Answers
[tex]y=\dfrac{sin(x^2)}{x^3}[/tex]
Apply the quotient rule:
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{x^3\frac{\mathrm d\sin(x^2)}{\mathrm dx}-\sin(x^2)\frac{\mathrm dx^3}{\mathrm dx}}{(x^3)^2}[/tex]
Chain and power rules:
[tex]\dfrac{\mathrm d\sin(x^2)}{\mathrm dx}=\cos(x^2)\dfrac{\mathrm dx^2}{\mathrm dx}=2x\cos(x^2)[/tex]
Power rule:
[tex]\dfrac{\mathrm dx^3}{\mathrm dx}=3x^2[/tex]
Putting everything together, we have
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{x^3(2x\cos(x^2))-\sin(x^2)(2x\cos(x^2))}{(x^3)^2}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x^3\cos(x^2)-2x\sin(x^2)\cos(x^2)}{x^6}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x^2\cos(x^2)-\sin(2x^2)}{x^5}[/tex]
When [tex]x=\sqrt{\frac\pi2}[/tex], we have
[tex]\cos\left(\left(\sqrt{\dfrac\pi2}\right)^2\right)=\cos\left(\dfrac\pi2\right)=0[/tex]
[tex]\sin\left(2\left(\sqrt{\dfrac\pi2}\right)^2\right)=\sin(\pi)=0[/tex]
so the derivative is 0.
Related Questions
Solve the equation
2r-3 3
———— = —
4 5
Answers
10r -15 = 12
10r = 27
r = 27/10
r = 2.7
Explanation
(2r - 3)/4 = 3/5
Use cross multiplication:
5(2r - 3) = 3 x 4
10r - 15 = 12
10r = 12 + 15
10r = 27
r = 27/10
.........................help
Answers
Your answer is last part(e part)
Irrational
Hope it helps :)
I only have 30 sec left help
Answers
Answer:
17
Step-by-step explanation:
first find the value of N
(8x2 + 9) - (3x2 + 2x + 5)
Answers
Answer:
5x^2 -2x +4
Step-by-step explanation:
(8x^2 + 9) - (3x^2 + 2x + 5)
Distribute the minus sign
(8x^2 + 9) - 3x^2 - 2x - 5
Combine like terms
5x^2 -2x +4
the H.C.F OF 64,96,128
Answers
Answer:
32
Step-by-step explanation:
[tex] 64= 2^6[/tex]
[tex] 96= 2^5\times 3[/tex]
[tex] 64= 2^7[/tex]
Common factor = [tex] 2^5[/tex]
Therefore,
H.C.F OF 64,96,128 = [tex] 2^5[/tex] = 32
Find the value of x.
Answers
Answer:
or,6x+6=9x-9
or,6+9= 9x-6x
or,15=3x
or,15/3=X
therefore,X=5ans
Answer:
x=3
Step-by-step explanation:
32/24=(6x+6)/(9x-9)
simplify by 8 in the left
4/3=6(x+1)/9(x-1)
simplify by 3 in the right
4/3=2(x+1)/3(x-1)
*3 *3
4=2(x+1)/(x-1)
(x+1)/(x-1)=4/2=2
so x+1=2(x-1)=2x-2
-x -x
1=x-2
+2 +2
3=x
so x=3
verify (6*3+6)/(9*3-9)=32/24
24/18=32/24
simplify by 6 in the left
4/3=32/24
simplify by 8 in the right
4/3=4/3 TRUE
Suppose that the function fis defined on the interval (-2,2) as follows.
find f(-1) f(0.5) f(1)
Answers
Answer:
Step-by-step explanation:
Hello,
-1 <= -1 < 0
so f(-1)=-1
0 <= 0.5 < 1
so f(0.5)=0
1 <= 1 < 2
so f(1)=1
Thank you.
Can Someone please help me....Like pretty please....It would mean everything to me, Please help me out 1. 2. 3. 4. 5.
