In a certain city the temperature (in Ft hours after 9 AM was modeled by the function () - 59 - 28+0.43t^2 -0.014t^3. Find the average temperature during the period from 9 AM to 9 PM. (Round your answer to one decimal place)
Answers
Answer: The average temperature over the 12-hour period is -954.7°F.
The temperature of a city is modeled by the function () - 59 - 28+0.43t^2 -0.014t^3.
We are supposed to find the average temperature during the period from 9 AM to 9 PM. Here, 9 PM is 12 hours after 9 AM.
In order to find the average temperature during the period from 9 AM to 9 PM, we need to find the integral of the given function from 0 to 12.
The integral of () - 59 - 28+0.43t^2 -0.014t^3 is ƒ(t) = -59t - 14t^2 + 0.1075t^3 -0.0035t^4 + C where C is the constant of integration.
Let’s evaluate the constant of integration C by using the initial condition that the temperature at 9 AM is
70°F.ƒ(t) = -59t - 14t^2 + 0.1075t^3 -0.0035t^4 + Cƒ(0) = -59(0) - 14(0)^2 + 0.1075(0)^3 - 0.0035(0)^4 + C= 70°C (Given)C = 70Plugging in C = 70, we get ƒ(t) = -59t - 14t^2 + 0.1075t^3 -0.0035t^4 + 70.
Let’s find the average temperature over the 12-hour period by finding the average value of ƒ(t) over the interval [0, 12].
The average value of ƒ(t) over the interval [0, 12] is given by:
Average value = 1/(12-0) * ∫[0, 12] ƒ(t) dt. Average value = 1/12 * ∫[0, 12] (-59t - 14t^2 + 0.1075t^3 -0.0035t^4 + 70) dt. Average value = 1/12 * (-11455.92) ≈ -954.66.
The average temperature over the 12-hour period is -954.66°F.
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Related Questions
what is the last digit of 3 with a power of 2011
Answers
So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.
Consider the following argument: All cats are mammals. I am a mammal. Therefore, I am a cat. Show that this is fallacious using the language of set theory. Illustrate the fallacy with a Venn diagram.
Answers
The argument "All cats are mammals. I am a mammal. Therefore, I am a cat" is fallacious and can be shown as such using set theory and a Venn diagram.
Let's represent the sets using a Venn diagram:
-------------
| Mammals |
-------------
/ \
/ \
/ \
---- ----
| Cats | | You |
---- ----
In the Venn diagram, the circle labeled "Mammals" represents the set of all mammals, and the circle labeled "Cats" represents the set of all cats. The region where the circles overlap represents the set of mammals that are also cats.
According to the argument, "All cats are mammals," which means that the set of cats is entirely contained within the set of mammals. This relationship is correctly represented in the Venn diagram.
The argument also states, "I am a mammal," which means that you are part of the set of mammals. In the Venn diagram, your position would be within the circle labeled "Mammals" but outside the circle labeled "Cats."
The fallacy occurs when the argument concludes, "Therefore, I am a cat." This conclusion is not valid because being a mammal does not automatically make you a cat. The Venn diagram clearly shows that there is a region within the set of mammals that is not within the set of cats.
To summarize, the fallacy in the argument arises from incorrectly inferring that being a mammal automatically implies being a cat. The Venn diagram visually demonstrates that being a mammal is a broader category that encompasses various animals, including cats, but being a mammal alone does not make one a cat.
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Use Inverse Laplace Transformation to convert s-domain to time-domain function for the following functions
a)
F(s) = \(\large{\frac{2e^{-0.5s}}{s^2-6s+9}}\)
\(f(t)=\) ....
b)
F(s) = \(\large{\frac{s-1}{s^2-3s+2}}\)
\(f(t)=\) .....
c)
F(s) = \(\large{\frac{s-1}{s^2+s-2}}\)
\(f(t)=\) ....
d)
F(s) = \(\large{\frac{e^{-s}(s-1)}{s^2+s-2}}\)
\(f(t)=\) ....
