The particular solution is [tex]y(t) = (1/2c) (t^2/2 + t/2 + 1/2c) + (2 - 1/(4c))e^(-2ct)[/tex].
[tex]dy/dt + 2cy = t^2 + 1[/tex]
To find the general solution of this differential equation, we can start by finding the integrating factor, which is given by:
I(t) = e^(∫2c dt) = [tex]e^(2ct)[/tex]
Next, we can multiply both sides of the differential equation by the integrating factor I(t):
[tex]e^(2ct) dy/dt + 2ce^(2ct) y = (t^2 + 1) e^(2ct)[/tex]
We can now recognize the left-hand side as the product rule of the derivative of the product of y and I(t):
[tex](d/dt)(y e^(2ct)) = (t^2 + 1) e^(2ct)[/tex]
Integrating both sides with respect to t gives:
[tex]y e^(2ct) = ∫(t^2 + 1) e^(2ct) dt + C[/tex]
The integral on the right-hand side can be solved using integration by parts, and we get:
∫([tex]t^2[/tex] + 1) [tex]e^(2ct) dt = (1/2c) e^(2ct) (t^2/2 + t/2 + 1/2c) + K[/tex]
where K is an arbitrary constant of integration.
Substituting this expression back into the previous equation, we get:
[tex]y e^(2ct) = (1/2c) e^(2ct) (t^2/2 + t/2 + 1/2c) + K[/tex]
Dividing both sides by e^(2ct), we obtain the general solution:
[tex]y(t) = (1/2c) (t^2/2 + t/2 + 1/2c) + Ke^(-2ct)[/tex]
where K is an arbitrary constant.
To find the particular solution that satisfies y(0) = 2, we can substitute t = 0 and y(0) = 2 into the general solution and solve for K:
[tex]y(0) = (1/2c) (0^2/2 + 0/2 + 1/2c) + Ke^(0)[/tex]
2 = 1/(4c) + K
Solving for K, we get:
K = 2 - 1/(4c)
Substituting this value of K back into the general solution, we get the particular solution:
[tex]y(t) = (1/2c) (t^2/2 + t/2 + 1/2c) + (2 - 1/(4c))e^(-2ct)[/tex]
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Complete the proof that the point (, −3) does or does not lie on the circle centered at the origin and containing the point (5, 0).
the radius of the circle is
The radius of the circle is 5.
To complete the proof, we need to find the radius of the circle centered at the origin and containing the point (5, 0). We can use the distance formula to find the distance between the origin (0, 0) and the point (5, 0):
distance = √((5 - 0)^2 + (0 - 0)^2) = √25 = 5
Therefore, the radius of the circle is 5.
Now, to determine whether the point (, −3) lies on the circle, we need to find the distance between the origin and the point (, −3):
distance = √((-3 - 0)^2 + (0 - 0)^2) = √9 = 3
Since the distance between the origin and the point (, −3) is not equal to the radius of the circle, which is 5, we can conclude that the point (, −3) does not lie on the circle centered at the origin and containing the point (5, 0).
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Hunter is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if he rolls a fair die in the shape of a pyramid that has four sides labeled 1 to 4, spins a spinner with four equal-sized sections labeled Red, Green, Blue, Orange, and flips a coin?
Hunter has 32 different possible outcomes if he rolls a pyramid-shaped die with four sides, spins a spinner with four equal-sized sections, and flips a coin.
There are different methods to approach this problem, but one possible way is to use the multiplication principle of counting, which states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks in sequence.
In this case, Hunter has three tasks: rolling the die, spinning the spinner, and flipping the coin.
For the first task, rolling the die, there are four possible outcomes.
For the second task, spinning the spinner, there are four possible outcomes as well.
For the third task, flipping the coin, there are two possible outcomes.
Using the multiplication principle, the total number of possible outcomes is:
4 x 4 x 2 = 32
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(1 point) Evaluate the line integral Sc 2y dx + 2x dy where is the straight line path from (4,3) to (9,6). Jc 2g dc + 2z du =
the value of the line integral ∫_C 2y dx + 2x dy along the straight line path from (4,3) to (9,6) is 84.
