Answer:
Given,
y=x³ ,0≤x≤2
We have to find the surface area of the surface by rotating the curve about the x axis.
For rotation about the x axis, the surface area formula is given by-
s=2π∫ᵇₐ y√1+(y)² dx
y=x³
y'=3x²
By rotating the curve y=x³ about the x axis in the interval [0,2]
s=2π∫₀²(x³)√1+(3x²)² dx
let u=1+9x⁴
du=36x³dx
dx/36x³
Substituting u and du in the integral,
s= 2π∫₀²(x³)√u du/36x³
s= 2π∫₀²√u du
s= 2π/36.2/3[u.3/2]₀²
s= π/27[(145)³/²-(1)³/²]
s= π/27 [1746.03-1]
s= π/27 [1745.03]
s= 64.67π
s= 64.67(3.14)
s=203.06 square units.
therefore, the exact surface area is 203.06 square units.
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Answer:
In order to find the surface area obtained by rotating the curve we need to find surface area for rotation along x axis then substituting values in the integral.
Given: y=3x, for x is in [1,125] about the y axis.
y=x³ ,0≤x≤2
Lets find the surface area of the rotating curve,
Finding surface area for rotation along x-axis,
s=2π∫ᵇₐ y√1+(y)² dx
y=x³
y'=3x²
By rotating the curve y=x³ about the x axis in the interval [0,2]
s=2π∫₀²(x³)√1+(3x²)² dx
Assuming u =1+9x⁴
du=36x³dx
=dx/36x³
Substituting respective values of u and du in the integral,
s= 2π∫₀²(x³)√u du/36x³
s= 2π∫₀²√u du
s= 2π/36.2/3[u.3/2]₀²
s= π/27[(145)³/²-(1)³/²]
s= π/27 [1746.03-1]
s= π/27 [1745.03]
s= 64.67π
s= 64.67(3.14)
s=203.06 square units.
hence, the surface area is 203.06 square units.
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I NEED HELP WITH THIS ASAP! Find x and y
Answer: D
Step-by-step explanation: a^2+b^2=c^2
so use y value for b2 and 6 square root 3 as a and check with it.
Is there anyone who help me in my math work
Answer:
LCM=72
Step-by-step explanation:
l.c.m by prime factorization
a)18,24
factor of 18=2*3*3
factor of 24=2*2*2*3
common and remaining factor=2*3*3*2*2= 72
Una estrategia de cálculo mental con
números decimales consiste en buscar
parejas de números cuya suma sea un
número entero. Aplica esta estrategia para
calcular mentalmente:
a. 15,75 + 1,2 + 0,25
b. (–1,8) + 2,45 + (–0,20)
c. 3,5 + 11,8 + 12,5
d. 7,38 – 1,5 + 2,62
Esta estrategia se puede aplicar sumando 15,75 + 0,25, –1,8 + –0,20, 3,5 + 12,5 y 2,62 + 7,38 antes de sumar el tercer número dado en cada caso.
¿En qué consiste está estrategia?La estrategia propuesta consiste en sumar dos números decimales que den como resultado un número entero antes de sumar el tercer número decima. Por ejemplo si teneos 1,4 + 0,6 + 1,2, se debe sumar primero 1,4 + 0,6 lo que es igual a 2 antes de sumar el 1,2.
¿Por qué utilizar esta estrategia?Este estrategia es beneficiosa porque facilita sumar números decimales.
¿Cómo aplicar está estrategia?15,75 + 1,2 + 0,25 = 16 (0,25+15,75) + 1,2 = 17,2 (–1,8) + 2,45 + (–0,20) = -2 (-1,8-0,20) + 2,45 = 0,453,5 + 11,8 + 12,5 = 16 (12,5+3,5) +11,8 = 27.87,38 – 1,5 + 2,62 = 10 (7,38+2,62) + 2,62 = 12,62Aprenda más sobre números decimales en: https://brainly.com/question/24620232
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True or false? the patient should be given a receipt for payments on account even if the account is not paid in full.
Answer:
Step-by-step explanation:
true
Answer:
False because the account isn't full
4. Which of the following can be used
to support the idea that the set of
polynomials is closed under
multiplication?
