Answer:
[tex]\displaystyle \large{y\prime = 2t \sin (2t) + 2t^2 \cos (2t)}[/tex]
Step-by-step explanation:
We are given a function:
[tex]\displaystyle \large{y = t^2 \sin (2t)}[/tex]
To differentiate a function, we are going to use the product rules since there are two functions which are t^2 and sin(2t) multiplying together.
From the product rules, [tex]\displaystyle \large{y = f(x)g(x) \to y\prime = f\prime (x) g(x)+f(x) g\prime (x)}[/tex]
Therefore, [tex]\displaystyle \large{y = t^2 \sin (2t) \to y\prime = (t^2)\prime \sin (2t) + t^2 (\sin (2t))\prime}[/tex]
Before we start differentiating, I’d like you to look at [sin(2t)]’. A function like this, you cannot just directly derive and answer. You need to use chain rules.
We know that, [tex]\displaystyle \large{y = \sin (x) \to y\prime = \cos (x)}[/tex] but what if the “x” is another function? Like sin(3x), sin(x^2) as examples. The insides are another function, can be expressed as fog(x) or gof(x) is composite function.
Basically, chain rule is a rule or formula for composite function and it’s the most common and useful as well as being always used in differentiation.
Chain Rules
[tex]\displaystyle \large{\frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx}}[/tex]
where u is another function in a bracket. From the formula above, it can be also written as:
[tex]\displaystyle \large{[f(g(x))]\prime = f(g(x))\prime \cdot g(x)\prime[/tex]
To simply say, you differentiate the whole function first then multiply with the chain or inner derived function.
So from the function, we obtain:
[tex]\displaystyle \large{y\prime = 2t \sin (2t) + t^2 \cos (2t) \cdot (2t)\prime}\\ \displaystyle \large{y\prime = 2t \sin (2t) + t^2 \cos (2t) \cdot 2}\\ \displaystyle \large{y\prime = 2t \sin (2t) + 2t^2 \cos (2t)}[/tex]
The factored form would be:
[tex]\displaystyle \large{y\prime = 2t ( \sin (2t) + t \cos (2t))}[/tex]
From above, for polynomial function, to differentiate, you can do by using the power rules.
Power Rules
[tex]\displaystyle \large{y = ax^n \to y\prime = nax^{n-1}}[/tex]
Solve for x.
3 (4-2x) = -2x
A)-1
B)1
C)2
D)3
[tex]3(4 - 2x) = - 2x[/tex]
Distribute 3 in the expression.[tex]12 - 6x = - 2x[/tex]
Solve the equation for x-term by making x as the subject.[tex]12 = - 2x + 6x \\ 12 = 4x \\ \frac{12}{4} = x \\ 3 = x[/tex]
Answer Check by substituting the value of x in the equation.[tex]3(4 - 2x) = - 2x \\ 3(4 - 2(3)) = - 2(3) \\ 3(4 - 6) = - 6 \\ 3( - 2) = - 6 \\ - 6 = - 6 \: \: \green{ \checkmark}[/tex]
The equation is true when x = 3. Therefore the answer is D. 3
Answer[tex] \large \boxed{x = 3} \: \: \sf{or} \: \: \large \boxed{ \sf{D \: \: choice}}[/tex]
Answer:
solution
Step-by-step explanation:
3 (4-2x)= -2x
12-6x= -2x
12= -2x+6x
12= 4x
12÷4= x
3= x
D
It snowed 134.46 inches on Monday and 8.3 inches on Tuesday. How much did it snow on Monday and Tuesday combined?
Answer:
142.76 inches
Step-by-step explanation:
This is a combination problem, so add the two quantities to find the sum.
134.46 inches + 8.3 inches = 142.76 inches
Fill in the blanks:
A perfect square is a ________ whose ________ value is an ________. If you ________ any integer you will always get a ________ number.
Answer:
A perfect square is a number whose product value is an integer. If you change any integer you will always get a even number.
Step-by-step explanation:
answer ???????????????????????
Answer:
6a + 6 is answer
Step-by-step explanation:
may be this is helpful!
