Answers
C. For each term in this expression, you can just apply the power rule.
[tex]y = 3x^2 - \sqrt x + \dfrac2x = 3x^2 - x^{\frac12} + 2x^{-1}[/tex]
[tex]\implies \dfrac{dy}{dx} = 2\cdot3x^{2-1} - \dfrac12 x^{\frac12-1} + (-1)\cdot2x^{-1-1}[/tex]
[tex]\implies \dfrac{dy}{dx} = 6x - \dfrac12 x^{-\frac12} - 2x^{-2}[/tex]
[tex]\implies \dfrac{dy}{dx} = 6x - \dfrac1{2\sqrt x} - \dfrac2{x^2}[/tex]
Every other choice involves composite functions that do require the chain rule to differentiate.
Option C : [tex]y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\[/tex] can be differentiated without using chain rule.
The differentiation of [tex]y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\[/tex] without using chain rule can be done as follows:
[tex]\begin{aligned}\dfrac{dy}{dx} &= \dfrac{d}{dx}(3x^2 - \sqrt{x} + \dfrac{2}{x})\\\\&= \dfrac{d}{dx}(3x^2 - x^{\frac{1}{2}} + 2x^{-1})\\&= 6x - (1/2)x^{-\frac{3}{2}} -2x^{-2}\\\end{aligned}[/tex]
The rest of the functions are composite, which means, that after differentiating them with some other base, you need to change the base and differentiate again, thus applying chain rule.
Thus, the function [tex]y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\[/tex] can be differentiated without using chain rule.
Thus, option C: [tex]y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\[/tex] is correct option.
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Related Questions
Camila is collecting button pins. Camila started her collection with 20 button pins and collects 5 button pins per month. Let y represent the total number of button pins Camila has collected and x represent the number of months Camila collects button pins.
Graph this linear relationship.
Select two points to graph the line.
Answers
Step-by-step explanation:
Camilla started her collection with 20 buttons, meaning that this number is a constant, and that it will not change: (+20)
She then collects 5 buttons per month. Month is represented by the variable, x (given by the question), and there are 5 per month (so you multiply).
Set the equation:
Total pins = Amount of pins per month x amount of months + Amount of pins started.
y = 5x + 20
In this case, plug in the amount of months (x) to obtain your total (y):
When x = 0, y = 20
y = 5(0) + 20
y = 0 + 20
y = 20
When x = 1 , y = 25
y = 5(1) + 20
y = 5 + 20
y = 25
When x = 2, y = 30
y = 5(2) + 20
y = 10 + 20
y = 30
When x = 3, y = 35
y = 5(3) + 20
y = 15 + 20
y = 35
When x = 4, y = 40
y = 5(4) + 20
y = 20 + 20
y = 40
~
Note: This is a linear graph, so you can choose any of these given points (and more if you want to plot more). I would choose two that aren't too close to each other, unless you want a really small graph size.
The length of a rectangle is 6 in less than 3 times the width. If the perimeter is 36 in, what is the width of the rectangle?
Answers
Answer:
width = 6
Step-by-step explanation:
We can think of the width as x and the height as 3x-6. the perimeter formula is (width + height)*2, since we have x as width and 3x-6 as height, we can put it in the formula, which will get you (x + 3x-6)*2 = 36, if we devide both sides by 2, we'll get (x + 3x - 6) = 18, when we simplify it, we will get 4x-6 = 18, which can then be simplified into 4x = 24, which will get you that x = 6
Hope it helped :)
1. The following sets of data shows the mean marks of 43 interviewees from a certain job interview that was conducted by a HR Consulting Firm in Mombasa: 23, 45, 79, 15, 47, 64, 33, 26, 34, 46, 31, 29, 49, 25, 45, 43, 39, 45, 22, 26, 28, 36, 42 Using the concept of sampling distribution, what sample size will give at least a 0.95 probability that the sample mean is greater than $8 of the population mean?