A (5x-1)(3x² +4x)
B
(9x³-5)(2x-17)
(10x0.5-8)(5x0.5 +4)
D(2x¹5x¹)(7x-2x5)
The option that can be used to support the idea that the set of polynomials is closed under multiplication is; Option C: (10x^(0.5) - 8)(5x^(0.5) + 4)
What is the Closure property under multiplication?When multiplying polynomials, the variables' exponents are added, according to the rules of exponents. It is pertinent to note that the exponents in polynomials are whole numbers. The whole numbers are closed under addition, which guarantees that the new exponents will be whole numbers. Thus, we can also say that the polynomials are closed under multiplication.
Now, looking at the options, we can say that option C is the only polynomial that is closed under multiplication because its' variables and exponents will not change;
(10x^(0.5) - 8)(5x^(0.5) + 4)
The output will retain the same thing.
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Help me for this easy question which is no for me!!!!
Answer:
4c=12
c=3
Step-by-step explanation:
Since 4c's make up one 12, it is safe to assume that 4c=12. This results in c=3 once simplified.
Answer:
4c = 12.
Step-by-step explanation:
There are 4 of the same objects marked c.
Find the value of n in this equation.
Answer:
D. 9=========================
GivenTriangle with:
Base of n² -3,Midsegment of 39.To findThe value of n.SolutionAs per definition of midsegment, it is connecting the midpoints of two sides and its length is half the length of the opposite side of the triangle.
So we have:
(n² - 3)/2 = 39Solve it for n:
n² - 3 = 78n² = 81n = √81n = 9Correct choice is D.
Consider this equation.
Use the graph to find the approximate solutions to this equations
The equation be 2(x-2)-5=√x+3-1 then the graphical solution of the equations exists approximately x = 3 and x = 6.
What is the solution of the equation?The solution of an equation creates that equation true.
The equation of can be simplified, therefore:
2(x-2)-5=√x+3-1
simplifying the above equation, we get
2x -9 =√x+2
4 x²-37x + 79 = 0
The graphical solution of the equations exists at approximately x = 3 and
x = 6
In ending, the solution of an equation makes the equation true.
Therefore, the graphical solution of the equations exists approximately x = 3 and x = 6
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A student is constructing a pair of perpendicular lines using a compass and ruler. Here are her first steps:
Step 1: The student draws her first line and labels it l. She marks a point A (not on the first line) for the second line to pass through.
Step 2: She puts the compass point on A and draws an arc that intersects l at two points. She labels the points B and C.
Step 3: Without changing the compass setting, she puts the compass point on B and draws a large arc.
What should be her next step?
The next step she should take is to use her ruler to join the given point to the point where the arcs intersect.
Steps in constructing perpendicular linesPlace your compass on the given point Draw an arc across the line on each side of the given point. Do not adjust the compass width when drawing the second arcFrom each arc on the line, draw another arc on the opposite side of the line from the given point. The two new arcs will intersect.Use your ruler to join the given point to the point where the arcs intersect.Use your compass and ruler to draw a perpendicular line from each given point to the line segmentFrom this, we can deduce that her next step is to use her ruler to join the given point to the point where the arcs intersect
Thus, the next step she should take is to use her ruler to join the given point to the point where the arcs intersect.
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
B) x-intercept: (6, 0)
y-intercept: (0, 7)
Step-by-step explanation:
Given equation: [tex]7x + 6y = 42[/tex]
What are the x- and y-intercepts?
The x-intercept is the point where the line intersects the x-axis. In short, it is when y = 0 — [tex](x, y) \Rightarrow (x, 0)[/tex]. The y-intercept is where the line intersects the y-axis, which is when x = 0 — [tex](x, y) \Rightarrow (0, y)[/tex].
