[tex]\displaystyle f(x)=\sin(3x)\\\\\\f'(x)=\lim_{h\to0}\dfrac{\sin(3(x+h))-\sin(3x)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{\sin(3x+3h)-\sin(3x)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{2\cos\left(\dfrac{3x+3h+3x}{2}\right)\sin\left(\dfrac{3x+3h-3x}{2}\right)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{2\cos\left(\dfrac{6x+3h}{2}\right)\sin\left(\dfrac{3h}{2}\right)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{2\cos\left(\dfrac{6x+3h}{2}\right)\sin\left(\dfrac{3h}{2}\right)}{\dfrac{3h}{2}}\cdot\dfrac{3}{2}[/tex]
[tex]\displaystyle f'(x)=\lim_{h\to0}2\cos\left(\dfrac{6x+3h}{2}\right)\cdot\dfrac{3}{2}\\\\f'(x)=\lim_{h\to0}3\cos\left(\dfrac{6x+3h}{2}\right)\\\\f'(x)=3\cos\left(\dfrac{6x+3\cdot 0}{2}\right)\\\\f'(x)=3\cos\left(\dfrac{6x}{2}\right)\\\\f'(x)=3\cos(3x)[/tex]
The derivative of sin 3x using first principles is; 3cos(3x)
We want to find the derivative of sin 3x using first principles.
Step 1;
f'(x) = [tex]\lim_{h \to \ 0} \frac{(sin3(x + h)) - sin(3x)}{h}[/tex]
Step 2; Expand the bracket to get;
f'(x) = [tex]\lim_{h \to \ 0} \frac{(sin(3x + 3h)) - sin(3x)}{h}[/tex]
Step 3: According to trigonometric identities, we know that;
sin A - sin B = [tex]2cos\frac{A + B}{2} sin\frac{A - B}{2}[/tex]
Applying that to the answer in step 2 gives;
f'(x) = [tex]\lim_{h \to \ 0} \frac{2(cos\frac{(3x + 3h + 3x)}{2}) sin\frac{(3x + 3h - 3x)}{2})}{h}[/tex]
Step 4; Simplify the brackets to obtain;
f'(x) = [tex]\lim_{h \to \ 0} \frac{2(cos\frac{(6x + 3h)}{2}) sin\frac{(3h)}{2})}{h}[/tex]
Step 5; Rewrite the denominator to get;
f'(x) = [tex]\lim_{h \to \ 0} \frac{2(cos\frac{(6x + 3h)}{2}) sin\frac{(3h)}{2})}{\frac{3h}{2}*\frac{2}{3}}[/tex]
Step 6; Input the limit of 0 for h to get;
f'(x) = [tex]\frac{2(cos\frac{(6x)}{2}) sin\frac{(0)}{2})}{\frac{0}{2}*\frac{2}{3}}[/tex]
⇒ f'(x) = [tex]\frac{2(cos3x)}{2/3} \frac{ 0}{{0}}[/tex]
0/0 = 1. Thus;
f'(x) = 3cos(3x)
Read more about differentiation from first principles at; https://brainly.com/question/5313449
Help please, I would really appreciate it. :)
Answer:
9, 13, 17, 21
Step-by-step explanation:
If x=2,
y=1+4(2)
y=9
This goes on, like a pattern. If x increases by 1, y inreases by 4. So, if y=3, x=13. If x=4, y=17, and so on.
There are 2 Rectangles, a red one and a blue one.The Blue rectangle has the perimeter of 250 km. If the area of the red rectangle is 2,500 square kilometers, what are its dimensions?
(Both of the rectangles have the same perimeter)
Answer:a
Step-by-step explanation:
Answer:
length = 100
width = 25
Step-by-step explanation:
Let L = length of red rectangle
Let H = height of red rectangle
Equation1: L+H=125 : we know the perimeter is 250 so L+H is 125
Equation2: L*H=2,500 : we know the area is 2,500
Equation3: L=125-H : subtracted H from both sides of Equation1
Equation4: (125-H)*H=2,500 : substituted "125-H" for L into Equation2
Solve equation4:
(125-H)*H=2,500 multiple terms on left side of equation
125H - H^2 = 2,500 rearrange into standard form
H^2 - 125H + 2,500 = 0
At this point you can "brute force" the answer with the quadratic formula:
H = (125 ± SQRT(125^2 - 4*1*2500) ) / 2
H = 100 or H = 25 : actually these are L and H
You could also factor the equation:
(H - 100) * (H - 25) = 0 : gives same answe
20 POINTS!!! Please Help! No nonsense answers please!
Answer:
[tex](2-\sqrt{7}, 2+\sqrt{7})[/tex]
Step-by-step explanation:
A wave has a time period of 0.2 s Calculate the frequency of the wave.
