Answers
The value of dy/dx for the functions are
(i) \(\frac{dy}{dx} = 4x^{2}sin2x.cos2x+ 2x. sin^{2}2x\)
(ii) \(\frac{dy}{dx} =\frac{- y(1+3x^{2})}{2x(1+x^{2}) }\)
DifferentiationFrom the question, we are to determine dy/dx for the given functions
(i) \(x^{2} sin^{2}2x\)
Let \(u = x^{2}\)
and
\(v = sin^{2} 2x\)
Also,
Let \(w= sin2x\)
∴ \(v = w^{2}\)
First, we will determine \(\frac{dv}{dx}\)
Using the Chain rule
\(\frac{dv}{dx} = \frac{dv}{dw}.\frac{dw}{dx}\)
\(v = w^{2}\)
∴ \(\frac{dv}{dw} =2w\)
Also,
\(w= sin2x\)
∴ \(\frac{dw}{dx} =2cos2x\)
Thus,
\(\frac{dv}{dx} = 2w \times 2cos2x\)
\(\frac{dv}{dx} = 2sin2x \times 2cos2x\)
\(\frac{dv}{dx} = 4sin2x . cos2x\)
Now, using the product rule
\(\frac{dy}{dx} = u\frac{dv}{dx} + v\frac{du}{dx}\)
From above
\(u = x^{2}\)
∴ \(\frac{du}{dx}=2x\)
Now,
\(\frac{dy}{dx} = x^{2} (4sin2x.cos2x)+ sin^{2}2x (2x)\)
\(\frac{dy}{dx} = 4x^{2}sin2x.cos2x+ 2x. sin^{2}2x\)
(ii) \(xy^{2}+y^{2}x^{3} +2=0\)
Then,
\(x.2y\frac{dy}{dx}+ y^{2}(1)+y^{2}.3x^{2} + x^{3}.2y\frac{dy}{dx} +0=0\)
\(2xy\frac{dy}{dx}+ y^{2}+3x^{2}y^{2} + 2x^{3}y\frac{dy}{dx} =0\)
\(2xy\frac{dy}{dx}+2x^{3}y\frac{dy}{dx} =- y^{2}-3x^{2}y^{2}\)
\(\frac{dy}{dx} (2xy+2x^{3}y)=- y^{2}(1+3x^{2})\)
\(\frac{dy}{dx} =\frac{- y^{2}(1+3x^{2})}{2xy+2x^{3}y}\)
\(\frac{dy}{dx} =\frac{- y^{2}(1+3x^{2})}{2xy(1+x^{2}) }\)
\(\frac{dy}{dx} =\frac{- y(1+3x^{2})}{2x(1+x^{2}) }\)
Hence, the value of dy/dx for the functions are
(i) \(\frac{dy}{dx} = 4x^{2}sin2x.cos2x+ 2x. sin^{2}2x\)
(ii) \(\frac{dy}{dx} =\frac{- y(1+3x^{2})}{2x(1+x^{2}) }\)
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Related Questions
Mr. Villegas can drive 280 miles in 4 hours. How long would it take him to drive 2.5 hours?
Answers
Vertical angles are two angles that are ___ of each other when two intersect. These angles are
Answers
Answer:
The two angles that are directly across the intersection point from each other are called vertical angles. Vertical angles are always congruent.
Step-by-step explanation:
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Vertical angles are two angles that are opposite of each other when two intersect. These angles are congruent.
What are vertical angles?Vertical angles are angles opposite to each other where two lines cross.
When two lines intersect, they naturally form two pairs of vertical angles. Vertical angles share the same vertex or corner, and are opposite each other.
These pair of angles are congruent which means they have the same angle measure.
Hence, Vertical angles are two angles that are opposite of each other when two intersect. These angles are congruent.
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3. How many different numbers can be created by selecting 4 of the digits from the number 8712395?
Answers
840 different numbers can be created selecting 4 of the digits from the number
How many different numbers can be created selecting 4 of the digits from the numberFrom the question, we have the following parameters that can be used in our computation:
Number = 8712395
Digits = 4
The count of digits in the number is 7
Using the above as a guide, we have the following:
First digit = any of the 7second digit = any of the remaining 6Third digit = any of the remaining 5Fourth digit = any of the remaining 4So, we have
Numbers = 7 * 6 * 5 * 4
Evaluate
Numbers = 840
Hence, 840 numbers can be formed
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Find an equation of the line described below. Write the equation in slope intercept form( solved for y) when possible through (8,5) and (5,8)
Answers
\((\stackrel{x_1}{8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{8}}} \implies \cfrac{ 3 }{ -3 } \implies - 1\)
\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 1}(x-\stackrel{x_1}{8}) \\\\\\ y-5=-x+8\implies {\Large \begin{array}{llll} y=-x+13 \end{array}}\)
What is the height of spanning tree obtained from Wn by the breadth-first search, starting at the central vertex of Wn?
