Find k such that x(t) = 10' is a solution of the differential equation dx/dt = kx k = ?
Answers
The value of k that makes x(t) = 10' a solution of the differential equation dx/dt = kx is k = ln(10).
The given differential equation is dx/dt = kx. To find the value of k such that x(t) = 10' is a solution of the differential equation, we substitute x(t) = 10' in the differential equation and solve for k.
dx/dt = kx
When x(t) = 10', we have x(t) = 10'. So, we substitute this in the above differential equation:
d(10')/dt = k(10')
Using the derivative of an exponential function, we get:
10'ln(10) = k(10')
Now, we can solve for k:
k = 10'ln(10)/10'
Simplifying this expression, we can use the property of logarithms that states:
loga(b^c) = c*loga(b)
Applying this property, we get:
k = ln(10)
Therefore, k = ln(10) makes x(t) = 10' a solution of the differential equation dx/dt = kx.
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Related Questions
consider the following problem: a farmer has 3600 ft of fencing and wants to fence off a rectangular field that borders a straight river. he does not need a fence along the river (see the figure). what are the dimensions of the field of largest area that he can fence? (let x be the width of the field in feet and l be the length of the field in feet.)
Answers
We can use the given information to write an equation for the area of the rectangular field in terms of its dimensions, and then use calculus to find the maximum value of the area.
Explanation:
Let x be the width of the rectangular field, and let l be its length. Since the field is rectangular and has no fence along the river, we can divide the 3600 ft of fencing into two equal lengths, which will be used for the length of the field, and the remaining two lengths, which will be used for the width of the field. This gives us the equation:
2x + 2l = 3600
Simplifying this equation, we get:
l = 1800 - x
The area of the rectangular field can be expressed as:
A = x * l = x(1800 - x)
To find the maximum value of A, we take the derivative of A with respect to x, and set it equal to 0:
dA/dx = 1800 - 2x = 0
Solving for x, we get:
x = 900
Substituting this value of x back into our equation for l, we get:
l = 900
Therefore, the dimensions of the rectangular field with the largest possible area are x = 900 ft (width) and l = 900 ft (length). The maximum area of the field is:
A = 900 * 900 = 810,000 square feet.
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the pharmacist says 5 g of a powder with 45cm³ of water to make a prescription medicine. How much powder mix with 81cm² of water to make a larger amounts of the same medicine?
Answers
Answer:
For 81cm³ of water we need 9g of powder.
Step-by-step explanation:
To have the same medicine in a larger amount, the concentration of the powder must be the same, and this concentration is given by the ratio between the amount of powder and the volume of water it is diluted. This ratio is
\(\frac{5}{45} = \frac{1}{9}\)
Since this ratio must be the same for a larger amount, the ratio of our desired amount of powder(let's call it x) by 81cm³ must be equal to this ratio.
\(\frac{x}{81} = \frac{1}{9}\)
Solving for x, we have
\(\frac{x}{81} = \frac{1}{9} \\\\\)
\(\frac{x}{81}\) × \(81= \frac{1}{9}\) × \(81\)
\(x = \frac{81}{9}\)
\(x = 9\)
For 81cm³ of water we need 9g of powder.
Selection of a white ball from a box with 5 white
balls, 8 red balls and 10 yellow balls.
Answers
Some jobs pay a commission plus a bonus at the end of the year. The bonus may be a percent of the salesperson's total commission for the year. a. Madelyn Carr is a sales representative. She receives 7 percent commission on all sales. At the end of the year, she receives a bonus of 5 percent of her commission. What is her total pay for a year in which she had sales totaling $412,454? b. What would Carr's total pay be if her sales were $316,250?
Answers
Answer:
Step-by-step explanation:
commision the end of the year is;
7
------- × 412454
100
= $28871.78
bonus is ;
5
--------- × 28871.78
100
= 1443.589
total pay is 1443.589 + 28871.78
= $30315.369.
(b)
5
----------- × 316250
100
= $15812.5
total pay is = 15812.5 + 316250
= $332062.5
he analysis of gas and how it behaves has been undertaken to develop several gas laws. Using applicable gas laws establish solutions for the following a) a mass of gas has a pressure of 450 kPa and temperature of 140°C. The pressure is doubled during a process but the volume remains unchanged. What is the new temperature so cooling systems can be designed? b) a mass of gas at a temperature of 160°C has a volume of 0.2mºis cooled down by 110°C with no change in pressure. Calculate the new volume of the gas.