To evaluate the line integral ∫_C 2y dx + 2x dy along the straight line path from (4,3) to (9,6), follow these steps:
Step:1. Parametrize the straight line path: Define a vector-valued function r(t) = (1-t)(4,3) + t(9,6) = (4+5t, 3+3t), where 0 ≤ t ≤ 1. Step:2. Calculate the derivatives: dr/dt = (5,3). Step:3. Substitute the parametric equations into the line integral: 2(3+3t)(5) + 2(4+5t)(3). Step:4. Calculate the line integral: ∫(30+30t + 24+30t) dt, where the integration is from 0 to 1. Step:5. Combine the terms and integrate: ∫(54+60t) dt from 0 to 1 = [54t + 30t^2] from 0 to 1.
Step:6. Evaluate the integral at the limits: (54(1) + 30(1)^2) - (54(0) + 30(0)^2) = 54 + 30 = 84.
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On March 1 a commodity's spot price is $60 and its August futures price is $59. On July 1 the spot price is $64 and the
August futures price is $63. 50. A company entered into futures contracts on March 1 to hedge its purchase of the
commodity on July 1. It closed out its position on July 1. What is the effective price (after taking account of hedging) paid
by the company?
The effective price paid by the company after taking account of hedging would be $63.50, which is the August futures price on July 1. Calculate the profit or loss on the futures contracts and subtract that from the spot price on July 1, to determine the effective.
By entering into futures contracts on March 1, the company was able to lock in the price of $59 for the commodity, when the spot price was $60 and the futures price was $59, the difference between the futures price and the spot price on March 1 was $1 ($60 - $59), so the company had to pay an extra $1 per unit to hedge its purchase.
When the spot price increased to $64 on July 1, the company was still able to purchase the commodity at the lower hedged price of $59, plus the cost of the futures contract, which resulted in an effective price of $63.50. Overall, hedging helped the company mitigate the risk of price volatility and ensured a more predictable cost for the commodity purchase.
Effective price = Spot price - Profit from futures contracts
Effective price = $64 - $0.50(The difference between the futures price and the spot price on July 1 was $0.50 ($64 - $63.50))
Effective price = $63.50 per unit
Therefore, the effective price paid by the company after taking into account hedging was $63.50 per unit.
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As a candle burns, its wick gets smaller over time. When first purchased, the wick is 150 mm in length. After 50 minutes, the wick is only 110 mm in length. Find the slope you would use in a linear model of mm per minute. 3 points Construct an equation that models the length of the wick over this time period. Your answer should be in the proper form using correct letters and numbers with no spaces. 2 points Use your linear model to predict the how many minutes it would take to have 74 mm remaining. 3 points
It would take approximately 95 minutes for the wick to have 74 mm remaining.
1) Finding the slope (mm per minute):
The wick was initially 150 mm in length and reduced to 110 mm after 50 minutes. To find the slope, we use the formula:
Slope = (change in length) / (change in time)
Slope = (110 mm - 150 mm) / (50 minutes - 0 minutes)
Slope = (-40 mm) / (50 minutes)
Slope = -0.8 mm/minute
2) Constructing the linear equation:
We now have the slope (-0.8) and the initial length (150 mm) to create a linear equation:
Length (L) = initial length + slope × time (t)
L = 150 - 0.8t
3) Predicting the time to have 74 mm remaining:
To find the time, plug in 74 mm for the length (L) in the equation and solve for t:
74 = 150 - 0.8t
76 = 0.8t
t = 95 minutes
So, it would take approximately 95 minutes for the wick to have 74 mm remaining.
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Find the area of the shaded region
The area of the shaded region of the circle is 89.75 mi².
What is the area of the shaded region?The area of a sector of a circle, you can use the formula:
A = (θ/360) × π × r²
Where A is the area of the sector, θ is the central angle of the sector, r is the radius of the circle, and π is a constant approximately equal to 3.14.
From the diagram, angle of the unshaded sector equals 150 degree.
