Answer:
The area of the surface is 2.72 units
Step-by-step explanation:
The area of a curve y = (x) a ≤x ≤ b rotated about the y axis is given by:
[tex]s=\int\limits^a_b {2\pi x\sqrt{1+(\frac{dy}{dx} )^2} } \, dx[/tex]
y = 4 - x²
dy / dx = -2x
(dy/dx)² = (-2x)² = 4x²
Hence:
[tex]s=\int\limits^a_b {2\pi x\sqrt{1+(\frac{dy}{dx} )^2} } \, dx\\\\s=\int\limits^0_3 {2\pi x\sqrt{1+4x^2} } \, dx\\\\Let\ u = 1+4x^2\ \\\frac{du}{dx}=8x\\\frac{du}{8x}=dx\\\\Substituting\ value\ of\ u \ and\ dx:\\ \\s=\int\limits^0_3 {2\pi x\sqrt{u} } \, \frac{du}{8x} \\\\s=\frac{\pi }{4} \int\limits^0_3 {\sqrt{u} } \, du\\\\s=\frac{\pi }{4}|\frac{2}{3}u^{3/2}|_0^3\\\\s=\frac{\pi }{4}*\frac{2}{3}(5.196)\\\\s=2.72\ units[/tex]
The area of the surface is 2.72 units
The area of the resulting surface is [tex]37.3437\pi[/tex].
Curve:
A curve is an object that is similar to a line, but that does not have to be a straight line. A curve may be regarded as a trace left by a moving point.
Given:
[tex]y=4-x^{2}[/tex] , [tex]0 \leq x\leq 3[/tex]
Surface area[tex]=2\pi \int_{a}^{b}x\sqrt{1+\left ( \frac{dx}{dy} \right )^{2}dy}[/tex]
[tex]x=\sqrt{4-y} \ , \ \frac{dx}{dy}=-\frac{1}{2\sqrt{4-y}}[/tex]
when [tex]x=0 \ , \ y=4[/tex]
[tex]x=3 \ , \ y=-5[/tex]
Area of surface[tex]=2\pi \int_{-5}^{4}\sqrt{4-y}\sqrt{1+\frac{1}{4\left ( y-4 \right )}dy}[/tex]
[tex]=2\pi \int_{-5}^{4}\sqrt{4-y+\frac{4-y}{4\left ( y-4 \right )}dy} \\ =2\pi \int_{-5}^{4}\sqrt{4-y+\frac{1}{4}dy} \\ =\frac{2\pi }{2}\int_{-5}^{4}\sqrt{17-y} \ dy \\ =\pi \int_{-5}^{4}\sqrt{17-y} \ dy[/tex]
Solving with calculator:
[tex]\Rightarrow \pi\left [ \frac{1}{6}\left ( 37\sqrt{37}-1 \right ) \right ][/tex]
[tex]=37.3437\pi[/tex]
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A publisher sells either digital copies of their new book, paperback copies or hardback copies. For every 4 digital sales they make, they make 5 paperback sales and 1 hardback sale. In the first week of sales, the company sells 308 more paperback copies of the book than hardback copies.
Answer:
This means in the first week the number sells of digital copies is 308, paperback sells was 385 copies and hardback sell was 77 copies
Step-by-step explanation:
Let the number of digital copies be x, the number of paperback copies be y and the number of hardback copies be z.
4 digital sales is equal to 5 paperback sales and 1 hardback sale.
5x = 4y, x = 4z, y = 5z
The company sells 308 more paperback copies of the book than hardback copies
y = 308 + z
But y = 5z
5z = 308 + z
4z = 308
z = 77
y = 5z = 5(77) = 385
x = 4z = 4(77) = 308
This means in the first week the number sells of digital copies is 308, paperback sells was 385 copies and hardback sell was 77 copies
Considere as mesas com 4 cadeiras, com 6 cadeiras e com 8 cadeiras. ©Shutterstock/jenjira Com base nessa sequência de imagens, qual expressão indica a quantidade de cadeiras utilizadas ao colocarmos n mesas lado a lado?
Responder:
C. Tₙ = 2n + 2Explicación paso a paso:
De la pregunta, la secuencia de imágenes, cuya expresión indica es 4 cadeiras, 6 cadeiras, 8 cadeiras ...
