Which of the following functions are of exponential order c? Find c, if the answer is yes. (a) y(t) = 5t? + 24 +1. (b) y(t) = sin(31) (c) y(t) = 42 y(t) = 93 (e) y(t) 12 if t = 3 gift 3 (1) y(t) = coste
(a) Not of exponential order.
(b) Not of exponential order.
(c) Exponential order with c = 2.
(d) Not of exponential order.
(e) Not of exponential order.
To determine if a function is of exponential order, we need to check if there exist positive constants M and c such that |y(t)| ≤ M[tex]e^{ct}[/tex] for all t ≥ t₀, where t0 is some starting point.
Let's analyze each function:
(a) y(t) = 5t² + 24 + 1
This function is not of exponential order since it contains a quadratic term (t²) and does not satisfy the exponential order condition.
(b) y(t) = sin(3t)
The sine function is periodic and oscillates between -1 and 1. It is not bounded by an exponential function. Therefore, it is not of exponential order.
(c) y(t) = 4[tex]e^{2t}[/tex]
The exponential function [tex]e^{2t}[/tex] grows exponentially as t increases. The constant multiplier 4 does not affect the exponential growth. Therefore, this function is of exponential order with c = 2.
(d) y(t) = [tex]e^{t^{2} }[/tex]
The exponent t² grows faster than any exponential function with a constant base. Therefore, this function is not of exponential order.
(e) y(t) = cost [tex]e^{3t}[/tex]
The exponential function [tex]e^{3t}[/tex] grows exponentially as t increases. However, the cosine function oscillates between -1 and 1, which prevents the overall function from being bounded by an exponential function. Therefore, it is not of exponential order.
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If money in a savings account earned 8% interest per annum, how much nterest would be earned on $150.00 over three years?
Answer:
$36
Step-by-step explanation:
Given :
Interest rate, r = 8% = 0.08
Principal, P = 150
Time, t = 3 years
Simple interest = (principal * rate * time)
Simple interest = (150 * 0.08 * 3)
Simple interest = $36
a parallelogram has one angle that measures 65 what are the other three angles
Answer:
Step-by-step explanation:
65,115,115
Let y+3=xy-6x². Use implicit differentiation to find y' or dy dx
the derivative of y with respect to x, or dy/dx, for the given equation is y' = (y - 12x) / (1 - x).
We start by differentiating both sides of the equation with respect to x.
For the left-hand side, the derivative of y + 3 with respect to x is simply dy/dx, or y'.
For the right-hand side, we need to apply the product and chain rules.
Differentiating xy with respect to x gives us x(dy/dx) + y.
Differentiating -6x² with respect to x gives us -12x.
Putting it all together, we have y' + 0 = x(dy/dx) + y - 12x.
Rearranging the equation, we get y' = (y - 12x) / (1 - x).
Therefore, the derivative of y with respect to x, or dy/dx, for the given equation is y' = (y - 12x) / (1 - x).
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I'll give you the brainliest
Answer:
>
Step-by-step explanation:
sqrt{17} > sqrt{11}
Answer: >
Step-by-step explanation: the square root of 17 is going to be larger than the square root of 11. since you add 3 to both equations, that is all you have to worry about.
Please help due two days ago helpp me please Which measure of center is the most appropriate for the data in Table 1 (Height) in Task 1? Give a reason for your answer. calculate the value of the most appropriate center value of the heights.
Answer:
I think the correct answer is....... The measure of center for table 1 is 61, 62, 58, and 57 inches. The most kids had the same number of inches in this category.
I'm not 100% sure so try at your own risk
Have a great day!
The center of measures of table 1 height (task1) are Mean of heights of siblings are 58.29. Median of the height of 24 siblings are 61.5. Mode of the height 24 siblings 57,58,61,62 are the heights in inches.
What is Measures of center?
Measures of center of data set is also "a way of describing data set. The two most widely used measures of the center is mean and median".
What is mean?
Mean is the process of "adding all values and then divided by total number of values".
What is median?
Median is the "process of arranging data value in ascending or descending order and then divided data set into two if 'n' is odd then middle point is the median or if 'n' is even then sum of two mid value and then divided by two".
What is Mode?Mode can be one, "two or more in the given data set. The number or data point which have more frequency is taken as mode".
According to the question,
Measures of center is the most appropriate for the data in Table 1 (Height) in Task 1.
Heights in inches Frequency
55 1
57 3
58 3
59 2
60 1
61 3
62 3
63 2
64 2
65 2
66 1
67 1
Total number of frequency = N = 1+3++3+2+1+3+3+2+2+2+1+1 =24. Number of siblings n =12
Mean = ∑(Height of inches × Frequency of height)/Total number of frequency.
= [tex]\frac{(55*1+57*3+58*3+59*2+60*1+61*3+62*3+63*2+64*2+65*1+66*1+67*1)}{24}[/tex]
= [tex]\frac{1399}{24}[/tex]
= 58.29.
