By calculations, Colleen's photo is smaller than Ali's photo
Determining if Colleen's photo larger or smaller than Ali's photo?From the question, we have the following parameters that can be used in our computation:
Area of Ali's photo = 91 square inches.
For Colleen's photo, we have
9 inches by 7 inches
This means that
Area of Colleen's photo = 9 * 7 square inches.
Evaluate
Area of Colleen's photo = 63 square inches.
63 square inches is lesser than 91 square inches
This means that Colleen's photo is smaller than Ali's photo
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Find the derivative of the functions and simplify:
f(x) = (x^3 - 5x)(2x-1)
The derivative of the function f(x) = (x³ - 5x)(2x-1) after simplification is 6x⁴ - 10x³ - 10x².
We apply the product rule and simplify to determine the derivative of,
f(x) = (x³ - 5x)(2x-1).
The product rule is used to determine the derivative of the given function f(x),
h(x) = a.b, then after applying product rule,
h'(x) = (a)(d/dx)(b) + (b)(d/dx)(a).
Applying this for function f,
f'(x) = 6x⁴ - 25x² - 10x³ + 15x²
f'(x) = 6x⁴ - 10x³ - 10x².
Therefore, f'(x) = 6x⁴ - 10x³ - 10x² is the derivative of f(x) after simplifying the function.
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What is the height, to the nearest tenth of a foot, of a tree that creates a 35-foot shadow when the sun is at an angle of elevation of 35⁰? (do NOT type in units, just the value)
The height of the tree is approximately 20.1 feet.
What is the height of a tree that produces a 35-foot shadow when the sun is at an angle of 35 degrees?To determine the height of the tree, we can use the tangent function, which relates the opposite side (the height of the tree) to the adjacent side (the length of the shadow) of a right triangle.
tan(35°) = height of tree / 35 feet shadow
Rearranging this formula, we get:
height of tree = 35 feet shadow x tan(35°)
Plugging in the given values and using a calculator, we get:
height of tree = 35 x tan(35°) ≈ 20.1 feet
Therefore, the height of the tree is approximately 20.1 feet.
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1⁄6 of the boys joined the basketball team and 2⁄9 of the boys joined the soccer team. How many boys are there in the soccer team? There are 540 boys
If 1/6 of the boys joined the basketball team, there are 160 boys in the soccer team.
If 1/6 of the boys joined the basketball team, then 5/6 of the boys did not join the basketball team. Similarly, if 2/9 of the boys joined the soccer team, then 7/9 of the boys did not join the soccer team.
Let's first find out how many boys did not join the soccer team:
7/9 x 540 = 380
Therefore, 380 boys did not join the soccer team.
To find out how many boys did join the soccer team, we can subtract the boys who did not join from the total number of boys:
540 - 380 = 160
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3cm on a map represents a distance of 60 if the scale is expressed in the ratio 1:n then n
What is the cost of 0. 7 kg of apples, if 1 kg of apples cost 89. 50
In the proportion, the cost of 0.7kg apple is Rs.62.65 .
What is proportion?
A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.
Here cost of 1kg apples = 89.50
Then cost of 0.7 kg apple = x.
Now using proportion,
=> 1 = 89.50
0.7= x
=> x = [tex]\frac{89.50\times0.7}{1}[/tex]
=> x = 62.65.
Hence the cost of 0.7kg apple is Rs.62.65 .
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Of the last 12 cakes sold at graces cakes,6 were carrot cakes. Find the experimental probability the next cake sold will be a carrot cake.in percentages.
Suppose the area of a trapezoid is 126 yd?. if the bases of the trapezoid are 17 yd and 11 yd long, what is the height?
a 4.5 yd
b. 9 yd
c. 2.25 yd
d. 18 yd
The height of the trapezoid is 9 yards. Therefore, the correct answer is option b. 9 yd.
To find the height of the trapezoid with the given area and base lengths, we will use the formula for the area of a trapezoid:
Area = (1/2) * (base1 + base2) * height
Here, the area is given as 126 square yards, base1 is 17 yards, and base2 is 11 yards. We need to find the height.