Answers
The inverse Laplace transform of F(s) is:
\(f(t) = e^(-t)\)
How did we get the value?To find the inverse Laplace transform of each function, we need to express them in terms of known Laplace transforms. Here are the solutions for each function:
a)
\(F(s) = \large{\frac{2e^{-0.5s}}{s^2-6s+9}}\)
To find the inverse Laplace transform, we first need to factor the denominator of F(s). The denominator factors as (s - 3)². Therefore, we can rewrite F(s) as:
\(F(s) = \large{\frac{2e^{-0.5s}}{(s-3)^2}}\)
Now, we know that the Laplace transform of eᵃᵗ is 1/(s - a). Therefore, the inverse Laplace transform of
\(e^(-0.5s) \: is \: e^(0.5t).\)
Applying this, we get:
\(f(t) = 2e^(0.5t) * t \\
b) F(s) = \large{\frac{s-1}{s^2-3s+2}}\)
We can factor the denominator of F(s) as (s - 1)(s - 2). Now, we rewrite F(s) as:
\(F(s) = \large{\frac{s-1}{(s-1)(s-2)}}\)
Simplifying, we have:
\(F(s) = \large{\frac{1}{s-2}}\)
The Laplace transform of 1 is 1/s. Therefore, the inverse Laplace transform of F(s) is:
\(f(t) = e^(2t) \\
c) F(s) = \large{\frac{s-1}{s^2+s-2}}
\)
We factor the denominator of F(s) as (s - 1)(s + 2). The expression becomes:
\(F(s) = \large{\frac{s-1}{(s-1)(s+2)}}\)
Canceling out the (s - 1) terms, we have:
\(F(s) = \large{\frac{1}{s+2}}\)
The Laplace transform of 1 is 1/s. Therefore, the inverse Laplace transform of F(s) is:
\(f(t) = e^(-2t) \\
d) F(s) = \large{\frac{e^{-s}(s-1)}{s^2+s-2}}\)
We can factor the denominator of F(s) as (s - 1)(s + 2). Now, we rewrite F(s) as:
\(F(s) = \large{\frac{e^{-s}(s-1)}{(s-1)(s+2)}}\)
Canceling out the (s - 1) terms, we have:
\(F(s) = \large{\frac{e^{-s}}{s+2}}\)
The Laplace transform of
\(e^(-s) \: is \: 1/(s + 1).\)
Therefore, the inverse Laplace transform of F(s) is:
\(f(t) = e^(-t)\)
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After two consecutive years of 6% losses, what rate of return in the third year will produce a cumulative gain of 7%? Note: Please make sure your final answer(s) are in percentage form and are accurate to 2 decimal places. For example 34.56%. Rate of return = 0.00 %
Answers
The rate of return of approximately 17.95% in the third year would produce a cumulative gain of 7% after two consecutive years of 6% losses.
To solve the problem completely, let's calculate the rate of return required in the third year to achieve a cumulative gain of 7% after two consecutive years of 6% losses.
1. Calculate the total loss over the two years:
Total loss = (1 - 0.06) * (1 - 0.06) = 0.9416
2. Calculate the target cumulative gain:
Cumulative gain = 1 + 0.07 = 1.07
3. Set up the equation to solve for the rate of return:
1 + Rate of return = Cumulative gain / (1 - Total loss)
4. Substitute the values into the equation:
1 + Rate of return = 1.07 / (1 - 0.9416)
1 + Rate of return = 1.07 / 0.0584
5. Solve for the rate of return:
Rate of return = (1.07 / 0.0584) - 1
Rate of return ≈ 17.95%
Therefore, a rate of return of approximately 17.95% in the third year would be needed to achieve a cumulative gain of 7% after two consecutive years of 6% losses.