Angle of the shaded region = 360 - 150 = 210 degree
Radius r = 7 miles.
We can substitute these values into the formula and solve for the area A.
A = (θ/360) × π × r²
A = ( 210/360 ) × 3.14 × 7²
A = ( 210/360 ) × 3.14 × 49
A = 89.75 mi²
Therefore, the area of the sector is approximately 89.75 mi².
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Let R be the region in the first quadrant bounded by the graph of y=x3 the line x=2 and the x-axis. R is the base of a solid whose cross sections perpendicular to the x-axis are equilateral triangles. What is the volume of the solid?
The volume of the solid will be 32/7 √3.
How to calculate the volumeSince base of a solid whose cross-sections is perpendicular to the w-axis are equilateral triangles
Now base of triangle. is f(x) = x³ and the Area of Equilateral Triangle is ✓3/4 base²
The volume of the solid will be:
= ✓3/4 (x^7/7)²
= ✓3/4 (128/7)
= 32/7 √3
Therefore, the volume of the solid will be 32/7 √3.
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ķojo and kofta were given 38000 to share. kojo had 7500 more than kofta find each of their shares Show working
Answer:
Kofta receives $15,250 and Kojo receives $22,750.
Step-by-step explanation:
Let x represent the amount of money that Kofta has.
x + (x +7,500) = 38,000
- 7,500 - 7,500
___________________
x + x = 30,500
2x = 30,500
÷ 2 = ÷2
-------------------
x = 15,250
Therefore, Kofta has $15,250.
Let k represent the amount of money that Kojo has.
k + 15,250 = 38,00
k = 38,000 - 15,250
k = $22,750
Therefore, Kojo has $22,750
pleaseeeeee help asapppp
During an elbow flexion exercise, the relative angle at the elbow was 10 degrees at 0. 5s and 120 degrees at 0. 71s. What was the angular velocity of the elbow?
The angular velocity of the elbow during the elbow flexion exercise was approximately 523.81 degrees/s
To calculate the angular velocity of the elbow during an elbow flexion exercise, we'll use the information given about the relative angle at different times. Here's the step-by-step explanation:
First, find the change in relative angle: Δθ = Final angle - Initial angle = 120 degrees - 10 degrees = 110 degrees.
Next, find the change in time: Δt = Final time - Initial time = 0.71s - 0.5s = 0.21s.
Now, calculate the angular velocity: ω = Δθ / Δt = 110 degrees / 0.21s ≈ 523.81 degrees/s.
So, the angular velocity of the elbow during the elbow flexion exercise was approximately 523.81 degrees/s.
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what is praportional to 18/6
a small plane leaves an airport and flies north at 240 mi/hr. a jet leaves the airport 30 minutes later and follows the small plane at 360 mi/hr. how long does it take the jet to overtake the small place?
According to the distance, it will take the jet 1 hour to overtake the small plane.
Let's first calculate the distance traveled by the small plane in the time it takes for the jet to overtake it. Since the small plane is flying for an extra 30 minutes, its travel time is "t + 0.5" hours. Therefore, the distance traveled by the small plane is:
Distance of small plane = Speed of small plane x Time of small plane
Distance of small plane = 240 x (t + 0.5)
Now, let's calculate the distance traveled by the jet in "t" hours:
Distance of jet = Speed of jet x Time of jet
Distance of jet = 360 x t
Since both planes are at the same point at the time of overtaking, we can set the distances traveled by both planes equal to each other:
240 x (t + 0.5) = 360 x t
We can solve for "t" using algebra:
240t + 120 = 360t
120 = 120t
t = 1
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Consider the following.g(x) = 2e−x + ln x; h(x) = 9x2.5Find the derivative for f(x) = g(x) · h(x).f '(x) =
This is the derivative of f(x) with respect to x:
f'(x) = (-2e^(-x) + 1/x)·(9x^2.5) + (2e^(-x) + ln(x))·(22.5x^1.5)
To find the derivative of f(x) = g(x) · h(x), we'll use the product rule, which states that (u·v)' = u'·v + u·v'. Let u = g(x) and v = h(x).
u = g(x) = 2e^(-x) + ln(x)
v = h(x) = 9x^2.5
Now, find the derivatives of u and v:
u' = g'(x) = -2e^(-x) + 1/x
v' = h'(x) = 22.5x^1.5
Now apply the product rule:
f'(x) = u'·v + u·v'
f'(x) = (-2e^(-x) + 1/x)·(9x^2.5) + (2e^(-x) + ln(x))·(22.5x^1.5)
This is the derivative of f(x) with respect to x.