Answers
a) The new temperature after doubling the pressure while keeping the volume constant is 80°C. b) The new volume of the gas after cooling it down by 110°C with no change in pressure is 0.0686 m³.
a) According to the gas law, when the volume remains constant (V₁ = V₂), the ratio of initial pressure (P₁) to final pressure (P₂) is equal to the ratio of initial temperature (T₁) to final temperature (T₂) for an ideal gas. Mathematically, P₁/T₁ = P₂/T₂. Plugging in the given values (P₁ = 450 kPa, T₁ = 140°C, P₂ = 2P₁), we can solve for T₂ to find that the new temperature is 80°C.
b) When the pressure remains constant, the ratio of initial volume (V₁) to final volume (V₂) is equal to the ratio of initial temperature (T₁) to final temperature (T₂) for an ideal gas. Mathematically, V₁/T₁ = V₂/T₂. Plugging in the given values (V₁ = 0.2 m³, T₁ = 160°C, T₂ = T₁ - 110°C), we can solve for V₂ to find that the new volume is approximately 0.0686 m³.
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The joint probability density function of x and y is given by f(x,y)=(x+y)/8 0 calculate the variance of (x+y)/2
Answers
The variance of (X + Y)/2 is 5/9. The variance of a random variable is defined as E[(X - E[X])^2], where E[X] is the expected value of the random variable.
We are given the joint probability density function of X and Y as f(x,y) = (x+y)/8 for 0 < x < 2 and 0 < y < 2.
We need to find the variance of (X + Y)/2.
Let Z = (X + Y)/2. Then, the expected value of Z is:
E[Z] = E[(X + Y)/2] = E[X]/2 + E[Y]/2
We can find E[X] and E[Y] as follows:
E[X] = ∫∫x f(x,y) dxdy = ∫∫x(x+y)/8 dxdy
= ∫0²∫0²x(x+y)/8 dydx = 2/3
Similarly, E[Y] = 2/3.
Therefore, E[Z] = 2/3.
Now, we need to find E[Z^2]:
E[Z^2] = E[(X + Y)^2/4] = E[X^2]/4 + E[Y^2]/4 + E[XY]/2
We can find E[X^2], E[Y^2], and E[XY] as follows:
E[X^2] = ∫∫x^2 f(x,y) dxdy = ∫0²∫0²x^2(x+y)/8 dydx = 2
E[Y^2] = ∫∫y^2 f(x,y) dxdy = ∫0²∫0²y^2(x+y)/8 dydx = 2
E[XY] = ∫∫xy f(x,y) dxdy = ∫0²∫0²xy(x+y)/8 dydx = 1/2
Therefore, E[Z^2] = (2/4) + (2/4) + (1/4) = 1.
Finally, we can find the variance of Z as:
Var(Z) = E[Z^2] - E[Z]^2 = 1 - (2/3)^2 = 5/9.
Therefore, the variance of (X + Y)/2 is 5/9.
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draw a number line and represent the following rational numbers on it:1:3/4
Answers
Answer:
It is your answer please mark me brainlist
Step-by-step explanation:
follow
Pls help PLEASE
x/3 + x-1/4=2+x.
Find X
Answers
Answer:
27/5
Step-by-step explanation:
x/3+x-1/4 = 2+x
4x+3x-3/12=2+x
7x-3=24+12x
7x-12x=24+3
5x=27
x=27/5
if 269 are sampled, what is the probability that the sample proportion will differ from the population proportion by less than 0.03? round your answer to four decimal places.
Answers
The probability will be 0.9940.
The provided parameters are
p = 0.05 (the true proportion or the mean )
n = 269 ( sample size )
we can calculate standard deviation as follows
σ = \(\sqrt{\frac{p(1-p)}{n} }\)
σ = 0.0132
Now the values that 'x' can take are
x = \(x_{1}\) ± \(x_{2}\)
x = 0.05 + 0.03, 0.05 - 0.03
x = 0.08 , 0.02
Also the z-score is
z = (x - μ)/σ
z = \(\frac{0.08-0.05}{0.0132}\) , \(\frac{0.02-0.05}{0.0132}\)
z = 2.27 , -2.27
we now find the p-values for the z-scores
p values are = 0.9970 , 0.0030
The difference in these values will give the probability
∴ P = 0.9970 - 0.0030
P = 0.9940
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The perimeter of the pentagon below is 58 units. Find the value of z.