Answer:
[tex]\huge\boxed{f = 5\ Hz}[/tex]
Step-by-step explanation:
Given:
Time period = T = 0.2 sec
Required:
Frequency = f = ?
Formula:
f = 1/T
Solution:
f = 1/0.2
f = 5 Hertz
Answer:
[tex] \boxed{\sf Frequency \ (f) \ of \ the \ wave = 5 \ Hz} [/tex]
Given:
Time Period (T) = 0.2 s
To Find:
Frequency (f) of the wave
Step-by-step explanation:
[tex] \sf Frequency (f) = \frac{1}{Time Period (T)} [/tex]
[tex] \sf f = \frac{1}{0.2} [/tex]
[tex] \sf f = \frac{1}{0.2} \times \frac{10}{10} [/tex]
[tex] \sf f = \frac{10}{2} [/tex]
[tex] \sf f = \frac{ \cancel{2} \times 5}{ \cancel{2}} [/tex]
[tex] \sf f = 5 \: Hz[/tex]
A survey of 100 people found that 35 people exercise in
the morning, 45 people exercise in the afternoon, and 20
people exercise at night. Tara claims that 35:55, 45:80,
and 20:65 are possible ratios from this data. Jim claims
that 35:100, 45:100, and 20:100 are possible ratios from
this data. Who is correct? Explain.
Answer:
Jim's claim is correct
Step-by-step explanation:
Total survey=100 people
Morning exercise=35 people
Afternoon exercise=45 people
Night exercise=20 people
Morning exercise : Total survey
=35 : 100
Afternoon exercise : Total survey
=45 : 100
Night exercise : Total survey
=20 : 100
Jim's claim is correct because in finding the ratio, one has to relate it with the total people involved in the survey.
Tara's claim however seems to relate one variable with two other variables
Example:
35 : 55
Morning exercise : (morning exercise + night exercise)
35 : (35+20)
35 : 55
Answer:
Sample Response: Jim is correct because 35:100, 45:100, and 20:100 are part-to-whole comparisons. There are other possible part-to-part ratios from the data.
Observe how the land division was planned for the preparation of a vegetable garden.
In it, lettuce, tomatoes, carrots, beets and corn will be planted.
Determine the monomial that represents the measure:
1-lettuce
2-beets
3-tomato
4-corn
5-carrot
Answer:
1-lettuce 4ab x 12ab = 48a²b²
2-beets 3ab x 3ab = 9a²b²
3-tomato 4ab x 5ab = 20a²b²
4-corn 2ab x 3ab = 6a²b²
5-carrot 12ab x 3ab = 36a²b²
Step-by-step explanation:
Over what axis was the square reflected in the first example?
The x-axis
The y-axis
Answer:
The x-axis!
Step-by-step explanation:
In the function above, the slope will be multiplied by -4, and the y-value of the y-intercept will be decreased by 1 unit. Which of the following graphs best represents the new function?
Answer: Answer Z :)
Step-by-step explanation:
Basic math for 20 points + brainliest!
Answer:
Look at photo
Step-by-step explanation:
It took Amir 2 hours to hike 5 miles. On the first part of the hike, Amir averaged 3 miles per hour. For the second part of the hike, the terrain was more difficult so his average speed decreased to 1.5 mile per hour.
