The surface area of revolution about the x-axis over the given intervals are: 33. 8π, 34. 32π/3, 35. 2π(2+ln(2)), 36. 8π/3, 37. 64π/15, 38. 2π, 39. (32/3)π, 40. 2π.
The surface area of revolution is given by
SA = 2π ∫[0,4] x√(1+(dy/dx)²) dx
Here, y = x and dy/dx = 1.
So, SA = 2π ∫[0,4] x√2 dx = 2π[2/3 * 2√2 * 4^(3/2) - 2/3 * 2√2] = 16π/3√2.
The surface area of revolution is given by
SA = 2π ∫[0,1] (4x+3)√(1+(dy/dx)²) dx
Here, y = 4x+3 and dy/dx = 4.
So, SA = 2π ∫[0,1] (4x+3)√17 dx = 2π[(4/15)*17^(3/2) + (3/8)*17^(1/2)] = 17π(8+3√17)/30.
The surface area of revolution is given by
SA = 2π ∫[0,2] x√(1+(dy/dx)²) dx
Here, y = x³ and dy/dx = 3x².
So, SA = 2π ∫[0,2] x√(1+9x⁴) dx. This integral cannot be evaluated analytically, so we must use numerical methods to approximate the value.
The surface area of revolution is given by
SA = 2π ∫[0,4] x√(1+(dy/dx)²) dx
Here, y = x² and dy/dx = 2x.
So, SA = 2π ∫[0,4] x√(1+4x²) dx. This integral cannot be evaluated analytically, so we must use numerical methods to approximate the value.
The surface area of revolution is given by
SA = 2π ∫[0,8] y√(1+(dx/dy)²) dy
Here, x = (4-y^(2/3))^(1/2) and dx/dy = -(2/3)y^(-1/3)(4-y^(2/3))^(-1/2).
So, SA = 2π ∫[0,8] (4-y^(2/3))^(1/2)√(1+(2/3)^2y^(-2/3)(4-y^(2/3))^(-1)) dy. This integral cannot be evaluated analytically, so we must use numerical methods to approximate the value.
The surface area of revolution is given by
SA = 2π ∫[0,1] e^(-x)√(1+(dy/dx)²) dx
Here, y = e^(-x) and dy/dx = -e^(-x).
So, SA = 2π ∫[0,1] e^(-x)√(1+e^(-2x)) dx = 2π[1 - (1/2)*e^(-2)].
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Can someone help me please?
The surface area of the cone is: A. 184π units².
What is the Surface Area of a Cone?Surface area of a cone = πr(l + r), where r is the radius and l is the slant height.
Given the following:
Slant height (l) = 15 unitsRadius = (r) = 8 unitsSurface area of a cone = π8(15 + 8)
Surface area of a cone = 184π units²
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Anyone know?? I’d appreciate it.
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: (1.6 \times 10 {}^{5} ) \sdot(2 .3 \times {10}^{1} )[/tex]
[tex]\qquad \sf \dashrightarrow \: (1.6 \times 2.3) \sdot(10 {}^{5} \times 10 {}^{1} )[/tex]
[tex]\qquad \sf \dashrightarrow \: 3.68 \times 10 {}^{6} [/tex]
pls answer fast , pls
Answer:
x is 14
1st is 14
2nd is 20
Step-by-step explanation:
4/7 (x ) = (34 - x )(2/5)
4x/7 + 2x/5 = 34 x 2/5 = 68/5
34x/35 = 68/5
x = 14
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Slope-intercept form?
Answer:
y=3x+4
Step-by-step explanation:
The original formula for slope-intercept is y=mx+b.
b is your y-intercept (where the line crosses the y-axis).
m is your slope which is 3/1 or just 3.
What does 6 * b equal??
Answer:
6b
You can just simply combine the variable, 6, and the coefficient, b.
The product of the square of a number x and 2 subtracted from 3 is y.
The algebraic expression for the given statement is: 2x² - 3 = y.
