(a) The area of the region would be given by the integral
[tex]\displaystyle\int_0^\pi y(t)\left|x'(t)\right|\,\mathrm dt = 8 \int_0^\pi \sin^2(t)\,\mathrm dt[/tex]
(b) The area of the surface of revolution would be given by
[tex]\displaystyle\int_0^\pi y(t)\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt = 4\int_0^\pi\sin(t)\sqrt{4\sin^2(t)+16\cos^2(t)}\,\mathrm dt[/tex]
NEED HELP ASAP!!
Which equations represent exponential growth?
Which equations represent exponential decay?
Drag the choices into the boxes to complete the table.
Exponential Growth:
Exponential Decay:
y = 1700(1.25)^t
y =240(1/2)^t
y = 4000(1.0825)^t
y = 1.5(10)^t
y = 12,000(0.72)^t
y = 8000(0.97)^t
Answer:
Growth: y = 1700(1.25)^t, y = 4000(1.0825)^t, y = 1.5(10)^t
Decay: y =240(1/2)^t, y = 12,000(0.72)^t, y = 8000(0.97)^t
Step-by-step explanation:
In an exponential equation, growth and decay are determined by the factor you are multiplying by exponentially. If it's under 1 you're basically exponentially dividing the initial value. Over 1 and you are increasing the value.
Which of the following best describes the number below square root of -7
A. Perfect square
B.composite
C.imaginary
D.positive
Answer: The ans is imaginary . option c
Which number is a solution of the inequality x less-than negative 4? Use the number line to help answer the question.
A number line going from negative 9 to positive 1.
–3
0
2
Answer:
-5 it is
Step-by-step explanation:
GED Academy Practice Test
What is the value of the expression?
4+(-2)
-3+3
Answer:
The first one is 2
The second one is 0
I hope this helps!
Answer:
First:
[tex]{ \tt{ = 4 + ( - 2)}} \\ = 4 - 2 \\ = 2[/tex]
Second:
[tex] - 3 + 3 \\ = 0[/tex]
Question:
which is a y-intercept of the graphed function?
Answers:
A. (-9,0)
B. (-3,0)
C. (0,-9)
D. (0,-3)
Answer:
(0, -9)
Step-by-step explanation:
The y intercept is the y value when x =0
(0, -9)
Jamal opens a savings account with a starting balance of $200 and plans to
deposit $75 each week after opening the account. His savings over time is
represented by the graph below. How would this graph change if Jamal
decided to deposit $100 each week instead?
the graph would steeper, meaning more savings over time
A differential equation is an equation involving an unknown function and its derivatives. Consider the differential equation 0. a. Show that satisfies the equation for any constant A. b. Show that satisfies the equation for any constant B. c. Show that satisfies the equation for any constants A and B.
Answer: hi your question is poorly written below is the correct question
answer :
a) y1 = Asint, y'1 = Acost , y"1 = -Asint
b) y2 = Bcost, y'2 = Bsint , y"2 = - Bcost
c) y = Asint + B cost satisfies the differential equation for any constant A and B
Step-by-step explanation:
y" + y = 0
Proves
a) y1 = Asint, y'1 = Acost , y"1 = -Asint
b) y2 = Bcost, y'2 = Bsint , y"2 = - Bcost
c) y3 = y1 + y2 , y'3 = y'1 + y'2, y"3 = y"1 + y"2
∴ y"1 + y1 = -Asint + Asint
y"2 + y2 = -Bcost + Bcost
y"3 - y3 = y"1 + y"2 - ( y1 + y2 )
= y"1 - y1 + y"2 - y2
= -Asint - Asint + ( - Bcost - Bcost ) = 0
Hence we can conclude that y = Asint + B cost satisfies the equation for any constant A and B
Find the direction cosines and direction angles of the vector. (Give the direction angles correct to the nearest degree.) c, c, c , where c > 0
Answer:
cos(∝) = 1/√3
cos(β) = 1/√3
cos(γ) = 1/√3
∝ = 55°
β = 55°
γ = 55°
Step-by-step explanation:
Given the data in the question;
vector is z = < c,c,c >
the direction cosines and direction angles of the vector = ?
