e^3x.cos4x.sin2x hii please solv this you have to differentiate
Answer:
[tex]y = e^{3x}.cos4x.sin2x[/tex]
[tex]=> y' =- 3e^{3x}.4sin4x.2cos2x=-24.e^{3x}.sin4x.cos2x[/tex]
[tex]dy=y'.dx => dy = -24e^{3x}.sin4x.cos2x.dx[/tex]
Step-by-step explanation:
The function [tex]e^3^x[/tex].cos4x.sin2x on differentiating gives the solution as 2[tex]e^3^x[/tex]cos2x.cos4x - 4[tex]e^3^x[/tex]sin2x.sin4x + 3[tex]e^3^x[/tex]cos4x.sin2x.
What is Product rule in Differentiation?Product rule in differentiation states that, for two functions f(x) and g(x),
[tex]\frac{d}{dx}[/tex] [f(x).g(x)] = f(x) . [tex]\frac{d}{dx}[/tex][g(x)] + g(x) . [tex]\frac{d}{dx}[/tex][f(x)]
The question is to differentiate y = [tex]e^3^x[/tex].cos4x.sin2x
We have three functions here.
Let u = [tex]e^3^x[/tex] and v = cos4x.sin2x
[tex]\frac{d}{dx}[/tex] [u . v] = u [tex]\frac{d}{dx}[/tex][v] + v [tex]\frac{d}{dx}[/tex][u]
= [tex]e^3^x[/tex] [tex]\frac{d}{dx}[/tex] [cos4x.sin2x] + cos4x.sin2x [tex]\frac{d}{dx}[/tex] [[tex]e^3^x[/tex] ]
= [tex]e^3^x[/tex] [tex]\frac{d}{dx}[/tex] [cos4x.sin2x] + cos4x.sin2x (3[tex]e^3^x[/tex])
[tex]\frac{d}{dx}[/tex] [u . v] = [tex]e^3^x[/tex] [tex]\frac{d}{dx}[/tex] [cos4x.sin2x] + 3[tex]e^3^x[/tex]cos4x.sin2x
Let the above equation be equation E.
Again apply the product rule for [tex]\frac{d}{dx}[/tex] [cos4x.sin2x].
Let u' = cos4x and v' = sin2x
[tex]\frac{d}{dx}[/tex] [u'. v'] = u' [tex]\frac{d}{dx}[/tex][v'] + v' [tex]\frac{d}{dx}[/tex][u']
= cos4x [tex]\frac{d}{dx}[/tex][sin2x] + sin2x [tex]\frac{d}{dx}[/tex][cos4x]
= cos4x [2cos2x] + sin2x [-4sin4x]
= 2cos2x.cos4x - 4sin2x.sin4x
Substituting this is equation E, we get,
[tex]\frac{d}{dx}[/tex] [u . v] = [tex]e^3^x[/tex] [2cos2x.cos4x - 4sin2x.sin4x] + 3[tex]e^3^x[/tex]cos4x.sin2x
= 2[tex]e^3^x[/tex]cos2x.cos4x - 4[tex]e^3^x[/tex]sin2x.sin4x + 3[tex]e^3^x[/tex]cos4x.sin2x
Hence the function [tex]e^3^x[/tex].cos4x.sin2x on differentiating gives 2[tex]e^3^x[/tex]cos2x.cos4x - 4[tex]e^3^x[/tex]sin2x.sin4x + 3[tex]e^3^x[/tex]cos4x.sin2x.
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60 POINTS PLS HELP WILL MARK BRAINLIEST EXPLAIN TOO PLS
Step-by-step explanation:
we need to find the slope of each line.
the slope is the ratio y/x indicating how many units y changes, when x changes a certain amount of units.
parallel lines have the same slope.
for a perpendicular line x and y in the slope ratio are put upside down, and the sign is flipped (+ to - and vice versa).
a.
2x - 8y = -24
2x + 24 = 8y
y = 2/8 x + 24/8 = 1/4 x + 3
the slope is 1/4 (always the factor of x).
4x + y = -2
y = -4x - 2
the slope is -4 = -4/1.
this line is therefore perpendicular to the first line.
x - 4y = 4
x - 4 = 4y
y = 1/4 x - 4/4 = 1/4 x - 1
the slope is 1/4.
this line is therefore parallel to the first line.
b.
3x - 9y = 9
9y = 3x - 9
y = 3/9 x - 9/9 = 1/3 x - 1
the slope is 1/3
3y = x + 12
y = 1/3 x + 4
the slope is 1/3.
this line is therefore parallel to the first line.
2x - 6y = 12
6y = 2x - 12
y = 2/6 x - 12/6 = 1/3 x - 2
the slope is 1/3.
this line is therefore parallel to the first line.