1. Substitute the given values into the formula:
126 = (1/2) * (17 + 11) * height
2. Simplify the equation:
126 = (1/2) * 28 * height
3. To isolate the height, divide both sides by (1/2) * 28:
height = 126 / ((1/2) * 28)
4. Calculate the result:
height = 126 / 14
height = 9
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Stacy has 3 collector’s cards. She receives 1 more card each week that she volunteers at the student center. Let x = the number of weeks. Let y = the number of cards
The equation would be: y = 3 + x
To include the terms you mentioned, we can set up an equation to represent the relationship between the number of weeks Stacy volunteers (x) and the number of cards she has (y).
Since Stacy starts with 3 collector's cards and receives 1 more card each week she volunteers, the equation would be:
y = 3 + x
In this equation, x represents the number of weeks Stacy volunteers, and y represents the total number of collector's cards she has.
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Students attending a technology summer camp were asked what technology class they would like to attend at the camp. They chose between one of the following classes: robotics, video game design, or website design. The camp director constructed a frequency table to analyze the students’ class choices.
Robotics Video Game Design Website Design Total
Females 116 94 152 362
Males 172 157 52 381
Total 288 251 204 743
A camp counselor says that about 68% of female students chose a design class and the camp director says that about 34% of female students chose a design class
The frequency table shows that 152 female students chose website design out of a total of 362 female students, which is about 0.421 or 42%.
The frequency table shows that out of the total 362 female students attending the technology summer camp, 152 chose website design, which is a design class. This means that the percentage of female students who chose a design class is 152/362 = 0.4202 or about 42%.
However, the camp counselor says that about 68% of female students chose a design class. It is unclear where the counselor obtained this information from as it is not reflected in the frequency table. It is possible that the counselor gathered this information from a different survey or observation.
On the other hand, the camp director's statement is more accurate as it is based on the frequency table.
The frequency table shows that 152 female students chose website design out of a total of 362 female students, which is about 0.421 or 42%. It is important to rely on data and accurate information when making statements or drawing conclusions.
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Each letter in these following problems will be transformed into a number based on their number in the alphabet. Solve these following problems based on this information.
1) n + e
2) t-j
3) d x e
4) p/b
The solution to the problems are given below:
n + e = 14 + 5 = 19t - j = 20 - 10 = 10d x e = 4 x 5 = 20p / b = 16 / 2 = 8How to solveGiving each of the letters numbers based on their numerical position on the English alphabet, we can solve below:
n (14) + e (5) = 14 + 5 = 19
t (20) - j (10) = 20 - 10 = 10
d (4) x e (5) = 4 x 5 = 20
p (16) / b (2) = 16 / 2 = 8
It can be seen that with the letter e for example is the 5th letter of the alphabet and the value is used to compute the addition of the problem.
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a) Find the general solution of the differential equation dy 2.cy dar 22 +1 3 b) Find the particular solution that satisfies y(0) 2
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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An oil slick on a lake is surrounded by a floating circular containment boom. as the boom is pulled in, the circular containment area shrinks. if the radius of the area decreases at a constant rate of 7 m/min, at what rate is the containment area shrinking when the containment area has a diameter of 80m?
The containment area is shrinking at a rate of 280π m²/min when the diameter is 80m and the radius is decreasing at a constant rate of 7m/min.
What is the rate of containment area shrinkage?
Let's begin by first finding the radius of the containment area when its diameter is 80m.
The diameter of the containment area is 80m, so its radius is half of that:
[tex]r = 80m / 2 = 40m[/tex]
Now, we need to find the rate at which the containment area is shrinking when the radius is decreasing at a constant rate of 7m/min.
We can use the chain rule of differentiation to find this rate:
[tex]dA/dt = dA/dr * dr/dt[/tex]
where A is the area of the containment, t is time, r is the radius of the containment, and dA/dt and dr/dt are the rates of change of A and r with respect to time, respectively.