How to Write an Algebraic Expression?To wrote an algebraic expression is translate a statement using numbers, variables, and mathematical sign into a mathematical statement.
Square of x is: x²
Product of x² and 2 is: 2x²
Thus, we would have:
2x² - 3 = y
The algebraic expression is: 2x² - 3 = y.
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Thanks!
1) You know that for any , neither sin nor cos can be greater than 1. How can you explain this using the unit circle definitions of sine and cosine? How can you explain it using the right triangle definitions of sine and cosine?
As a follow-up question, consider why it is important to have both the right triangle definitions of sine and cosine and the unit circle definitions of sine and cosine.
2) Can you give examples of situations that might be modeled with trigonometric functions? That is, can you give examples of phenomena that take on a series of values over and over again?
The trigonometric function gives the ratio of different sides of a right-angle triangle. The value of sine and cosine will be always less than a unit.
How to explain the trigonometry?In a unit circle, the radius of the circle represents the hypotenuse of the triangle. Since the hypotenuse is the largest side of the triangle, the ratio of the perpendicular to the hypotenuse and the base to the hypotenuse both will be less than the hypotenuse, therefore, 1. Hence, the value of sine and cosine will be always less than a unit.
In construction, we use trigonometry. For figuring areas of triangular shapes, similar to many concepts and phenomena in mathematics.
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4+4-3-4-2-5-1-8-9-0=a+c=a
Simplification of the expression gives 2a + c = -24
How to simplify the equation
4+4-3-4-2-5-1-8-9-0=a +c + a
First, let's add
[tex]8 -3 -4-2-5-1-8-9-0 = a+ c + a[/tex]
Then, let's substract
[tex]-24 = a + c + a[/tex]
[tex]-24 = 2a + c[/tex]
We then have,
[tex]2a + c = -24[/tex]
Thus, simplification of the expression gives 2a + c = -24
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I dentist the slope and a point on the line
Answer:
2/3 (0,-3) is one possible answer.
Step-by-step explanation:
y -1 = 2/3(x-6) We want to get this into the slope intercept form of a line. We want it to be in the form y = mx + b. Let's clear the fraction first by multiplying the whole equation through by 3.
3(y - 1) = 3[2/3(x - 6)]
3y -3 = 2(x -6)
3y - 3 = 2x -12
3y = 2x - 9 Now divide all the way through by 3 to get
y = 2/3x - 3
y = mx + b. The m part is the slope. In this equation the slope is 2/3
There are in infinite amount of points on a line. I do not know if they give you a picture or if you are just to create your own. I am going to create a point that have x = 0. I get to pick the point. I could pick any number. 0 is just usually really easy. So, if I substitute 0 for x I will get:
y = 2/3(0) - 3
y = 1 so my point is (0,-3)
Now that I think about it, I do not think that I would start out clearing the fraction even though it works. I think that I would do it like this"
y - 1 = 2/3(x - 6) Distribute the 2/3 through (x - 4) to get
y-1 = 2/3x -4 I can make -6 a fraction by putting it over 1. Now we have 2/3(-6/1) multiply across to get -12/3. A positive times a negative is a negative. -12 divided by 3 is -4.
y - 1 = 2/3x -4 now add 1 to both sides.
y = 2/3x -3
A sample of workers exhibit the following production rates before and after a workshop. Worker Before After 1 20 22 2 25 23 3 27 27 4 23 20 5 22 25 6 20 19 7 17 18 The point estimate for the difference between the means of the two populations is: Group of answer choices
The point estimate here is 0.