Answer:
Times
first part x = 1,33 h second part y = 0,66 h
distances d₁ (first part ) d₁ = 4 miles d₂ (second part ) d₂ = 0,999 miles
Step-by-step explanation: IMPORTANT NOTE: EVEN PROBLEM STATEMENT DID NOT ASK ANY QUESTION WE WILL ASSUME QUESTION ARE: LENGTH ( IN MILES ) AND SPENT TIME OF EACH PART OF THE HIKE
We formulate a two-equation system according to:
x = time for the first part
y = time for the second part
then x + y = 2 or y = 2 - x
And 3 m/h * x(h) + 1,5 m/h * y (h) = 5
3*x + 1,5*y = 5
3*x + 1,5 * ( 2 - x ) = 5
3*x + 3 - 1,5*x = 5
1,5*x = 2
x = 2/1,5 (h)
x = 1,33 (h)
And y = 2 - 1,33 y = 0,66 (h)
Distances are
first part d₁ = 3*1,33 d₁ = 4 miles
second part d₂ = 1,5*0,66 d₂ = 0,999 miles
the points (-2,1), (1,1), (0,-2), and (-3,-2) are vertices of a polygon. what type of polygon is formed by these points? A. rectangle B. square C. pentagon D. parallelogram
Answer:
[tex]\boxed{\sf D. \ Parallelogram}[/tex]
Step-by-step explanation:
When we graph the points, the polygon is a quadrilateral with opposite parallel sides. The type of polygon formed by these points is a parallelogram.
Answer:
Parallelogram
Step-by-step explanation:
We'll graph all of the points from which we'll come to know that it is a parallelogram having opposite sides equal and parallel.
See the attached file for more understanding.
in a 10 team league, each teams play every other team exactly twice. find the total number of games played in the league
Addition can be defined as the process of adding two numbers. The total number of games played in the league is 90.
What is Addition?Addition can be defined as the process of adding two numbers such that the result is the combined value of the two numbers.
Given that in a 10-team league, each team play every other team exactly twice. Therefore, the total number of games that will be played by the first team is 18, similarly, the number of games that will be played by the second team is 16.
Therefore, as mentioned above the series will continue with a common difference of -2 and will continue till 0. Thus, the total number of games played in the league is,
Total number of games = 18 + 16 + 14 + 12 + 10 + 8 + 6 + 4 + 2 = 90
Learn more about Addition:
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Write the equation for the line that passes through the points (4, 5) and
(6,9). *
O y = 2x-3
O y = 0.5x - 3
O y = 0.5x + 6
O y = 2x + 6
None of the Above
Answer:
Step-by-step explanation:
(9-5)/6-4)= 4/2= 2
y - 5 = 2(x - 4)
y - 5 = 2x - 8
y = 2x - 3 is the solution
Answer:
the answer is y = –2x – 5 hope this helps:) give brainliest if it does
Step-by-step explanation:
i got it right on edge
Web site W receives orders for its products every day. What is the standard deviation of the numbers of orders that Web site W received daily for the past 5 days?(1) The average (arithmetic mean) number of orders that Web site W received per day for the past 5 days is equal to the greatest of the numbers of orders that Web site W received daily for the past 5 days.(2) The range of the numbers of orders that Web site W received daily for the past 5 days is equal to 0.
Answer:
The standard deviation is zero
Step-by-step explanation:
Given that:
Web site W receives orders for its products every day.
What is the standard deviation of the numbers of orders that Web site W received daily for the past 5 days?
If :
(1) The average (arithmetic mean) number of orders that Web site W received per day for the past 5 days is equal to the greatest of the numbers of orders that Web site W received daily for the past 5 days.
SO, IF the average (arithmetic mean) is greatest , therefore, this implies that the number of orders per day remains the same. Then the standard deviation will be zero because the set of values for the number of orders per day for the five days is the same.( i.e contains identical numbers).
.(2) The range of the numbers of orders that Web site W received daily for the past 5 days is equal to 0.
The range is the difference between the greatest value and the smallest value.
i.e
greatest value - smallest value = 0
greatest value = smallest value
Therefore , the range is zero and the standard deviation will remain the same (zero)
with a tax rate of 0.0200, a tax bill of 1050 corresponds to an assessed valuation of
Answer:
$52,500
Step-by-step explanation:
1050/0.0200=52500
Answer:
B. 52,500
Step-by-step explanation:
-5y+6>26 does the inequality sign flip?