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WILL MARK BRAINLIEST 100 POINTS
Answer:
The answer is the fourth option - 0.63
Step-by-step explanation:
Write a system of inequalities whose solution is the set of all points in quadrant I not including the axis's.
The set of all points in quadrant I not including the axis's can be represented by the following system of inequalities:
x > 0
y > 0
Inequalities are useful in modeling situations where there are constraints or limitations. For illustration, in real- life scripts, there may be limited coffers or capacity, or certain variables must fall within a specific range. Systems of inequalities are frequently used to represent these constraints or limitations graphically. One common operation of systems of inequalities is in optimization problems, where the thing is to maximize or minimize a particular function subject to certain constraints.
In these situations, the doable region, or the set of all points that satisfy the constraints, is frequently represented as a shadowed region on a graph. The optimal result is also set up by relating the point( s) within this region that maximize or minimize the function.
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The diagram shows a track composed with a semicircle on each end. The area of the rectangle is 5,500 square meters. What is the perimeter of the th rack? Use 3.14 for π
The perimeter of the track is of 377 m.
What is the measure of the circumference of a circle?The circumference of a circle of radius r is given by the equation presented as follows:
C = 2πr.
Considering the rectangle with area 5500 m² and base 110 m, the height h, representing the diameter d of the circumference, is obtained as follows:
110d = 5500
d = 550/11
d = 50 m.
The radius is half the diameter, hence it is given as follows:
r = 25 m.
The perimeter is given as follows:
Circumference of two-half-circles = one circle of radius 25 m.Two segments of 110 m.Hence it is given as follows:
P = 2 x 110 + 2 x 3.14 x 25
P = 377 m.
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what is the answer to 8 units away from zero.
Answer:
Step-by-step explanation:
Find the necessary sample size.
A population is normal with a variance of 99. Suppose you wish to estimate the population mean μ. Find the sample size needed to assure with 68. 26 percent confidence that the sample mean will not differ from the population mean by more than 4 units.
A. 9
B. 7
C. 613
D. 25
To estimate a population mean with 68.26% confidence that the sample mean will not differ from the population mean by more than 4 units, a sample size of 7 is needed. So, the correct answer is B).
The formula to calculate the sample size needed to estimate the population mean with a specified margin of error, assuming the population standard deviation is known, is
n = ((z-score * σ) / E)²
where
n = sample size
z-score = the z-score corresponding to the desired confidence level (in this case, the 68.26% confidence level corresponds to a z-score of 1)
σ = population standard deviation
E = the desired margin of error
Substituting the given values, we get
n = ((1 * √(99)) / 4)²
n = 6.1875
Since we need to have a whole number for the sample size, we must round up to the nearest integer. Therefore, the necessary sample size is 7.
So, the answer is B) 7.
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Use the ratio test to find the radius of convergence of the power series 3x+36x^2+243x^3+1296x^4+6075x^5+
The radius of convergence is 1/3. To find the radius of convergence for the power series using the ratio test, we need to analyze the general term of the series. The given series is:
Σ(an * x^n)
where an is the coefficient of the term with x raised to the power n. The coefficients in the given series are:
a1 = 3
a2 = 36
a3 = 243
a4 = 1296
a5 = 6075
...
