Answers
[tex]\textbf{(i)}\\\\y=f(x)= \dfrac{x}{4+x}\\\\\\\dfrac{dy}{dx}= \lim \limits_{h \to 0} \dfrac{f(x+h)-f(x)}{h}\\\\\\~~~~~=\lim \limits_{h \to 0}\dfrac{\dfrac{x+h}{4+x+h}-\dfrac{x}{4+x}}{h}\\\\\\~~~~~~=\lim \limits_{h \to 0}\dfrac{\tfrac{(x+h)(4+x)-x(4+x+h)}{(4+x+h)(4+x)}}{h}\\\\\\~~~~~~= \lim \limits_{ h \to 0} \dfrac{4x+x^2 +4h+hx -4x-x^2 -hx}{h(4+x+h)(4+x)}\\\\\\~~~~~~=\lim \limits_{ h \to 0}\dfrac{4h}{h(4+x+h)(4+x)}\\\\\\~~~~~~=\lim \limits_{h \to 0} \dfrac{4}{(4+x+h)(4+x)}\\[/tex]
[tex]~~~~~~~~= \dfrac{ 4}{(4+x+0)(4+x)}\\\\\\~~~~~~~~= \dfrac{4}{(4+x)^2}[/tex]
[tex]\textbf{(ii)}\\\\\text{Given that,}~ y = f(x) = \sin 2x\\\\\\\dfrac{dy}{dx} = \lim \limits_{h \to 0} \dfrac{f(x+h) - f(x) }{h}\\\\\\~~~~~~=\lim \limits_{h \to 0} \dfrac{\sin(2x+2h)-\sin 2x}{h}\\\\\\~~~~~~=\lim \limits_{h \to 0} \dfrac{2 \sin \left( \dfrac{2x +2h -2x}{2} \right) \cos \left(\dfrac{2x+2h+2x}{2} \right)}{h}\\\\\\~~~~~~=\lim \limits_{h \to 0} \dfrac{2 \sin \left( \dfrac {2h}2 \right) \cos \left(\dfrac{ 4x+2h} 2\right)}{h}\\\\\\[/tex]
[tex]~~~~~~=\lim \limits_{h \to 0} \dfrac{2 \sin h \cdot \cos \left[ \dfrac{2(2x+h)}{2}\right] }{h}\\\\\\~~~~~~=\lim \limits_{h \to 0} \dfrac{2 \sin h \cdot \cos(2x+h) }{h}\\\\\\~~~~~~=2\left(\lim \limits_{h \to 0} \dfrac{\sin h}{ h} \right) \cdot \lim \limits_{h \to 0} \cos (2x+h)\\\\\\~~~~~~=2\cdot 1 \cdot \cos(2x+ 0)\\\\\\~~~~~~=2 \cos 2x[/tex]
Related Questions
What is the length of the missing side of this triangle?
13
?
9
A
250
В
22
С
15.81
Answers
Answer: C - 15.81
Step-by-step explanation:
pythagorean theorum: a^2 + b^2 = c^2
13^2 + 9^2 = c^2
169 + 81 = c^2
c^2 = 250
root both sides
c = 15.81
Which list of numbers is ordered from greatest to least?
Answers
Answer:
the option b is correct answer
Answer:
c
Step-by-step explanation:
that was arrange from greatest to lowest
When multiplying two matrices does AB = BA?
Answers
Answer:
AB = BA
Step-by-step explanation:
In general, AB = BA, even if A and B are both square. If AB = BA, then we say that A and B commute. For a general matrix A, we cannot say that AB = AC yields B = C. (However, if we know that A is invertible, then we can multiply both sides of the equation AB = AC to the left by A−1 and get B = C.)
Select ALL the true statements about the scatter plot below.
A. The graph shows a linear association
B. The graph has no outliers
C. The graph shows a nonlinear association
D. The graph shows a positive association
E. The graph could be used to show an association between the hours worked and the amount earned
Answers
A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. The true statements are A, D, and E.
What is a scatter plot?A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. One more variable can be presented if the points are programmed.
The following points about the scatter plot are true,
A. The graph shows a linear association
As there can be drawn a line between the two axes of the graph, and this line will give the approximate values, therefore, the graph shows a linear association. Thus, the statement is true.
B. The graph has no outliers
The graph has an outlier lying at the bottom right of the graph. Thus, the statement is False.