Se puede ver la secuencia una progresión aritmética de la forma 4, 6, 8 ... Para obtener la expresión que indica la cantidad de cadenas utilizadas o colocaremos n tablas una al lado de la otra, tendremos que encontrar el enésimo término de la secuencia que usa la fórmula para encontrar el enésimo término de una secuencia aritmética.
El enésimo término de un AP se expresa como Tₙ = a + (n-1) d donde;
a es el primer término
n es el número de términos es la diferencia común
De la secuencia generada, a = 4, d = 6-4 = 8-6 = 2
Tₙ = 4+ (n-1) 2
abre el paréntesis
Tₙ = 4 + 2n-2
Tₙ = 2n + 4-2
Tₙ = 2n + 2
Por lo tanto, la expresión que indica la cantidad de cadenas utilizadas o colocaremos n tablas una al lado de la otra es 2n + 2
Question 1 (1 point) How many terms are in the polynomial? 3x3 + 4x2 - 8x - 5 3 4 7
Answer:
4
Step-by-step explanation:
The polynomial 3x^3 +4x^2 -8x -5 has 4 terms. A term is a product or single variable or constant separated from other terms by a plus or minus sign.
The four terms are ...
3x^34x^2-8x-5Express the set x≥2x≥2 using interval notation. Use "oo" (two lower case o's) for ∞∞.
Answer: [x/2 , 1]
Step-by-step explanation: Convert the inequality to interval notation.
The union consists of all of the elements that are contained in each interval. There is No Solution.
I hope this helps you out. If not, my apologizes.
-Leif Jonsi-
math help on this question!
Answer:
none
Step-by-step explanation:
110 + 60 = 170
but 170 is obviously not 180 sooo none will be 60 degrees
Solve for x in the equation 3x-5=2x²
Answer:
[tex]3x - 5 = 2 {x}^{2} \\ = > 3x = 2 {x}^{2} + 5 \\ = > x = \frac{2 {x}^{2} + 5 }{3} [/tex]
What is the solution of the equation below ?
Answer:
d = ±7i
Step-by-step explanation:
d^2 -1 = -50
Add 1 to each side
d^2 -1 = -50
d^2 = -49
Take the square root of each side
sqrt(d^2) = sqrt(-49)
d = sqrt(-1) sqrt(49)
d = i( ±7)
d = ±7i
Answer:
A.
Step-by-step explanation:
d^2-1= -50
First, add 1 to both sides.
d^2= -49
Take the square root of both sides:
d=√-49
Since i^2=-1
d=i√49
d= ±7i
Hope this helps!
Find the sum of -6x^2-1−6x 2 −1 and x+9x+9.
Answer:-6x^2+10x-5.
Step-by-step explanation: -6x^2-1−6x 2−1+x+9x+9 -6x^2-1−6x 2−1+10x+9 -6x^2-1-12−1+10x+9 -6x^2+10x-1-12-1+9 6x^2+10x-5
The sum of the two expressions are -6x²+22x+9
What are like and unlike terms in an expression?In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions.
Given here the expressions here as -6x²+1+6x ×2-1, x+9x+9
The sum is -6x²+1+6x ×2-1 +x+9x+9=-6x²+22x+9
Hence, The sum of the two expressions are -6x²+22x+9
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Represent the following expression using an exponent.
12 x 12 x 12 x 12
Answer:
12<4 (12 to the power of 4)
Step-by-step explanation:
an exponet is used when a number is repeated multiplied against itself. sinec 12 is being multiplied against itself 4 times, we can use the exponent of 4
Answer: [tex]12^4[/tex]
Step-by-step explanation:
Concept to know: for exponents, the amount of same number that is multiplied together will be the number of exponents
--------------------------------------
12×12×12×12
There are in total 4 [12]'s multiplied together, so we will get [tex]12^4[/tex]
Hope this helps!! :)
Please let me know if you have any question or need further explanation
5/8 + 7/12
A 1/2
B 5/24
C 1 5/24
Step-by-step explanation:
The answer is not in the option.
The answer is 29/24.
Simplify ten to the eighth divided by ten to the negative third.
Answer:
[tex]10^{11}[/tex]
Step-by-step explanation:
A statement is given i.e. "ten to the eighth divided by ten to the negative third."
It means that 10 to power 8 divided by 10 to the power -3.
