Describe the method of establishing and evaluating for a triple integral. Provide an example using one of the following options: (a) iterated triple integral, (b) use of spherical coordinates, (c) use of cylindrical coordinates.
In: Math
Consider f(x) = 2 + 3x2 − x3
a) Find local max and min values
b) Find intervals of concavity and infection points
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Find all the vectors in R4 that are perpendicular to the three vectors <1,1,1,1>, <1,2,3,4>, and <1,9,9,7>
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(a) Find symmetric equations for the line that passes through the point
(5, −5, 6)
and is parallel to the vector
−1, 3, −2
.
−(x − 5) = 3(y + 5) = −2(z − 6).
x + 5 =
| y + 5 |
| 3 |
=
| z − 6 |
| −2 |
.
| x − 5 |
| −1 |
=
| y + 5 |
| 3 |
=
| z − 6 |
| −2 |
.
| x + 5 |
| −1 |
=
| y − 5 |
| 3 |
=
| z + 6 |
| −2 |
.
−(x + 5) = 3(y − 5) = −2(z + 6).
(b) Find the points in which the required line in part (a)
intersects the coordinate planes.
point of intersection with
xy-plane
point of intersection with
yz-plane
point of intersection with
xz-plane
In: Math
Let g(x) = 1/(x + 1)
(a) Does g satisfy the conditions of the Mean Value Theorem over the interval [1, 3]? Explain.
(b) Find a number c that satisfies the conclusion of the Mean Value Theorem for g over [1, 3], or explain why no such number exists.
(c) Does g satisfy the conditions of the Mean Value Theorem over the interval [−3, 0]? Explain.
(d) Find a number c that satisfies the conclusion of the Mean Value Theorem for g over [−3, 0], or explain why no such number exists.
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Draw a convex quadrilateral ABCD, where the diagonals intersect at point M. Prove: If ABCD is a parallelogram, then M is the midpoint of each diagonal.
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The Alaskan oil fields, in operation since 1977, had an estimated reserve of 4.9 billion barrels in 1999. In 2009, the fields had an estimated reserve of 3.5 billion barrels. Assume the rate of depletion is constant.
(a) Find a linear equation that relates the amount A, in millions of barrels, of oil left in the fields at any time t, where t is the year.
(b) If the trend continues, when will the fields dry out?
(c) Interpret the slope and y-intercept in this context.
(d) The Jack Field, discovered in the Gulf of Mexico off the coast of Louisiana in 2006, is estimated to contain up to 15 billion barrels of oil. At the same rate of depletion, how long will this field last?
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A box has a bottom with one edge 7 times as long as the other. If the box has no top and the volume is fixed at ?V, what dimensions minimize the surface area?
dimensions = ________________
Enter the dimensions as a comma-separated list, e.g., 3,sqrt(12),8. (Your answer may involve V.)
The top and bottom margins of a poster are 2 cm and the side margins are each 6 cm. If the area of printed material on the poster is fixed at 384 square centimeters, find the dimensions of the poster with the smallest area.
Width = ______________(include units)
Height =_____________ (include units)
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f(t) = 1- t 0<t<1
a function f(t) defined on an interval 0 < t < L is given. Find the Fourier cosine and sine series of f and sketch the graphs of the two extensions of f to which these two series converge
In: Math
a dead body was found within a closed room of a house
where the temperature was at 21°C. at the time of discovery the
core temperature of the body was determined to be 28°C. One hour
later the second measurement show that the core temperature
of the body was 25°C. assume that the time of death corresponds to
t = 0 and that the core temperature at the time was 37°C. determine
how many hours elapsed before the body was found. [ Hint: Let t1
> 0 denote the time that the body was discovered.] (Round your
answer to one decimal place.)
_____ hr
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a) How many ways can the letters of the word COMPUTER be arranged in a row?
b) How many ways can the letters of the word COMPUTER be arranged in a row if O and M must remain next to each other as either OM or MO?
c) How many permutations of the letters COMPUTER contain P, U and T (all three of them) not to be together in any order?
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A road perpendicular to a highway leads to a farmhouse located 22 mile away. An automobile traveling on the highway passes through this intersection at a speed of 55mph.55mph.
How fast is the distance between the automobile and the farmhouse increasing when the automobile is 11 miles past the intersection of the highway and the road?
The distance between the automobile and the farmhouse is increasing at a rate of miles per hour.
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Belirli bir radyoaktif maddenin, miktarıyla orantılı bir hızla yok olduğu bilinmektedir. Eğer başlangıçta 50 mg madde varsa ve 2 saat sonra maddenin başlangıçtaki kütlesinin %10 unun yok olduğu gözlenmiş ise
a) Herhangi bir t anında kalan maddenin kütlesi için bir ifade bulunuz ?
b) 4 saat sonra maddenin kütlesini bulunuz ?
c) maddenin başlangıçtaki kütlesinin yarısına indiği zamanı bulunuz?
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Consider the boundary value problem X ′′ +λX=0 , X ′ (0)=0 , X′(π)=0 . Find all real values of λ for which there is a non-trivial solution of the problem and find the corresponding solution.
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Consider the function f(x) = 3/(3x+ 4), c= 0 a)Find the power series for the function centered at c b)Determine the interval of convergence
In: Math