Answers
Using the Central Limit Theorem, it is found that a sample size of 13 is needed.
In a normal distribution 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]
It 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, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].For this problem, using a calculator:
The mean is [tex]\mu = 37.9[/tex]The standard deviation is [tex]\sigma = 14.07[/tex]The sample size needed is n when [tex]s = 4[/tex], as by the Empirical Rule, 95% of the measures are within 2 standard errors of the mean, hence [tex]2s = 8 \rightarrow s = 4[/tex]
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
[tex]4 = \frac{14.07}{\sqrt{n}}[/tex]
[tex]4\sqrt{n} = 14.07[/tex]
[tex]\sqrt{n} = \frac{14.07}{4}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{14.07}{4}\right)^2[/tex]
[tex]n = 12.37[/tex]
Rounding up, a sample size of 13 is needed.
A similar problem is given at https://brainly.com/question/24663213
Can someone help me solve these problems?
Answers
Answer:
Step-by-step explanation:
1) add all angles to 180
2) exterior angle = P + Q
i can add remaining ones also
Help help help help help help help help
Answers
Answer:
7
Step-by-step explanation:
15-8 is 7
16-8 is 7
17-10 is 7
18-11 is 7
this fits the eqation.
hope this helps you
Octavia is making cotton candy. She uses 17.5 cups of sugar to make 5 bags of cotton candy. At this rate, how many cups of sugar are used to make 1 bag of cotton candy?
Answers
Answer:
3.5 cups of sugar per bag.
Step-by-step explanation:
17.5/5
3.5 cups of sugar are used to make 1 bag of cotton candy
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
For 5 bags of candy = 17.5 cups of sugar needed
and, For 1 bags of candy
=17.5/ 5
=3.5 cups of sugar needed
hence, 3.5 cups of sugar are used to make 1 bag of cotton candy
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At a concert the ratio of adults to children is 4:5. There are 720 children in a concert how many adults are there?
BRAINLIEST QUEATION !!
Answers
Answer:
576 adults
Step-by-step explanation:
The 5 part of the ratio relates to 720 children, then
720 ÷ 5 = 144 ← value of 1 part of the ratio , then
4 parts = 4 × 144 = 576 ← number of adults
Answer:
576
Step-by-step explanation:
Adults : Children
4 : 5
x : 720
Let the number of adults be x.
Use cross multiplication.
[tex]4 : 5\\ x : 720\\[/tex]
[tex]4 *720=5*x[/tex]
[tex]\frac{4*720}{5} =\frac{5x}{5}[/tex]
4 × 144 = x
576 = x
Hope this helps you.
Let me know if you have any other questions :-)
Helps me please help help me
Answers
Answer:
(2, -6)
Step-by-step explanation:
1. The rule for reflecting a point across the y-axis is (x, y) -> (-x, y)
This means that when reflecting across the y-axis, the x-coordinate changes signs.[tex](-(-2),-6)[/tex] [tex](2,-6)[/tex]Therefore, the ordered pair that describes the location of C' is (2, -6).
Answer:
(2, -6)
Step-by-step explanation:
share £650 in the ratio of 4:9
Answers
Answer:
200:450 that would be the answer i believe
When bisecting segments and angles, which step is the same?
Answers
what is perpendicular lines
Answers
Perpendicular lines are lines, segments or rays that intersect to form right angles. The symbol ⊥ means is perpendicular to . In the figure, PR⊥QS. The right angle symbol in the figure indicates that the lines are perpendicular. PLS MARK BRAINLIEST :D
Round to 2 decimal places 0.966
Answers
Answer:
Step-by-step explanation:
round to 2 places 0.966: 1.00
Simplify the following expression
3x + 2(x +6) -4 -2x
A. 3x + 2
B. 7x + 8
C. 3x + 8
D.7x + 10
Answers
Answer:
C
Step-by-step explanation:
3x+2(x+6)-4-2x.