Notice that each coefficient is a multiple of 3^n. Thus, we can write the general term as:
an = 3^n
Now, we apply the ratio test. The ratio test states that the series converges if the limit as n approaches infinity of the absolute value of the ratio of consecutive terms is less than 1:
lim (n → ∞) |(a(n+1) * x^(n+1)) / (an * x^n)|
= lim (n → ∞) |(3^(n+1) * x^(n+1)) / (3^n * x^n)|
To simplify, divide 3^(n+1) by 3^n:
= lim (n → ∞) |(3 * x)|
The series converges when |3 * x| < 1. To find the radius of convergence, solve for |x|:
|x| < 1/3
The radius of convergence is 1/3.
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Please answer now! Please show the Example
Mr. Bilo received 8 P50-bills, 5 P100-bills, and 5 P20-bills.
How many P50, P100, and P20 bills did Mr. Pilo get?The number of P50, P100, and P20 bills Mr. Pilo got is calculated as follows;
Amount from P50-bills: 2/5 x P1,000 = P400
Amount from P100-bills: 1/2 x P1,000 = P500
The total amount he received from the P50-bills and P100-bills = P400 + P500
The total amount he received from the P50-bills and P100-bills = P900. The amount left to be changed into P20-bills = P1,000 - P900
The amount left to be changed into P20-bills = P100.
The number of bills will then be:
Number of P50-bills: P400 ÷ P50 = 8
Number of P100-bills: P500 ÷ P100 = 5
Number of P20-bills: P100 ÷ P20 = 5
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Complete question:
Mr Bilo has a P1,000-bill and asked someone to exchange in to 2/5 P50-bill and 1/2 P100-bill and the rest into 20-bill. How many P50,P100 and P20 bills did he get.
If the range of f (x) = startroot m x endroot and the range of g (x) = m startroot x endroot are the same, which statement is true about the value of m?
The only possible value of m that would make the ranges of f(x) and g(x) the same is any positive real number.
The range of a function is the set of all possible output values. In this case, we are given that the ranges of two functions, f(x) and g(x), are the same.
The function f(x) = √(mx) has a domain of x ≥ 0, since the square root of a negative number is not a real number. The function g(x) = m√x has a domain of x ≥ 0 for the same reason.
To find the range of these functions, we need to consider the possible values of the input x. For f(x), as x increases, the output √(mx) also increases, and as x approaches infinity, so does the output. For g(x), as x increases, the output m√x also increases, and as x approaches infinity, so does the output.
Therefore, if the ranges of f(x) and g(x) are the same, this means that they both have the same maximum and minimum values, and these values are achieved at the same inputs.
In particular, if we consider the minimum value of the range, this is achieved when x = 0, since both functions are defined only for non-negative inputs. At x = 0, we have f(0) = g(0) = 0, so the minimum value of the range is 0.
To find the maximum value of the range, we need to consider the behavior of the functions as x approaches infinity. As noted above, both functions increase without bound as x increases, so the maximum value of the range is infinity.
Therefore, the only possible value of m that would make the ranges of f(x) and g(x) the same is any positive real number.
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Peter eats 3 carrot sticks, with 1 cup of peanut butter, p, every day before lacrosse practice. he practices 4 days a week.
select all the equivalent expressions that represents how much peter eats before practice in one week.
To find out how much Peter eats in one week (which is 7 days), we need to multiply this expression by 7.
How much Peter eats before practice in one week?Peter eats 3 carrot sticks and 1 cup of peanut butter before lacrosse practice every day, so in one day he eats:
3 + p
To find out how much he eats in one week (which is 7 days), we need to multiply this expression by 7:
7(3 + p)
Distributing the 7, we get:
21 + 7p
So the equivalent expressions that represent how much Peter eats before practice in one week are:
3 + 4p + 3p
4(3 + p)
21 + 7p
7(3p + 1)
So the correct answers are:
4(3 + p)
21 + 7p
7(3p + 1)
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The alverado's have a monthly income of $6,000.
3. how much more do they spend on taxes than on clothing?
pls help fast! my teacher is gonna get mad!
The Alverados spend $1,200 more on taxes than on clothing.
How we get the tax spend on clothing?To determine how much more the Alverados spend on taxes than on clothing, we need to know how much they spend on each.
