find a power series representation for the function. f(x) = x5 4 − x2
Answers
The power series representation for the given function f(x) is given by:
\(x^(5/4) - x^2= (5/4)x^(1/4)x - (5/32)x^(-3/4)x^2 + (25/192)x^(-7/4)x^3 - (375/1024)x^(-11/4)x^4 + ...\)
The given function is f(x) =\(x^5/4 - x^2.\)
We are required to find a power series representation for the function.
Let's find the derivatives of f(x):f(x) = \(x^_(5/4) - x^2\)
First derivative:
f '(x) = \((5/4)x^_(-1/4) - 2x\)
Second derivative:
f ''(x) = \((-5/16)x^_(-5/4) - 2\)
Third derivative:
f '''(x) =\((25/64)x^_(-9/4)\)
Fourth derivative:
f ''''(x) =\((-375/256)x^_(-13/4)\)
The general formula for the Maclaurin series expansion of f(x) is:
\(f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + … + f(n)(0)x^n/n! + …\)
Therefore, the Maclaurin series expansion of f(x) is:
f(x) =\(x^_(5/4)\)\(- x^2\)
= f\((0) + f '(0)x + f ''(0)x^2/2! + f '''(0)x^3/3! + f ''''(0)x^4/4! + ...\)
=\(0 + [(5/4)x^_(1/4)\)\(- 0]x + [(-5/16)x^_(-5/4)\)\(- 0]x^2/2! + [(25/64)x^_(-9/4)\)\(- 0]x^3/3! + [(-375/256)x^_(-13/4)\)\(- 0]x^_4/\)\(4! + ...\)
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Related Questions
in what one year period of the study did the rabbit populations see the greatest decrease?
Answers
Answer- The rabbit population decreased in 2013 and 2015 in some areas of up to 80%
Consider a falling object accounting for both gravity and air resistance, with the latter proportional to the square of the velocity. Find v(t) and determine the terminal velocity 2. The following nonlinear equation is not separable. However, the substitution y zr(z) converts the equation into a separable equation for v(x). Use this substitution to solve the equation (be sure to express your final answer in terms of y). dy dx 3. One snowy day a forensics team was brought to a hotel two miles outside of town to investigate a homicide that occured in a suite where the temperature was held fixed at 70°. When the team arrived at 2:15pm the temperature of the body was 90° and one hour later it was 85°. Determine the time of the murder. (Assume Newton's law of cooling and a normal body temperature of 98.6 at the time of death). Who committed the murder? 4. Suppose Euler's Method is used to solve the following Initial Value Problem on the interval t e [0,T]. dy dt 9 =y, y(0) = 30, Write down Euler's iteration formula for this equation, and use this to determine yi, y2. ys and yn in terms of yo. Evaluate yn in the limit n -oo, i.e. h-0. 5. The equation of motion for the velocity, vd of an object dropped down a hole bored through the center of the earth is du dt gmr where r is the distance from the center of the earth to the object, and R is the radius of the earth. Suppose u o initially, i.e. when r # R. Recall from the chain rule that ar Use this fact to solve for the velocity of the mass as a function of r. Then set v in your resulting expression to obtain a nonlinear equation for r. Solve this equation subject to the initial condtion r(0) - R. How long will it take for the object to reach the other side of the earth, i.e. when r-R? (g 32ft/s2, and R- 2.1 x 107ft).
Answers
The time it takes for the object to reach the other side of the earth is \((2gR^2/u_o) sec\).
1. The equation for a falling object accounting for both gravity and air resistance is given by:
\(m*dv/dt = -mg - kv^2\),
where m is the mass of the object, g is the gravitational acceleration, and k is a constant dependent on air resistance. The velocity of the object, v(t), can be determined by solving this differential equation. The terminal velocity is given by \(v_t = (mg/k)\).
2. The substitution y = zr(z) transforms the nonlinear equation into a separable equation for v(x). This can be expressed as:
\((dy/dx)/y = (dz/r(z))/z\).
Integrating both sides of the equation and rearranging gives:
ln(abs(y)) = ln(C) + ln(abs(z)) + ln(abs(r(z)))
where C is an integration constant. This equation can be solved for y in terms of z, r(z), and C.