Mean of heights of siblings are 58.29
Median of the height of 24 siblings are sum of 61 and 62 divided by 2.
= [tex]\frac{61+62}{2}[/tex] [since 'n' is odd]
=61.5.
Median of the height of 24 siblings are 61.5.
Mode of the height 24 siblings 57,58,61,62 are the heights in inches.
Hence, the center of measures of table 1 height (task1) are Mean of heights of siblings are 58.29. Median of the height of 24 siblings are 61.5. Mode of the height 24 siblings 57,58,61,62 are the heights in inches.
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4x - 2y can be simplified as ____________
Answer:
4x - 2y can be simplified as 2(2x - y)
The temperature at the beginning of the day was 6 degrees F. The temperature dropped 9 degrees F by the end of the day. What was the temperature at the end of the day?
Temperature is an average measure of the kinetic energy of particles of matter.
Temperature can be in negative degrees.
The temperature at the end of the day is -3°F.
What is temperature?Temperature is an average measure of the kinetic energy of particles of matter.
The Celsius scale is generally used for measuring most temperatures.
The Fahrenheit (°F) temperature scale is also used.
We have,
The temperature at the beginning of the day = 6°F
The temperature drop by the end of the day = 9°F
Temperature can also be in negative degrees.
The temperature at the end of the day:
= 6°F - 9°F
= -3°F
Thus the temperature at the end of the day is -3°F.
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PLEASE ANSWER THIS ASAP I WILL MARK YOU THE BRAINLIEST
SHOW YOUR WORK!!!
Calculate the volume of the following three-dimensional object
Answer: 6773.27
Step-by-step explanation: volume formula for the cone is pie(radius)^2(height/3) just plug in your information into the formula and viola
Evaluate the work done between point 1 and point 2 for the conservative field F.
F = 6x i + 6y j + 6z k; P 1(4, 3, 5) , P 2(5, 6, 7)
a)W = - 180
b)W = 480
c)W = 0
d)W = 180
The correct answer is option (c) W = 0.
Given information :F = 6xi + 6yj + 6zk; P1(4, 3, 5), P2(5, 6, 7)The formula for work done by the conservative force is given by: W = U(P2) - U(P1)Where U(P) is the potential energy at point P. The force is conservative. Hence, work done is independent of path and is equal to the difference in potential energy between points 1 and 2.To find the potential energy U at any point, we use the formula: U(x, y, z) = - ∫F.dr where F is the force, and dr is the infinitesimal displacement vector.
To find the potential difference between two points, we integrate the formula: W = - ∫F.dr over a path between those two points, P1 and P2.Now we will find the potential energy at points 1 and 2.∴U(P1) = -∫F.drbetween the limits (4,3,5) and (5,6,7)Let us take the path from P1 to P2 along the straight line. Then the position vector of the path is:r = (5 - 4) i + (6 - 3) j + (7 - 5) k = i + 3j + 2k.dr = dx i + dy j + dz k= i dx + j dy + k dz = i dt + 3j dt + 2k dt = (i + 3j + 2k) dt∴∫F.dr= ∫6x i . (i + 3j + 2k) dt + ∫6y j . (i + 3j + 2k) dt + ∫6z k . (i + 3j + 2k) dt= ∫6x dt + 3 * 6y dt + 2 * 6z dt= (6x + 18y + 12z) |_P1^P2= (6 * 5 + 18 * 6 + 12 * 7) - (6 * 4 + 18 * 3 + 12 * 5)= 30 + 108 + 84 - 24 - 54 - 60= 84Thus, U(P2) - U(P1) = 0 - 84 = -84. Hence, work done = -(-84) = 84Option (d) W = 180 is incorrect as the value of work done is 84.
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tory buys a bag of cat food that has a mass of 5 kilograms. torys cat has a mass of 4 kilograms, 575 grams,. what is the difference in mass, in grams, between the bag of food and torys cat?
Answer:
5
Step-by-step explanation:
Answer 424
Step-by-step explanation: you have to change 5 kg to 5,000 grams. then you have to change 4 kg to 4,000 grams. then add 575 to 4,000. then subtract 5,000 by 4,575now your answer is 424Move point C and observe how the
angle measures change.
When AC changes,
m_ABC and mŁADC
vand are
to each other.
Answer:
[tex]\angle ABC[/tex] and [tex]\angle ADC[/tex] will change
[tex]\angle ABC[/tex] equal [tex]\angle ADC[/tex]
Step-by-step explanation:
Given
See attachment for complete question
Required
What happens when AC changes
(a) [tex]\angle ABC[/tex] and [tex]\angle ADC[/tex] are formed from points A and C. So, a change in AC will result to a change in the measures of [tex]\angle ABC[/tex] and [tex]\angle ADC[/tex].