Mathematically,
[tex]\dfrac{10^8}{10^{-3}}[/tex]
We know that, [tex]\dfrac{x^a}{x^b}=x^{a-b}[/tex]
Here, x = 10, a = 8 and b = -3
So,
[tex]\dfrac{10^8}{10^{-3}}=10^{8-(-3)}\\\\=10^{8+3}\\\\=10^{11}[/tex]
So, the answer is [tex]10^{11}[/tex]
Solve x+9=7 show work
Answer: x = -2
x + 9 = 7, Move the constant to the right.
x =7 -9 now calculate that.
then you get x = -2
Hope that helps ya out :D
Answer:
x+9=7
So x= 7-9
( 9 became -9 because we brought it back to the other side to have the x alone and the digits alone )
So x= -2
Angle Terminology with Equations
Answer:
∠ B = 54°
Step-by-step explanation:
Supplementary angles sum to 180°.
Sum A and B and equate to 180, that is
7x + 14 + 5x - 26 = 180, that is
12x - 12 = 180 ( add 12 to both sides )
12x = 192 ( divide both sides by 12 )
x = 16
Thus
∠ B = 5x - 26 = 5(16) - 26 = 80 - 26 = 54°
The width of a rectangle is 4 inches (in) and the area of the rectangle is 32 in2? Which of the following represents the length of the rectange?
a. 8 in
b. 128 in
c. 28 in
d. 36 in
Answer:
A. 8
Step-by-step explanation:
32 divided by 4 = 8
The answer is a. 8 in.
Since the width of the rectangle is 4 inches (in) and the area of the rectangle is 32 in², we need to find the length of the rectangle.
We know that the area of a rectangle with length, L and width, W is A = LW.
Since we need to find the length of the rectangle, we make the length, L subject of the formula.
Since A = LW,
L = A/W
Given that A = 32 in² and W = 4 in
Substituting the values of the variables into the equation, we have
L = 32 in²/4 in
L = 8 in
So, the length of the rectangle is 8 in
So, the answer is a. 8 in.
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The measure of ZAOC is 90 degrees. Find the value of x.
Answer:
14 + 3x + 46 = 90
3x + 60 =90
3x = 30
x = 10
Answer:
Step-by-step explanation:
If u see it is right angle so 90 - 14 u will get an or bc 76
3x+46=76
3x=76-46
3x=30
X=30/3
10
0 to 100 miles per hour in a mere 0.8 seconds. Calculate its acceleration. Show your work and include units.
Answer:
Answer: so the answer is 80 miles per 0.8 Step-by-step explanation: consistence
Integral- Volumes by Slicing and Rotation About an Axis..Volume of a Pyramid... Could you help me solving this question, please?
Answer: volume is 9 cubic units
===================================================
Explanation:
Each cross section is a square with side length x, so the area of this cross section is x^2
We're integrating from x = 0 to x = 3
So we have
[tex]\displaystyle f(x) = x^2\\\\\\\displaystyle g(x) = \int x^2 dx = \frac{1}{3}x^3+C\\\\\\\displaystyle \int_{a}^{b} f(x) dx = g(b) - g(a)\\\\\\\displaystyle \int_{0}^{3} x^2 dx = g(3) - g(0)\\\\\\\displaystyle \int_{0}^{3} x^2 dx = \left(\frac{1}{3}(3)^3+C\right) - \left(\frac{1}{3}(0)^3+C\right)\\\\\\\displaystyle \int_{0}^{3} x^2 dx = 9\\\\\\[/tex]
Simplify 55/66 to lowest terms ?
Answer:
5/6
Step-by-step explanation:
To simplify this fraction, we need to find the GCF (greatest common factor) of the numerator and denominator. In this case, the GCF of 55 and 66 is 11. Now, all we have to do is divide both the numerator and denominator by the GCF. The numerator will become 55 / 11 = 5 and the denominator will become 66 / 11 = 6 so the simplified fraction is 5 / 6.