3. Using Newton's law of cooling, the temperature of the body, T(t), can be expressed as:
\(T(t) = 98.6 + (90 - 98.6)e^(-kt)\),
where k is a constant of proportionality and t is the time. This equation can be solved for k and then used to determine the time of the murder, \(t_m\). Since the murderer is the one who fixed the temperature of the suite, the murderer can be identified as the one who set the temperature at 70°.
4. Euler's iteration formula for this equation is given by:
\(yi+1 = yi + hf(xi,yi)\),
where h is the step size, xi and yi are the independent and dependent variables, respectively, and f(xi,yi) is the right-hand side of the differential equation. Using this formula, the values of yi, y2, ys, and yn can be determined in terms of yo. Taking the limit as h -> 0 gives yn -> 30.
5. Using the chain rule, the velocity of the object, vd, can be expressed as:
\(vd = (dr/dt) = (1/r)*(du/dt)\).
Substituting this into the equation of motion and rearranging gives a nonlinear equation for r:
du/dt + gmr = 0.
This equation can be solved subject to the given initial condition to obtain r(t). Setting r = R in the resulting expression gives \(t = (2gR^2/u_o)\)sec, which is the time it takes for the object to reach the other side of the earth.
The time it takes for the object to reach the other side of the earth is \((2gR^2/u_o) sec\).
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what annual medical costs will ronald pay using the sample medical expenses provided if he enrolls in the blue cross/blue shield plan?
Answers
Annual Medical cost = 1269.86
monthly premium cost to Ronald for the Blue Shield plan = $48.48.
For all doctor office visits, prescriptions, and major medical charges, Ronald will be responsible for 35 percent and the insurance company will cover 65 percent of covered charges.
The annual deductible cost = $630.
Ronald decided to review his medical bills from the previous year to see what costs he had incurred and to help him evaluate his choices. He visited his general physician 6 times during the year at a cost = $105 for each visit.
He also spent $71 and $95 on two prescriptions during the year.
= (Monthly premium cost × 12) + Deductible cost + (Coinsurance percent × Coinsurance expenses)
= (48.48 x 12) + 630 + (0.35 x 166)
= 1269.86
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conservationists tagged 80 black-nosed rabbits in a national forest in 1990. in 1991, they tagged 160 black-nosed rabbits in the same range. if the rabbit population follows the exponential law, how many rabbits will be in the range 9 years from 1990?
Answers
The total number of rabbits in the range 9 years from 1990 is 4094.
Exponential growth occurs when the growth rate of the value of a mathematical function is proportional to the function’s current value, resulting in its growth with time being an exponential function. In other words, when the growth of a function increases rapidly in relation to the increase in the total number, then it is exponential.
\(A = A_{0} * e^{kt}\) --- (1)
where A is the initial value, \(A_{0}\) is the previous value, k is the exponential constant, and t is the time.
Now, substitute the values to determine the value of 'k'.
160 = 80 * \(e^{k*1}\)
2 = \(e^{k}\)
ln2 = k
k = 0.6931
Now, at t = 9 the expression (1) becomes:
\(A = 80 * e^{0.6931*9}\)
A = 4094 rabbits
Thus, the total number of rabbits in the range 9 years from 1990 is 4094.
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The foot size of each of 16 men was measured, resulting in the sample mean of
27.32 cm. Assume that the distribution of foot sizes is normal with o = 1.2 cm.
a.
Test if the population mean of men's foot sizes is 28.0 cm using o = 0.01.
b. If = 0.01 is used, what is the probability of a type II error when the population
mean is 27.0 cm?
C.
Find the sample size required to ensure that the type II error probability
B(27) = 0.1 when a = 0.01.