We know that dr/dt = -7 m/min (negative because the radius is decreasing), and we can find dA/dr by differentiating the formula for the area of a circle with respect to r:
A = π[tex]r^2[/tex]
[tex]dA/dr = 2πr[/tex]
So, when r = 40m, we have:
[tex]dA/dt = dA/dr * dr/dt[/tex]
= (2πr) * (-7)
= -280π [tex]m^2[/tex]/min
Therefore, the containment area is shrinking at a rate of 280π m^2/min when the radius is decreasing at a constant rate of 7m/min and the diameter of the containment area is 80m.
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A company randomly assigns employees four-digit security codes using the numbers
1 through 4 to activate their e-mail accounts.
Any of the digits can be repeated. Is it likely that more than 3 of the 1,280 employees will be assigned the code 4113? PLEASE I WILL GIVE U BRAINLIEST!!
Answer:
1email is given by its boss and another email is given by its assistent
Ao
Del
5. An archway has vertical sides 10 feet high. The top of an archway can
be modeled by the quadratic function f(x) = -0. 5x2 + 10 where x is the
horizontal distance, in feet, along the archway. How far apart are the
walls of the archway? Round your answer to the nearest tenth of a foot.
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
293
The walls of the archway are approximately 8.9 apart.
Find out the distance between the walls of the archway?To find the distance between the walls of the archway, we need to find the horizontal distance where the function f(x) intersects the x-axis. This is because the archway's walls are vertical, and their distance apart is the same as the horizontal distance between the points where the archway meets them.
To find the x-intercepts of the function f(x) = -0.5x^2 + 10, we need to set f(x) = 0 and solve for x:
0 = -0.5x^2 + 10
0.5x^2 = 10
x^2 = 20
x = ±√20
Since the archway is a physical object, we can discard the negative value for x, which means the archway meets the walls at x = √20 feet.
To find the distance between the walls of the archway, we can double this value:
2√20 ≈ 8.94
Then it's concluded that the walls of the archway are approximately 8.9 feet apart.
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Consider the concentration, C, (in mg/liter) of a drug in the blood as a function of the amount of drug given, x, and the time since injection, t For 0 <= x <= 5 and t >= 0 hours, we have C = f(x,t) = 26te^-(5-x) f (3,5) = _____
Using the given function, we can plug in x=3 and t=5 to find the concentration of the drug in the blood:
C = f(x,t) = 26te^-(5-x)
C = f(3,5) = 26(5)e^-(5-3)
C = f(3,5) = 130e^-2
Using a calculator, we can simplify this to:
C = f(3,5) ≈ 32.22 mg/liter
Therefore, the concentration of the drug in the blood 3 hours after injection with a dosage of 5 mg is approximately 32.22 mg/liter.
Hi! To find the concentration C at f(3,5), you'll need to plug in the values for x and t into the given function f(x,t) = 26te^-(5-x).
So, f(3,5) = 26(5)e^-(5-3) = 130e^(-2).
Now, calculate the exponential value: e^(-2) ≈ 0.1353.
Finally, multiply this value by 130: 130 * 0.1353 ≈ 17.589.
Thus, f(3,5) = 17.589 mg/liter (rounded to 3 decimal places).
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7. If angle GFE ~ angle CBE, find FE.
The value of FE comes out to be 35.
What is angle?An angle is a geometric figure formed by two rays or line segments that share a common endpoint, called the vertex. The measure of an angle is typically given in degrees or radians, and it describes the amount of rotation needed to move one of the rays or line segments to coincide with the other. Angles are used in many areas of mathematics, physics, engineering, and other sciences to describe and analyze various phenomena.
What is parallel line?Parallel lines have the same slope and will never meet, no matter how far they are extended. Parallel lines are important in geometry and other areas of mathematics, as well as in engineering, architecture, and other fields where precise measurements and constructions are required.