True or false? For any two integers x and y, |x+y| = |x| + |y|
Answer:
False
Step-by-step explanation:
|x+y| = |x| + |y|
To show this is false, all we have to do is find one example where it is false
Let x = -1 and y = 4
|-1+4| = |-1| + |4|
|3| = |1| + |4|
3 = 5
This is false so we have a set of integers where the statement is not true
(6^2)^x =1 I need to now ASAP
Answer:
x =0
Step-by-step explanation:
[tex]\left(6^2\right)^x=1\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}\\\left(6^2\right)^x=6^{2x}\\\\6^{2x}=1\\\mathrm{If\:}f\left(x\right)=g\left(x\right)\mathrm{,\:then\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)\\\ln \left(6^{2x}\right)=\ln \left(1\right)\\\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)\\\ln \left(6^{2x}\right)=2x\ln \left(6\right)\\2x\ln \left(6\right)=\ln \left(1\right)\\[/tex]
[tex]\mathrm{Solve\:}\:2x\ln \left(6\right)=\ln \left(1\right):\\\quad x=0[/tex]
Jessica always uses the same ratio of green beads to blue beads when she makes necklaces. The graph shows these equivalent ratios. Which table shows the same data?
Answer:
table 2
Step-by-step explanation:
see attached
Answer:
table no. 2
Step-by-step explanation:
Solve the given initial-value problem by finding, as an appropriate integrating factor.
(x2 + y2 − 3) dx = (y + xy) dy, y(0) = 1
Answer:
hello attached below is the detailed solution
answer : In |x+1| + [2/(x+1)] + [1/(1+x)^2] - [y^2/2(1+x)^2] = 5/2
Step-by-step explanation:
Given
(x^2 + y^2 - 3) dx = ( y + xy ) dy, y(0) = 1
solving the given initial-value problem
Rounding whole number which number could round to 80,600 80,532 80,549 80,617 80, ,651
Answer:
80,617
Step-by-step explanation:
the 1 in the tens place puts the number back down to 600
Someone help!! Need answer fast!
Answer:
the area of the triangle is 20 units, and the answer to the expression is also 20, so its equal to each other. 20=20
the area of the trapezoid is 38.5 units
Step-by-step explanation:
14. Line AD is parallel to line EG. If
m<3 is 70°, what is m 24?
F 10°
H 110°
G 20°
| 290°
15. Which angle is congruent to Z 3?
H 22
C 26
B 24
D 28
Answer:
14. H. 110°
15. D. <8
Step-by-step explanation:
14. Given that line AD and line EG are parallel as shown above, m<3 and m<4 are linear pairs and are supplementary. That is, m<3 + m<4 = 180°.
If m<3 = 70°, therefore, m<4 = 180° - 70°
m<4 = 110°
15. <3 corresponds with <8. Corresponding angles are congruent. Therefore, <3 = <8.
What is 4.56 x 105in standard form? a.0.00000456 b.0.0000456 c.0.000456 d.456,000
Answer:
the answer is b
Step-by-step explanation:
What is the equation of the slant asymptote of the rational function? f(x)=6x3−15x2+x−43x2−1 y=x−5 y=2x−5 y=x−17/3 y=2x−17/3
Answer:
2x − 5
Step-by-step explanation:
To solve, divide the numerator by the denominator. The result (not including the remainder) will be the equation of the slant asymptote.
We can tell the first term of the quotient will be 2x, so the answer will be either 2x − 5 or 2x − 17/3.
The easiest method here is to simply multiply these by denominator.
(3x² − 1) (2x − 5) = 6x³ − 15x² − 2x + 5
(3x² − 1) (2x − 17/3) = 6x³ − 17x² − 2x + 17/3
So the answer must be 2x − 5.
Alternatively, you can use long division.