I believe the answer is B.
Answer:
Yes, B is correct, the horizontal line test is used to test if an INVERSE is a function.
Step-by-step explanation:
Sketch the graph of this linear equation
4y = -7x + 1
Answer:
use desmos to graph it
.....
A man walked 6 kilometres per hour. How far does he walk between 9:30a.m 12 noon
Answer:
15
Step-by-step explanation:
if he walks 6 kilometres per hour multiply 6 times 2 and you get 12 and he walked for half an hour and half of 6 is 3 so 12 plus 3 equals 15
Answer:
15 km
Step-by-step explanation:
given:
1 hour=6 km
9:30--12:00=2.5 hours
•°•2.5×6=15 km
margo is repaying a loan from her parents. she has already paid $315 and still owes them $1245. write an equation to find the original amount a of the loan
Answer:
n-315=1245
Step-by-step explanation:
n stands for the original amount of the loan. Margo has paid $315, so the original number minus what Margo has paid, and the equality is the amount that Margo still owes.
Maths question, someone pls help me solve it
what do many prefixes and suffixes have in common?
The gitman siblings are in a fight, and they split up the play-room, but sarah needs/wants 1/3 of the house to make a cake. which part(s) of the house, should she get?
bathroom
Step-by-step explanation:
19 - 6n = - 5 - 3 (2n - 6)
Answer:
Its 50
Step-by-step explanation:
3y=9-12x I need the slope for this equation and the steps
Answer:
slope = -4
Step-by-step explanation:
3y = 9 - 12x
Rearrange the right-hand side:
3y = - 12x + 9
Next, Divide both sides by 3 to isolate y:
[tex]\frac{3y}{3} = \frac{-12x + 9}{3}[/tex]
y = -4x +3 this is the slope-intercept form where the slope, m = -4, and the y-intercept, b = 3.
Therefore, the slope = -4.
Please mark my answers as the Brainliest if you find this helpful :)
20 points and brainliest!
Express each sentence below as an equation or inequality.
1. Bob has two less than half of the document of points Leroy has.
2. To be in the platinum tier for a ranked video, you must have at least 1000 ranked points.
Answer
Step-by-step explanation:
B=Bob, b=2-(1/2xL)
L= leroy
P<1000
Which of the following is a characteristic of a line?
[tex]\huge\rm\purple{\underline{Line:-}}[/tex]
➜ A line is a figure in geometry which has only length with no breadth in a two dimensional plane , and extended infinitely in opposite directions .
➜ A line may be of any length and breadth . An infinite number of combination of long, short , thick or thin lines can Accord to their application unify , divide , balance , or unbalance a pictorial area . This emotion dynamic is set up by lines measures .
⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀
[tex]\large\sf\orange{\underline{Characteristics\:of\:line:}}[/tex]
Line type : dotted , short dashed , long dashed and continuous line.Line width : extra dark , thick , medium annd thinLine quality : the quality of line depends largely upon the drawing medium⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀
Tristen is making cookies and cream ice cream to sell at the school fair. He making 80 gallons of ice cream. He wants to make sure there is a full cookie in every 1/4 cup of ice cream. If there are 16 cups in a gallon, how many cookies will trustees need to make the ice cream? I need help asap
Answer:
5120 cookiesStep-by-step explanation:
Find the number of cups in 80 gallons:
80*16 = 1280 cupsNow multiply the number of cups by 4 since each cup of ice cream is equivalent of 4 cookies:
1280*4 = 5120Middle school math pls help
Answer:
2 3/4
Step-by-step explanation:
You need to find the greatest common factor of 4 and 2 then you multiply the 2 by 2 to get a 4 and multiply the 1, then you add those together to get 2 3/4.
The sides of a triangle are in the ratio 12:17: 25 and its perimeter is 540cm. The area is:
a) 1000 sq.cm.
b) 5000 sq.cm.
c) 9000 sq.cm.
d) 8000 sq.m
1000
Step-by-step explanation:
Find the height of the triangle using the Pythagoras theorem
Then, use it to calculate the area of the triangle
A toy factory can produce approximately 36,000 building blocks in just one minute! The function B(t)=36,000t approximates the total number of blocks produced over t minutes. In this context, what is the largest possible domain of B(t)?
Answer:
all real numbers greater than or equal to 0
Step-by-step explanation:
All real numbers greater than or equal to 0.