Cosines are the angle made with the respect to the axes.
cos(∝) = z < 1,0,0 > / |z|
so
cos(∝) = < c,c,c > < 1,0,0 > / √[c² + c² + c²] = ( c + 0 + 0 ) / √[ 3c² ]
cos(∝) = c / √[ 3c² ] = c / c√3 = 1/√3
∝ = cos⁻¹( 1/√3 ) = 54.7356° ≈ 55°
cos(β) = < c,c,c > < 0,1,0 > / √[c² + c² + c²] = ( 0 + c + 0 ) / √[ 3c² ]
cos(β) = c / √[ 3c² ] = c / c√3 = 1/√3
β = cos⁻¹( 1/√3 ) = 54.7356° ≈ 55°
cos(γ) = < c,c,c > < 0,0,1 > / √[c² + c² + c²] = ( 0 + 0 + c ) / √[ 3c² ]
cos(γ) = c / √[ 3c² ] = c / c√3 = 1/√3
γ = cos⁻¹( 1/√3 ) = 54.7356° ≈ 55°
Therefore;
cos(∝) = 1/√3
cos(β) = 1/√3
cos(γ) = 1/√3
∝ = 55°
β = 55°
γ = 55°
Not sure what to pick
Answer:
option d is correct answer
Answer:
Step-by-step explanation:
D looks good
By recognizing the series as a Taylor series evaluated at a particular value of x, find the sum of each of the following convergent series
1 + 3 + 9/2! + 27/3! + 81/4! + .....
Answer:
the answer should be e^3
Step-by-step explanation:
i hope it helps you
Math pweasee 15 points
Answer:
Step-by-step explanation:
a = 5
b = 15
c = ?
c^2 = a^2 + b^2
c^2 = 5^2 + 15^2
c^2 = 25 + 125
c^2 = 250
sqrt(c^2) = sqrt(250)
c = sqrt(250)
The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.8 millimeters and a standard deviation of 0.07 millimeters. Find the two diameters that separate the top 8% and the bottom 8%. These diameters could serve as limits used to identify which bolts should be rejected. Round your answer to the nearest hundredth, if necessary.
Answer:
5.70 < X < 5.89
Step-by-step explanation:
Z = ±1.40507156
z = (x - μ)/σ
1.40507156 = (x - 5.8)/.07
5.70 < X < 5.89
Which of the following sets of points are NOT coplanar?
admins, pls delete this, I messed up and don't know how
Please help with this
Answer:
i think you answer is correct as it has to be less that 64 yards since it is not on a big slant. using reference from the first section forty yards is not as big as the sectuon you are looking for therefore using estimation, the answer is most likely b 53 and 1 thirds
A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 310.
(a) Find an expression for the number of bacteria after
hours.
(b) Find the number of bacteria after 3 hours.
(c) Find the rate of growth after 3 hours.
(d) When will the population reach 10,000?
Answer:
a) The expression for the number of bacteria is [tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex].
b) There are 2975 bacteria after 3 hours.
c) The rate of growth after 3 hours is about 3365.3 bacteria per hour.
d) A population of 10,000 will be reached after 4.072 hours.
Step-by-step explanation:
a) The population growth of the bacteria culture is described by this ordinary differential equation:
[tex]\frac{dP}{dt} = k\cdot P[/tex] (1)
Where:
[tex]k[/tex] - Rate of proportionality, in [tex]\frac{1}{h}[/tex].
[tex]P[/tex] - Population of the bacteria culture, no unit.
[tex]t[/tex] - Time, in hours.
The solution of this differential equation is:
[tex]P(t) = P_{o}\cdot e^{k\cdot t}[/tex] (2)
Where:
[tex]P_{o}[/tex] - Initial population, no unit.
[tex]P(t)[/tex] - Current population, no unit.