Find the x-intercept (by substituting 0 for y):
[tex]\\\implies 7x + 6y = 42\\\\\implies 7x + 6(0) = 42\\\\\implies 7x = 42\\\\\implies \dfrac{7x}{7}=\dfrac{42}{7}\\\\\implies \boxed{x=6}[/tex]
Coordinate: [tex](6, 0)[/tex]
Find the y-intercept (by substituting 0 for x):
[tex]\\\implies 7x + 6y = 42\\\\\implies 7(0) + 6y = 42\\\\\implies 6y = 42\\\\\implies \dfrac{6y}{6}=\dfrac{42}{6}\\\\\implies \boxed{y=7}[/tex]
Coordinate: [tex](0, 7)[/tex]
Which graph shows the solution to this system of in
y>-1/3x+1
y> 2x-3
Answer:
Step-by-step explanation:
the graph is down below
I need help finding the quotient of this equation in simplified form.
by breaking it down u can write it as
15p^-4/_20p^-12 * q^-6/q^-3
15/-20=-3/4
using law of indices we have
-3/4p^-4+12 * q^-6+3
-3/4p^8q^-3
the answer is the first own
answer the last question that is blank
The solutions to the given quadratic equation are as follows:
x = 1.10, x = 10.9.
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which:
[tex]\Delta = b^2 - 4ac[/tex]
For this problem, the equation in item D is:
-x² + 12x - 12 = 0
x² - 12x + 12 = 0
Hence the coefficients are:
a = 1, b = -12, c = 12.
Then the solutions to the equation are found as follows:
Delta = (-12)² - 4 x 1 x 12 = 96x1 = 0.5(12 + sqrt(96)) = 10.9x2 = 0.5(12 - sqrt(96)) = 1.10The solutions are:
x = 1.10, x = 10.9.
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the area of a piece of land is 4.08km^2. it is bought at a piece of $6000 per square km. calculate the total cost of the land, giving our answer to the nearest $100
Answer:
22480.000
Step-by-step explanation:
Cost of 1km²=6000
So,
Cost of 4.08km²=6000x4.08
=22480.000
I don't know what nearest $100 means tho maybe nearest hundredth but I'm not sure.
The total cost nearest 100 is = $22500.
What is area?Modern mathematics heavily relies on the concept of area. The area is the quantity that shows the amount of space occupied by a two-dimensional figure or shape or planar lamina in the plane. Simply put, the area is the amount of cloth or other material with the specified thickness needed to build a model of the form or the quantity of paint required to cover the shape's surface in a single layer, or "coat," of paint.
According to the given Information:Cost of 1km2 = 6000
So,
Cost of 4.08km2 = 6000 * 4.08
= 22480.000
Rounding off to 100;
Cost = 22500.00
Hence,
Total cost of the land nearest 100 is = $22500.
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Select the correct answer. What is the value of the limit lim x 2 (x^2+3x+1/x^3+x+1) ? A. B. 1 C. D.
So by direct evaluation we can see that the limit when x tends to 2 is equal to 1.
How to get the value of the limit?
Here we want to get the limit:
[tex]\lim_{x \to \ 2} \frac{x^2 + 3x + 1}{x^3 + x + 1}[/tex]
First, we can try to evaluate directly in x = 2 and see if it does not generate any problem, we will get:
[tex]\lim_{x \to \ 2} \frac{x^2 + 3x + 1}{x^3 + x + 1} = \frac{2^2 + 3*2 + 1}{2^3 + 2 + 1} = 1[/tex]
So by direct evaluation we can see that the limit when x tends to 2 is equal to 1.
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write the expression as the sine or cosine of an angle
The expression, written as the sine of an angle is sin (7π/10)
Trigonometry IdentitiesFrom the question, we are to write the given expression as the sine or cosine of an angle.