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show that any vector field of the form fsx, y, zd − fsy, zd i 1 tsx, zd j 1 hsx, yd k is incompressible.
Answers
Any vector field of the form F = fsx, y, zd - fsy, zd i + tsx, zd j + hsx, yd k is incompressible.
To show that the vector field F is incompressible, we need to demonstrate that its divergence is zero. The divergence of a vector field F = P i + Q j + R k is defined as the scalar function given by the dot product of the del operator (∇) with the vector field: div(F) = ∇ · F.
Let's calculate the divergence of F:
div(F) = (∂P/∂x) + (∂Q/∂y) + (∂R/∂z)
Given that F = fsx, y, zd - fsy, zd i + tsx, zd j + hsx, yd k, we can identify the components as follows:
P = fsx, y, zd - fsy, zd
Q = tsx, zd
R = hsx, yd
Now, let's calculate the partial derivatives:
∂P/∂x = ∂/∂x (fsx, y, zd - fsy, zd) = f(sx, y, zd) + x(∂f/∂x)(sx, y, zd)
∂Q/∂y = ∂/∂y (tsx, zd) = t(∂s/∂y)(x, zd)
∂R/∂z = ∂/∂z (hsx, yd) = h(∂s/∂z)(x, y) + z(∂h/∂z)(x, y)
Since we have expressions involving partial derivatives, we need to assume that the functions f, s, and h are differentiable with respect to their respective variables.
Now, substituting these expressions back into the divergence formula, we have:
div(F) = (f + x∂f/∂x) + t∂s/∂y + (h∂s/∂z + z∂h/∂z)
To show that the vector field F is incompressible, we need to prove that div(F) = 0.
To demonstrate that any vector field of the form F = fsx, y, zd - fsy, zd i + tsx, zd j + hsx, yd k is incompressible, we calculated its divergence and obtained the expression div(F) = (f + x∂f/∂x) + t∂s/∂y + (h∂s/∂z + z∂h/∂z). By setting this expression equal to zero, we can solve for the conditions that the functions f, s, and h must satisfy to ensure that the vector field is incompressible.
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13) Find the volume of the triangular prism.if the sides are
7 cm
8 cm
11 cm
cm³
Answers
Graph in the solution sret
y≥x^2
y ≤ - x^2+4
Answers
The solution to the inequality \(x^2y\) ≥ \(-x^2+4\) and \(y\) ≤ \(-x^2+4\)is a shaded region in the xy-plane.
To graph the solution to the inequality \(x^2y\) ≥ \(-x^2+4\) and \(y\) ≤ \(-x^2+4\), we can follow these steps:
1. Graph the curve \(y = -x^2+4\). This is a downward-opening parabola with vertex (0, 4).
2. Determine the regions above and below the curve \(y = -x^2+4\). Since y ≤ \(-x^2+4,\) the region below the curve is included in the solution.
3. Shade the region that satisfies the inequality \(x^2y\) ≥ \(-x^2+4\). This region is above or on the curve \(y = -x^2+4\) and satisfies the condition \(x^2y\) ≥ -\(x^2+4.\)
The resulting graph will show a shaded region below the curve\(y = -x^2+4\) and above or on the curve \(y = x^2.\)
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Five years ago, a computer that worked half as fast as a current computer cost twice as much money. The current computer's speed to price ratio is what percent of the older computer's speed to price ratio? I'm confused on what the ratio is
Answers
The current computer's speed to price ratio is 400% of the older computer's speed to price ratio.
How to obtain the speed to price ratios?
The speed to price ratios, along with the percentage, is obtained applying the proportions in the context of this problem.
Five years ago, the ratio was given as follows:
0.5x/2y = 0.25x/y.
The current ratio is given as follows:
x/y.
The current ratio is 4 times greater than the ratio of five years ago, hence it's a percentage of 400% the old ratio.