C. The graph shows a nonlinear association
As the graph has a linear association, it can not have a non-linear association. Thus, the statement is False.
D. The graph shows a positive association.
As the slope of the imaginary line is positive, the graph shows a positive association. Thus, the statement is true.
E. The graph could be used to show an association between the hours worked and the amount earned.
The above situation can be depicted by the given graph. Thus, the statement is true.
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Help
This
Is
Hard
Thanks
Answers
Answer:
x = 28
y = 13/7
Step-by-step explanation:
2x + 2y = 160
xy = 52
y = 80-x
80 - x = 52
-x = -28
x = 28
y = 13/7
Assume the acceleration of the object is a(t) = −9.8 meters per second per second (Neglect air resistance.) A baseball is thrown upward from a height of 3 meters with an initial velocity of 7 meters per second. Determine its maximum height. (Round your answer to two decimal places.)
Answers
Answer:
height = 5.682 meters
Step-by-step explanation:
height = -9.8x^2 + 7x + 3
Find the axis of symmetry: x = -b/(2a)
a = -9.8 b = 7 c = 3
x = -7/(2*-9.8) = -7/-19.6 = .357 = x = +.357 secs is when max height occurs
Find the height, replace x with .561
height = -9.8(.357^2) + 11(.357) + 3
height = -9.8(.127) + 11(.357) + 3
height = -1.245+3.927+3
height = 5.682
https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.292302.html
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Find the area of the
parallelogram.
10.7 ft.
5.5 ft.
14 ft.
Answers
Answer: [tex]823.9ft^{2}[/tex]
Step-by-step explanation:
The formula for the area of a parallelogram is : [tex]l * w * h[/tex]
l = length
w = width
h = height
You did not specify which integer was which, but it does not matter as the order in which you multiply them together does not matter.
10.7 * 5.5 * 14 = 823.9
Since you are finding the area, you have to square the units; 823.9 ft^2
If you found this answer helpful, I would greatly appreciate it if you gave me brainliest :D.
What is the volume in cubic in, of a rectangular prism with a height of 19in, a width
of 17in, and a length of 18in?
Answers
Answer:
5,814 inches cubed
Step-by-step explanation:
lengthxwidthxheight=volume of a rectangular prism.
19 times 17 times 18 equals 5,814 inches cubed. It is cubed because it is a three-dimensionsal shape. Hope this helps!
Use the graph below to answer the question that:
What are the amplitude, period, and midline of the function? (1 point)
Amplitude: 6; period: 2π; midline: y = −3
Amplitude: 6; period: π; midline: y = −3
Amplitude: 3; period: π; midline: y = −2
Amplitude: 3; period: 2π; midline: y = −2
Answers
The amplitude is equal to 3, the period is π midline y = -1.
For this case the amplitude is given by:
A = (l-5l + 1) / 2
A = 6/2
A = 3
The middle line is given by:
y = -1
What is the formula for period?The period of the function is given by,
T = l x2 - x1 l
T = l 0 - pi l
T = l - pi l
T = pi
Therefore the amplitude: 3; period is π; midline: y = -1.
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In hopes of encouraging healthier snacks at school, Wanda brought in a tray of carrot sticks and apple slices to share. The tray had a total of 30 snacks, of which 30% were carrot sticks. How many carrot sticks did Wanda bring?
Answers
Answer:
Wanda brought 9 carrot sticks.
Step-by-step explanation:
Convert 30% to a decimal by removing the percent sign and dividing by 100: 30 ÷ 100 = 0.30Substitute 0.30 for 30% in the equation: 30% x 30 = Y becomes 0.30 * 30 = YDo the math: 0.30 x 30 = 9Y = 9So 30% of 30 is 9Double check your answer with the original question: How many carrot sticks did Wanda bring? Multiply 0.30 x 30 = 9Yo math hard. so 25 points, i really need it
Answers
Answer:
10 feet
Step-by-step explanation:
Given,
Volume of right cylinder = 2000 π cubic feet.
Length ( l ) = 20 feet
To find : Radius ( r )
Formula : -
Volume of right cylinder = πr²h
πr²h = 2000 π
Divide π on both sides,
r²h = 2000
r² = 2000 / h
r² = 2000 / 20
r² = 100
= 10 x 10
r²= 10²
r = 10 feet
Hence,
the radius is 10 feet.