The given expression is
sin(π/5)cos(π/2) + sin(π/2)cos(π/5)
Let A = π/5
and
B = π/2
Thus, we get
sinA cosB + sinB cosA
From the given information, we have that
sin(A ± B) = sinA cos B ± cosA sinB
∴ sin(A + B) = sinA cos B + cosA sinB
Now,
sinA cosB + sinB cosA = sinA cosB + cosA sin B
∴ sinA cosB + sinB cosA = sin (A + B)
Put A = π/5
and
B = π/2
sinπ/5 cosπ/2 + sinπ/2 cosπ/5 = sin (π/5 + π/2)
sinπ/5 cosπ/2 + sinπ/2 cosπ/5 = sin (7π/10)
Hence, the expression, written as the sine of an angle is sin (7π/10)
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(3x^{4} +3x^{3}+5x^{2})-(x^{4}-6x^{3}+5x^{2} )
Answer: x^{3}(2x+9)
Step-by-step explanation:
Eliminate redundant parentheses:
(3x^{4}+3x^{3}+5x^{2})-1(x^{4}-6x^{3}+5x^{2})
3x^{4}+3x^{3}+5x^{2}-1(x^{4}-6x^{3}+5x^{2})
Distribute:
^{4}+3x^{3}+5x^{2}{-1(x^{4}-6x^{3}+5x^{2})}
3x^{4}+3x^{3}+5x^{2}
Combine like terms UNTIL YOU FIND ONE FACTOR
35 Points + Brainest
Answer:
5/12a + 1/3b
Step-by-step explanation:
2/3a + 1/6b + (-1/6a) + 3/18b + (-1/12a)
[2/3a + (-1/6a) + (-1/12a)] + [3/18b + 1/6b]
5/12a + 1/3b
Use a right-hand sum with 4
intervals to approximate the area
under f(x) = 4 - x² between
x = 0 and x = 2.
Answer:
17 / 4
Step-by-step explanation:
To find the right sum, you need to....
Step #1: Find Δx
Step #2: Find [tex]x_k[/tex]
Step #3 Make the right-hand sum equation: ∑[tex]^n_{k=1}f(x_k)[/tex]Δx
Step #4: Solve the right-hand sum equation
complete the remainder of the table for the given function rule.
Answer:
following the (x,y) coordinate system,
(0,4) ; (1,1) ; (2,-2)
Step-by-step explanation:
youre given the value of the x variable in the table, so all you need to do is substitute x and follow pedmas!! hope this helps<3
Find using appropriate Properties:
6/7 x -2/3 + 3/5 + 5/8 x -6/7
The simplified form of the expression is given as 83x/56 -(97/105)
Finding the value of unknown variablesAlphabets are usually represented as unknown variables in a equation or expression.
Given the following expression shown below
6/7 x -2/3 + 3/5 + 5/8 x -6/7
Collect the like terms to have;
6/7 x+ 5/8 x -2/3 + 3/5 -6/7
Simplify
48x+35x/56 - (70-63 + 90)/105
The final expression will be given as;
83x/56 -(97/105)
Hence the simplified form of the expression is given as 83x/56 -(97/105)
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Eight and one-half foot-pounds of work is required to compress a spring 4 inches from its natural length. Find the work required to compress the spring an additional one-half inch. (Round your answer to two decimal places.) ft-lb
Using proportions, it is found that the work required to compress the spring an additional one-half inch is of 1.0625 ft-lb.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
For 4 inches, 8.5 ft-lb of work is needed, hence for a single inch the amount needed is:
8.5/4 = 2.125.
Hence for half an inch, the amount if:
0.5 x 2.125 = 1.0625 ft-lb.
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I need help with this question
Answer:
2.72 / 16 x 28 = $4.76
Step-by-step explanation:
Since they give you $2.72 for 16 ounces you put in:
2.72 / 16 x 28 = $___
Then you just solve it to get $4.76:
2.72 / 16 = 0.17
0.17 x 28 = 4.76
You have $30 to buy muffins. However, at the shop you can buy 1 muffin for $4. (a) Write an inequality from the above information. (b) Solve this inequality to find the number of muffins you can buy. (c) How much money will you have left over?
Answer:
Let m be the number of muffins.
a) 4m <= 30
b) m <= 7.5, so the maximum number of muffins to buy is 7.
c) $4 × 7 = $28, so $2 will be left over.
math related!!!! What are the restrictions on the variable
in the quotient
See my explanation in the pic
Find the explicit form of the arithmetic function of p if the first term is 12 and the common difference is 2. Then find the seventh term.
The explicit form of the arithmetic function as described is; f(p) = 2(p-1) + 12. and the seventh term is; 24.
What is the seventh term of the arithmetic function?Since it follows from the task content, that the first term is 12 and the common difference is 2.