11
2z
32-2
10
2+3
Z=
0
X
Answers
The perimeter of a pentagon is equal to the sum of the lengths of all its sides. If the perimeter of the pentagon is 58 units, we can set up an equation to solve for z:
11 + 2z + 32 - 2 + 10 + 2 + 3 = 58
Simplifying the equation:
60 + 2z = 58
Subtracting 60 from both sides:
2z = -2
Dividing both sides by 2:
z = -1
So, the value of z is -1.
A recipe for lemonade is shown. Select the two true statements about the ratios in this recipe.
Lemonade recipe
2 cups sugar
3 cups lemon juice
8 cups water
There is 14 cup of sugar for each cup of water.
There are 2 cups of sugar for each cup of water.
There are 4 cups of water for each cup of sugar.
There are 8 cups of water for each cup of sugar.
Answers
Answer:
it is There are 4 cups of water for each cup of sugar
Step-by-step explanation:
√8 as an irrational number rounded to nearest hundredth
Answers
Answer:
2.83
Step-by-step explanation:
Simplify 6c-5c+2c-8c
HELP
Answers
Answer:
I believe the answer is -5c
a*b= 1
b*c=4
c*d=9
d*e= 16
e*a=25
Answers
Step-by-step explanation:
To solve the given equations, let's assign variables to each equation and solve them step by step.
Let's assume:
a = x
b = y
c = z
d = w
e = v
From the given equations:
a * b = 1 -> x * y = 1 (Equation 1)
b * c = 4 -> y * z = 4 (Equation 2)
c * d = 9 -> z * w = 9 (Equation 3)
d * e = 16 -> w * v = 16 (Equation 4)
e * a = 25 -> v * x = 25 (Equation 5)
Now, let's solve the equations using substitution:
From Equation 1 (x * y = 1), we can rewrite it as y = 1/x.
Substituting y in Equation 2, we get (1/x) * z = 4, which gives us z = 4x.
Substituting z in Equation 3, we have (4x) * w = 9, which gives us w = 9/(4x).
Substituting w in Equation 4, we get (9/(4x)) * v = 16, which simplifies to v = (16 * 4x)/9.
Finally, substituting v in Equation 5, we have [(16 * 4x)/9] * x = 25.
Simplifying the equation, we get:
(64x^2)/9 = 25.
To solve for x, we can cross multiply and solve the quadratic equation:
64x^2 = 225.
Dividing both sides by 64, we get:
x^2 = 225/64.
Taking the square root of both sides, we have:
x = ±(√(225/64)).
So, x = ±(15/8).
Now, substituting the values of x in the respective equations, we can find the values of y, z, w, and v.
For x = 15/8:
y = 1/(15/8) = 8/15
z = 4 * (15/8) = 30/4 = 15/2
w = 9/(4 * (15/8)) = 9/(30/8) = 9 * (8/30) = 12/5
v = (16 * 4 * (15/8))/9 = (60/2)/9 = 60/18 = 10/3
For x = -15/8:
y = 1/(-15/8) = -8/15
z = 4 * (-15/8) = -30/4 = -15/2
w = 9/(4 * (-15/8)) = 9/(-30/8) = -9 * (8/30) = -12/5
v = (16 * 4 * (-15/8))/9 = (-60/2)/9 = -60/18 = -10/3
Therefore, the possible solutions for the variables are:
x = 15/8, y = 8/15, z = 15/2, w = 12/5, v = 10/3
or
x = -15/8, y = -8/15, z = -15/2, w = -12/5, v = -10/3.
Note: The solution includes both positive and negative values for the variables.
How to solve for x also what is an equation that I could do?
Answers
Answer:
x=15
Step-by-step explanation:
5x+17+36=128
5x+53=128
5x=75
x=15
What is the equation of the line that passes through the point (-8,-8)(−8,−8) and has a slope of 22?
Answers
The slope intercept form of the required line is 2x - y = -8
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If \(\theta\) is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = \(tan\theta\)
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Slope of the line = 2
The line passes through (-8, -8)
Equation of the required line-
\(y - (-8)= 2(x - (-8))\\y + 8 = 2(x + 8)\\y + 8 = 2x + 16\\2x - y = 8 -16\\2x - y = -8\)
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3. Solve for x: (x-3)2 =16
Answers
Answer:
x = 11
Step-by-step explanation:
(x - 3)2 = 16
simplify
2x - 6 = 16
add 6 to both sides
2x -6 + 6 = 16 + 6
2x = 22
divide by 2
2x/2 = 22/2
x = 11
Answer:
x=11
Step-by-step explanation:
11-3=8
8x2=16
Hope this helps you! Happy holidays!