Answers
Answer:
The height of the spanning tree is one by the breadth-first search at the central vertex of Wn.
Step-by-step explanation:
The graph is connected and has a spanning tree where the tree can build using a depth-first search of the graph. Start with chosen vertex, the graph as the root, and root add vertices and edges such as each new edge is incident with vertex and vertices are not in path. If all vertices are included, it will do otherwise, move back to the next level vertex and start passing. It is for depth-first search. For breadth-first search, start with chosen vertex add all edges incident to a vertex. The new vertex is added and becomes the vertices at level 1 in the spanning tree, and each vertex at level 1 adds each edge incident to vertex and other vertex connected to the edge of the tree as long as it does not produce.
7. Write a biconditional for the following conditional. Determine the truth value
of the new statement. If two lines have the same slope, then they are parallel.
Answers
Line AB is parallel to CD, for instance, as indicated by the formula AB ll CD.
How do parallel lines work?
Lines in a plane that are regularly spaced apart are known as parallel lines. Parallel lines don't overlap each other. Perpendicular lines are those that cross at a straight angle of 90 degrees.Only if the slopes of two lines are equal can they be said to be parallel. If two lines have different y-intercepts and equal slopes, they are said to be parallel. In a plane, parallel lines are two lines that never cross (meaning they will continue on forever without ever touching). The equal slopes of parallel lines are a distinctive feature. The rise (change in Y coordinates) over the run (change in X coordinates) of a line, or its steepness, is referred to as the slope of a line. The most typical way to depict parallel lines is with two vertical lines (ll). Line AB is parallel to CD, for instance, as indicated by the formula AB ll CD.Learn more about parallel lines
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every us state has 2 senators (there are 50 states). if there are 500 members in congress, what percent of the congress is made up of senators?
Answers
Answer:
20% of the Congress is made of Senators.
Step-by-step explanation:
Our whole here is 500, since the House of Representatives and Senate combined would have 500 members in this case. So, we now need to find out how many senators there are.
\(2\) x \(50\) = \(100\)
Now, since we know the fact that there are 100 senators in Congress, we will find out what percent of 500 is 100.
100 = 20% of 500. To check, we will multiply 5 by 100. We get 500.
Therefore, the answer is 20%.
Brittany asked her classmates: How much time, in minutes, do you spend reading each day? Here are the results: 10, 20, 20, 20, 30, 30, 30, 30, 30, 40, 40, 40, 60, 60, 60 Display the data in a line plot, a histogram, and a box plot. Next to each graph, write down something you notice about the data. Upload your completed plots here.
Answers
The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.
Line Plot:
A line plot displays data points on a number line, representing the frequency or count of each value.
In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.
For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.
Histogram:
A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.
The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.
The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.
The height of each bar in the histogram will represent the number of students falling into each interval.
Box Plot:
A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.
The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.
The box will represent the interquartile range (IQR), showing the middle 50% of the data.
The line within the box will represent the median value.
The whiskers will indicate the minimum and maximum values, excluding outliers.
By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.
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What are the coordinates of the endpoints of the midsegment for A RST that is parallel TS? Enter your answer by filling in the boxes. (_ , _) and (_ , _)
Answers
Answer:
2,4 3,5
Step-by-step explanation:
John estimated the height of his office building to be 13m . The actual height of his office building was 14.7m .
Find the absolute error and the percent error of John's estimate. If necessary, round your answers to the nearest tenth.
Answers
Answer:
Percent error = 11.6%
Step-by-step explanation:
Given the following data;
Actual height, A = 14.7 m
Estimated height, E = 13 m
a. To find the absolute error;
Absolute error = A - E
Absolute error = 14.7 - 13
Absolute error = 1.7
b. To find the percent error;
Percent error can be defined as a measure of the extent to which an experimental (estimated) value differs from the actual or theoretical value.