If we know that [tex]P_{o} = 100[/tex], [tex]t = 1\,h[/tex] and [tex]P(t) = 310[/tex], then the rate of proportionality is:
[tex]P(t) = P_{o}\cdot e^{k\cdot t}[/tex]
[tex]\frac{P(t)}{P_{o}} = e^{k\cdot t}[/tex]
[tex]k\cdot t = \ln \frac{P(t)}{P_{o}}[/tex]
[tex]k = \frac{1}{t}\cdot \ln \frac{P(t)}{P_{o}}[/tex]
[tex]k = \frac{1}{1}\cdot \ln \frac{310}{100}[/tex]
[tex]k\approx 1.131\,\frac{1}{h}[/tex]
Hence, the expression for the number of bacteria is [tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex].
b) If we know that [tex]t = 3\,h[/tex], then the number of bacteria is:
[tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex]
[tex]P(3) = 100\cdot e^{1.131\cdot (3)}[/tex]
[tex]P(3) \approx 2975.508[/tex]
There are 2975 bacteria after 3 hours.
c) The rate of growth of the population is represented by (1):
[tex]\frac{dP}{dt} = k\cdot P[/tex]
If we know that [tex]k\approx 1.131\,\frac{1}{h}[/tex] and [tex]P \approx 2975.508[/tex], then the rate of growth after 3 hours:
[tex]\frac{dP}{dt} = \left(1.131\,\frac{1}{h} \right)\cdot (2975.508)[/tex]
[tex]\frac{dP}{dt} = 3365.3\,\frac{1}{h}[/tex]
The rate of growth after 3 hours is about 3365.3 bacteria per hour.
d) If we know that [tex]P(t) = 10000[/tex], then the time associated with the size of the bacteria culture is:
[tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex]
[tex]10000 = 100\cdot e^{1.131\cdot t}[/tex]
[tex]100 = e^{1.131\cdot t}[/tex]
[tex]\ln 100 = 1.131\cdot t[/tex]
[tex]t = \frac{\ln 100}{1.131}[/tex]
[tex]t \approx 4.072\,h[/tex]
A population of 10,000 will be reached after 4.072 hours.
what graph shows the solution to the equation below log3(x+2)=1
Answer:
The solution to the equation log3(x+2)=1 is given by x=1
Step-by-step explanation:
We are given that
[tex]log_3(x+2)=1[/tex]
We have to find the graph which shows the solution to the equation log3(x+2)=1.
[tex]log_3(x+2)=1[/tex]
[tex]x+2=3^1[/tex]
Using the formula
[tex]lnx=y\implies x=e^y[/tex]
[tex]x+2=3[/tex]
[tex]x=3-2[/tex]
[tex]x=1[/tex]
Write an equation that represents the line.
Use exact numbers
Explain relationship between ≠2 and the factor x – 2.
Answer:
It has a difference of x=2 of -4
Step-by-step explanation:
It has a difference of x=2 of -4
What is factor ?A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor in mathematics. As an illustration, 3 and 6 are factors of 12 because 12 3 = 4 and 12 6 = 2, respectively. 1, 2, 4, and 12 are the other components that make up 12.Given ,
x ≠ 2 ,
x - 2 =0
So, we put x = -2 because in question x ≠ 2 .
Then, x - 2 = 0
-2 -2 = 0
- 4 =0
Therefore, it has a difference of x= -2 of -4.
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What is the measure of L?
A. 390
B. 25°
C. Cannot be determined
D. 32°
Answer:
∠L = 25°
Step-by-step explanation:
Two sides are equal. so , it is an isosceles triangle.
Angles opposite to equal sides are equal.
∠L = 25
Each side of a square is increasing at a rate of 4 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 25 cm2
Answer:
The area of the square is increasing at a rate of 40 square centimeters per second.
Step-by-step explanation:
The area of the square ([tex]A[/tex]), in square centimeters, is represented by the following function:
[tex]A = l^{2}[/tex] (1)
Where [tex]l[/tex] is the side length, in centimeters.