(b) [tex]\angle ABC[/tex] and [tex]\angle ADC[/tex] are in the same segment, meaning that they will always have the same measure
Watch help video
What is the image of (-9,9) after a dilation by a scale factor of 2 centered at the
origin?
Answer:
It would be C since a scale factor of 2 makes the original A coordinate of (3,3) times 2 therefore the new coordinates being (6,6)
Step-by-step explanation:
Let W = {a + 2x + bx2 € Pz: a, b E R} with the standard operations in P2. Which of the following statements is true? W is not a subspace of P2 because 0 € W. W is a subspace of P2. a The above is true The above is true None of the mentioned O 1+xEW
The statement "W is a subspace of P2" is true, as W satisfies the conditions for being a subspace: closure under addition and scalar multiplication, and containing the zero vector.
The statement "W is a subspace of P2" is true.
To show that W is a subspace, we need to verify the three conditions for subspace:
W is closed under addition: For any two polynomials p(x) = a + 2x + bx^2 and q(x) = c + 2x + dx^2 in W, their sum p(x) + q(x) = (a + c) + 4x + (b + d)x^2 is also in W. Therefore, W is closed under addition.
W is closed under scalar multiplication: For any polynomial p(x) = a + 2x + bx^2 in W and any scalar k, the scalar multiple kp(x) = ka + 2kx + kbx^2 is also in W. Therefore, W is closed under scalar multiplication.
W contains the zero vector: The zero polynomial 0 = 0 + 0x + 0x^2 is in W since a = b = 0. Therefore, W contains the zero vector.
Since W satisfies all three conditions for subspace, it is indeed a subspace of P2.
Hence, the statement "W is a subspace of P2" is true.
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(a) what is the effect on the period of a pendulum if you double its length?
If we double the length of the pendulum, the period of the pendulum will be approximately 1.4 times longer than it was before. This relationship between the length and period of a pendulum is very important, as it allows us to calculate the length of a pendulum needed to produce a desired period. This relationship is also used in many applications, such as clocks and metronomes.
The period of a pendulum is the time it takes to swing back and forth through one complete cycle. The period of a pendulum is affected by the length of the pendulum, the acceleration due to gravity, and the amplitude of the swing. If the length of a pendulum is doubled, the period of the pendulum will also double. The reason for this is that the period of a pendulum is directly proportional to the square root of its length.
This means that if the length of the pendulum is increased by a factor of 2, the period of the pendulum will increase by a factor of sqrt(2).
Mathematically, this can be expressed as: T = 2π * sqrt(L/g).
Where T is the period of the pendulum, L is the length of the pendulum, and g is the acceleration due to gravity.
If we double the length of the pendulum (L), the equation becomes T = 2π * sqrt(2L/g).
Taking the ratio of the new period to the original period, we get: T_new/T_old = sqrt(2).
Therefore if we double the length of the pendulum, the period of the pendulum will be approximately 1.4 times longer than it was before. This relationship between the length and period of a pendulum is very important, as it allows us to calculate the length of a pendulum needed to produce a desired period. This relationship is also used in many applications, such as clocks and metronomes.
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HELP PLEASEE
I’m stuck
Answer:
:-):-)
Step-by-step explanation:
1) p<1000
2)p>500
3)By combining the above two, we get: 500<p<1000
Andre will agree as he thinks that the no. of paper clips in the box is less than 1000. But lin will not as she thinks that the no. of clips is more than 500.
4)This time, they both will agree as the no. of paper clips is more than 500 but less than 1000.
complete the proof given: AB x BE =CB x BD prove: triangle ABC triangle DBE
The complete proofs with all the reasons and statements; have been enumerated below
Triangle Proofs
The image showing the given triangle is missing and so i have attached it.
From the attached image, we can deduce that;
Statement 1; AB * BE = CB * BD
Reason 1; Given
Statement 2; CB/BE = AB/BD
Reason 2; Property of Cross Multiplication
Statement 3; ∠ABC ≅ ∠DBE
Reason 3; Vertical Angles
Statement 4; ΔABC ~ ΔDBE
Reason 4; SAS property of similarity
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If the measure of arc KM is 112°, find the measure of arc LM
What is the factored form of the expressions 4x2 - 25?
Answer:
Explanation: Realize that 4x2−25 is a difference of squares. Differences of squares, such as a2−b2 , can be factored into (a+b)(a−b) . Since 4x2=(2x)2 and 25=(5)2 , we can say that 4x2−25=(2x+5)(2x−5)
Step-by-step explanation:
Answer:
(2x + 5)(2x - 5)
Step-by-step explanation:
a² - b² = (a + b)(a - b)
4x² = 2²x²= (2x)²
25= 5* 5 = 5²
4x² - 25 = (2x)² - 5² {a= 2x ; b = 5}
= (2x + 5)(2x - 5)
Convert the time. Enter your answers in the boxes.