Mathematically, it is given by this expression;
\( Percent \; error = \frac {experimental \;value - theoretical \; value}{ theoretical \;value} *100\)
Substituting into the equation, we have;
\( Percent \; error = \frac {13 - 14.7}{14.7} *100\)
\( Percent \; error = \frac {1.7}{14.7} *100\)
\( Percent \; error = 0.1157 *100\)
Percent error = 11.57 ≈ 11.6%
4.1 Draw the four different views of the object, as indicated below, on square grid paper. Left Back Front Right
Answers
Remember to make use of the grid paper to maintain accuracy and proportionality across all four views.
Certainly! Below is a verbal description of how you can draw the four different views of the object on square grid paper:
Left View: Start by drawing the left side of the object as you would see it from a leftward perspective.
Capture its shape, height, and any visible features. Use the grid lines to maintain proportion and accuracy.
Back View: Move to the back of the object and draw what you see from that viewpoint.
Focus on its rear-facing details, contours, and any distinguishing characteristics. Utilize the grid paper to ensure proper alignment.
Front View: Now, face the object directly and draw its front view. Pay attention to its overall shape, dimensions, and any frontal features or patterns.
Utilize the grid lines to maintain symmetry and precision.
Right View: Finally, position yourself on the right side of the object and draw its appearance from that angle.
Portray the right-facing side, capturing its unique attributes and maintaining consistency with the previous views.
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Please help
The formula for the Volume...
Answers
Answer:
cones
Step-by-step explanation:
Volume of a cone:
V = (1/3)πr2h
Who knows this answer!!
Answers
12.84 + 53.87 = y
66.71 = y
Sooo the predicted height at the time of 6 weeks is 66.71 and then you’d put inches or centimeters or whatever unit after that. :) hope this helps!
Energy is generated from solar and wind power. Solar power must be at most 6units/day or the panels will burn out. Wind must be strong enough to power 1 unit/ day or else the turbines won’t turn. The wind power must be less than twice the solar power less one, or the batteries wont charge properly. Find the optimal production of wind and solar that will maximize overall power output
Answers
Efficiency.Compared to solar panels' efficiency range of 18% to 22%, wind turbines typically capture 60% of the energy that flows through them.
What is more efficient wind or solar energy?Efficiency.Compared to solar panels' efficiency range of 18% to 22%, wind turbines typically capture 60% of the energy that flows through them.This proves that a single home wind turbine can generate more electricity than a number of solar panels.By the movement of air in relation to the Earth's surface, wind energy, a type of solar energy, is created.When the Earth's surface is heated unevenly by the Sun, this type of energy is created. The Earth's rotation and surface topography then alter this energy.Photovoltaic (PV) panels or solar radiation-concentrating mirrors are two ways that solar technologies turn sunlight into electrical energy.Electricity can be produced from this energy, which can also be used to store energy thermally or in batteries.To learn more about solar energy refer
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Annabelle works in a department store selling clothing. She makes a guaranteed
salary of $500 per week, but is paid atommision on top of her base salary equal to
30% of her total sales for the week. How much would Annabelle make in a week in
which she made $2400 in sales? How much would Annabelle make in a week if she made x dollars in sales?
Earnings when selling $2400:
Earnings when selling $x:
Answers
Answer:
$1220
$500 + $0.3x
Step-by-step explanation:
First of all, Ana makes a guaranteed $500. We set that aside, like a constant.
Now, we proceed. We're old she earns 30% extra on her total sales for the week. This means her earnings will be.
$500 + 0.3x, where x is her total sales for the week. Thus, in a week she made $2400 sales, she'd earn
$500 + 0.3 * 2400
$500 + $720
$1220
That means, she earns $1220 in that week
Given the equation -4x + y = 8, what are the x- and y-intercepts
Answers
y-intercept(s): (0,8)
The scale of a truck is 3.7 cm
Answers
Answer:
that truck must be straight fire
help me answer this please
Answers
Answer:
3,952 ft
Step-by-step explanation:
Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.
sin8°=\(\frac{550}{c}\)
csin8°=550
c=550/sin8°
c= 3,952
De un grupo de fichas numeradas del 1 al 15, ¿cuál es la probabilidad de elegir una ficha al azar y que esta sea par y múltiplo de 3?
Answers
Answer:
2/15
Step-by-step explanation:
Comenzaremos escribiendo el número de mosaicos. Esto se ilustra a continuación:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15.