[tex]4x-1/x+5 = 60/24\\5x+25= 8x-2\\27= 3x\\x=9[/tex]
Therefore FE= 4×(9)-1
=35
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A square pyramid is contained within a cone such that the vertices of the base of the pyramid are touching the edge of the cone. They both share a height of 20 cm. The square base of the pyramid has an edge of 10 cm. Using 3.14 as the decimal approximation for T, what is the volume of the cone? 1046.35 cubic centimeters 2093.33 cubic centimeters O 4185.40 cubic centimeters 06280.00 cubic centimeters
To find the volume of the cone, we first need to find its radius. Since the pyramid is contained within the cone such that the vertices of the base of the pyramid are touching the edge of the cone, the diagonal of the square base of the pyramid is equal to the diameter of the base of the cone. The diagonal of the square base of the pyramid is:
d = √(10^2 + 10^2) = √200 = 10√2 cm
Therefore, the diameter of the base of the cone is 10√2 cm, and the radius is 5√2 cm.
The volume of the cone can be calculated using the formula:
V = (1/3)πr^2h
where r is the radius of the base of the cone and h is the height of the cone.
Substituting the given values, we get:
V = (1/3)π(5√2)^2(20)
V = (1/3)π(50)(20)
V = (1/3)(1000π)
V = 1000/3 * π
Using 3.14 as the decimal approximation for π, we get:
V ≈ 1046.35 cubic centimeters
Therefore, the volume of the cone is approximately 1046.35 cubic centimeters. The answer is A.
How do you solve this cube root function?
The solutions for the cube function are x=64 or x= -64.
Power RulesThe main power rules are presented below.
Multiplication with the same base: you should repeat the base and add the exponents.Division with the same base: you should repeat the base and subtract the exponents.Power. For this rule, you should repeat the base and multiply the exponents.Exponent negative - For this rule, you should write the reciprocal number with the exponent positive.Zero Exponent. When you have an exponent equal to zero, the result must be 1.The question gives the equation [tex]x^{2/3}[/tex]=16, you can rewrite it as: [tex]\sqrt[3]{x^2}[/tex]=16.
For eliminating the cubic root, you should apply the power 3 ib both sides. See:
[tex](\sqrt[3]{x^2})^3[/tex]= 16³
x²= 4096
Finally, you have x=64 or x=-64
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Question 11
It took Fred 12 hours to travel over pack ice from one town in the Arctic to another town 360 miles
away. During the return journey, it took him 15 hours. Assume the pack ice was drifting at a constant
rate, and that Fred's snowmobile was traveling at a constants
What was the speed of Fred's snowmobile?
The speed of Fred's snowmobile was 30 miles per hour.
This is calculated by dividing the distance traveled by the time taken for each journey, which gives a speed of 30 mph for both the outward and return journeys.
To find Fred's speed, we can use the formula speed = distance/time. We know that Fred traveled a distance of 360 miles in 12 hours on the outward journey, so his speed was 360/12 = 30 mph.
Similarly, on the return journey, he traveled the same distance of 360 miles, but it took him 15 hours, so his speed was again 360/15 = 24 mph.
However, we are asked to find his constant speed, so we take the average of the two speeds, which gives us (30 + 24)/2 = 27 mph. Therefore, Fred's snowmobile was traveling at a constant speed of 30 mph on both journeys.
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what the root of this question?
Answer:
[tex] \sqrt{125 {p}^{2} } = p \sqrt{25} \sqrt{5} = 5p \sqrt{5} [/tex]
D is the correct answer.
The high temperature in Jackson, WY, on July 13 was 80°F. Use the formula, C = (F - 32), where C is Celsius degrees and
Fis Fahrenheit degrees, to convert 80°F to Celsius degrees. Round to the nearest tenth of a degree
The temperature of 80°F is equivalent to 48°C.
How to convert temperature from Fahrenheit to Celsius using a specific formula?To convert 80°F to Celsius degrees using the formula C = (F - 32), we substitute the given Fahrenheit temperature into the formula.
C = (80 - 32) = 48
Therefore, the temperature of 80°F is equivalent to 48°C.
The Celsius scale is commonly used in scientific and international contexts, while the Fahrenheit scale is more prevalent in the United States. The conversion formula allows us to convert temperatures between these two scales.