A point has a positive x-coordinate and a positive y-coordinate. which quardrant is in it
Answers
Answer: 1
Step-by-step explanation: look at the image attached to show which quadrant is what.
when the x coord is +, it's on the right half of the graph, so by this, quadrants 1 and 4 are possible answers.
when the y coord is +, it's on the top half of the graph, this makes quadrants 1 and 2 possible answers.
look for the consistency, in this case since 1 is the only possible answer between both, the answer is 1
Can someone help quick?I don't fully get how to do this. Find the measure of the following arcs or angles. There are two images.
Answers
Answer:
AE is 77
AB is 65
CPD is 77
BPE is 142
ADC is 257
ACD is 180
Step-by-step explanation:
line CE and AD are splitting the circle in half
1/16+3/18? Find the lowest common denominator?
Answers
Answer:
48 is the lowest common denominator.
Step-by-step explanation:
\(\frac{1}{16}+\frac{3}{18}\)
\(\frac{18+16(3)}{16*18}\)
\(\frac{66}{288}\) /2
\(\frac{33}{144}\) /3
\(\frac{11}{48}\)
Therefore the lowest common denominator of both the fractions is 48.
area of square increasing at 112 centimeters squared per second, rate of change when side is 7 centimeters
Answers
The area rate of change of side of square is 8 cm/s;
dA/dt = 112 cm²/s;
Area = (r)²; where r is the side of square;
dA/dt = (dA/dr)(dr/dt);
dA/dr = 2r and dA/dt = 112 cm²/s;
Therefore; dr/dt = 112/2r at r = 7;
dr/dt = 112/14 = 8 cm/s;
Rate of change of side of square is 8 cm/s;
area is the quantity that expresses the extent of a area on the plane or on a curved floor. The location of a aircraft region or plane place refers to the location of a shape or planar lamina, at the same time as surface place refers to the vicinity of an open floor or the boundary of a 3-dimensional object.
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Select all the correct answers.
Which expressions are equivalent to log4 (²) ?
Answers
Answer:
A: -1 + 2 log4^x
C: log4 (1/4) + log4 x^2
Step-by-step explanation:
Apply logarithm properties:
log4 (1/4x^2) = log4 (1/4) + log4 x^2
Evaluate: log4 (1/4)
log4 (1/4) = -1
Substitute the value back:
-1 + lg4 x^2
Apply logarithm properties:
-1 + 2 log4 ^x
Draw a conclusion:
The expressions equivalent to: log4 (1/4x^2) are:
Answer Choices: A, and C
A= -1 + 2 log4^x
C= log4 (1/4) + log4 x^2
Hope this helps!
help me please . I don't know which method to use. maybe the time=
\( \frac{distance}{speed} \)
or....
![help me please . I don't know which method to use. maybe the time=[tex] \frac{distance}{speed} [/tex]or....](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/TOTS7oheFy4rJS7Dact4sqNgXQ7fR1lM.jpeg)
Answers
An isosceles triangle MNP has one angle, N, with a measure of 20". The
angles M and Pare congruent. Which is the measure of angle P?
Answers
P=80º
Start by doing 180-20 since N=20
M and P are congruent, so P = 160/2
P=80
You are flipping two coins. Find the probability of flipping two tails.
A. 1/2
B. 1/24
C. 1/8
D. 1/4
Answers
Answer:
D. 1/4
Step-by-step explanation:
The probability of flipping a tail is 1/2. To find the probability of flipping two tails, multiply.
1/2 x 1/2 = 1/4
Answer: Here we will learn how to find the probability of tossing two coins.
Let us take the experiment of tossing two coins simultaneously:
When we toss two coins simultaneously then the possible of outcomes are: (two heads) or (one head and one tail) or (two tails) i.e., in short (H, H) or (H, T) or (T, T) respectively; where H is denoted for head and T is denoted for tail.
Therefore, total numbers of outcome are 22 = 4
The above explanation will help us to solve the problems on finding the probability of tossing two coins.
Step-by-step explanation:
THE ANSWER MUST BE AT LEAST 1/4 OR 1/8
IF THAT IS WRONG LET ME KNOW!