Then, we derive (1) in time to calculate the rate of change of the area of the square ([tex]\frac{dA}{dt}[/tex]), in square centimeters per second:
[tex]\frac{dA}{dt} = 2\cdot l \cdot \frac{dl}{dt}[/tex]
[tex]\frac{dA}{dt} = 2\cdot \sqrt{A}\cdot \frac{dl}{dt}[/tex] (2)
Where [tex]\frac{dl}{dt}[/tex] is the rate of change of the side length, in centimeters per second.
If we know that [tex]A = 25\,cm^{2}[/tex] and [tex]\frac{dl}{dt} = 4\,\frac{cm}{s}[/tex], then the rate of change of the area of the square is:
[tex]\frac{dA}{dt} = 2\cdot \sqrt{25\,cm^{2}}\cdot \left(4\,\frac{cm}{s} \right)[/tex]
[tex]\frac{dA}{dt} = 40\,\frac{cm^{2}}{s}[/tex]
The area of the square is increasing at a rate of 40 square centimeters per second.
A card is drawn from a well shuffled pack of 52 cards . find the probability of '2' of spades
Answer:
[tex] \frac{1}{52} [/tex]Step-by-step explanation:
Given,
Total no. of cards = 52
No. of 2 of spades cards = 1
Therefore,
Probability of getting 2 of spades
[tex] = \frac{no. \: of \: required \: outcomes}{total \: outcomes} [/tex]
[tex] = \frac{1}{52} (ans)[/tex]
find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] Find the associated radius of convergence R. f(x) = 6(1 − x)−2 Step 1 The Maclaurin series formula is f(0) + f '(0)x + f ''(0) 2! x2 + f '''(0) 3! x3 + f (4)(0) 4! x4 + .
Answer:
= ∑ 6*n*x^n-1
Radius of convergence = 1
Step-by-step explanation:
f(x) = 6(1-x)^-2
Maclaurin series can be expressed using the formula
f(x) = f(0) + f '(0)x + f ''(0)/ 2! (x)^2 + f '''(0)/3! (x)^3 + f (4)(0) 4! x4 + .
attached below is the detailed solution
Radius of convergence = 1
The Maclaurin series for f(x) = 6 / (1 - x )^2 = ∑ 6*n*x^n-1 ( boundary ; ∞ and n = 1 )
express the ratio as a fraction in it's lowest terms.3kg to 800g
Answer:
15 / 4
Step-by-step explanation:
1 kg = 1000 g
3 kg
= 3 x 1000
= 3000 g
3kg to 800g
= 3kg : 800g
= 3000 : 800
= 30 : 8
= 30 / 8
= 15 / 4
15/4 is the fraction representing the ratio of 3 kilograms to 800 grams.
To express the ratio of 3 kilograms to 800 grams as a fraction in its lowest terms.
we need to convert both the quantities to the same units. Since 1 kg is equal to 1000 g, we can convert 3 kg to grams as follows:
3 kg = 3 * 1000 g = 3000 g
Now, we have the quantities in the same unit, and the ratio becomes:
3000 g to 800 g
To express this ratio as a fraction, we place the quantities over each other:
3000 g
-------
800 g
Now, to simplify the fraction to its lowest terms, we find the greatest common divisor (GCD) of the two numbers (3000 and 800) and divide both the numerator and denominator by this GCD.
The GCD of 3000 and 800 is 200, so dividing both by 200 gives us:
3000 ÷ 200 = 15
800 ÷ 200 = 4
Therefore, the ratio 3 kg to 800 g expressed as a fraction in its lowest terms is 15/4.
In summary, we first converted the units to the same (grams) to make the ratio easier to handle. Then, we represented the ratio as a fraction and simplified it to its lowest terms using the GCD method. The final answer, 15/4, is the fraction representing the ratio of 3 kilograms to 800 grams.
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PLEASE HELP :) I will give all points
answer choice a
x^2 - 5x - 1 = 0
a=1, b=-5, and c=-1
next you plug in the numbers into the quadratic formula
-(-5) plus or minus the square root of (-5)^2 - 4(1)(-1)/ 2(1)
after you simply, you should get 5 plus or minus the square root of 29, which is answer choice a
HELP! AAHHHHH SOMEBODY HELP!