First, we do the parenthesis.
This gives us: 3x+2x+12-4-2x.
Then, we reorder so like terms are together.
This gives us: 3x+2x-2x+12-4.
Then, we combine like terms.
This gives us: 3x+8, which is C.
use a calculator to find the square for 7.6
Answers
Answer:
Using a calcuator, [tex]7.6^{2} =57.76[/tex]
Answer:
Hey mate....
Step-by-step explanation:
This is ur answer....
Shows me 57.76 well....Hope it helps!
Brainliest pls!
Follow me! ♧
28. Marta Sanchez purchased a sweater for $15.67, a pair of socks for $2.13, and a bracelet for $6.78. For all
purchases she must pay the state sales tax of 7.5% and the county tax of 0.5%. What is the tax on her
purchases?
Answers
Answer:
$ 1.94
Hope I helped
Calculate the difference and enter it below. -9-(-10) Answer here
Answers
Answer:
-9-(-10)
=-9+10
=1
help on math review edu
Answers
Answer:
Answer is A
Step-by-step explanation:
Subtract 47 from both sides to get 0
3x² - 18x - 42 = 0
Use Quadratic formula to get
[tex]3+\sqrt{23} \\3-\sqrt{23}[/tex]
Answer:
Step-by-step explanation:
plzz help asap plzzzzz
Answers
Answer:
5.45 then 6.454 then 5425 then 12825
Step-by-step explanation:
Taylor buys candy at the store that costs $1.50 per candy bar.
Create a table that could represent Taylor’s cost per candy bar.
Candy
Cost
0 /0
1 /1.50
? ?
? ?
? ?
Answers
Answer:
2/ 3.00
3/4.50
4/6.00
Step-by-step explanation:
A dealership is allowing residents to test drive the following vehicles: 2 sports cars, 3 vans, and 3 trucks. If you select a random car to test drive, what are the odds it is not a sports car? Write your answer in the form a:b as a fully reduced ratio.
Answers
Answer:3:1
Step-by-step explanation:
There are 2 sports cars out of a total of 8 total cars, so there are 2 favorable outcomes, and 8−2=6 unfavorable outcomes.
The odds against choosing a sports car are 6:2.
Both numbers are divisible by 2, so this ratio can be simplified to 3:1.
Colin got a new video game. He scored 31 points on the first level, 31 points on the second level, 31 points on the third level, and 31 points on the fourth level. What kind of sequence is this? both, neither ,arithmetic, geometric
Answers
Answer:
Both
Step-by-step explanation:
An arithmetic sequence is given by the next form:
[tex]a_{n} = a_{1} + (n-1)d[/tex]
Where [tex]a[/tex] is the [tex]n^{th}[/tex] term of the sequence, [tex]a_{1}[/tex] the first term of the sequence and [tex]d[/tex] the common difference between terms.
So the given sequence is of the form, because the common difference between terms is 0.
[tex]a_{n} = 31 + (n - 1) 0 = 31[/tex]
A geometric sequence is given by the next form
[tex]ar^0, ar^1, ar^2, ar^3, ar^4, \cdot \cdot \cdot[/tex]
When [tex]r\neq 0[/tex]
In this occasion our [tex]a=31[/tex] and the [tex]r = 1[/tex]
So both sequence represent the given one.
Select the correct answer
Consider the given solids with the dimensions shown. Which solids are similar?
Aonly figure 1 and figure 2
B.only figure 2 and figure 3
c.only figure 1 and figure 3
D. all three figures
E none of the figures
Answers
only figure 1 and figure 3 are similar.
What is similarity?Two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.
In figure 1, two of the sides (16 and 9 ) are perfect square and third is not.
If we take the ratio of three side as
16:9:12
(4)²:(3)²:(2√3)²
Similarly, In figure 3 two of the sides (64 and 36 ) are perfect square and third is not.