Calculating the Mean of Each Set
The sample set of production rates exhibited by workers before workshop, S1 = {20, 25, 27, 23, , 22, 20, 17}
The sample set of production rates exhibited by workers after workshop, S2 = {22, 23, 27, 20, 25, 19, 18}
The mean of set S1 = (20+25+27+23+22+20+17)/7
= 154/7
= 22
The mean of set S2 = (22+23+37+20+25+19+18)/7
= 154/7
=22
Calculating the Point Estimate
The formula for point estimate is given as,
Point Estimate = The mean of set S1 - The mean of set S2
Point Estimate = 22-22
Point Estimate = 0
Therefore, the point estimate for the difference between the means of the two populations or sets is 0
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The counting numbers beginning with 101 and ending with 200 are listed. How many of the numbers have a 6 as a digit
Counting numbers from 101 to 200, those with 6 as a digit are 19
The numbers
Let's start by listing all the number between 101 and 200
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200
Now, let's count the numbers with 6 as a digit
= 19 numbers has 6 as a digit
Thus, counting numbers from 101 to 200, those with 6 as a digit are 19
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Given: quadrilateral MNOL with MN ≅ LO and ML ≅ NO
Prove: MNOL is a parallelogram.
Quadrilateral L M N O is shown. Sides M N and L O are congruent. Sides L M and O N are congruent.
Complete the paragraph proof.
We are given that MN ≅ LO and ML ≅ NO. We can draw in MO because between any two points is a line. By the reflexive property, MO ≅ MO. By SSS, △MLO ≅ △
. By CPCTC, ∠LMO ≅ ∠ and ∠NMO ≅ ∠LOM. Both pairs of angles are also , based on the definition. Based on the converse of the alternate interior angles theorem, MN ∥ LO and LM ∥ NO. Based on the definition of a parallelogram, MNOL is a parallelogram.
The answers to the quadrilateral are ONM, NOM, and alternate interior angles.
How to explain the quadrilateral?Based on the SSS postulate, the two triangles △MLO and △ONM are congruent since three sides of △MLO are respectively equal to the three sides of △ONM.
Based on CPCTC, all of the corresponding angles of △MLO and △ONM are congruent as well since the two triangles are congruent, that is,
∠LMO≅∠NOM and ∠NMO≅∠LOM.
Since the pair ∠LMO and ∠NOM as well as ∠NMO and ∠LOM are angles on the inner side of two lines but on opposite sides of the transversal MO, these pairs of angles are also alternate interior angles.
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Answer: ONM
NOM
alternate interior angles
Step-by-step explanation: Complete the paragraph proof.
We are given that MN ≅ LO and ML ≅ NO. We can draw in MO because between any two points is a line. By the reflexive property, MO ≅ MO. By SSS, △MLO ≅ △
✔ ONM
. By CPCTC, ∠LMO ≅ ∠
✔ NOM
and ∠NMO ≅ ∠LOM. Both pairs of angles are also
✔ alternate interior angles
, based on the definition. Based on the converse of the alternate interior angles theorem, MN ∥ LO and LM ∥ NO. Based on the definition of a parallelogram, MNOL is a parallelogram.
Triangle ABC was dilated using the rule Do,4. Triangle
A'B'C' is the result of the dilation.
3
A
B
C
A'
В'
C
What is OB'?
O 1.5 units
3 units
O4.5 units
O6 units
The value of OB based on the information given about the triangle is 3 units.
How to illustrate the information?It should be noted that dilation is the process of enlarging or shrinking of an object.
In this case, the triangle is dilated. Therefore, the length of OB will be:
= 3/4 × 4 = 3 units.
Therefore, the correct option is B.
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y=x The point F is the foot of the perpendicular from the point (1, 9) to the line y=x. Find the coordinates of F.
Answer: (5,5)
Step-by-step explanation:
The perpendicular to y=x has slope -1, and thus the equation of the perpendicular from (1,9) is [tex]y=-x+10[/tex].
Finding the point where they intersect, since both equations are set equal to y, we know that -x+10=x, and thus x=5.
If x=5, then y=5 as well.
So, F has coordinates (5,5).
A magazine provided results from a poll of 1000 adults who were asked to identify their favorite pie. Among the 1000 ​respondents, 14​% chose chocolate​ pie, and the margin of error was given as +3 percentage points. What values do ​, ​, ​n, E, and p​ represent? If the confidence level is ​%, what is the value of ​?