PLEASE HELP WILL GIVE BRAINLIEST
A family has two cars. The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. During
one particular week, the two cars went a combined total of 1325 miles, for a total gas consumption of 75 gallons. How many gallons were consumed by each of
the two cars that week?
Answer:
40 and 35
Step-by-step explanation:
If we say the first car uses x gallons then the second car must use 75 - x gallons.
The distance travelled is the number of gallons used * the efficiency of the car.
20x + 15(75-x)=1325
20x + 1125 - 15x = 1325
5x = 200
x = 40
This means that the first car uses 40 gallons and the second car uses 75-40= 35 gallons
Which system of equations has only one solution? 0 4x+2y=8 -4x-2y=3 -5x+y = 6 5x-ya-6 0 -3x+4y= 2 3x-4y 0 0 2x+4y= 6 3x - 4y - 9
Answer:
D) 2X + 4Y = 6
3X - 4Y =9
Step-by-step explanation:
Hope this helps
Answer:
first one buddy
Step-by-step explanation:
Help please.
Solve for the unknown variable for the following similar shapes.
Help me figure out x= 2, 6, 3.75
9514 1404 393
Answer:
x = 2
Step-by-step explanation:
The product of secant lengths to the near and far circle intercepts is the same for both secants:
3 · (3+5) = 4 · (4+x)
24 = 4(4 +x) . . . . simplify
6 = 4 +x . . . . . . . .divide by 4
2 = x . . . . . . . . . subtract 4
The longest sea bridge, the Jiaozhou Bay Bridge in China, spans 26.4 miles. The longest sea bridge in the United States is the Lake Pontchartrain Causeway in Louisiana, which spans 41,940 yards. How much longer is the Jiaozhou Bay Bridge, in units of feet, than the Lake Pontchartrain Causeway
Answer:
2.57 yards longer
Step-by-step explanation:
Step one:
given data
We are told that the Jiaozhou Bay Bridge in China, spans 26.4 miles
Also, The longest sea bridge in the United States is the Lake Pontchartrain Causeway in Louisiana, which spans 41,940 yards
Required
Unit conversion from yards to miles
Step two:
let us convert 41,940 yards to miles
We know that 1 yard is 0.000568182 miles
hence 41,940 yards is x miles
cross multiply we have
x= 41,940*0.000568182
x=23.83 yards
Hence the difference in their lengths is
=26.4-23.83
=2.57 yards
Tyson is 6 feet 2 inches tail. There are 2.5 centimeters in 1 inch What is Tyson's height in centimeters
Answer:
187.96cm
Step-by-step explanation:
Answer:
187.96 centimeters tall
What is the formula for finding slope
Answer:
M = rise/run is the formula
Step-by-step explanation:
That's it
What is the area of the figure?
Answer:
252 in²
Step-by-step explanation:
Just separate them into different shapes and add their areas together.
Answer:
252 Inches
Step-by-step explanation:
We first section off all the areas we can, find the area of each of those, add them all up, and you get 252 inches.
A farmer notes that in a field full of horses and geese there are 36 heads and 106 feet. How many of each animal are there?
Answer:
17 horses and 19 geese
Step-by-step explanation:
Let x be the number of horses and y be the number of geese
We know that, horses have four feet and geese have 2 feet
It is given that
x+y=36 (i)
and
4x+2y=106 (ii)
Solve the two equations simultaneously by substitution,
From equation (i)
y=36-x (iii)
Substitute y with 36-x in equation (ii)
4x+2(36-x)=106
4x+72-2x=106
4x-2x=106-72
2x=34
x=17
Then
Substitute x=17 to equation (iii)
y=36-17=19
x=17, y=19
We therefore have 17 horses and 19 geese
Tyler sells 20 of his records (r) and has 74 left. Which equation best
represents this scenario?
Answer:
Equation: r-20=74
Step-by-step explanation:
So he started with 94. I got B
What is the solution to the equation? sqrtx + 3 = 12 HINT: It's not C.