Answers
a. Perform a one-sample t-test using the given sample mean, population mean, sample size, and standard deviation, with a significance level of 0.01, to test the population mean of men's foot sizes.
b. Calculate the probability of a type II error when the population mean is 27.0 cm, assuming a specific alternative hypothesis and using a significance level of 0.01.
c. Determine the sample size required to achieve a type II error probability of 0.1 when the significance level is 0.01.
a. To test if the population mean of men's foot sizes is 28.0 cm, we can perform a one-sample t-test. The null hypothesis (H0) is that the population mean is equal to 28.0 cm, and the alternative hypothesis (H1) is that the population mean is not equal to 28.0 cm.
Given that the distribution is normal with a known standard deviation of 1.2 cm, we can calculate the t-value using the sample mean, population mean, sample size, and standard deviation. With a significance level (α) of 0.01, we compare the calculated t-value to the critical t-value from the t-distribution table to determine if we reject or fail to reject the null hypothesis.
b. To find the probability of a type II error when the population mean is 27.0 cm, we need to specify the alternative hypothesis more precisely. If we assume the alternative hypothesis is that the population mean is less than 28.0 cm, we can calculate the probability of a type II error using the given information, sample size, and the desired significance level (α).
This can be done by calculating the power of the test, which is equal to 1 minus the type II error probability.
c. To find the sample size required to ensure that the type II error probability B(27) = 0.1 when α = 0.01, we need to use the power calculation. We can determine the required sample size by specifying the desired power level, the significance level, the population mean, and the population standard deviation.
By solving for the sample size, we can determine the number of observations needed to achieve the desired power while maintaining a certain level of significance.
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Im having a brain fart moment rn. Does f(27) mean to replace the x with 27 or f(x) with 27
Answers
Answer:
it means replace x with 27
Step-by-step explanation:
\( \sqrt[3]{27 + 98} + 5 = \sqrt[3]{125} + 5 = 5 + 5 = 10\)
Answer:
10
Step-by-step explanation:
f(27) means to replace the x, not f(x). This means the equation would be \(f(27)=\sqrt[3]{27+98}+5\). First, take the cube root of 27 + 98 (125), which equals 5. Then add this to the 5 on the outside of the cube root to get 10.
Davon has only red tulips and white tulips in his garden. Three-fourths of his tulips are white. What is the
ratio of red tulips to white tulips in Devon's garden?
1 to
Answers
Answer:
3:1
Step-by-step explanation:
Out of 4/4 tulips...
Davon has 3/4 white tulips.
Davon therefore has 1/4 red tulips.
3/4:1/4 is basically 3:1 (After dividing 1/4 by 3/4)
Quis mode Easy
hasil dari
T²⁵⁴÷T²⁴³=
Answers
Answer:
T²⁵⁴÷T²⁴³=
T²⁵⁴-²⁴³=
=T¹¹
done and thank you
exercise 1 (lump-sum taxes). consider a two-period economy. households preferences are described by the utility function ln c1 ln c2, where c1 denotes consumption in period 1 and c2 denotes consumption in period 2. in period 1, households receive an endowment y1
Answers
The optimal tax is equal to the households' endowment in period 1.
The utility function for the households is given by ln(c1) + ln(c2), where c1 is the consumption in period 1 and c2 is the consumption in period 2. The households receive an endowment of y1 in period 1, which can be either consumed or saved for period 2. The interest rate is given by r.
a) To maximize utility, we can use the Lagrangian method. Let L = ln(c1) + ln(c2) + λ(y1 - c1 - (1+r)s), where λ is the Lagrange multiplier and s is the amount saved from period 1 to period 2. Taking partial derivatives with respect to c1, c2, and s, we get:
dL/dc1 = 1/c1 - λ = 0
dL/dc2 = 1/c2 - λ = 0
dL/ds = -λ(1+r) = 0
Solving for λ and substituting into the first two equations, we get:
1/c1 = 1/c2
c2 = c1
Using the budget constraint, we have:
y1 = c1 + (1+r)s
Substituting c2 = c1 into this equation and solving for s, we get:
s = (y1 - 2c1)/(2(1+r))
b) If the government imposes a lump-sum tax of T in period 1, the households' budget constraint becomes:
y1 - T = c1 + (1+r)s
Substituting the expression for s from part (a), we get:
y1 - T = c1 + (1+r)(y1 - 2c1)/(2(1+r))
Simplifying, we get:
c1 = (y1 - T)/3
c2 = (y1 - T)/3
The households' utility with the tax is ln[(y1-T)/3]^2.
c) To find the optimal tax, we can differentiate the households' utility with respect to T and set it equal to zero:
d/dT [2ln((y1-T)/3)] = -2/(y1-T) = 0
Solving for T, we get:
T = y1
Therefore, the optimal tax is equal to the households' endowment.