If we take the ratio of three side as
64:36:48
(8)²:(6)²:(4√3)²
Comparing the ratios of both figure, the figure 3 has twice the measurement of figure 1 sides.
Hence, only figure 1 and 3 are similar.
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50 pencils cost £3. How much would 8 pencils
cost
What is the answer
Answers
X = 12/25 or 0.48
Answer:
0.48£
Step-by-step explanation:
(3x8)/50=0.48£
BETWEEN WHAT TWO INTEGERS IS THE SECOND ZERO?
Answers
Answer:
between 2 and 3
Step-by-step explanation:
see how it crosses the x axis a little after 2, so it's between 2 and 3
After watching some fish 55 feet below the surface of the water, a scuba diver went up 25 feet to explore a coral reef. Use a number line to help you create an equation that shows the location of the coral reef in relation to the water's surface.︎︎︎︎︎︎︎ ︎︎︎︎
It might be A
I really dont know lol
Answers
Answer:
The answer is C.
Step-by-step explanation:
Consider 5 1/2 as 5.5 to make it less confusing. Now, subtract 8 from 5.5.
5.5 - 8
=> -2.5
Now, let's turn -2.5 back in fraction form.
=> -2 1/2
Therefore, C is the answer
epic gamer question, i'll mark brainlist
Answers
Answer:
It has to be an isosceles because it has 2 congruent sides (and angles) in the same relative position. The two congruent angles both measure 30 degrees each; the total of degrees in any triangle is always 180. So, the other side has an angle measure of 120 degrees, which is more than 90. Therefore, it is
an obtuse isosceles
Does this graph represent a function? Why or why not?
Ay
10
8
8+
2+
1
-10-8-64
2
+ c
240
-
ON
10
4
-8-
-8-
-10
O A. No, because it fails the vertical line test.
O B. Yes, because it passes the vertical line test.
O C. No, because it is not a straight line.
O D. Yes, because it passes the horizontal line test.
Answers
The answer would e number B.
Moneysaver's Bank offers a savings account that earns 5% interest compounded continuously. If Ravi deposits $3200, how much will he have in the account
after six years, assuming he makes no withdrawals?
Do not round any intermediate computations, and round your answer to the nearest cent
x
5
?
Answers
the answer is 4160$
After 6 years of investment of $3200 compounded continuously, final amount in the account will be $4319.55.
Moneysaver's Bank offers a saving account with the features as,
Rate of interest = 5% annualTime of investment = 6 yearsPrincipal amount = $3200Expression to calculate the final amount when compounded continuously,
Final amount = [tex]P.e^{rt}[/tex]
Here, P = Principal amount
r = Rate of interest
t = Duration of investment
By substituting the values in the expression,
Final amount = [tex]3200.e^{0.05\times 6}[/tex]
= 3200(1.3498588)
= 4319.548
≈ $4319.55
Therefore, after 6 years of investment of $3200, final amount in the account will be $4319.55.
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Look at UVZ and WVZ in the image below.
Which of the following is the best description for this pair of angles?
A) supplementary
B) acute
C) straight
D) complementary
Answers
Answer:
A Supplementery
Step-by-step explanation:
they show on usa test prep
The best description for the given pair of angles is supplementary as shown in the figure. which is the correct answer would be an option (A).
What are supplementary angles?Supplementary angles are two angles that add up to 180 degrees. In other words, if you have two angles and you add their measures together, the sum will be 180 degrees if the angles are supplementary.
For example, consider the following pair of angles:
Angle A measures 80 degrees.
Angle B measures 100 degrees.
The sum of the measures of these two angles is 80 + 100 = 180 degrees, so angle A and angle B are supplementary angles.
As per the given figure, we have two angles UVZ and WVZ
As indicated in the image, the best description for the given pair of angles is supplementary.
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Type the correct answer in each box
The point on the number line shows the opposite of ____, or the opposite of the opposite _____.