Rounding to the nearest tenth of a degree, we find that 48°C remains unchanged.
It's worth noting that the Celsius scale sets the freezing point of water at 0°C and the boiling point at 100°C at standard atmospheric pressure. In contrast, on the Fahrenheit scale, water freezes at 32°F and boils at 212°F.
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can someone did this step by step correctly and not give the wrong answer
A cylinder has the net shown.
net of a cylinder with diameter of each circle labeled 3.8 inches and a rectangle with a height labeled 3 inches
What is the surface area of the cylinder in terms of π?
40.28π in2
22.80π in2
18.62π in2
15.01π in2
h(t) = -16t^2 +90t
how many seconds will it take for the ball to reach its maximum height
The amount of time it would take for the ball to reach its maximum height is 2.1825 seconds.
How to determine the time when the ball would reach its maximum height?Based on the information provided, we can logically deduce that the height (h) in feet, of this ball above the ground is related to time by the following quadratic function:
Next, we would determine the maximum height of this ball by taking the first derivate in order to determine the time (t) it takes as follows;
h(t) = -16t² + 90t
h'(t) = -32t + 90
90 = 32t
t = 90/32 = 2.1825 seconds.
h(2.1825) = -16(2.1825)² + 90(2.1825)
h(2.1825) = 120.21 feet.
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In triangle ABC, the length of side AB is 12 inches and the length of side BC is 20 inches. Which of the following could be the length of side AC?
Applying the triangle inequality theorem, the possible length of side AC is: C. 18 inches.
How to Determine the Length of a Triangle Using Triangle Inequality Theorem?The triangle inequality theorem states that lengths of the two sides of a triangle, when added together must be greater than the third side of any given triangle.
Therefore, to determine the possible length of side AC, we can use the triangle inequality theorem, stated above and applying this to triangle ABC, we have the following:
AC < AB + BC
AC < 12 + 20
AC < 32
This implies that, length of side AC must be less than 32 inches. Thus, the answer is: C. 18 inches.
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True or false:
True or false cultural traits diffused from one group usually are changed or adopted over time by the people in the receiving cultural
All diffused elements of cultural are successfully integrated into other cultures
False. Cultural traits that are diffused from one group are not always changed or adopted over time by the people in the receiving culture.
This is because different cultures have their own unique values, beliefs, and practices that may not align with the diffused cultural trait. Additionally, some cultural traits may be seen as a threat to the receiving culture and therefore not adopted.
Moreover, not all diffused elements of culture are successfully integrated into other cultures. Some may be rejected outright, while others may only be partially integrated or adapted to fit the receiving culture. It's important to note that cultural diffusion is a complex and ongoing process that involves a multitude of factors, including social, economic, and political influences, as well as individual attitudes and beliefs.
Therefore, the success of cultural diffusion and integration can vary greatly from one context to another.
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Express the volume of the sphere x^2+ y^2 + z2 < 36 that lies between the cones z = √ 3x^2 + 3y^2 and z = √(x^2+y^2)/3
The volume of the sphere that lies between the two cones is approximately 43.53 cubic units.
How to calculate the volume of the sphereTo find the volume of the sphere that lies between the given cones, we first need to determine the limits of integration.
Since the sphere has a radius of 6 (since x² + y² + z² = 36), we can use spherical coordinates to express the volume as an integral. Let's first consider the cone z = √3x² + 3y².
In spherical coordinates, this is equivalent to z = ρcos(φ)√3, where ρ is the radial distance and φ is the angle between the positive z-axis and the line connecting the origin to the point.
Similarly, the cone z = √(x²+y²)/3 can be expressed in spherical coordinates as z = ρcos(φ)/√3.
Since we're only interested in the volume of the sphere between these cones, we can integrate over the limits of ρ and φ that satisfy both inequalities.
The limits of ρ will be 0 (the origin) to 6 (the radius of the sphere).
To find the limits of φ, we need to solve for the intersection points of the two cones.