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A family reunion has 184 people together at a local hotel. They travel in groups of 13 from the airport by van. How many vans will be needed to take the people to the hotel?
Answers
184 people
groups of 13
to find:How many vans needed to take the people to the hotel.
solution:\( \frac{184}{13} \)
\( = 14.1538461538\)
\(nearest \: whole \: number = 14\)
therefore, they'll need 14 vans to take the people to the hotel.
answer= option B
I
need the details why we choose answer c
109) Use the following random numbers to simulation crop yield for 10 years: 37, 23, 92, 01, 69, 50, 72, 12, 46, 81. What is the estimated crop yield from the simulation? A) 425 B) 442 C) 440 D) 475 A
Answers
The estimated crop yield from the simulation is 443 (option b).
To estimate the crop yield from the given random numbers, we need to assign a specific meaning to each random number. Let's assume that each random number represents the crop yield for a particular year.
Given random numbers: 37, 23, 92, 01, 69, 50, 72, 12, 46, 81
To find the estimated crop yield, we sum up all the random numbers:
37 + 23 + 92 + 01 + 69 + 50 + 72 + 12 + 46 + 81 = 443
Therefore, the estimated crop yield from the simulation is 443. The correct option is b.
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The function y f(x) is graphed below. What is the average rate of change of the
function f(x) on the interval
4
_ _
Answers
The average rate of change of the function f(x) on the interval [2, 6] is 1.
To find the average rate of change of a function, we need to calculate the change in the function over the given interval, and divide by the length of the interval.
In this case, we want to find the average rate of change of the function f(x) on the interval [2, 6], which has a length of 4.
From the graph, we can see that the value of the function at x=2 is approximately f(2)=3, and the value of the function at x=6 is approximately f(6)=7.
Therefore, the change in the function over the interval is f(6) - f(2) = 7 - 3 = 4.
The length of the interval is 6 - 2 = 4, so the average rate of change of the function on the interval is:
average rate of change = (f(6) - f(2)) / (6 - 2) = 4 / 4 = 1
Therefore, the average rate of change of the function f(x) on the interval [2, 6] is 1.
In general, the average rate of change of a function on an interval measures how much the function changes on average per unit of distance traveled on the x-axis. In this case, we found that the function increases by an average of 1 unit for each unit of distance traveled on the interval [2, 6].
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what is the value of x when y= -1
Answers
Answer:
x=+1
Step-by-step explanation:
the value of x will be positive 1 for we will take x=0 y=-1 where we inter change the values to be x=y-1=0
Graph: y - 10 = -2(x – 10) Y χ y 30 20 10 X -10 10 20 -10 Draw Click or tap the graph to plot a point.
Answers
BROO PLS SOMEONE HELP IM SO CONFUSED
The start of an arithmetic sequence is shown below.
Work out the nth term
Work out the 30th term in this sequence.
4 - 13 - 22 - 31
Answers
The 30th term of the arithmetic sequence is 265
What is an arithmetic sequence in math?
Arithmetic sequences are those in which each term is increased by the addition or subtraction of a constant k. In contrast to a geometric sequence, where each term rises by being multiplied by or divided by a constant k,A series of numbers is considered to be an arithmetic progression or sequence if there is a constant difference between the terms. Consider the mathematical progression with a common difference of 2 in the numbers 5, 7, 9, 11, 13, and so on.An is equal to a1 + d(n - 1), where d is the common difference across terms in the series, and a1 is the first term in the sequence.This is an arithmetic sequence since there is a common difference between each term. In this case, adding 9 to the previous term in the sequence gives the next term. In other words, \(a_{n}\)= \(a_{1}\)+ d ( n - 1 )
Arithmetic Sequence: d = 9
This is the formula of an arithmetic sequence.