AND IF YOU NEED A TUTOR I AM OPEN FOR HELP JUST CONTACT ME IF YOU HAVE ANY QUESTIONS!
ill mark braillest if right
Answers
Answer: try b
Step-by-step explanation:
This is for geometry I need to know step by step appreciate it
Answers
For the given similar triangles, the value of x = 5.
What are similar triangles used for?Similar triangles share the same associated angle measurements and proportional side lengths.
Due to their similar shapes, two figures that are not always the same size can appear comparable. We might claim, for instance, that all circles are equivalent. Squares and equilateral triangles share similar characteristics. Although similar figures need not be congruent in order to be comparable, congruent figures are always comparable.
Despite having the same shape, similar triangles have different diameters. In identical triangles, corresponding angles are equal. In analogous triangles, the ratio of the corresponding sides is the same. Any pair of equivalent sides' squares and any comparable triangle's area have the same ratio.
As the given triangles are similar,
the sides are in same ratio,
⇒ 56 / 8x - 5 = 24 / 15
⇒ 8x - 5 = 35
⇒ 8x = 40
⇒ x = 5
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Expedition Everest, a major thrill ride at Walt Disney World, often has a demand of over 3,000 riders an hour causing long waiting times for guests wishing to ride. The attraction averages 1,800 riders an hour. The roller coaster has a design capacity of 2,050 riders an hour and an effective capacity of 1,900 riders an hour.
a. What is the efficiency of Expedition Everest?
b. What is the utilization of Expedition Everest?
c. Is the operation overcapacity or undercapacity?
Answers
a. The efficiency of Expedition Everest is approximately 87.8%.
b. The utilization of Expedition Everest is approximately 94.7%.
c. The demand is greater than the effective capacity, the operation is considered overcapacity. This means that the ride cannot accommodate all the riders who wish to ride, resulting in long waiting times for guests.
To calculate the efficiency and utilization of Expedition Everest, we need to compare the actual number of riders with the design capacity and effective capacity.
Given:
Demand = 3,000 riders/hour
Average riders = 1,800 riders/hour
Design capacity = 2,050 riders/hour
Effective capacity = 1,900 riders/hour
a. Efficiency:
Efficiency is calculated as the average riders divided by the design capacity, multiplied by 100%.
Efficiency = (Average riders / Design capacity) * 100%
= (1,800 / 2,050) * 100%
≈ 87.8%
Therefore, the efficiency of Expedition Everest is approximately 87.8%.
b. Utilization:
Utilization is calculated as the average riders divided by the effective capacity, multiplied by 100%.
Utilization = (Average riders / Effective capacity) * 100%
= (1,800 / 1,900) * 100%
≈ 94.7%
Therefore, the utilization of Expedition Everest is approximately 94.7%.
c. Capacity Analysis:
To determine if the operation is overcapacity or undercapacity, we compare the demand with the effective capacity.
Demand > Effective capacity
3,000 > 1,900
Since the demand is greater than the effective capacity, the operation is considered overcapacity. This means that the ride cannot accommodate all the riders who wish to ride, resulting in long waiting times for guests.
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3. In a survey of 200 people about a bus company, 77 said they were satisfied with the bus
company's performance. What percent of the people were satisfied with the bus company's
performance?
O 23%
38.5%
061.5%
077%
Answers
The percentage of the people that were satisfied with the bus company's performance is: B. 38.5%
Given the following data:
Population = 200 peopleSatisfied people = 77 peopleTo determine the percentage of the people that were satisfied with the bus company's performance:
In this exercise, you're required to find the number of the people that were satisfied with the bus company's performance as a percentage of the total population in this survey.
Thus, we would use this formula:
\(Percentage = \frac{Satisfied\;people}{Population} \times 100\)
Substituting the given parameters into the formula, we have;
\(Percentage = \frac{77}{200} \times 100\\\\Percentage = \frac{77}{2}\)
Percentage = 38.5%
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Mae Ling earns a weekly salary of $365 plus a 5.0% commission on sales at a gift shop. How much she make in a workweek if she sold $4,800 worth of merchandise?
Answers
The amount that she make in a workweek if she sold $4,800 worth of merchandise will be $605.
How to calculate the value?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Here, Mae Ling earns a weekly salary of $365 plus a 5.0% commission on sales at a gift shop.
The amount that she make in a workweek if she sold $4,800 worth of merchandise will be:
= $365 + (5% × $4800)
= $605
The amount is $605.
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