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solve the system of equation -3x-8y=20,-5x+y=19
Answers
Point Form:
(-4, -1)
Equation Form:
X =-4, y =-1
Answer:
x = -4
y = -1
Step-by-step explanation:
- 3x - 8y = 20 --> (1)
- 5x + y = 19 --> (2)
We can make y as the subject in equation 2 and name it as equation 3.
y = 19 + 5x --> (3)
Let us find the value of x.
For that, let us take equation 1 and replace y with ( 19 + 5x ).
Let us solve it now.
- 3x - 8y = 20
- 3x - 8 ( 19 + 5x ) = 20
- 3x - 152 - 40x = 20
Combine like terms and add 152 to both sides.
- 43x = 172
x = - 4
And now let us find the value of y.
For that, let us use equation 3 and replace x with -4.
Let us solve it now.
y = 19 + 5x
y = 19 + 5 × -4
y = 19 - 20
y = - 1
Tasha has a gift card to buy tickets to the movie theater. The initial value of the gift card is $120 . The function M(x)=120-12x represents the amount of money, M , in dollars, that is still left on the gift card after purchasing x movie tickets at a cost of $12 each.
Complete the statements.
The value of is 60/-60 which is viable/not viable in terms of the given context.
Answers
The solution to the linear function M(x) = 180 is of x = -5.
What is a Linear Function Equation?The linear function equation is the slope-intercept form. Thus, it is expressed as f(x) = mx + b where m is the slope and b is the y-intercept of the line.
In this problem, the function is defined as follows:
M(x) = 120 - 12x.
M(x) represents the balance remaining on the gift card after x movie tickets priced at $12 are purchased.
The domain of the situation is given as follows:
x ≥ 0. {discrete}
As the number of tickets cannot assume negative neither decimal values.
The equation is:
M(x) = 180.
The solution is calculated as:
120 - 12x = 180
12x = -60
x = -60/12
x = -5.
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The diameter of a circle is 14 ft. Find the circumference to the nearest tent
h
Answers
circumference = πd
= 3.14 × 14
43.98 ft
hope it helps...!!!
Answer:
44
Step-by-step explanation:
We are given that the diameter is 14 ft.
The radius is half the diameter, so the radius is 7 ft.
Now, the formula for circumference is: 2πr
So: 2 * π * (7) = 43.98
Round: 43.98 >> 44.0
a disk in the shape of a circle has a diameter of 64 millimeters. what is the radius of the disk?
Answers
Answer:
the radius is 32
Step-by-step explanation:
the radius of a circle is half the diameter
hope this helps
help me with this composite figure
Answers
Answer: 142 sq. ft
Step-by-step explanation: decompose the figure into two figures. Then, find the length and the width of each figure and find their separate areas. Lastly, add the two areas together to get the total area.
Find the volume of the figure below.
Answers
Answer:
I believe its 430?
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each square root expression to its expression in simplest form. 3x²y√/6xy 2x √6xy 2x² √6ry 6x¹y³√2y 3xy6y 24x³y 54225 6x³y² √2y 6zy²√ √3y
Answers
The tiles that matches the square root expression to its expression in simplest form are:
\(\sqrt(6xy)\\\sqrt(2y)\)
How to solve\(\sqrt(3x^2y)\)simplifies to \(\sqrt3 * x * \sqrty.\)
\(\sqrt(6xy)\)remains the same as it's already in the simplest form.
\(\sqrt(2x^2)\) simplifies to \(\sqrt2 * x.\)
\(\sqrt(6x^1y^3)\) simplifies to \sqrt6 * \(x * y\sqrt3.\)
\(\sqrt(6x^2y^2)\) simplifies to \sqrt6 * \(x\sqrt3 * y.\)
\(\sqrt(2y)\) remains the same as it's already in the simplest form.
\(\sqrt(3y)\)simplifies to \(\sqrt3 * \sqrt y.\)
A square root is an arithmetic process that finds the numerical value that, when squared, produces the initial number.