The completion of the tabs are:
The value of [tex]\bar p[/tex] is the sample proportion.The value of [tex]\bar q[/tex] is found by evaluating [tex]1-\=p[/tex]The value of n is the sample size.The value of E is the margin of error.The value of p is the population proportion. α = 0.05.What is the margin of error.?You may calculate how many percentage points your findings will deviate from the actual population figure by using something called a margin of error.
In conclusion
The worth of p^ is the fraction of the sample.The worth of p^ is discovered by assessingThe sample size is given by the number n.The margin of error is expressed as E's value.The population percentage is represented by the value of p. α = 0.05.In conclusion,
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6x + -2y² + 4xy² + 3x² + 5xy² simplify it
[tex]\large\displaystyle\text{$\begin{gathered}\sf 6x+-2y^{2}+4xy^{2}+3x^{2} +5xy^{2} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Group\:like\:terms \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf =3x^2+6x-2y^2+4xy^2+5xy^2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Sum\:similar\:elements:\:4xy^2+5xy^2=9xy^2 \end{gathered}$}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf 3x^2+6x-2y^2+9xy^2 \end{gathered}$} }[/tex]
NEED HELP PLEASE!!!!!
What is c−1(x) given c(x)=x3−5?
A. c−1(x)= ∛x+5
B. c−1(x)= ∛x+x
C. c−1(x)= ∛x- ∛5
D. c−1(x)= ∛x-5
Answer: A
Step-by-step explanation:
Let c(y)=x.
[tex]\implies x=y^3 -5\\\\x+5=y^3\\\\y=\sqrt[3]{x+5}\\\\c^{-1}(x)=\sqrt[3]{x+5}[/tex]
This market is a duopoly and the demand schedule as well as the total revenue is provided below. The number of customers you see and the total revenue is for the total market, not for an individual firm.
Answer:
??
Step-by-step explanation:
PLEASE HELP DUE TONIGHT
The height & speed are mathematically given as
t = 0.2 s
u = 4 m/s
What is the height & speed?Generally, the equation for height is mathematically given as
h = 0.2gt^2
Therefore
0.2 = 0.5 * 9.8 *[tex]t^2[/tex]
0.2 = 4.9 *[tex]t^2[/tex]
t = 0.2 s
b)
In conclusion, the initial speed is
s = ut
Therefore
u = 0.8 / 0.2
u = 4 m/s
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2. Mary receives $2.00 weekly as an allowance. If
she saves $0.70 of it, what percent does she
save?
Answer:
35%
Step-by-step explanation:
She is saving $0.70/$2.00 weekly.
To convert this into a percentage we covert it to decimal then multiply by 100 :
$0.70/$2.00 = 0.35
0.35 × 100 = 35%
Our final answer is 35%.
Hope this helped and have a good day
Please help me with this
Answer:
altitude: 16 cmbase: 12 cmStep-by-step explanation:
The given relation can be used with the formula for the area of a triangle to give an equation for the altitude or base.
SetupLet b represent the length of the base. Then the altitude (height) is (b+4). The area formula tells us the area is ...
A = 1/2bh
Using given values, the equation becomes ...
96 = 1/2b(b +4)
SolutionSimplifying the equation and multiplying by 2, we have ...
192 = b² +4b
Adding (4/2)² = 4 will complete the square.
196 = b² +4b +4 = (b +2)²
Taking the square root gives ...
14 = b +2 . . . . . . we are not interested in the negative root
12 = b . . . . . . . . subtract 2
16 = b+4 . . . . . find the altitude
The base is 12 cm; the altitude is 16 cm.
Question 5(Multiple Choice Worth 1 points)
(02.01 LC)
Which of the following tables represents a function?
its the first one
a system can only be a function if there is only one value of y for each value of x. there cannot be two or more values of y for one single value of x in a function.
Determine the volume of a cube with a side length of 5 1/3 in.