Find the linear equations giving brainlest
Answers
Answer:
Step-by-step explanation:
Slope-intercept form of a linear equation: y = mx + b
m is the slopeb is the y-intercept - when x = 0Problem 17: y = -4x + 2
slope: -4y-intercept: (0, 2)Problem 18: y = 1/7x - 5
slope: 1/7y-intercept: (0, -5)Problem 19:
y = 1x + 3
slope: 1y-intercept: (0, 3)Hope this helps!
Clearly, we can tell that the equation is in slope intercept form.
Formula:
Slope intercept form: y = (m)x + (b) [m = Slope; b = y-intercept]
Let us compare the slope intercept form equation with the given equation to determine the slope and the y-intercept.
⇒ y = (m)x + (b) and y = -4x + 2
When comparing both equations, we can observe that:
"-4" takes the place as "m" "2" takes the place as "b"Therefore, the slope and the y-intercept are -4 and 2 respectively.
Determining the coordinates of the y-intercept;
Note: The y-intercept of the line ALWAYS has an x-coordinate of 0.
⇒ Coordinates of y-intercept: (0, y-intercept) ⇒ (0, 2)
Final answers:Slope = -4Coordinates of y-intercept = (0, 2)________________________________________________________
18) y = x/7 - 5Clearly, we can tell that the equation is in slope intercept form.
Formula:
Slope intercept form: y = (m)x + (b) [m = Slope; b = y-intercept]
Let us compare the slope intercept form equation with the given equation to determine the slope and the y-intercept.
⇒ y = (m)x + (b) and y = x/7 - 5
When comparing both equations, we can observe that:
"x/7" takes the place as "m" "-5" takes the place as "b"Therefore, the slope and the y-intercept are x/7 and -5 respectively.
Determining the coordinates of the y-intercept;
Note: The y-intercept of the line ALWAYS has an x-coordinate of 0.
⇒ Coordinates of y-intercept: (0, y-intercept) ⇒ (0, -5)
Final answers:Slope = x/7Coordinates of y-intercept = (0, -5)________________________________________________________
19) y = x + 3Clearly, we can tell that the equation is in slope intercept form.
Formula:
Slope intercept form: y = (m)x + (b) [m = Slope; b = y-intercept]
Let us compare the slope intercept form equation with the given equation to determine the slope and the y-intercept.
⇒ y = (m)x + (b) and y = 1x + 3 [x = 1x]
When comparing both equations, we can observe that:
"1" takes the place as "m" "3" takes the place as "b"Therefore, the slope and the y-intercept are 1 and 3 respectively.
Determining the coordinates of the y-intercept;
Note: The y-intercept of the line ALWAYS has an x-coordinate of 0.
⇒ Coordinates of y-intercept: (0, y-intercept) ⇒ (0, 3)
Final answers:Slope = 1Coordinates of y-intercept = (0, 3)The radius of the earth is 6.371 X 10^3 km. Write the value of this scientific notation and express the radius in words.
Answers
Answer:
6371. six thousand three hundred and seventy-one
PLS PLS HELP HELP ME ITS EASY ITS FREE PONTS LOL
Answers
Answer:
92 degrees
Step-by-step explanation:
180-88
=92
~rere
4. Add
f(x)= 4x?+5x-1
g(x) = 2x2 + 5x+3
Answers
A. 3x² +6
Explanation:(f-g)(x) = f(x) -g(x) = (4x²+1) -(x²-5) . . . . . substitute the function definitions
... = 4x² +1 -x² +5 . . . . . . . . . . . eliminate parentheses
... = (4-1)x² +(1+5) . . . . . . . . . . . collect like terms
... = 3x² +6
A disadvantage of the Harvard step test is:
A. it is not accurate.
B. it requires too much equipment.
C. it is difficult to find the heart rate easily.
D. it is difficult to administer.
Answers
D) it is difficult to administer.
Step-by-step explanation:
Harvard step, main aim is to measure cardiovascular endurance. It is difficult to administer as, it creates problems while identity the cardio endurance of tall and short person.Pls ingore all of the questions below, but help me with the attached image
What is the only number that has the same number of letters as it's meaning? ...
What number doesn't have its own Roman numeral? ...
What is the only even prime number? ...
What is the smallest perfect number? ...
What is our current numerical system based on? ...