\(a_{n}\) = \(a_{1}\) + d ( n - 1 )
Substitute in the values of \(a_{1}\) = 4 and d = 9
\(a_{n}\)= 4 + 9 ( n - 1 )
\(a_{n}\)= 4 + 9n - 9
\(a_{n}\) = 9n - 5
.30th term = \(a_{n}\) = \(a_{1}\)+ d ( n - 1 )
= \(a_{30}\)= 4 + 9 ( 30 -1 )
\(a_{30}\)= 4 + 9 x 29
\(a_{30}\)= 265
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i toss a penny and observe whether it lands heads up or tails up. suppose the penny is fair; that is, the probability of heads is 1/2 and the probability of tails is 1/2. this means that:
Answers
a
A container has 14 yellow chips, 10 blue chips and 12 red chips in it.
One chip is randomly chosen from the container, then a second chip is
randomly chosen after replacing the first chip. What is the probability
that both chips are red?
Answers
Answer:
1/9 is the probability that its red chip.
Step-by-step explanation:
total chips = 14 + 10 + 12 = 36 chips
first probability = 12/36 = 1/3
second probability = 12/36 = 1/3...........total remains same, 36 as its replaced
therefore probability = 1/3 * 1/3 = 1/9
The graph of function f is shown. Function g is represented by the table. x -2 -1 0 1 2 g(x) -32 -16 -8 -4 -2 Which statement correctly compares the two functions on the interval [0, 2]? A. Function f is increasing, and function g is decreasing. B. Both functions are increasing, but function f is increasing faster. C. Both functions are increasing, but function g is increasing faster. D. Both functions are increasing at the same rate.
Answers
Answer:
Both functions are increasing, but function g is increasing faster
Step-by-step explanation:
Correct on a plato test. Have a great day!
Answer:
B. fashoooooooo
Step-by-step explanation:
Both functions are increasing, but function f is increasing faster.
Waterway Industries reported income taxes of $418,100,000 on its 2022 income statement and income taxes payable of $313,010,000 at December 31, 2022, and $596,640,000 at December 31, 2022. What amount of cash payments were made for income taxes during 2022
Answers
Waterway Industries made cash payments of $124,130,000 for income taxes during 2022.
To determine the cash payments made for income taxes during 2022, we need to consider the change in income taxes payable from the beginning to the end of the year. The change in income taxes payable represents the net increase or decrease in the amount owed to tax authorities. In this case, the income taxes payable at the beginning of the year (December 31, 2021) was $313,010,000, and the income taxes payable at the end of the year (December 31, 2022) was $596,640,000. Therefore, the change in income taxes payable is calculated as follows:
Change in income taxes payable = Income taxes payable at December 31, 2022 - Income taxes payable at December 31, 2021
= $596,640,000 - $313,010,000
= $283,630,000
The change in income taxes payable represents the amount of income taxes that were paid during 2022. Thus, Waterway Industries made cash payments of $283,630,000 for income taxes during the year.
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which of the following functions are solutions of the differential equation y′′−9y′ 18y=0? a. y(x)=e6x b. y(x)=e−x c. y(x)=e3x d. y(x)=0 e. y(x)=6x f. y(x)=3x g. y(x)=ex
Answers
Only one of the following functions is a solution of the differential equation y′′−9y′+18y=0.
The second-order homogeneous linear differential equation is given as:y'' - 9y' + 18y = 0This differential equation is a linear homogeneous equation. We will have two roots of the characteristic equation: r1 = 3, r2 = 6So, the general solution to the differential equation is given as:y = c1e3x + c2e6xwhere c1 and c2 are arbitrary constants.a. y(x) = e6x is a solution because it is a part of the general solution of the differential equation.y(x) = e−x, y(x) = 0, y(x) = 6x, y(x) = 3x, y(x) = ex are not solutions because they don't satisfy the differential equation. Hence, the correct options are:a. y(x) = e6xTherefore, only one of the following functions is a solution of the differential equation y′′−9y′+18y=0.