Answers
================================
Explanation:
SSS stands for "Side side side" indicating there are 3 pairs of sides that are same length. Visually we use tickmarks to show how the sides pair up. Eg: sides that have 1 tickmark only are the same length. If we know that all 3 pairs of sides are congruent, then we have enough info to conclude the triangles are congruent.SAS means "side angle side". The angle is between the two sides. The sides in question are the ones with tickmarks to indicate how they pair up. We have two angles and a side between them. So we use ASA this time. It stands for "Angle side angle". This is slightly different from AAS.We'll use AAS here. The side is not between the two angles. So this is why AAS is different from ASA. Some books may call "AAS" as "SAA", but they're the same thing. HL stands for hypotenuse leg. This only applies to right triangles (since the hypotenuse is a special term for the longest side of a right triangle). The hypotenuse is always opposite the 90 degree angle. This is the only time when SSA will work. Otherwise, SSA is ambiguous and it is not a valid congruence theorem.Find the sum of the sequence. 42+43+44+45+...+107
Answers
Answer:
4917
Step-by-step explanation:
Given sequence:
42, 43, 44, 45, ..., 107This is AP with common difference of 1, the first term of 42 and the last term of 107
Number of terms:
107 - 42 + 1 = 66Sum of the terms:
Sₙ= 1/2*n*(a₁+aₙ)Sₙ= 1/2*66*(42+107) = 4917Answer is: 4917
Cooper bought a washing machine with a sticker price of $900. If he paid $12
a week for two years, what was the approximate markup rate on the washing
machine?
A. 27.9%
B. 38.7%
C. 69.3%
D. 72.1%
Answers
1 year = 52 weeks. 2 years would be 104 weeks.
$12 per week x 104 weeks = $1248 total.
1248 - 900 = $348
348 /900 = 0.3866 = 38.7%
The answer is B
an administrator is asked to file papers in a box which has the following dimensions:height 15cm, width 300mm and depth 0.2m. calculate the volume of the box. give your answer in cm
Answers
Answer:
900cm^3
Step-by-step explanation:
1 cm= 10 mm
x=300mm (criss cross)
1cm*300mm/10mm= 10mm*x/10mm
30cm=x
30cm=300mm
1m=100cm
0.2m=x
1m*x/1m=0.2m*100cm/1m
x=0.2*100cm
x=20cm
0.2m=20cm
l=15cm
w=30cm
h=20cm
v=l*w*h
v=15cm*30cm*20cm
v=450cm^2*20cm
v=900cm^3
Answer:
9000cm^3
Step-by-step explanation:
Width:300mm=30cm
Height:15cm=15cm
Depth:0.2m=20cm
V=DxWxH
V= 20x30x15
V=9000cm^3
Which of the following equations represents a line parallel to the line given by y=5x +9?
Answers
Answer:
y = 5x + 1
Step-by-step explanation:
Lines that are parallel to each other on a graph would have the same slope but different y-intercepts. When option A's equation is graphed along with the line given in the question, the lines appear to be parallel.
Option A should be the correct answer.
What is the meaning of the ∝ sign?
Answers
Answer:
"proportional to"
Step-by-step explanation:
The sign ∝ means 'is proportional to'. This is used to show that one variable of value is proportional to another value or variable.
Example:
x ∝ y ('x' is proportional to 'y')Hope this helps.
real numbers are ____ integers
OPTION A: Always
OPTION B: Sometimes
OPTION C: Never
Answers
Answer:
B
Step-by-step explanation:
Which of the following is an example of the difference of two squares
a 22 - 9
B + +9)
C23 -9
D(2 - 9)
Answers
Complete Question: Which of the following is an example of the difference of two squares?
A x² − 9
B x³ − 9
C (x + 9)²
D (x − 9)²
Answer:
A. [tex] x^2 - 9 [/tex].
Step-by-step explanation:
An easy way to spot an expression that is a difference of two squares is to note that the first term and the second term in the expression are both perfect squares. Both terms usually have the negative sign between them.
Thus, difference of two squares takes the following form: [tex] a^2 - b^2 = (a + b)(a - b) [/tex].
a² and b² are perfect squares. Expanding [tex] (a + b)(a - b) [/tex] will give us [tex] a^2 - b^2 [/tex].