Setting the two equations equal to each other, we get:
ρcos(φ)√3 = ρcos(φ)/√3
Solving for φ, we get:
tan(φ) = 1/√3 Using the inverse tangent function, we find that: φ = π/6, 7π/6
So the limits of integration for φ will be π/6 to 7π/6.
Finally, we need to integrate over the full range of θ (the angle between the positive x-axis and the line connecting the origin to the point).
This will be 0 to 2π.
Putting it all together, the volume of the sphere between the two cones is:
∫∫∫ ρ^2sin(φ) dρ dφ dθ
With limits of integration:
0 ≤ ρ ≤ 6 π/6 ≤ φ ≤ 7π/6 0 ≤ θ ≤ 2π
Evaluating this integral gives:
V = 288π/5 - 216√3π/5
So the volume of the sphere that lies between the two cones is approximately 43.53 cubic units.
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Find the value(s) of k for which u(x,t) = e¯³ᵗsin(kt) satisfies the equation uₜ = 4uxx
The two values of k that satisfy the given equation are approximately 0.1449/t and 1.096/t.
We have the partial differential equation uₜ = 4uₓₓ. Substituting u(x,t) = e¯³ᵗsin(kt) into this equation, we get:
uₜ = e¯³ᵗ(k cos(kt) - 3k sin(kt))
uₓₓ = e¯³ᵗ(-k² sin(kt))
Now, we can compute uₓₓ and uₜ and substitute these expressions back into the partial differential equation:
uₜ = 4uₓₓ
e¯³ᵗ(k cos(kt) - 3k sin(kt)) = -4k²e¯³ᵗ sin(kt)
Dividing both sides by e¯³ᵗ and sin(kt), we get:
k cos(kt) - 3k sin(kt) = -4k²
Dividing both sides by k and simplifying, we get:
tan(kt) - 1 = -4k
Letting z = kt, we can write this equation as:
tan(z) = 4z + 1
We can graph y = tan(z) and y = 4z + 1 and find their intersection points to find the values of z (and therefore k) that satisfy the equation. The first intersection point is approximately z = 0.1449, which corresponds to k ≈ 0.1449/t. The second intersection point is approximately z = 1.096, which corresponds to k ≈ 1.096/t. Therefore, the two values of k that satisfy the given equation are approximately 0.1449/t and 1.096/t.
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A vehicle has a mass of 1295 kg and uses petrol. Another vehicle has a mass of 1290 kg and uses diesel fuel, 1L of petrol has a mass of 737g and 1L of diesel has a mass of 820g. How many litres of fuel will result in the two vehicles having the same mass? Round to the nearest tenth of a litre.
Answer:
Another vehicle has a mass of 1290 kg and uses diesel fuel. 1 L of petrol has a mass of 737 g. 1L of diesel has a mass of 820g.
PLEASE HELP!! LIKE ASAPP
Answer:
12(8) + (1/2)(13)(20) + (1/4)π(8^2)
= 96 + 130 + 4π = 226 + 16π ft^2
= about 276.27 ft^2
Determine whether the geometric series is convergent or divergent. If it is convergent, find the sum. (If the quantity diverges, enter DIVERGES.) 00 7 80 3| n n = 1
|r| = 7/80 < 1, the series is convergent. The sum = 0/(1-7/80) = 0. the sum of the geometric series is 0.
The geometric series with first term 0 and common ratio 7/80 is given by 0, 7/80, (7/80)², (7/80)³, ... In general, the nth term is (7/80)ⁿ⁻¹.
To determine whether this series is convergent or divergent, we can use the formula for the sum of an infinite geometric series:
sum = a/(1-r)
where a is the first term and r is the common ratio. In this case, a = 0 and r = 7/80.
If |r| < 1, then the series converges to the sum given by the above formula. If |r| ≥ 1, then the series diverges.
In this case, |r| = 7/80 < 1, so the series is convergent. The sum is given by:
sum = 0/(1-7/80) = 0
Therefore, the sum of the geometric series is 0.
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