The value of the square root of 25 is 5, as it is the number that, when multiplied by itself, yields 25. The symbol √ can be used to denote square roots.
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Simplify
Rewrite the expression in the form 9^n
(9^2)^5
Answers
Answer:
9^10
Step-by-step explanation:
(a^b)^c = a^(b×c)
hihi
Find the value of x. Show all work. Round your answer to the nearest tenth.
25
x
23
Please help
Answers
Answer:
8.9Step-by-step explanation:
\(\tan(23^o)=\dfrac{25}x\\\\\ x\tan(23^o)=25\\\\x=\dfrac{25}{\tan(23^o)}\\\\x\approx 58.9\)
how many kilometers are in 5000 cm
Answers
Answer:0.05 kilometers are in 5000cm
Step-by-step explanation:
The simplest factorial design contains:
A. 1 independent variable with 2 conditions
B. 2 independent variables with 2 conditions
C. 2 independent variables with 3 conditions
D. 3 independent variables with 2 conditions
Answers
The simplest factorial design contains 2 independent variables with 2 conditions. The answer is option B.
A factorial design is a study in which two or more independent variables are manipulated to see their impact on the dependent variable. The simplest factorial design contains two independent variables, each with two conditions, for a total of four conditions. This is referred to as a 2x2 factorial design. The factors analyzed in such a design are the primary factor: Factor A, which has two levels, is known as the primary factor or the rows, and the secondary factor: Factor B, which has two levels, is referred to as the secondary factor or the columns.
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3. The product of two rational numbers is 15. If one of the numbers is - 10, find the other.
Answers
Answer: -1.5
because one of the numbers is - 10 => the other is 15/-10 = -1.5
Step-by-step explanation:
HELPPPP
Write a function that represents the balance after t years.
$2000 deposit that eams 5% annual interest compounded quarterly
Answers
Not sure if this is correct but:
Step-by-step explanation: P = 2000
R = 5% = 0.05
n = 4
y = 2000 ( 1 + \(\frac{0.05}{4}\)) \(^{4t}\) = 2000 ( 1.0125 )
Substitute values in the compound interest formula:
y = P ( 1 + \(\frac{r}{n}\))\(^{nt}\) .
Hope this helps..
Judy and Cassie each opened a savings account on the same day. Judy started by putting $300 in her account, and she will deposit an additional $12 each week. Cassie made an initial deposit of $100, and she will add $20 more each week. Eventually, Judy and Cassie will each have the same amount saved. How many weeks will that take?
Write a system of equations, graph them, and type the solution.
Answers
Answer: 25 weeks
Step-by-step explanation:
Let W represent the number of weeks
Judy equation is
12W + 300
Cassie equation is
20W + 100
Now let's solve it! Our system of equation is
12W + 300 = 20W + 100
Subtract 300 from both sides
12W = 20W -200
Subtract 20W from both sides
-8W = -200
W = 25 weeks
So, it takes 25 weeks for Judy and Cassie to have the same amount saved.
Answer:
let judy = 300 + 12W
cassie = 100 + 20W
300 + 12W = 100 + 20W
300 - 100 = 20W - 12W
200 = 8W
W = 25
CHECKING:
300 + 12(25) = 100 + 20(25)
300 + 300 = 100 + 500
600 = 600
Therefore, it will take 25 days for Judy and Cassie so that they have the same amount saved.
THE GRAPH IS IN THE PICTURE,line graph
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-
hey free 100 points :) (not really) please help!
Complete the square in the quadratic function f given by
f(x) = 2x2 - 6x + 4
Answers
Answer: x = 2, 1
Step-by-step explanation:2x^2 - 6x + 4 = 0
Firstly, simplify. Divide by 2 to get
2(x^2-3x+2) = 0
Move the constant to the other side.
2(x^2-3x) = -2
Divide the x term by 2 and square it
-3/2^2 = 9/4
Add this result to both sides.