Therefore, an example of the difference of two squares, from the given options, is [tex] x^2 - 9 [/tex].
[tex] x^2 - 9 [/tex] can be factorised as [tex] x^2 - 3^2 = (x + 3)(x - 3) [/tex].
for simplicity, let X=M G = 1 I = 2 if you like decimals C = 3 + 0.75Y or if you prefer fractions C = 3 + 3/4Y the simple multiplier is equal to
Answers
Answer:
the simple multiplier is equal to 4
Step-by-step explanation:
In an economic model,
Y= C + I + G + (X - M)
the average expenditure Y must be equal to the totality of the output
If C = 3 + 0.75Y
where;
marginal propensity to consume MPC = 0.75
Then,
Y = 3 + 0.75Y + 2 + 1
Y = 6+0.75 Y
Y - 0.75 Y = 6
0.25 Y = 6
Y = 6/0.25
Y = 24
However, the simple multiplier can be expressed as:
[tex]=\dfrac{1}{1 - MPC}[/tex]
[tex]=\dfrac{1}{1 - 0.75}[/tex]
[tex]=\dfrac{1}{0.25}[/tex]
= 4
What is 325.623 rounded to the nearest tenth?
Answers
Explanation: because 1-4 rounds down and 5-9 rounds the numbers up
PLEASE HELP ME, I DON'T UNDERSTAND!
Answers
Hello,
First of all, dividing by 0 is not defined we will take x different from 1/3 (because -1+3x= 0 <=> x = 1/3)
Then, dividing this polynomial by (-1+3x) means that you have to have Q(x), a polynomial of degree 1 and R a real number such that
[tex]\dfrac{9x^2-6x+2}{-1+3x}=Q(x)+\dfrac{R}{-1+3x}\\\\\text{We can multiply by (-1+3x)}\\\\9x^2-6x+2=(-1+3x)Q(x)+R[/tex]
Either you do the division and you can select the correct answer or you check the different answer to identify the correct one.
For instance, for the first answer, let's estimate
[tex](-1+3x)(3x-3)+\dfrac{-1+3x}{3x-1}\\\\=-3x+3+9x^2-9x+1\\\\=9x^2-12x+4[/tex]
and this is not equal to our initial polynomial, so this is not the correct answer.
Second Answer.
[tex](-1+3x)(3x-1)+\dfrac{-1+3x}{3x-1}\\\\=-3x+1+9x^2-3x+1\\\\=9x^2-6x+2[/tex]
And this is our initial polynomial. So this is the [tex]\large \boxed{\sf \bf \text{correct answer}}[/tex]
Thank you.
PS: in this example, you can even notice the following (so it makes the division trivial)
[tex](3x-1)^x=9x^2-6x+1 \\\\\text{So}\\\\9x^2-6x+2= (3x-1)^2+1\\\\\text{And, then.}\\\\\dfrac{9x^2-6x+2}{-1+3x}=3x-1+\dfrac{1}{3x-1}[/tex]
Let (6,-5) be a point on the terminal side of θ. Find the exact values of sin θ, sec θ, and tan θ.
Answers
Answer:
sinθ = -5/√61
secθ = √61/6
tanθ = -5/6
Step-by-step explanation:
From the given coordinate (6, -5), x = 6 and y = -5. This shows that the point lies in the 4th quadrant. In the fourth quadrant, only cos θ is positive, both sin θ and tan θ are negative.
Let us get the value of the radius 'r' first before calculating the trigonometry identities.