324 minutes =
hours,
minutes
Answer:
5 hours and 24 minutes
Step-by-step explanation:
sorry if im wrong
Answer:
5.4 hours
Step-by-step explanation:
I'm not 100 percent sure
hope this helped ;)
Do,k= (0,2) (0,6) the scale factor is
3
0
1/3
Answer:
Step-by-step explanation:
3
Please answer this is my last few points
Answer:
first is some and second is all
Step-by-step explanation:
PLEASE GIVE BRAINLIEST!!!!!!!!!!
Answer:
1. All
2. Some
Step-by-step explanation:
I belive this awnser is correct
When rolling a die, calculate the probability as a fraction of rolling a 3. The probability is
Answer:
1/6
Step-by-step explanation:
there is only one side in which there is 3 out of total six sides so 1/6
x+10=?
I NEED HELP WE JUST STARTED THIS LESSON
Answer:
I need more info to answer that question.
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
The X is invisible and doesn't have a value causing the answer to still be 10.
Suppose a regression was run between y and one x variable. The coefficient of the x variable (slope coefficient) was -0.76. The associated standard error of the slope coefficient was 0.04, and p value of the slope coefficient was 0. The t stat of the slope coefficient is: ________
The t-statistic of the slope coefficient is -19 is the answer.
Suppose a regression was run between y and one x variable.
The coefficient of the x variable (slope coefficient) was -0.76.
The associated standard error of the slope coefficient was 0.04, and p value of the slope coefficient was 0.
The t stat of the slope coefficient is -19.
To find the t-statistic value, divide the slope coefficient by the standard error.
This is given as t = slope / SE.
We have the values of the slope and the SE in the problem.
Substitute these values to get the t-statistic.t = -0.76 / 0.04 = -19
From this calculation, we can see that the t-statistic of the slope coefficient is -19.
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I need help with this math promblem will anybody help me
Answer:
d = 83
Step-by-step explanation:
Answer:
d=83°
Step-by-step explanation:
the sum of the inner angles is equal to 360°
so
127+67+d+d=360
194+2d=360
2d=166
d=83°
help me with the whole problem plssss i do anything plss.
Answer:
8 people can go
Step-by-step explanation:
Nia increased her class average by 3%. She now has a 92% in her math class.
Nia's original class average was 89%. After increasing it by 3%, she now has a 92% in her math class.
1. Let's assume Nia's original class average was X.
2. She increased her class average by 3%, which can be represented as X + (3/100)X.
3. According to the question, X + (3/100)X = 92.
4. Simplifying the equation, we have (103/100)X = 92.
5. To find X, we divide both sides of the equation by (103/100): X = (92 * 100) / 103.
6. Calculating the value, X ≈ 89.32.
7. Therefore, Nia's original class average was approximately 89.32%.
8. After increasing it by 3%, her new class average is 89.32% + (3/100) * 89.32% ≈ 92%.
Note: The values have been rounded for simplicity.
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Let D be the region enclosed by the two paraboloids z = 3x2 + + y2 z = 16 – x2 Then the projection of D on the xy-plane is: 2 *-* = 1 = 1 16 = 1 4 16 O This option O This option x None of these 16 4
The projection of the region D onto the xy-plane is an ellipse centered at the origin, with a major axis length of 4 and a minor axis length of 2.
To find the projection of the region D onto the xy-plane, we need to determine the intersection curve of the two paraboloids in the xyz-space. Setting the equations of the paraboloids equal to each other, we have:
3x^2 + y^2 = 16 - x^2.
Combining like terms, we get:
4x^2 + y^2 = 16.
This equation represents an ellipse in the xy-plane. To visualize the projection, let's rewrite the equation in terms of standard form:
(x^2)/4 + (y^2)/16 = 1.
Comparing this equation to the standard equation of an ellipse, (x^2)/(a^2) + (y^2)/(b^2) = 1, we can see that the major axis of the ellipse is along the y-axis, with a length of 4, and the minor axis is along the x-axis, with a length of 2.
Therefore, the projection of the region D onto the xy-plane is an ellipse centered at the origin, with a major axis length of 4 and a minor axis length of 2. The shape of the ellipse will have its major axis along the y-axis and its minor axis along the x-axis.
In summary, the projection of the region D onto the xy-plane is an ellipse centered at the origin, with a major axis length of 4 and a minor axis length of 2.
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The last time you bough pizza, 3 pizzdis was enough for 7 people. At that rate, how
many pizzas should you buy for a party for 35 people.
Answer:
15 pizzas.
Step-by-step explanation:
The rate is 3 pizzas for every 7 people. If there are 35 people at the party (7 times 5), the amount of pizzas you should buy is 15 pizzas (3 times 5). Hope I explained that well (^^'')