2r=5s/2-s/4 (solve for s)
Answer:
s=8r/9
Step-by-step explanation:
2r=5s/2-s/4 multiply both sides by 4
8r=10s-s (5s times 4 = 20s and 20s/2=10s) combine like terms
8r=9s divide by 9 to isolate s
8r/9=s
18+ (-30)=
helpppppp
Answer:
[tex]18 + ( - 30) = 18 - 30 = - 12[/tex]
I hope I helped you^_^
help me with this pelases
Answer:
32 square units
Step-by-step explanation:
You can split this shape into four different shapes:
2 unit by 2 unit triangle
2 unit by 2 unit square
2 unit by 6 unit triangle
To find the length of the big triangle, add the lengths of the small triangle,the square,and the bigger leg of the other triangle:
2 + 2 + 6 = 10
10 unit by 4 unit triangle
Then solve all these areas:
( 2 x 2 ) / 2 = 4 / 2 = 2
2 x 2 = 4
( 2 x 6 ) / 2 = 12 / 2 = 6
( 10 x 4 ) / 2 = 40 / 2 = 20
Then add all these areas together to get the total area of the composite shape:
2 + 4 + 6 + 20 = 32
Higher Order Thinking A farmer grows
128 red tomato
plants and 102 yellow tomato plants. Each plant produces
about 32 tomatoes. The farmer plans to
sell each tomato
for a $2. Explain how to find a reasonable estimate for the
total amount of money the farmer will earn if she sells all
of the tomatoes.
Answer: 14720 dollars, or $14720
Step-by-step explanation:
128 red tomato plants plus 102 yellow tomato plants = 230 tomato plants in total.
230 plants with 32 tomatoes each = 7360 tomatoes in all
7360 x 2 dollars = 14720 dollars
PLEASE HELP ME WITH THIS ONE
Answer:
b answer
Step-by-step explanation:
hope helpful
if wrong sorry
I need help. I’m a little bit confused
Answer: 65 degrees
Explanation:
The adjacent angle directly above angle 8 is congruent to the 115 degree angle (due to the corresponding angles theorem). This only works because p || q and q || r, so by the transitive property of parallel lines, we know that p || r.
Since the 115 degree angle and angle 8 pair up to form a straight line, we know that the two angles must add to 180 degrees
115+(angle 8) = 180
angle 8 = 180 - 115
angle 8 = 65 degrees
Answer:
[tex]m[/tex]∠8 = 65°
Step-by-step explanation:
The other side (angle) of 115 is [tex]n[/tex] and [tex]n =[/tex] ∠8
To find [tex]n[/tex] you need to subtract 180 - 115 giving you 65, and since n is angle 8, angle 8 is also 65 since the angles have a state of congruence...
What does this mean
Find the area and perimeter of the shape
Please help.
A sports outlet received a shipment of
baseball gloves. Of the gloves, 13 were
black and the rest were tan. If there were
85 gloves in the shipment, how many were
tan gloves? Write an equation and solve.
Step-by-step explanation:
72 tan gloves and 13 black
Which mathematical operation is being used here?
Eight and some number
Answer:
All math operation
Basic Operations. The basic arithmetic operations for real numbers are addition, subtraction, multiplication, and division.
Step-by-step explanation:
evaluate the expression when z= -5
100 divided (-z2)
Answer:the anwser is 4
Step-by-step explanation:
You buy 50 feet of fence to place around a rectangular yard. If the length of the yard is 13 feet, what is the constraint for the width of the yard? Let w represent width *
Step-by-step explanation:
a fence represents the circumference, the perimeter of the lot or yard.
remember, a rectangle has 2 parallel sides called the length, and 2 parallel sides called the width (altogether 4 sides).
therefore
perimeter = 2×length + 2×width
or with short variables
p = 2×l + 2×w
so, now we have 50 ft of fence available for the perimeter. and the length l = 13 ft.
since we have 2 lengths in the perimeter, these 13 ft are twice (2×13 = 26 ft) in the perimeter.
now, how much fence do we have left for the width ?
well, 50 - 26 = 24 ft
and again, this is the size of 2 sides (2×width) :
p = 2×l + 2×w
50 = 2×13 + 2×w = 26 + 2×w
2×w = 24
w = 12 ft
so, the width of the yard must not be bigger than 12 ft.
c) Sarah and Maya must split the $15 they earned
scorekeeping a volleyball game. Sarah says, "There
is only one way to split this money, we both get
$7.50." Maya argued that there were an infinite
number of ways to divide up the money. Who is
correct? Prove their argument.
(I really need help, who is right, and tell me why please!)
Answer:
I think that Maya is right because the question doesn't state that they had to split it equally, you could split it infinite ways.
Step-by-step explanation:
You could give one person 8$ and the other7$. you could do it infinitely.
When the same probability is assigned to each outcome of a sample space, the experiment is said to have _______ ________ outcomes.
Answer:
Equally likely
Step-by-step explanation:
Hope this is right!