Using the Pythagoras theorem;
[tex]r^2 = x^2 + y^2\\r^2 = 6^2 + (-5)^2\\r^2 = 36+25\\r^2 = 61\\r = \sqrt{61}[/tex]
Using SOH, CAH, TOA to get the trigonometry identities;
Given x = 6, y =5 and r = √61
[tex]sin \theta = opp/hyp = y/r\\sin \theta = 5/\sqrt{61} \\[/tex]
Since sin θ, is negative in the fourth quadrant, [tex]sin \theta = -5/\sqrt{61} \\[/tex]
[tex]cos \theta = adj/hyp = x/r\\cos \theta = 6/\sqrt{61} \\[/tex]
[tex]sec \theta = \frac{1}{cos \theta} \\sec \theta = \frac{1}{6/\sqrt{61} } \\sec \theta = \frac{\sqrt{61} }{6}[/tex]
For tanθ:
[tex]tan \theta = \frac{opp}{adj} = \frac{y}{x} \\tan \theta = \frac{5}{6}\\[/tex]
Since tan θ, is negative in the fourth quadrant, [tex]tan \theta = -5/6[/tex]
[tex]SIN\Theta=\frac{-5}{\sqrt{61} }[/tex],
[tex]SEC\Theta=\frac{\sqrt{61} }{6}[/tex]
[tex]TAN\Theta=\frac{-5}{6}[/tex].
Given coordinate of point be (6, -5).
So the point lies in the 4th quadrant. In the fourth quadrant, only cos θ is positive, both sin θ and tan θ are negative.
Since (6, -5) is on the terminal side that puts us in the fourth quadrant. If we plot that point and draw a diagonal to it from the origin, we will be able to draw a right triangle with that diagonal as the hypotenuse.That means the adjacent side is 6 and opposite side it -5.
By Pythagorean theorem, we find that the hypotenuse
[tex]H=\sqrt{6^{2} +(-5)^{2} }[/tex]
[tex]H=\sqrt{61}[/tex]
We know from trigonometric ratios,
[tex]SIN\Theta=\frac{Perpendicular}{hypotenuse} \\[/tex]
[tex]SIN\Theta=\frac{5}{\sqrt{61} }[/tex]
Since [tex]SIN\Theta[/tex] is negative in 4th quadrant,
so,
[tex]SIN\Theta=\frac{-5}{\sqrt{61} }[/tex]
Similarly,
[tex]SEC\Theta=\frac{hypotenuse}{base}[/tex]
[tex]SEC\Theta=\frac{\sqrt{61} }{6}[/tex]
And,
[tex]TAN\Theta=\frac{perpendicular}{base}[/tex]
[tex]TAN\Theta=\frac{-5}{6}[/tex]
Hence, [tex]SIN\Theta=\frac{-5}{\sqrt{61} }[/tex], [tex]SEC\Theta=\frac{\sqrt{61} }{6}[/tex] and [tex]TAN\Theta=\frac{-5}{6}[/tex].
For more details follow the link:
https://brainly.com/question/1201366
Three weeks ago John bought stock at 4944; today the stock is valued at 4971g. We could say the stock is performing at which of the
following?
A. Below par
B. Above par
C. On par
D. Par equality
Answers
Answer:
Step-by-step explanation:
B: Above par. Stock has gained a bit of value since it was purchased.
Andre has been practicing his math facts. He can now complete 135 multiplication
facts in 90 seconds.
a. If Andre is answering questions at a constant rate, how many facts can he
answer per second?
b. Noah also works at a constant rate, and he can complete 75 facts in 1 minute.
Who is working faster? Explain or show your reasoning.
Answers
135 : 90
b. Noah can answer 1.25 facts per second.
75 : 60
Andre is working faster.
Division is one of the four fundamental arithmetic operations. Andrew is faster than Noah.
What is Division?The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given that Andre can now complete 135 multiplication facts in 90 seconds.
A.) If Andre is answering questions at a constant rate, then the number of facts that Andre can answer per second can be written as,
Number of facts per seconds = 135 facts / 90 seconds
= 1.5 facts per seconds
B.) Noah also works at a constant rate, and he can complete 75 facts in 1 minute. Therefore, the number of facts that Noah can answer per second can be written as,
Number of facts per seconds = 75 facts / 60 seconds
= 1.25 facts per seconds
Now, since the number of facts that Andrew can read in a second is 1.5 facts, while the number of facts that Noah can read in a second is 1.25 facts.
Hence, Andrew is faster than Noah.