If we assume that the Alverados spend 25% of their income on taxes, that would be:
0.25 x $6,000 = $1,500
If we assume that the Alverados spend 5% of their income on clothing, that would be:
0.05 x $6,000 = $300
To find how much more they spend on taxes than on clothing, we can subtract the amount spent on clothing from the amount spent on taxes:
$1,500 - $300 = $1,200
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The table shows the purchases made by two customers at a meat counter. you want to buy 2 pounds of sliced ham and 3 pounds of sliced turkey. can you determine how much you will pay? explain.
The cost of purchasing 2 pounds of sliced ham and 3 pounds of sliced turkey from the meat counter is $30.95.
The table provided shows the purchases made by two customers at a meat counter. To determine how much you will pay for 2 pounds of sliced ham and 3 pounds of sliced turkey, you need to first look at the prices listed in the table. For sliced ham, the price per pound is $4.99, and for sliced turkey, the price per pound is $6.99.
To calculate the cost of 2 pounds of sliced ham, you can multiply the price per pound ($4.99) by the number of pounds (2), which gives you a total cost of $9.98. Similarly, to calculate the cost of 3 pounds of sliced turkey, you can multiply the price per pound ($6.99) by the number of pounds (3), which gives you a total cost of $20.97.
Therefore, the total cost for 2 pounds of sliced ham and 3 pounds of sliced turkey would be $9.98 + $20.97 = $30.95.
In conclusion, by using the prices listed in the table, it is possible to determine the cost of purchasing 2 pounds of sliced ham and 3 pounds of sliced turkey from the meat counter. It is important to remember to multiply the price per pound by the number of pounds needed for each item, and then add the costs together to get the total price.
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The data set shown below represents the number of times some families went out for dinner the previous week. 4, 2, 2, 0, 1, 6, 3, 2, 5, 1, 2, 4, 0, 1 an unnumbered number line labeled numbers of dinners out. create a dot plot to represent the data. what can you conclude about the dot plot of the data set? check all that apply. the range of the number line should be 0 to 7 to represent the frequency. four families said they ate out twice the previous week. one family said they ate out 5 times the previous week. the data set is symmetrical. the median best represents the data set.
Answer: B, C, E
Step-by-step explanation: Other dude posted wrong answer.
Claire flips a coin 4 times. using the table, what is the probability that the coin will show tails at least once?
2.
number of tails
probability
0
0.06
1
0.25
3
0.25
4
0.06
?
o 0.06
o 0.25
0.69
o 0.94
mark this and return
save and exit
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sunmit
The probability of flipping a coin and getting tails at least once in four flips is 15/16 or approximately 0.94. (option d).
To determine the probability of flipping a coin and getting tails at least once in four flips, we can use a probability table. The table shows all the possible outcomes of flipping a coin four times.
Flip 1 Flip 2 Flip 3 Flip 4
Outcome 1 H H H H
Outcome 2 H H H T
Outcome 3 H H T H
Outcome 4 H H T T
Outcome 5 H T H H
Outcome 6 H T H T
Outcome 7 H T T H
Outcome 8 H T T T
Outcome 9 T H H H
Outcome 10 T H H T
Outcome 11 T H T H
Outcome 12 T H T T
Outcome 13 T T H H
Outcome 14 T T H T
Outcome 15 T T T H
Outcome 16 T T T T
In the table, H represents heads, and T represents tails. There are 16 possible outcomes when flipping a coin four times. We can see that getting tails at least once is possible in 15 of these outcomes: Outcome 2, Outcome 3, Outcome 4, Outcome 6, Outcome 7, Outcome 8, Outcome 10, Outcome 11, Outcome 12, Outcome 14, Outcome 15, and Outcome 16.
Therefore, the probability of flipping a coin and getting tails at least once in four flips is the number of outcomes where tails appear at least once divided by the total number of outcomes, which is 15/16 or approximately 0.94. (option d).
