Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = 2 cos(t), 2t, 2 sin(t)

Question 5

Find all solutions of this system.

4x + 2y + 3z = 0 3x y + 2z = 0 x + 2y − z = 0

Compare the value of the determinant of the coefficient matrix to zero using the nature of the solution.

if you a square that is 3' 5" in width, length and height. How many five point stars (2" in size) filled with air will fit into the square? Please show all work.

For each statement, determine whether the statement is true or false. Give a sentence justifying your answer.

a. If tan(t)=0, then cos(t)=1 .

b. The function f(x)=sin(x)cos(x) has period 2π.

c. The graph of r = 1 is the unit circle.

d. Two angles with the same cosine value must have the same sine value.

e. The point (0, -3) in Cartesean coordinates can also be described by the ordered pair (-3, π/2) in polar coordinates

What other application's can we think of related to this topic leasing.

For each of the following integrals find an appropriate trigonometric substitution of the form x=f(t)x=f(t) to simplify the integral.

the inteagral

a) ∫x(3x^2+30x+73)^(1/2)dx

b)∫x/(−25−3x^2+18x)^(1/2)dx

1) Find the maximum and minimum values of the function y = 13x³ + 13x² − 13x on the interval [−2, 2].

2) Find the minimum and maximum values of the function f(x) = 4 sin(x) cos(x) + 8 on the interval [0, pi/2].

3)  Find the maximum and minimum values of the function y = 5 tan(x) − 10x on the interval [0, 1]

4) Find the maximum and minimum values of the function f(x) =ln(x)/x  on the interval [1,4]

5)  Find the maximum and minimum values of the function y = |x − 16| on the interval [0, 17] by comparing values at the critical points and endpoints.

A linear system of equations Ax=b is known, where A is a matrix of m by n size, and the column vectors of A are linearly independent of each other. Please answer the following questions based on this assumption, please explain all questions, thank you~.

(1) Please explain why this system has at most one solution.

(2) To give an example, Ax=b is no solution.

(3) According to the previous question, what kind of inference can be made to the size of A at this time? (What is the size of m and n,please explain also it thanks.)

Joanne sells​ silk-screened T-shirts at community festivals and craft fairs. Her marginal cost to produce one​ T-shirt is $ 2.50 . Her total cost to produce 60 ​T-shirts is  $ 220 comma and she sells them for ​$8 each. a. Find the linear cost function for​ Joanne's T-shirt production. b. How many​ T-shirts must she produce and sell in order to break​ even? c. How many​ T-shirts must she produce and sell to make a profit of ​$500​?

1. Consider the 2^nd order NHDE below

d2xdt2+k2x=F0eωt

            With the following initial conditions x0=0 and x'0=0. (Assume k≠ω)

1. Find the complimentary solution yc(t)

2. Find the particular solution yp(t)

3. Find the general solution for the IVP.

1 = Derivative of a Constant; 2 = Power Rule; 3 = Product Rule; 4 = Quotient Rule; 5 = Derivative of Exponential Function; 6 = Derivative of Logarithmic Function; 7 = Chain Rule
1. Circle the number(s) indicating the rule(s) used to find the derivative of each function. Then differentiate the function.
(a.) f(x) = ln7 1 2 3 4 5 6 7
(b.) p(y) = y3.7 1 2 3 4 5 6 7
(c.) g(x) = √x2ex 1 2 3 4 5 6 7
(d.) j(z) = 1 z2+1 1 2 3 4 5 6 7
(e.) h(x) = x lnx 1 2 3 4 5 6 7
2. Simplify each function, if possible. All exponents should be positive and factor out common factors. Do not find the derivative

. (a.) f(x) = x−4(x + 6)5

(b.) g(x) = e9x(x−2)2 + 9e9x(x−2)

(c.) h(x) = x x+2

(1 point) The count in a bacteria culture was 600 after 10 minutes and 11613 after 20 minutes. Assume the growth can be modelled exponentially by a function of the form Q(t)=AertQ(t)=Aert, where tt is in minutes.

(a) Find the relative growth rate, with at least the first 5 digits after the decimal point entered correctly:
r=r=

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(b) What was the initial size of the culture? Round your answer to the closest integer.

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(c) Find the doubling period (in minutes).

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(d) Find the population after 65 minutes. Use your answer to part (b) as the initial amount.

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(e) When will the population reach 13000? After

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Q-1)1 to 5 in bag A; 1 to 11 in bag B there are numbered cards. A random from the randomly selected bag card is selected. Since there is an odd number on the selected card, A
What is the probability of being chosen from the bag? Note: Make a tree diagram and
express your results with Bayes Theorem and
Confirm.

Q-2)ABCD is a rectangle whose long edge is twice the short edge. Long midpoint X of edge AB; The midpoint of the short edge AD is Y. This choice with the XAY triangle. A randomly selected point in a rectangle Find the probability of being selected in the XAY triangle.

Q-3)Ali and Ahmet are playing matches. Ali’s probability of winning the match
3 times the probability of winning. Ali and Ahmet’s chances of winning
Find and using the Binomial distribution:
a) In the event of 3 matches, the probability of Ali winning twice
You calculate.?
b) At least 1 win of Ali in case of 3 matches
Calculate the probability.?

Thanks

Find the point on the plane curve xy = 1, x > 0 where the curvature takes its maximal value.