It therefore follows from convention that the explicit function is; f(p) = 2(p-1) + 12 and by substituting n= 7 into, the equation, we have; f(7) = 24.
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In the expansion of (3a + 4b)8, which of the following are possible variable terms? Explain your reasoning.
a2b3; a7b; ab8; b8; a4b4; a6b2; a3b4; a8
pls help
The terms b⁸, a⁶ · b², a⁴ · b⁴, a⁷ · b and a⁸ are part of the expansion of (3 · a + 4 · b)⁸.
How to find the missing terms of a power polynomials
In this case, we have to expand a power binomial by means of the Pascal's triangle, which offers a useful and quick resource to expand expressions of this kind, now we proceed to present the result of this approach:
(3 · a + 4 · b)⁸ = 6 561 · a⁸ + 69 984 · a⁷ · b + 326 592 · a⁶ · b² + 870 912 · a⁵ · b³ + 1 451 520 · a⁴ · b⁴ + 1 548 288 · a³ · b⁵ + 1 032 192 · a² · b⁶ + 393 216 · a · b⁷ + 65 536 · b⁸
Such combinations of products between variables a and b are also supported by the theorem of the binomial. Finally, the terms b⁸, a⁶ · b², a⁴ · b⁴, a⁷ · b and a⁸ are part of the expansion of (3 · a + 4 · b)⁸.
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HELPPPP (x-y)^3-(y-x)^2
Answer:
(x-y)(x-y)(x-y)= x²-yx+x²-yx-yx+y²-yx+y²
2x²-4yx+2y²
(y-x)(y-x)= y²-yx-yx+x²
y²-2yx+x²
-(y²-2yx+x²) = -y²+2yx-x²
2x²-4yx+2y²-y²+2yx-x²= x²-2yx+y²
or
(x−y−1)(x−y)² ≡ x³−x²+3xy²+2xy−y³−y²−3yx³
a. A number is doubled and then increased by 2, the result is equal to 14 more than
5 times the number. What is the number?
Answer:
OK
Let x=the number
2x=double the number
2x+5=the doubled number increased by 5
And we are told that this equals -47
sooooo
2x+5=-47 subtract 5 from each side2x=-47-5=-52
2x=-52
x=-26------the number
CK
2*(-26)=-52
-52 increased by 5=-52+5=-47
-47=-47
Hope this helps- Clara ☆*: .｡. o(≧▽≦)o .｡.:*☆
Step-by-step explanation:
❄ Hi there,
let us start by letting the number be r. The problem tells us that r is doubled and then increased by 2.
This is what it looks like –
[tex]\triangleright \ \sf{2r+2}[/tex]
Also the result is 14 more than 5r.
We end up with an equation that looks like this –
[tex]\triangleright \ \sf{2r+2=14+5r}[/tex]
To find the number we should solve the equation for r –
[tex]\large\begin{gathered} \sf{2r+2=14+5r} . \ Solve \ for \ r: \\ \sf{2r-5r+2=14}\\ \\ \sf{-3r+2=14}\\\sf{-3r=14-2}\\\sf{-3r=12}\\\sf{-r=4}\\\sf{r=-4}\end{gathered}[/tex]
❄
In quadrilateral qrst, angle r s t measures (5x 15)°. angle tqr measures (4x 3)°. circle p is inscribed with quadrilateral q r s t. what is the measure of angle rst?
The measure of the angle rst is [tex]105^{o}[/tex].
What is the inscribed quadrilateral theorem?According to the theorem, a quadrilateral can be inscribed by a circle if and only if its opposing angles are supplementary. A quadrilateral that may be encircled by a circle is known as a cyclic quadrilateral.
The sum opposite angles of a quadrilateral is 180 degrees.
We can see that the angles rst and angle tqr are opposite angles of quadrilateral qrst, hence supplementary angles.
Therefore,
<RST + <TQR = 180
5x+15 + 4x+ 3 = 180
9x + 18 = 180
9x = 180 - 18
9x = 162
x = 162/9
x = 18
Since <RST = 5x+15
<RST = 5(18) + 15
<RST = 90 + 15
<RST = 105degrees
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