Learn more about Division:
https://brainly.com/question/369266
#SPJ2
When a number is increased by 3 and that number is doubled, the result is -8. What was the original number?
Answers
Answer:
The original number is -7.
Step-by-step explanation:
In this section, we are trying to figure out a mysterious number. Let's call this number y. To find the value of y, we need to create an equation. Our equation will be based on clues hidden in the text. So, what do we know?
- A number, aka y, is increased by 3. (y+3)
-That number is doubled. 'That number' refers to the answer of y+3. So, (y+3)x2.
-Finally, the end result is -8.
Great! Now we know our equation: 2(y+3)=-8. We need to figure out what y equals, so let's isolate the y term with some algebra.
2(y+3)=-8; Original formula
2y+6=-8; Distribute the (y+3)
2y=-14; Carry the 6 to the other side of the equation.
y=-7: Divide
Thus, our mysterious number is -7. Hope this helps:)))
Give 5 different names for this line? Will give to the brainliest! Thank you.
Answers
Step-by-step explanation: The figure shown here is a straight path between points that extends forever in both directions, so it's called a line.
Since a line doesn't have endpoints, it doesn't matter which
two points on the line we use to name the line.
I have attached 5 possible names for the line below.
Answer:
DE ED DF FD and line lStep-by-step explanation:
e Because lines continue infinitely, we can name them forwards or backwards. We can also use any two points on a line to identify it, unlike with rays or segments. The l and the end of the line can also be used to identify it.
Different names for the line include: DE ED DF FD and line l.
I'm always happy to help :)What is the y-intercept of the graph of the following data? a (-1, 0) b (0, 3) c (0, -3) d (1, 6).
Answers
Answer:
b
Step-by-step explanation:
The y- intercept is the point on the y- axis where the graph crosses.
On the y- axis the x- coordinate is always zero.
From the table when x = 0 , y = 3, thus
(0, 3 ) is the y- intercept → b
Change the decimal to fraction form or mixed number form and reduce if possible 73.437
Answers
Answer:
73.437= 74 437/1000
Step-by-step explanation:
73.437 to fraction.
Let's acknowledge the presence of a decimal and how many digit we have after the decimal point.
Actually, the numbers after the decimal point will determine the amount of 10s to be divided with.
What I'm saying is this
73.437= 74 437/1000
In this case, 437 is a prime number
So
73.437= 74 437/1000
Which expression is equivalent to -6(-2/3+2x)
Answers
Answer:
Step-by-step explanation:
Using the Distributive Property of Multiplication, we get
12
---- - 12x. or 4 - 12x, or 4(1 - 3x)
3
can u answer this plz
Answers
Answer:
The answer is 14 :)
Step-by-step explanation:
We have,
∠PQS = 90°∠PQR = 76°Find the measure of ∠ x ?
∠PQR + ∠RQS = ∠PQS
⇒ 76° + x = 90°
⇒ x = 90° - 76°
⇒ x = 14°
An elevator descends into mine shaft at the rate of 6m/min. If the descend starts from 10m above the ground level , how long will it take to reach the shaft which is 350m below the ground level?
Answers
Answer: Hi!
So first, I'm going to convert "350 below ground level" to -350, as this is what "below ground level" represents.
Now, we should find the total distance traveled. Take the absolute value of -350 (350) and add it to 10, the metres above ground level. This is 360.
We already know the rate of travel; 6m/min. All we have to do now is divide the total distance (360) by the rate of travel (6)!
360 ÷ 6 = 60
So, it took 60 minutes, or one hour, for the elevator to travel down the shaft!
Hope this helps!
What is the standard form of nine million, twenty thousand, twenty-nine
Answers
Answer:
9000000+20000+20+9
Step-by-step explanation:
simplify -4(x+6)+2(x-2)
Answers
Answer:
[tex]-2x-28[/tex]
Step-by-step explanation:
We can apply the distributive property then combine like terms for a simpler equation.
[tex]-4(x+6)+2(x-2)\\\\-4x-24+2x-4\\\\-2x-28[/tex]
Hope this helped!
Answer:
-2x -26
Step-by-step