A. 225
B. 81
C. 3
D. No solution
Given the equation: - 4 √x - 3 = 12
solve for x;
Divide both sides by -4 in [1]; we get;
√x - 3 = -3
Squaring both sides we get;
x -3 = (3)²
or
x - 3 = 9
Add 3 both sides we get;
x - 3 + 3 = 9 + 3
Simplify:
x= 12
Extraneous solution states that it is a root of a transformed equation that is not a root of the original equation because it was excluded from the domain of the original equation.
Substitute x= 12 in [1]
- 4√12 - 3 = 12
- 4√9 = 12
-4. 3 = 12
-12 = 12 False.
Therefore, the value of x is 12 and it is an extraneous solution.
Learn more about equations at
https://brainly.com/question/2972832
#SPJ2
Tim has 54 golf balls. He wants to put an equal number of golf balls in each of 9
baskets. How many golf balls will be in each basket?
CLEAR
SUBMIT
5 golf balls
6 golf balls
7 golf balls
8 golf balls
true or false determine key stage statement is true or false 1.a trapezoid has at least one pair of parallel sides
2.the legs of any trapezoid are congruent
here’s a picture .... 6th grade math
Answer:
The second pack with 18
Step-by-step explanation:
2.97/11= 0.27
4.74/18=0.26333
Answer: You should probably go for the $4.74
Step-by-step explanation:
Because you can pay that price and get 18 slices, but on the other hand, if you get the other you would be paying 2.97 for only ONE package of sliced cheese. So you would pay for the $4.74 package of cheese to get more for your money.
~I hope this was clear and answered your question~
the radius of a circle is 9 M what is the circle's circumference use 3.14 for pi
Answer:
56.52 is the circumference. If the radias is 9 and the diameter is then 18.
Step-by-step explanation:
Answer:
56.52 is the circumference. If the radias is 9 and the diameter is then 18.
Step-by-step explanation:
1. Simplify: (-9x3 + 4x2 – 5) - (14x2 - 10x - 3)
Show work please
Answer:
I got -9x^3-10x^2+10x-2
Step-by-step explanation:
Which equation represents the following table?
Answer:
y=2x-4
Step-by-step explanation:
gdgdvdjsksevsg
11/(x+9)=5
I am struggling with this question. Is there a solution?
Answer:
x=-6.8
[tex] \\ step \: by \: step \: explanation \\ \frac{11}{(x + 9)} = 5 \\ 11 = 5(x + 9) \\ 11 = 5x + 45 \\ 5x = 11 - 45 \\ 5x = - 34 \\ x = \frac{ - 34}{5} = - 6.8[/tex]
Convert to an improper fraction.
2 1/5
Answer:
11/5
Step-by-step explanation:
2 x 5 = 10
10 + 1 = 11
11/5
Solve the system of equations-2x+3y=-1 and 7x-8y=16 by combining the equations
Answer:
( 40 37 , − 39 37 )
Step-by-step explanation:
Perry had $23 to spend on 4 raffle tickets. After buying them he had 15 dollars left. How much did each ticket cost
Answer: 5.75
Step-by-step explanation:
Answer:
5.75
Step-by-step explanation:
you divide 23 by 4 and it will give you your answer . the first answer is also correct
Please help! 15 points!!
Answer:
none of the answers are correct because 2 and 5 are across
( don't know how to explain it) and they have to be the same
Solve 3|x – 6| = 12. Question 13 options: No solutions x = 4 or x = –4 x = 10 or x = 2 x = 2
Answer:
x=10
Step-by-step explanation:
divide by 3 on both sides then add 6 on both sides
Answer:
the answer is x=10, x=2
Step-by-step explanation:
hope that helps
A composite figure is formed by combining a square and a triangle. Its total area is 60.5 ft2. The area of the triangle is 35.5 ft2. What is the length of each side of the square? Complete the explanation.
Answer:
5 feet
Step-by-step explanation:
Total Area = Area of Triangle + Area of Square
60.5 = 35.5 + Area of Square (s²)
s² = 25
s = 5
Answer:
5 feet
Step-by-step explanation:
if i did the math correctly then its 5 feet have a nice day
SOLVE:
24 - 24 : 3 + 1
Answer
17
its a division sign for : so 24-24 divided by 3 + 1