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A tray of lasagna comes out of the oven at 200°F and is placed on a table
where the surrounding room temperature is 70°F. The temperature T (in °F) of
the lasagna is given by the function (0) -e(486753-1) +70, 0 s t, where tis time
(in hours) after taking the lasagna out of the oven. What is the rate of change
in the temperature of the lasagna exactly 2 hours after taking it out of the
oven?
Rate of change in the temperature of lasagna given by function T(t) = 70 + (200 - 70) × [tex]e^{(-0.0001t)}[/tex] exactly 2 hours after taking it out of oven is -0.013 °F/hour.
Surrounding room temperature is equal to 70°F
Temperature at which lasagna comes out of the oven = 200°F
The temperature T (in °F) of the lasagna at time t (in hours) after taking it out of the oven is equal to,
T(t) = 70 + (200 - 70) × [tex]e^{(-0.0001t)}[/tex]
To find the rate of change in the temperature of the lasagna exactly 2 hours after taking it out of the oven,
Find the derivative of the temperature function with respect to time t.
T'(t) = -0.013[tex]e^{(-0.0001t)}[/tex]
Substituting t = 2 into this expression gives:
T'(2) = -0.013[tex]e^{(-0.0001\times 2)}[/tex]
= -0.013[tex]e^{-0.0002}[/tex]
= -0.013 × 0.99980
= -0.0129974
= -0.013
Therefore, the rate of change in the temperature of the lasagna exactly 2 hours after taking it out of the oven is approximately -0.013 °F/hour.
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The given question is incomplete, I answer the question in general according to my knowledge:
A tray of lasagna comes out of the oven at 200°F and is placed on a table where the surrounding room temperature is 70°F. The temperature T (in °F) of the lasagna is given by the function T(t) = 70 + (200 - 70) × [tex]e^{(-0.0001t)}[/tex] where t is time(in hours) after taking the lasagna out of the oven. What is the rate of change in the temperature of the lasagna exactly 2 hours after taking it out of the oven?
please write neatly and check awnser to make sure
Question 4 < > Find the volume of the solid obtained by rotating the region bounded by y 4x2, 1 = 1, and y = 0, about the x-axis. V Submit Question
The volume of the solid obtained by rotating the region bounded about the x-axis is 3π/4 cubic units.
How to find the volume of a solid by rotating a region?To find the volume of the solid obtained by rotating the region bounded by y = 4x^2, y = 1, and y = 0 about the x-axis, we can use the method of cylindrical shells.
First, we need to find the limits of integration. The region is bounded by y = 4x^2 and y = 1, so we can set up the integral as follows:
V = ∫[0,1] 2πx(1-4x^2)dx
Next, we can simplify the integrand:
V = ∫[0,1] 2πx dx - ∫[0,1] 8πx^3 dx
V = π - 2π/4
V = 3π/4
Therefore, the volume of the solid obtained by rotating the region bounded by y = 4x^2, y = 1, and y = 0 about the x-axis is 3π/4 cubic units.
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The mean of 28 numbers is 18.
A number is added and the mean becomes 20.
What’s the new number?
Answer:
76
Step-by-step explanation:
If the mean of 28 numbers is 18 then the sum of those numbers=28×18=504
if one number is added then 29×20=580
the new number therefore=580-504=76
For each of the following functions find f(- x) and - f * (x) , then determine whether it is even, odd or neither. Justify your answer. F(x)= x^3-7/x
The function is neither even nor odd.
To find f(-x), we substitute -x for x in the function f(x):
f(-x) = (-x)^3 - 7/(-x) = -x^3 - 7/x
To find -f(x), we multiply the function f(x) by -1:
-f(x) = -1 * (x^3 - 7/x) = -x^3 + 7/x
To determine if the function is even, odd or neither, we compare f(-x) and -f(x).
If f(-x) = f(x), the function is even.
If f(-x) = -f(x), the function is odd.
If neither of these is true, the function is neither even nor odd.
Comparing f(-x) and -f(x), we have:
f(-x) = -x^3 - 7/x
-f(x) = -x^3 + 7/x
Since f(-x) and -f(x) are not equal, and f(-x) is not the negative of -f(x), the function is neither even nor odd.
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