Is Pi a rational or irrational number?
Answers
Answer:
A = 51
Step-by-step explanation:
I'm not sure if it is correct but here is my working
180=41+2a+a-14
180=3a+27
153=3a
51=a
Answer:
a=51
Explaination-
ABC + ACB + BAC = 180°
(a-14)° + 2a + 41° = 180°
a=51
Pls help me and show work! Thank you <3
Answers
Answer: 15
Step-by-step explanation:
By the alternate interior angles theorem, [tex]5x+9=84 \longrightarrow x=\boxed{15}[/tex]
A cube has an edge length of 10 inches. What is its volume, in cubic in?
Answers
Answer: 1000
Step-by-step explanation: V=a to the 3rd power=10 to the 3rd power=1000
What's the answer to this?
Answers
Answer:
Q' = (-4, -2)
R' = (4, -2)
S' = (4, 2)
T' = (-4, 2)
Step-by-step explanation:
First, we can create a matrix to scale this rectangle by putting all the x coordinates in the top row and all the y coordinates in the bottom row and multiply it by 4.
Our initial matrix to multiply:
[tex]4\left[\begin{array}{cccc}-1&1&1&-1\\-2&-2&-1&-1\end{array}\right][/tex]
Moved to the origin:
[tex]4\left[\begin{array}{cccc}-1&1&1&-1\\-0.5&-0.5&0.5&0.5\end{array}\right][/tex]
Multiplied by four:
[tex]\left[\begin{array}{cccc}-4&4&4&-4\\-2&-2&2&2\end{array}\right][/tex]
This gives us the points of
Q' = (-4, -2)
R' = (4, -2)
S' = (4, 2)
T' = (-4, 2)
which are our answers.
PLEASE HELP!!!! A triangle has sides of lengths a=17, b=36, c=45 km.
Find the measures of the 3 angles
Enter your answer as a number; answer should be accurate to 2 decimal places.
Angle A =____?
Angle B = ____?
Angle C = ____?
Explain how you found the 3 angles below. Be sure to show all of your work.
Answers
Answers:
Angle A = 20.64 degreesAngle B = 48.29 degreesAngle C = 111.07 degreesYou may or may not have to type in the word "degrees", and/or use the degree symbol. I would ask your teacher for clarification.
A diagram is shown below.
============================================================
Explanation:
We'll need the law of cosines to solve for angle A.
a^2 = b^2 + c^2 - 2*b*c*cos(A)
17^2 = 36^2 + 45^2 - 2*36*45*cos(A)
289 = 3321 - 3240*cos(A)
289 - 3321 = -3240*cos(A)
-3032 = -3240*cos(A)
-3240*cos(A) = -3032
cos(A) = (-3032)/(-3240)
cos(A) = 0.935802
A = arccos(0.935802)
A = 20.64 degrees
which is approximate to 2 decimal places.
Note: The "arccos" refers to "arccosine" which is the same as inverse cosine (denoted as [tex]\cos^{-1}[/tex] on many calculators).
-----------------------------
Do a similar set of steps for angle B.
b^2 = a^2 + c^2 - 2*a*c*cos(B)
36^2 = 17^2 + 45^2 - 2*17*45*cos(B)
1296 = 2314 - 1530*cos(B)
1296 - 2314 = -1530*cos(B)
-1018 = -1530*cos(B)
-1530*cos(B) = -1018
cos(B) = (-1018)/(-1530)
cos(B) = 0.665359
B = arccos(0.665359)
B = 48.29 degrees
Also approximate to 2 decimal places.
-----------------------------
As you can probably guess by now, we could use the law of cosines to find angle C. But a much quicker shortcut is to use the fact that for any triangle, the interior angles always add to 180 degrees.
This shortcut is only possible since we know the two other angles.
Solve for C.
A+B+C = 180
C = 180-A-B
C = 180 - 20.64 - 48.29
C = 111.07 degrees
Like the others, this is approximate to 2 decimal places.
You can use a graphing tool like GeoGebra to confirm the answers. See below. Due to the SSS (side side side) triangle congruence theorem, only one triangle is possible. This means only one answer is possible per angle.
Find equation of a line with the given slope that passes through the given point. Write the equation in the form Ax + By = C.
M = -5, (-4,-8)
Answers
Answer:
5x + y = -28
Step-by-step explanation:
Hi there!