A continuación, escribiremos el múltiplo de 3. Esto se ilustra a continuación:
3 × 1 = 3
3 × 2 = 6
3 × 3 = 9
3 × 4 = 12
3 × 5 = 15
Por tanto, los múltiplos de 3 son:
3, 6, 9, 12 y 15
A continuación, determinaremos el número par entre 3, 6, 9, 12 y 15
Esto se ilustra a continuación:
NOTA: Los números pares son divisibles por 2 sin residuo.
3/2 = 1,5
6/2 = 3
9/2 = 4,5
12/2 = 6
15/2 = 7,5
Por tanto, los números pares son: 6 y 12
Finalmente, determinaremos la probabilidad de elegir una loseta par y múltiplo de 3. Esto se puede obtener de la siguiente manera:
Espacio muestral (S) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
nS = 15
Par y múltiplo de 3 (E) = {6,12}
nE = 2
Probabilidad de elegir una loseta par y múltiplo de 3, P (E) =?
P (E) = nE / nS
P (E) = 2/15
Por lo tanto, la probabilidad de elegir una loseta par y múltiplo de 3 es 2/15
What is the solution of the equation 3/4x + 5 = -9
PLEASE HELPPPP
Answers
Answer:
-18 2/3 or -56/3
Step-by-step explanation:
A bag with 8 marbles has 4 red marbles, 3 blue marbles, and 1 yellow marble.A marble is chosen at random. What is the probability that it is red? Write your answer as a fraction in simplest form.
SOMEONE PLEASE HELP ME IM SO STUCK
Answers
Answer:
1/4
Step-by-step explanation:
First you add all of the marbles in the bag which is 16 marbles. The fraction of red marbles to the total would be 4/16. In the simplest form that is 1/4. You can also just do 4 divide by 16 which gives you 0.25 and in decimal form that is 1/4.
what pattern can be observed from the data?
Answers
Answer:
Clustering Data
Step-by-step explanation:
8
A cress seed took of a week to sprout. An artichoke seed took
7
8 17
What question does ÷ help us answer in this situation?
7 7
17
7
weeks to sprout.
Answers
This equation suggests that , How many times as long did the cress seed take to sprout as the artichoke seed.
What is sprouting ?
Sprouting is that the natural action by that seeds or spores germinate and place out shoots, and already established plants manufacture new leaves or buds, or alternative structures expertise additional growth.
Main body:
According to question:
A cress seed took 8/7 of week to sprout.
8/7 of week = (8/7)*7
total days taken by cress seed = 8 days
An artichoke seed took 17/7 week to sprout.
17/7 of week = (17/7)*7
total days taken by artichoke = 17 days.
⇒ (8/7)/(17/7)
⇒ \(\frac{8}{7} *\frac{7}{17}\)
⇒8/17
Therefore is it shows how many times as long did the cress seed take to sprout as the artichoke seed.
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Answer: D
Step-by-step explanation: DID IT ON KHAN
I need help with this pls ASAP
Answers
Jose has 3/5 kilograms of peppermints and 2/3 kilogram of candy canes. How many kilograms of candy does he have?
Answers
Answer: 1-4/15 kilograms of candy.
Step-by-step explanation: 3/5 + 2/3 = 1-4/15.
Answer:
19/15 kilo.
Step-by-step explanation:
First they have to have a common demonitator. Both of them are factors of 15. 3/5 = 9/15. 2/3 = 10/15. Now add the numerators and leave the denominators. 19/15.
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the costs of equipment for the track team is shown in the table at the right ⬆️
Answers
the total cost of equipment for the boy's team is $5700 and the total cost of equipment for the girl's team is $6305.
How to determine?
To find the total cost of equipment for each team, we can use matrix multiplication. Let's first create a matrix of the costs of each item:
Cost matrix =
[25
125
165]
Then we can create a matrix of the quantities of each item for each team:
Quantity matrix =
[38 18 20 32
15 17 0 0]
To find the total cost of equipment for each team, we can multiply the cost matrix by the quantity matrix:
Total cost matrix = Cost matrix x Quantity matrix
Total cost matrix =
[25 125 165] x [38 18 20 32
15 17 0 0]
Total cost matrix =
[(25 x 38) + (125 x 18) + (165 x 20) (25 x 32) + (125 x 15) + (165 x 17)]
Total cost matrix =
[5700 6305]
Therefore, the total cost of equipment for the boy's team is $5700 and the total cost of equipment for the girl's team is $6305.
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Jacob spends 13/4 dollars to paint 9/3 square feet. Find the cost to paint a
square feet per dollar.
