Solve the recurrence relation with the given initial conditions.
b0 = 0, b1 = 4, bn = 2bn ? 1 + 2bn ? 2 for n ? 2
In: Math
A city council consists of eight Democrats and eight Republicans. If a committee of six people is? selected, find the probability of selecting four Democrats and two Republicans.
In: Math
he function
f(x)equals=0.030.03xplus+500500
represents the rate of flow of money in dollars per year. Assume a 10-year period at
88%
compounded continuously. Find (A) the present value, and (B) the accumulated amount of money flow at
tequals=10.
(A) The present value is
$nothing
In: Math
3. Find the quotient and remainder using long division. x3 + 7x2 − x + 1 x + 8
quotient = ?
remainder = ?
4. Simplify using long division. (Express your answer as a quotient + remainder/divisor.)
f(x) = 8x2 − 6x + 3
g(x) = 2x + 1
5.
Find the quotient and remainder using long division.
| 9x3 + 3x2 + 22x |
| 3x2 + 5 |
| quotient | |
| remainder |
6.
Use the Remainder Theorem to evaluate P(c).
P(x) = x4 + 7x3 − 6x − 12, c = −1
f(−1) =
7.
Use the Remainder Theorem to evaluate P(c).
P(x) = 9x5 − 3x4 + 4x3 − 2x2 + x − 6, c = −6
P(−6) =
8.
Consider the following.
P(x) = x3 − 9x2 + 27x − 27
Factor the polynomial as a product of linear factors with complex coefficients.
9.
Consider the following.
P(x) = x3 + 2x2 − 3x − 10
Factor the polynomial as a product of linear factors with complex coefficients.
10.
The polynomial P(x) = 5x2(x − 1)3(x + 9) has degree (?). It has zeros 0, 1, and (?). The zero 0 has multiplicity (?), and the zero 1 has multiplicity (?). (answer all (?)
12.
Use the Factor Theorem to find all real zeros for the given polynomial function and one factor. (Enter your answers as a comma-separated list.)
f(x) = 6x3 + x2 − 41x + 30; x + 3
x =
13.
Use the Factor Theorem to find all real zeros for the given polynomial function and one factor. (Enter your answers as a comma-separated list.)
f(x) = 3x3 − 17x2 + 30x − 16; x − 1
x =
14.
Use the Factor Theorem to find all real zeros for the given polynomial function and one factor. (Enter your answers as a comma-separated list.)
2x3 + 7x2 − 12x − 42; 2x + 7
x =
15.
A polynomial P is given.
P(x) = x3 + x2 + 3x
(a) Find all zeros of P, real and complex. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
| x = |
? |
(b) Factor P completely.
| P(x) = |
? |
In: Math
1) find the are of the region that lies inside of the curve r= 1+ cos theta and outside the curve r=3 cos theta.
2) find the sum"
En=1 3^{1-n}:2^{n+2}
3) find
integration ( 2x^2 +1) e^x^2 dx
4) Does:
E n=12 ((2n)!/(n!)^2) converge or diverge ? justify your answer ( what test?)
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1) find all values of theta E [ 0,2 pi], where the curve r= 1- sin theta has a horizontal tangent line
2)find all values of theta E [ 0,2 pi] where the curve r=1- sin theta has a vertical tangent line
3) find the area of the region enclosed by the intersection of the curves"
r= sin theta and r= cos theta
In: Math
Design a google spreadsheet that will illustrate Riemann summation. Share the unlisted link on the forum. The entries should be (a) function f(x)=x^2 , (b) lower limit x=0, (c) upper limit x=2, (d) n = 4. The result should be three fields: left endpoint, midpoint approximation, right endpoint approximation.
In: Math
For each function given below, find the open intervals of
increase/decrease, all local extreme values, the intervals of
concavity, and inflection points.
(a) f(x) = x^2 + 2/x
(b) f(x) = xe^-x
In: Math
A company is creating a new fertilizer additive for lawn seed, which will be a mixture of nitrogen, phosphate, and potash. Based on their research, the total amount fertilizer added must be at least 14 oz. per 5 lb. bag of lawn seed, but should not exceed 20 oz. per 5 lb. bag. At least ¼ oz. of nitrogen must be used for every ounce of phosphate, and at least 1 oz. of potash must be used for every ounce of nitrogen. The costs per ounce of nitrogen, phosphate, and potash are $0.30, $0.18, and $0.54, respectively. Determine the mixture of the three ingredients in a 5 lb. bag that minimizes costs, as well as that cost.
In: Math
f(x) = 15x^4-3x^5 / 256. f'(x) = 60x^3 - 15x^4 / 256 f''(x) = 45x^2 - 15x^3 / 64
Find the horizontal and vertical asymptotes
Find the local minimum and maximum points of f(x)
Find all inflection points of f(x)
In: Math
A rectangular box with no top is to be made to hold a volume of 32 cubic inches. Which of following is the least amount of material used in its construction?
a.) 80 in2
b.) 48 in2
c.) 64 in2
d.) 96 in2
In: Math
The illumination of an object by a light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. If two light sources, one four times as strong as the other, are placed 16 ft apart, how far away from the stronger light source should an object be placed on the line between the two sources so as to receive the least illumination? (Round your answer to two decimal places.)
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Solve the differential equation using method of undetermined coefficients.
y'''- 8y = 6xe2x
In: Math
q=5000−100p
b. The cost of producing q units is given by
C(q)=3000−20q+0.03q2
Find the marginal profit for production level 500 units
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A company produces a special new type of TV. The company has fixed costs of $476,000 and it costs $1300 to produce each TV. The company projects that if it charges a price of $2300 for the TV, it will be able to sell 750 TVs. If the company wants to sell 800 TVs, however, it must lower the price to $2000. Assume a linear demand.
What price should the company charge to earn a profit of $734,000?
It would need to charge $
In: Math