If each square of the grid below is $0.5\text{ cm}$ by $0.5\text{ cm}$, how many square centimeters are in the area of the blue figure?
Answer:
8.50 cm²
Step-by-step explanation:
The dimension of each square is given as 0.5cm by 0.5cm
The area of the a square is, a²
Where, a = side length
Area of each square = 0.5² = 0.25cm
The number of blue colored squares = 34
The total area of the blue colored squares is :
34 * 0.25 = 8.50cm²
Use the graph of y=-2(x-3)^2+2 to find the vertex. Decide whether the vertex is a maximum or a minimum point.
Answer: B. Vertex is a maximum point at (3, 2)
The vertex is the point at the peak of the graph: (3, 2)Since the graph opens downward, it's the maximum pointSuppose that two balanced, six sided dice are tossed repeatedly and the sum of the two uppermost faces is determined on each toss. (a) What is the probability that we obtain a sum of 3 before we obtain a sum of 7
Answer:
[tex]\frac{(2/36)}{(1-(28/36))} = 1/4[/tex]
Step-by-step explanation:
!PLEASE HELP WILL GIVE BRAINLIEST!
An internet service charges $34 per month for internet access. Write an equation to represent the total cost based on the number of months of internet access.
Answer:
34m = c
Step-by-step explanation:
For every month (m) you pay 34 dollars. However many months youu use that service time 34 equals your total cost (c).
Answer:
[tex]let \: cost \: be \: { \bf{c}} \: and \: months \: be \: { \bf{n}} \\ { \bf{c \: \alpha \: n}} \\ { \bf{c = kn}} \\ 34 = (k \times 1) \\ k = 34 \: dollars \\ \\ { \boxed{ \bf{c = 34n}}}[/tex]
At a local community college, 57% of students who enter the college as freshmen go on to graduate. Five freshmen are randomly selected.
a. What is the probability that none of them graduates from the local community college? (Do not round intermediate calculations Round your final answer to 4 decimal places Probability
b. What is the probability that at most four will graduate from the local community college? (Do not round intermediate calculations. Round your final answer to 4 decimal places.)
c. What is the expected number that will graduate? (Round your final answer to 2 decimal places)
Answer:
a) 0.0147 = 1.47% probability that none of them graduates from the local community college.
b) 0.9398 = 93.98% probability that at most four will graduate from the local community college.
c) The expected number that will graduate is 2.85.
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they will graduate, or they will not. The probability of a student graduating is independent of any other student graduating, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
57% of students who enter the college as freshmen go on to graduate.
This means that [tex]p = 0.57[/tex]
Five freshmen are randomly selected.
This means that [tex]n = 5[/tex]
a. What is the probability that none of them graduates from the local community college?
This is P(X = 0). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.57)^{0}.(0.43)^{5} = 0.0147[/tex]
0.0147 = 1.47% probability that none of them graduates from the local community college.
b. What is the probability that at most four will graduate from the local community college?
This is:
[tex]P(X \leq 4) = 1 - P(X = 5)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{5,5}.(0.57)^{5}.(0.43)^{0} = 0.0602[/tex]
So
[tex]P(X \leq 4) = 1 - P(X = 5) = 1 - 0.0602 = 0.9398[/tex]
0.9398 = 93.98% probability that at most four will graduate from the local community college.
c. What is the expected number that will graduate?
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
In this question:
[tex]E(X) = 5*0.57 = 2.85[/tex]
The expected number that will graduate is 2.85.
Write the range of the function using interval notation.
Given:
The graph of a function.
To find:
The range of the given function using interval notation.
Solution:
Range: The set of y-values or output values are known as range.
From the given graph, it is clear that the function is defined for [tex]0<x<4[/tex] and the values of the functions lie between -2 and 2, where -2 is excluded and 2 is included.
Range [tex]=\{y|-2<y\leq 2\}[/tex]
The interval notation is:
Range [tex]=(-2,2][/tex]
Therefore, the range of the given function is (-2,2].