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16 days 5 hours 23 minutes. how many minutes and hours come out in total?
Answers
Answer:
389 hours and 23 minutes
Step-by-step explanation:
16x24=384
384+=5=389
and 23 minutes
ed psych which of the following statements best describes a control group? question 9 options: a) a control group is a comparison group treated in every way like the other group, except for the manipulated factor. b) a control group is a comparison group that does not participate in the experiment, but fills out a questionnaire instead. c) a control group is a group of individuals randomly assigned to a variety of treatments. d) a control group is a group of individuals who design the procedures of an experiment.
Answers
A control group is a comparison group treated like the other group, except for the manipulated factor.
A control group is a comparison group used in an experiment that is treated like the other group, except for the factor that is being manipulated. The purpose of a control group is to have a baseline to compare the results of the experiment with. It allows the researcher to measure the effects of the manipulated factor on the results. A control group is often used in medical trials, such as drug trials, to compare the effects of a new drug to the effects of a placebo. In other types of experiments, the control group is used to measure the effects of the manipulated factor, such as the effects of different teaching methods on student learning. The control group is also used to rule out any other factors that could be influencing the results of the experiment.
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What is joule per meter second?
Answers
Joule per meter second is the unit of measurement for momentum flux or power per unit area. It is commonly used in physics and engineering to quantify the rate of energy transfer or momentum flow per unit area.
Joule per meter second (J/m^2s) is not the correct unit for momentum flux or power per unit area. The correct unit for momentum flux is Newton per square meter (N/m^2), also known as Pascal (Pa), while the correct unit for power per unit area is watt per square meter (W/m^2). The joule per meter second (J/m^2s) is actually the unit for volumetric energy dissipation rate, which measures the rate at which energy is being dissipated within a fluid volume per unit volume. It is used in the study of fluid dynamics and turbulence.
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What is the reciprocal of -11/30
Answers
1.1 Use calculus to verify that is a solution of v(t) = gm Cd n (Joca m tanh t dv dt m Do NOT solve this problem by hand. Use MATLAB's symbolic algebra capability.
Answers
The given solution v(t) = gm Cd n is valid, as it satisfies the original differential equation.
The differential equation that represents the vertical velocity of a falling object, subject to air resistance, is given by:
v(t) = gm Cd n (Joca m tanh t dv/dt m)
Where:
g = the acceleration due to gravity = 9.8 m/s^2
m = the mass of the object
Cd = the drag coefficient of the object
ρ = the density of air
A = the cross-sectional area of the object
tanh = the hyperbolic tangent of the argument
d = the distance covered by the object
t = time
To verify the given solution, we first find the derivative of the given solution with respect to time:
v(t) = gm Cd n (Joca m tanh t dv/dt m)
Differentiating both sides with respect to time gives:
dv/dt = gm Cd n (Joca m sech^2 t dv/dt m)
Substituting the given solution into this equation gives:
dv/dt = -g/α tanh (αt)
where α = (gm/CdρA)^(1/2)n
Now we substitute this back into the original equation to check if it is a solution:
v(t) = gm Cd n (Joca m tanh t dv/dt m)
= gm Cd n (Joca m tanh t (-g/α tanh (αt) ))
= -g m tanh t
This means that the given solution is valid, as it satisfies the original differential equation.
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Which equation matches the table?
Answers
An equation that matches the table include the following: y = x + 5.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (6 - 5)/(1 - 0)
Slope (m) = 1/1
Slope (m) = 1.
At data point (0, 5) and a slope of 1/, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 5 = 1(x - 0)
y - 5 = x
y = x + 5
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The temperature of a bowl of soup, in degrees Fahrenheit, is
S (t) = 76 + 54e-0.1621
where is the time since it was served, measured in minutes.
Determine how long you need to wait, to the nearest minute, for the soup to cool to 115°F.
Answers
To determine how long you need to wait for the soup to cool to 115°F, we need to find the value of t in minutes when S(t) = 115°F.
The function S(t) represents the temperature of the soup in degrees Fahrenheit as a function of time t since it was served. According to the given function, S(t) = 76 + 54e^(-0.1621t).