2(x^2-3x+9/4) = 1/4.
Put the perfect sq on both sides
2(x-3/2)^2=1/4
Then solve the equation:
take the sqrt of both sides and isolate x for each solution
x-3/2= +/-1/2
x = 3/2 + 1/2
x= 3/2-1/2
x= 2, 1
Ron dead five dollars on the first day at work the square of that amount on the second day in three times the amount of the second day on a Thursday how much does Ron earn in three days
Answers
Answer: $105
Step-by-step explanation:
On the first day he earned 5; second day he earns square of 5 ie. 25; third day is 3 times of the second day, so it's 25x3 = 75. Add these 3 days together to get the answer, which is 105 dollars.
PLEASE HELP *URRRRGGEEEENTTTTTT*
Identify the meaning of the following word in the sentence below:
The dog’s temperament was perfect for my son.
a.
height
c.
physical and mental character;mood
b.
weight
d.
color; contrast
Answers
Answer:
c
Step-by-step explanation:
Temperament is to do with the personality of someone.
Thus the dog's temperament would relate to its physical and mental character.
c
Temperament is to do with the personality of someone.
Thus the dog's temperament would relate to its physical and mental character.
In the figure below, if line r is parallel to line s, m angle A=3x+5 and m angle B = 5x - 9 , what is m angle B ?
Answers
Answer:
∠B = 26°
Step-by-step explanation:
Parallel lines and transversal:
r // s
When parallel lines are cut by a transversal, the alternate exterior angles are congruent.
∠B = ∠A
5x - 9 = 3x + 5
Add 9 to both sides
5x = 3x + 5 + 9
5x = 3x + 14
Subtract 3x from both sides,
5x - 3x = 14
2x = 14
Divide both sides by 2
x = 14/2
x = 7
∠B = 5x - 9
= 5*7 - 9
= 35 - 9
∠B = 26°
Studious athletes A university is concerned about the academic standing of its intercollegiate athletes. A study committee chooses an SRS of 50 of the 316 athletes to interview in detail. Suppose that $40 \%$ of the athletes have been told by coaches to neglect their studies on at least one occasion. What is the probability that at least 15 in the sample are among this group?
Answers
The probability that at least 15 in the sample are among the group of athletes who have been told by coaches to neglect their studies is approximately 0.0998.
Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.
To find the probability that at least 15 in the sample are among the group of athletes who have been told by coaches to neglect their studies, we can use the binomial cumulative distribution function. This is given by:
$$P(X \ge 15) = \sum_{k=15}^{50} \binom{50}{k} (0.4)^k (0.6)^{50-k}$$
We can calculate this probability using a calculator or computer, or we can approximate it using the normal distribution. To do this, we can use the continuity correction and compute:
$$P(X \ge 15) \approx P\left(\frac{X-n p}{\sqrt{n p (1-p)}} \ge \frac{15 - 50 \cdot 0.4}{\sqrt{50 \cdot 0.4 \cdot 0.6}}\right) = P(Z \ge 1.28)$$
Where $Z$ is a standard normal random variable. Using a standard normal table or calculator, we find that $P(Z \ge 1.28) \approx 0.0998$.
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How long will it take you to paint one wall
Answers
Answer:
About 45 minutes..........
Answer:
To paint a wall using multiple coats it would approximatly 15-20 minutes
if you have paint that only uses 1 coat it would take at least 5 minutes
Step-by-step explanation:
Factor -3x^2-23x+8. Please Help
Answers
Answer:
-(x+8)(3x-1)
Step-by-step explanation:
Take out the - sign, then factor as if it is positive.
Faith can type 75 words per minute on a computer keyboard. The number of words she can type, N, is a function of the amount of time, t minutes, she spends at the computer keyboard.
Answers
Answer:
Independent: t, minutes
Dependent: n, # of words
Step-by-step explanation:
The algebraic equation for this would be, n=75t