Answer:
Yes
Step-by-step explanation:
Answer:
y < -4
Step-by-step explanation:
-5y+6>26
subtract 6 from each side
-5y+6-6>26-6
-5y > 20
Divide each side by -5. remembering to flip the inequality
-5y/-5 < 20/-5
y < -4
On a plane trip, baggage over 40 pounds is charged at the rate per pound of 1% of the one-way fare. The charge for a bag weighing 52 pounds on a trip where the one-way fare is $98 is:
Answer:
$11.76 is the charge for bag.
Step-by-step explanation:
Given:
One way fare = $98
Weight of bag = 52 pounds
Rate per pound Charges on baggage over 40 pounds = 1% of the one-way fare
To find:
Charge for bag = ?
Solution:
Pounds more than 40 pounds = Weight of baggage - 40 pounds
[tex]\Rightarrow 52-40 = 12\ pounds[/tex]
Charges on extra baggage = 1% of one-way fare multiplied by pounds more than 40.
Here one way fare is $98.
So, charges on extra baggage will be:
[tex]1\%\ of\ 98 \times (52-40) \\\Rightarrow 1\%\ of\ 98\times (12)\\\Rightarrow \dfrac{1}{100}\ of\ (98 \times 12)\\\Rightarrow \dfrac{1}{100}\times (98 \times 12)\\\Rightarrow \bold{\$11.76}[/tex]
So, the charge for the baggage is $11.76.
David’s family is driving from New York to Florida. They know the distance they will travel is about 1100 miles . If a map has a scale of 1 in = 80 mi about how far will the trip be on the map ?
You can do the proportion
1 inch/ 80 miles =x inch/ 1100 miles
1100=80x
11oo divided by 80 equals 13.75
The trip would be about 13.75 inches on the map
Feel free to brainliest :)
Answer:
13.75 inches
Step-by-step explanation:
To find an estimated distance on the map, we can simply create a proportion.
Let X represent the unknown distance in inches on the map.
1100 miles / 80 miles = X inches / 1 inch
Now let's solve for X.
X inches = (1100 miles / 80 miles) * 1 inch
X inches = 13.75 inches
So the approximate travel distance on the map will be 13.75 inches.
Write a real-life problem that you can solve using a 45 degree, -45 degree, -90 degree triangle with an 18-ft hypotenuse. Describe your solution
Answer:
A triangle with angles:
"45°, 45°, 90°"
Is a triangle rectangle, with two catheti of equal length.
Now, there is a lot of problems that you can solve with this:
"Suppose that you want to find the height at which you need to attach a wire in a tree, such that the distance between the tree and the ground is 18ft, and the distance between the base of the tree and the two points where the wire is fixed is exactly the same"
Well, here we have a triangle rectangle with a hypotenuse of 18 ft, with cathetus of equal length (the catheti are the tree and the distance between the base of the tree and the point where the wire is attached at the ground)
And because the catheti are equal, then the angles are 45°, 45° and 90°.
9/2 divided by 1/4= ? in simplest form
Answer: 18
Do Keep Change Flip (KCF)
Keep: 9/2
Change: ÷ into ×
Flip: 1/4 into 4/1
Your new problem should be 9/2×4/1
Multiply
9/2×4/1=36/2
36/2=18
Final Answer: 18
The angle of elevation of top of pole from point x to horizontal ground is 32degree. If x is 68m away from the foot. Calculate height FT
Answer:
h = 108.8 m
Step-by-step explanation:
x = tanФ h
x = 68m
Ф = 32°
h = unknown
68 = tan(32°) * h
h = 68 / tan(32°)
h = 108.8 m
Solve: 5x2 + 25x = 0
Answer:
x = -0.4
x = -(2/5)
Answer:
x = ± √5
Step-by-step explanation:
Please indicate exponentiation by using the symbol " ^ ":
5x^2 + 25x = 0
Divide all three terms by 5. We get:
x^2 + 5 = 0, or x^2 = -5
Then x = ± √5
What is the volume of this rectangular prism?
4/3
4/3
4/3
Answer:
[tex]\frac{64}{27}[/tex] cm³
Step-by-step explanation:
The volume (V) of the prism is calculated as
V = lbh ( l is length, b is breadth and h is height ), thus
V = [tex]\frac{4}{3}[/tex] × [tex]\frac{4}{3}[/tex] × [tex]\frac{4}{3}[/tex] = [tex]\frac{4^3}{3^3}[/tex] = [tex]\frac{64}{27}[/tex] cm³
Answer:
64/27 would be your answer.Step-by-step explanation:
I am more than happy to answer anymore questions. If needed an explanation I can put one in the comments.