Answers
The cost to paint a is 12/13 square feet per dollar.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Jacob spends 13/4 dollars to paint 9/3 square feet.
\(\dfrac{\dfrac{9}{3}}{ \dfrac{ 13}{4}} = \dfrac{9}{3} \times \dfrac{ 4}{13}\\\\= \dfrac{ 36}{39}\\\\= \dfrac{ 12}{13}\)
Hence, the cost to paint a is 12/13 square feet per dollar.
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Mr. McDowell's class read the first $52$ pages of a book during the first week of school, $46$ pages during the second week, $51$ pages during the third week, $42$ pages during the fourth week, $30$ pages during the fifth week, and $44$ pages during the sixth week. There are $75$ pages left to read. How many pages does the book have in all?
Answers
Answer:
340 pages total
Step-by-step explanation:
52+46+51+42+30+44+75=340
hope this helped!
Answer:
340 pages total
Step-by-step explanation:
Just add all the numbers together :)
Determine whether the following statement makes sense or does not make sense, and explain your reasoning. I found the expected value for the number of boys for a family with five children to be 2.5. I must have made an error because a family with 2.5 boys cannot occur. Question content area bottom Part 1 The statement ▼ does not make sense makes sense because the expected value of 2.5 represents the ▼ average number total number of boys for all the families with five children. In a five-child family, ▼ all the children half the children are expected to be boys, so the expected value of 2.5 is ▼ inconsistent. consistent.
Answers
This is due to the fact that the anticipated value is determined by multiplying the likelihood of each potential occurrence by its value, then adding the results.
what is probability ?Probability is a metric for determining the possibility of an event happening in mathematics and statistics. It is a number between 0 and 1, where 0 denotes that the action is impossible and 1 denotes that it is guaranteed to occur. Usually, the likelihood of a particular occurrence is calculated through dividing the number of possible outcomes by the number of alternative ways the event could happen. As an illustration, the likelihood of rolling a six on a regular die is 1/6 since there is just one method for scoring a six and a total of six options. Many practical applications of probability can be found in the fields of insurance, banking, and gaming. Also, it aids in risk management and assessment throughout scientific research and decision-making processes.
given
The assertion "I discovered that there should be 2.5 more boys in a household of five than was anticipated. A family of 2.5 boys cannot exist, thus I must have made a mistake "contradicts itself.
A family cannot have 2.5 males just because the number of boys in a household of five is supposed to be 2.5. Instead, it suggests that a family with five children may typically anticipate to have 2.5 boys.
This is due to the fact that the anticipated value is determined by multiplying the likelihood of each potential occurrence by its value, then adding the results.
It is indeed impossible to have 2.5 males in a family of five.
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The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four 10s, etc., down to four 2s in each deck.
You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. (a) Are the outcomes on the two cards independent? Why?
No. The events cannot occur together. Yes. The events can occur together. No. The probability of drawing a specific second card depends on the identity of the first card. Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card.
(b) Find P(ace on 1st card and jack on 2nd). (Enter your answer as a fraction.)
(c) Find P(jack on 1st card and ace on 2nd). (Enter your answer as a fraction.)(d) Find the probability of drawing an ace and a jack in either order. (Enter your answer as a fraction.)
Answers
Answer:
(a) (C) No. The probability of drawing a specific second card depends on the identity of the first card.
(b)\(\dfrac{4}{663}\)
(c)\(\dfrac{4}{663}\)
(d)\(\dfrac{8}{663}\)
Step-by-step explanation:
(a)The outcomes on the two cards are not independent because since the cards are drawn without replacement, the probability of drawing a specific second card depends on the identity of the first card.
(b)P(ace on 1st card and jack on 2nd).
Number of Ace = 4
Number of Jack = 4
P(ace on 1st card and jack on 2nd)
\(=\dfrac{4}{52} \times \dfrac{4}{51}\\=\dfrac{4}{663}\)
(c) P(jack on 1st card and ace on 2nd).
Number of Ace = 4
Number of Jack = 4
\(=\dfrac{4}{52} \times \dfrac{4}{51}\\=\dfrac{4}{663}\)
(d) Probability of drawing an ace and a jack in either order.
=P(Ace and Jack) Or P(Jack and Ace)
=P(Ace and Jack) + P(Jack and Ace)
\(=\dfrac{4}{52} \times \dfrac{4}{51}+\dfrac{4}{52} \times \dfrac{4}{51}\\=\dfrac{4}{663}+\dfrac{4}{663}\\=\dfrac{8}{663}\)