Answer:
151 19/27 in^3
Step-by-step explanation:
volume of cube is (side length)^3
(5 1/3)^3 = (16/3)^3 = 4096/27 = 151 19/27
how meny grams are in 6 ounces?
Answer:
170.097 grams are in 6 ounces
Answer:
170.097 g to nearest thousandth
Step-by-step explanation:
1 ounce = 28.34952 g
6 = 170.09712 g
Chandra invests $75 every month at 4.8%/a compounded monthly for 8 years. What is the total amount of Chandra's investments after 8 years?
The total amount of Chandra's investments after 8 years is $110.03
Compound interestThe formula for calculating the compound interest is expressed as;
A = P(1+r/n)^nt
where
P is the amount invested = $75
r is the rate. = 0.048
t is the time =8years
n = 12 (monthly)
Substitute
A = 75(1+0.048/12)^96
A = 75(1.467)
A = 110.03
Hence the total amount of Chandra's investments after 8 years is $110.03
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Simplify the expression.
Answer:
D
please mark brainiest
What is the repayment amount after one month on a simple interest loan of $2,500 at 7% interest?
Payment Every Month = $2,514.58
Total of 1 Payments = $2,514.58
Total Interest = $14.58
What is simple intertest ?
Simple interest is calculated based on the principal of a loan or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accumulated.
Solution:
Principal value = $2500
Interest rate = 7%
Time = One month
Formula for simple interest calculation:
[tex]=\frac{Principalamount*rate *time}{100} \\=\frac{2500*7*(\frac{1}{12}) }{100}\\ =14.588[/tex]
Total Simple interest on $2500 for month $14.588.
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pls help tysm!!!!!!!!!
Answer:
Second choice
Step-by-step explanation:
Analyse each sentences: The sum of x and y is 5 can be mathematically expressed as [tex]\displaystyle{x+y = 5}[/tex] since both are sum together and equal to 5.
Next, the value of y is one more than value of x can be mathematically expressed as [tex]\displaystyle{y=x+1}[/tex] because value of y is one more than value of x so y will be the value of x add with 1.
Therefore, form the simultaneous equation:
[tex]\displaystyle{\left \{ {{x+y=5} \atop {y=x+1}} \right}[/tex]
Hence, the answer is second choice.
A long oval is shown. Two lines are drawn where the sides are straight to form right angles.
How can you decompose the composite figure to determine its area?
as two semicircles and a rectangle
as two circles and a rectangle
as a circle and a square
as two semicircles and a trapezoid
The figure which is like a long oval can be decomposed to two semicircles and a rectangle so as to find the area.
Given a long oval and two lines are drawn where the sides are straight to form right angles.
We are required to find the way how we can decompose the composite figure to determine its area.
Area means the amount of space occupied by a two dimensional shape or object. The area of a figure can be decomposed to smaller figures so as to find the area.
The composed figure can be decomposed to two semicircles and a rectangle so as to find the area.
Hence the composite figure can be decomposed to two semicircles and a rectangle so as to find the area.
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Answer:
a
Step-by-step explanation:
The lengths of two sides of a triangle are shown below:
Side 1: 3x² - 2x - 1
Side 2: 9x + 2x² - 3
The perimeter of the triangle is 5x³+4x2 - x - 3.
Part A: What is the total length of the two sides, 1 and 2, of the triangle? (4 points)
Part B: What is the length of the third side of the triangle? (4 points)
Part C: Do the answers for Part A and Part B show that the polynomials are closed under
addition and subtraction? Justify your answer. (2 points)
(10 points)
Part A
[tex]3x^2 -2x-1+9x+2x^2 -3=\boxed{5x^2 + 7x-4}[/tex]
Part B
[tex](5x^3 +4x^2 - x-3)-(5x^2 + 7x-4)=\boxed{5x^3 - x^2 - 8x+1}[/tex]
Part C
No, because although they provide examples for specific polynomials being closed under addition and subtraction, there is a loss of generality.