Which parent function is f(x)= |3|
A. The quadratic parent function
B.The linear parent function
C. An exponential parent function
D. The absolute value parent function
Answer:
D. Absolute value parent function
we can know fro the symbol |x| in the question written f(x)= |3|
Write an expression for the shaded area
Answer:
4x(x+2) - x(3x+5)
Step-by-step explanation:
the area of the whole box is 4x(x+2)
to find the area of the shaded portion you have to subtract the area of the tiny box from the big box
the area of the tiny box is x(3x+5)
so, 4x(x+2) - x(3x+5) is the expression you can use to find the area of the shaded portion
find the area of a sector with a central angle of 150 and a diameter of 7.8 cm
Answer:
19.9 cm²
Step-by-step explanation:
The following data were obtained from the question:
Angle at the centre (θ) = 150°
Diameter (d) = 7.8 cm
Area of sector =.?
Next, we shall determine the radius.
This can be obtained as illustrated below:
Radius (r) = Diameter (d) /2
r = d/2
Diameter (d) = 7.8 cm
Radius (r) =.?
r = d/2
r = 7.8/2
r = 3.9 cm
Finally, we shall determine the area of the sector as follow:
Angle at the centre (θ) = 150°
Radius (r) = 3.9 cm
Pi (π) = 3.14
Area of sector (A) =.?
A = θ/360 × πr²
A = 150/360 × 3.14 × 3.9²
A = 15/36 × 3.14 × 15.21
A = 19.9 cm²
Therefore, the area of the sector is 19.9 cm²
What is the inverse of the function g(x)=-3(x+6)? g^-1(x)=
Answer:
[tex]g^{-1}(x)=-6-\frac{x}{3} =-\frac{x}{3} -6[/tex]
Step-by-step explanation:
First assign a letter "y" to g(x) and get rid of parenthesis on the right:
[tex]g(x)=-3\,(x+6)\\y=-3x-18[/tex]
Now, solve for "x":
[tex]3x=-18-y\\x=\frac{-18-y}{3}\\x=-6-\frac{y}{3}[/tex]
now replace y with x, and call x : [tex]g^{-1}(x)[/tex]
[tex]x=-6-\frac{y}{3} \\g^{-1}(x)=-6-\frac{x}{3}[/tex]
Answer:
-6 - [tex]\frac{x}{3}[/tex]
Step-by-step explanation:
Simplify 18-2[x + (x - 5)].
O8-4x
28 - 4x
28 - 2x
Answer:
28-4x
Step-by-step explanation:
Step 1: Open most inner bracket and simplify
=18-2(x+x-5)
=18-2(2x-5)
Step 2: Expand brackets by multiplying 2 in and simplify
=18-2(2x)-2(-5)
=18-4x+10
=28-4x
Therefore the answer is 28-4x
What is the value of m in the equation 1/2m - 3/4n = 16, when n = 8?
Answer: m= 44
Step-by-step explanation:
1/2m - 3/4n = 16 when n is 8 put it into the equation and solve for m.
1/2m - 3/4(8) = 16
1/2m - 6 = 16
+6 +6
1/2m = 22
m = 44
Answer:
44
Step-by-step explanation:
● (1/2 )× m - (3/4) × n = 16
Replace n by 8 and the fraction by decimal numbers (1/2 = 0.4 and 3/4 =0.75)
● 0.5 × m - 0.75 × 8 = 16
● 0.5m - 6 = 16
Add 6 to both sides
● 0.5 m - 6 + 6 = 16+ 6
● 0.5 m = 22
Multiply both sides by 2
● 0.5m × 2 = 22 × 2
● m = 44
Translate the following phrase into an algebraic expression using the variable m. Do not simplify
the cost of renting a car for one day and driving m miles if the rate is $48 per day plus 50 cents per mile
Answer:
y = 0.5X + 48
Answer:
48 + 0.50m
Step-by-step explanation:
m, the variable, equals to the number of miles driven. Since there is a base fare of $48, that will be the constant. It is $0.50 per mile, so it's 0.50m. Substituting for m, the miles driven, will give you the final cost.