We're given that a line has a slope of -5 and contains the point (-4, -8)
We want to write the equation of this line in standard form
Standard form is given as ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be zero, and a cannot be negative
Before we write the equation in standard form however, we need to write it in slope-intercept form, which is y=mx+b, where m is the slope & b is the y intercept
As we are already given the slope, we can immediately plug that in for m in y=mx+b
y=-5x+b
Now to find b:
As the equation passes through the point (-4, -8), we can use its values to help solve for b
Substitute -4 as x and -8 as y:
-8 = -5(-4) + b
Multiply
-8 = 20 + b
Subtract 20 from both sides
-8 = 20 + b
-20 -20
__________
-28 = b
substitute -28 as b
y = -5x - 28
We found the equation in slope-intercept form, but remember, we want it in standard form
In standard form, both x and y are on the same side; so, let's move 5x to the other side; to do this, we need to add 5x to both sides
y = -5x - 28
+5x +5x
_________
5x + y = -28
Hope this helps!
Total points in a board game based on the average number of hours played is predicted using the least-square regression line, 9 = 280.3 + 85.7x, where y
represents the total points scored and x represents the average number of hours spent playing the game. A player plays the game for an average of 3 hours
and has a point total of 550. What is the residual for the player?
O 3.15
03
0-126
0-3.15
O 12.6
Answers
Using the line of best-fit, it is found that the residual for the player is of 12.6.
What is the residual for a line of best-fit?A residual is given by the difference between the observed point and the predicted point.
In this problem, the expected score over x hours is given by:
f(x) = 280.3 + 85.7x.
Hence, for 3 hours, the predicted score is given by:
f(3) = 280.3 + 85.7 x 3 = 537.4.
The observed score was of 550, hence the residual is given by:
R = 550 - 537.4 = 12.6.
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Order these numbers from least to greatest.
8.461, 169/20, 8 6/11, 8.49
Hurry please
Answers
Answer:
169/20, 8.461, 8.49, 8 6/11
Step-by-step explanation:
You can convert all of them to decimals. 169/20 = 8.45 and 8 6/11= 8.545. Then you order the from least to greatest.
Find the area of the shaded region. 10 ft 10 ft
Answers
Answer: Its 10 ft
Step-by-step explanation: because if one side is the number the other side is going to be the same number
please choose me as brainly
1. What is the surface area of the composite figure?
4 ft
8 ft
3 ft
2 ft
6 ft
Answers
Answer:
c. 132
Step-by-step explanation:
find the area for each space than add them for sa
a = l x w
sa = a
Julieta was offered a job that paid a salary of $49,000 in its first year. The
salary was set to increase by 3% per year every year. If Julieta worked at the
job for 21 years, what was the total amount of money earned over the 21
years, to the nearest whole number?
Answers
Answer:
he will get a total of 41%
Julieta has a job for $49000 which increases at the rate of 3% per year, so the money earned after 21 years is $79870.
What is Simple interest?A quick and simple way to figure out interest on that money is to use the simple interest approach, which adds interest at the same rate for each daily cycle, and it is to the initial principal amount.
A way to figure out how much interest will be charged on an amount of money at a specific rate and for a specific duration of time is by using simple interest.
As per the information received from the question,
Principle amount, P = $49000
Rate, R = 3%
Time, T = 21 years.
SI = ($49000 × 3 × 21)/100
SI = 30870
So, the total amount earned in 21 years is $30870, and the total money he is having after 21 years is $79870.
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Are EFG and HIJ similar?
Answers
If the area of a circle is 40 pi square cm, find the radius.
Answers
area equation is pi*r^2. divide by pi then square root. so the answer is the square root of 40
Answer:
√40 centimeters
Step-by-step explanation:
Given :
Area of circle = 40π cm²
===========================================================
Formula for area of a circle :
Area = πr²
===============================================================
Equating the given term and formula to find r :
⇒ 40π = πr²
⇒ r² = 40
⇒ r = √40 centimeters
Using the diagram below what is the measure of <1
The measure of <1=[m]
Answers
Answer:
The angle measure of 1 is 62 degrees.
Step-by-step explanation:
You need to the exterior angle theorem.
This means that all the exterior angles have to equal up to 360 degrees.
You need to add everything up which should equal 298 degrees.
Then subtract 360 by 298.
The angle measure of 1 is 62 degrees.
