3 (1/2)^{4}[/tex] = 1/4 [tex]\frac{15}{16}[/tex]
4 [tex]^4C_4 (1/2)^{4}[/tex] = 1/16 1
Rewrite with only sin x and cos x.
sin 2x - cos x
Answers
Answer:
2sinxcosx - cosx OR cosx(2sinx - 1)
Step-by-step explanation:
Use the double angle identity for sin2x.
sin2x = 2sinxcosx
Substitute sin2x with 2sinxcosx.
2sinxcosx - cosx
Factor out cosx, if needed.
cosx * (2sinx - 1)
Answer:
[tex]{ \tt{ \sin2x - \cos x }} \\ = { \tt{(2 \sin x \cos x) - \cos x }} \\ = { \tt{ \cos x(2 \sin x - 1) }}[/tex]
Karl wants to fertilize his 6 acres. If it takes 7 StartFraction 2 Over 3 EndFraction bags of fertilizer for each acre, how much fertilizer does Karl need to buy?
Answers
Answer:
46
Step-by-step explanation:
Just multiply 6 by 7 2/3 to get 46.
Answer:
The answer is 46 bags
Step-by-step explanation:
Have a good summer!!!
The sum of two consecutive integers is -5. If 4
is subtracted from the smaller integer and 2 is
added to the larger integer, what is the quotient
when the larger of the two resulting numbers is
divided by the smaller number?
Please help me
Answers
Answer:
sim eu também preciso desta respota
9,16,25,36 arithmetic or geometric?
24,18,12,arithmetic or geometric?
500,100,20 ,4 arithmetic or geometric?
Answers
Answer:
9,16,25,36 neither, 24,18,12 arithmetic, 500,100,20 ,4 geometric
Step-by-step explanation:
1. has no common number
2. goes down by 6 each time
3. is divided by 5 each time
What is it quadratic, radical, rational?
Answers
Answer:
quadratic formula is ur answer for letter B
Paige and her family went to the movies. They bought 4 tickets and paid $12 for popcorn. They spent $40. How much did each ticket cost?
I need equation and cost :)
Answers
Answer:
Cost of tickets: $7. Equation: 40 = 4x + 12.
Step-by-step explanation:
Answer:
4*t +12 = 40
Each ticket cost 7 dollars
Step-by-step explanation:
tickets + popcorn = total cost
4*t +12 = 40
Subtract 12 from each side
4t +12-12 = 40-12
4t = 28
Divide by 4
4t/4 = 28/4
t = 7
Each ticket cost 7 dollars
You need to take a dosage of 10 ml of medicine every 8 hours for 9 days. How many fluid ounces of
medicine should you purchase? Round up to the next whole fluid ounce.
ounces
Answers
Answer:
270 ml
Step-by-step explanation:
30x9=270
Câu 1 (2 điểm). Cho hệ các vector
U = {(1,2,2); (0,-1,-1);(2,3,3);(1,0,0).
a) tìm số chiều và một cơ sở W của không gian con sinh bởi hệ vector U
b) tìm tham số k để u=(2,3,k^2 +1) là một tổ hợp tuyến tính cảu W, và suy ra [u]w
giải hộ mình với
Answers
Answer:
Step-by-step explanation:
Will mark Brainlest helppp plllllssss
Answers
Answer:
2h
Step-by-step explanation:
f(3 + h) = 2(3 + h)^2 + 1
= 2(3^2 + h^2) + 1
= 2(9) + 2h^2 + 1
= 18 + 2h^2 + 1
= 2h^2 + 19
f(3) = 2(3)^2 + 1
= 2(9) + 1
= 18 + 1
= 19
2h^2 + 19 - 19 / h
2h^2 / h
2h