Answer:
2x-5
Step-by-step explanation:
f(x)=(6x^3−15x^2+x−4 )/(3x^2−1)
To find the slant asymptote,divide the numerator by the denominator
2x +(-15x^2+3x-4)/ (3x^2-1)
-5 + (3x-9)/(3x^2-1)
The divisor is (2x-5) and the remainder is ( 3x-9)
roll two standard dice and add the numbers. what is the probability of getting a number larger than 8 for the first time on the third roll
Answer:
[tex]Probability = \frac{845}{5832}[/tex]
Step-by-step explanation:
Given
Two standard dice
Required
Probability that the outcome will be greater than 8 for the first time on the third roll
First, we need to list out the sample space of both dice
[tex]S_1 = \{1,2,3,4,5,6\}[/tex]
[tex]S_2 = \{1,2,3,4,5,6\}[/tex]
Next, is to list out the sample when outcome of both dice are added together[tex]S = \{2,3,4,5,6,7,3,4,5,6,7,8,4,5,6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11,7,8,9,10,11,12\}[/tex]
Next, is to get the probability that an outcome will be greater than 8
Represent this with P(E)
[tex]P(E) = \frac{Number\ of\ outcomes\ greater\ than\ 8}{Total}[/tex]
[tex]P(E) = \frac{10}{36}[/tex]
[tex]P(E) = \frac{5}{18}[/tex]
Next, is to get the probability that an outcome will noy be greater than 8
Represent this with P(E')
[tex]P(E) + P(E') = 1[/tex]
[tex]P(E') = 1 - P(E)[/tex]
[tex]P(E') = 1 - \frac{5}{18}[/tex]
[tex]P(E') = \frac{18 - 5}{18}[/tex]
[tex]P(E') = \frac{13}{18}[/tex]
Now, we can calculate the required probability;
Probability of a number greater than 8 first on the third attempt is:
Probability of outcome not greater than 8 on the first attempt * Probability of outcome not greater than 8 on the second attempt * Probability of outcome greater than 8 on the third attempt
Mathematically;
[tex]Probability = P(E') * P(E') * P(E)[/tex]
Substitute values for P(E) and P(E')
[tex]Probability = \frac{13}{18} * \frac{13}{18} * \frac{5}{18}[/tex]
[tex]Probability = \frac{13 * 13 * 5}{18 * 18 * 18}[/tex]
[tex]Probability = \frac{845}{5832}[/tex]
Let p be a prime number. The following exercises lead to a proof of Fermat's Little Theorem, which we prove by another method in the next chapter. a) For any integer k with 0 ≤ k ≤ p, let (p k) = p!/k!(p - k)! denote the binomial coefficient. Prove that (p k) 0 mod p if 1 ≤ k ≤ p - 1. b) Prove that for all integers x, y, (x + y)^p x^? + y^p mod p.c) Prove that for all integers x, x^p x mod p.
Hello,
a) We know the binomial coefficients are all integers, so
[tex]\dfrac{p!}{k!(p-k)!}[/tex]
is an integer.
And we can notice that the numerator p! is divisible by p.
If we take [tex]1\leq k\leq (p-1)[/tex]
It means that k! does not contain p, and we can say the same for (p-k)!
So, we have no p at the denominator so the binomial coefficient is divisible by p, meaning this is 0 modulo p.
b) We can write that
[tex]\displaystyle (x+y)^p=\sum_{i=0}^{p} \ {\dfrac{p!}{i!(p-i)!}x^{p-i}y^i[/tex]
We use the result from question a) and the binomial coefficients are 0 modulo p for i=1,2 , ... p-1 so there are only two terms left and then,
[tex](x+y)^p=x^p+y^p \text{ modulo p}[/tex]
c) Let's prove it by induction.
step 1 - for x = 0
This is trivial to notice that
[tex]0^p=0 \text{ modulo p}[/tex]
Step 2 - we assume that this is true for k
meaning [tex]k^p=k \text{ modulo p}[/tex]
and we need to prove that this is true for the k+1
We use the results of b)
[tex](k+1)^p=k^p+1^p=k^p+1 \text{ modulo p}[/tex]
and we use the induction hypothesis to say
[tex](k+1)^p=k^p+1^p=k^p+1=k+1 \text{ modulo p}[/tex]
And it means that this is true for k+1
Step 3 - conclusion
We have just proved by induction the Fermat's little theorem.
p a prime number, for for all x integers
[tex]\Large \boxed{\sf \bf x^p=x \textbf{ modulo p}}[/tex]
Thank you
5(x - 10) = 30 - 15x
Answer:
x = 4
Step-by-step explanation:
We can first expand 5(x-10), getting 5x - 50.
Thus, 5x - 50 = 30 - 15x
We can then isolate x, getting (5+15) x = 30 + 50
20 x = 80
x = 4.
Answer:
5(x - 10) = 30 - 15x
We distribute 5 (x-10)
So 5x-50 = 30 -15x
5x+15x=50+30
(-15x became 15x because we brought it back to the other side and -50 became 50 because we brought it back to the other side to put the x's with the x's and the digits with the digits.)
So 20x=80
x= 50/20
We simplify 80/20
So x=4