To find the time needed for the soup to cool to 115°F, we set S(t) = 115 and solve for t.
115 = 76 + 54e^(-0.1621t)
Subtracting 76 from both sides, we have:
39 = 54e^(-0.1621t)
Dividing by 54, we get:
0.7222 = e^(-0.1621t)
Taking the natural logarithm (ln) of both sides to eliminate the exponential function, we have:
ln(0.7222) = -0.1621t
Solving for t, we get:
t = ln(0.7222) / -0.1621 ≈ 7.86 minutes.
Therefore, you need to wait approximately 8 minutes (rounded to the nearest minute) for the soup to cool to 115°F.
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at what points does the curve r(t) = ti (3t − t2)k intersect the paraboloid z = x2 y2? (if an answer does not exist, enter dne.)
Answers
To determine the points of intersection between the curve and the paraboloid, we need to find the values of t that satisfy the equations of both curves.
The curve is defined as r(t) = ti (3t - \(t^2\))k, and the paraboloid is defined as z = \(x^2\) \(y^2\). We can substitute the components of the curve into the equation of the paraboloid to find the points of intersection.
Substituting the values of x, y, and z from the curve into the equation of the paraboloid, we get \((ti)^2\)(3t - \(t^2\))\(^2\) = \((ti)^2\) (3\(t^2\) - 2\(t^3\)). Simplifying the equation, we have \((ti)^2\)(3t - \(t^2\) - 3\(t^2\) + 2\(t^3\)) = 0.
To find the values of t that satisfy this equation, we can set each term equal to zero. Thus, we have three possibilities: ti = 0, 3t -\(t^2\) = 0, and 3\(t^2\) - 2\(t^3\) = 0.
Solving these equations, we find that ti = 0 gives t = 0, 3t - \(t^2\) = 0 gives t = 0 or t = 3, and 3\(t^2\) - 2\(t^3\) = 0 gives t = 0 or t = 1/2. Therefore, the points of intersection between the curve and the paraboloid are (0, 0, 0), (0, 0, 0), (3, 3, 27), and (1/2, 1/2, 1/16).
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Use the information given in the diagram to prove that triangle PUX is congruent to triangle QSY. I have multiple photos I would like to upload on here.
Answers
SOLUTION
We want to use the information in the diagram to prove that
\(\Delta PUX\cong\Delta\text{QSY}\)Now, we have been given for number 1
2.
\(\begin{gathered} RS=VU \\ \text{Definition of congruent segments } \end{gathered}\)3.
\(\begin{gathered} RU=RS+SU,VS=VU+SU \\ \text{Segment addition postulate } \end{gathered}\)4.
\(\begin{gathered} VS=RS+SU \\ Substitution\text{ property of equality} \end{gathered}\)5.
\(\begin{gathered} RU\cong VS \\ Transitive\text{ property of equality } \end{gathered}\)6.
\(\begin{gathered} RU=VS \\ \text{Definition of congruent segments} \end{gathered}\)7.
\(\begin{gathered} \Delta PUR\cong\Delta QSV \\ \text{ASA congruence theorem } \end{gathered}\)8.
\(\begin{gathered} m\angle RUX\cong m\angle VSY \\ m\angle PUR\cong m\angle QSV \\ \text{Corresponding parts of congruent triangles are congruent } \end{gathered}\)9. and 10. is good (correct)
11.
\(\begin{gathered} m\angle PUX=m\angle QSY \\ \text{Substitution property of equality} \end{gathered}\)12.
\(\begin{gathered} m\angle QSY=m\angle PUR+m\angle RUX \\ \text{Transitive property of equality} \end{gathered}\)13.
\(\begin{gathered} m\angle PUX=m\angle QSY \\ \text{Definition of congruent angles } \end{gathered}\)14.
\(\begin{gathered} \Delta PUX\cong\Delta\text{QSY} \\ \text{ASA congruence theorem} \end{gathered}\)HELP PLS
what is the best estimate for √333
A. 111
B. 19
C. 18
D. 18.2
Answers
Answer:
the answer is 18.248 so it would either be c or d.