4. [22 pts] For the function ?(?) = 2?5 − 9?4 + 12?3 − 12?2 + 10? − 3 answer the following:
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a. [2 pts] Determine whether the function represents a polynomial. Justify your answer. |
b. [4 pts] Determine whether the function satisfies the Intermediate Value Theorem on the interval [0, 5]. Justify your answer. |
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c. [2 pts] Determine the number (quantity) of complex zeros that the function has, provided the each zero is counted by its multiplicity. |
d. [4 pts] List all the possible rational zeros: |
e. [2 pts] Use part (d) result and a calculator to find the actual rational zeros. List the zeros here: { ____________________ } |
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f. [4 pts] Use the previous result, synthetic division, long division, quadratic formula, or square root property to find all the remaining zeros of f(x). |
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g. [4 pts] Use the previous result to rewrite f(x) as a product of linear factors. |
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In: Math
Find the area of the region that lies inside the curve r=1+cos(theta) but outside the curve r=3cos(theta)
In: Math
Answer the following questions thoroughly. Use correct grammar and punctuation.
1) A student observes the following spinner and claims that the color red has the highest probability of appearing, since there are two red areas on the spinner. What is your reply? Your answers should include facts, rules, any definitions necessary to explain why the student is correct or incorrect.
2) In class, an experiment of flipping a coin is performed.
Pretend that you are introducing the concept of probability and introducing the terms 1) experiment, 2) outcomes, 3)sample space, 4) theoretical probability, and 5) empirical probability. Explain these terms, as if you were speaking to a 5th grade class, as if they knew nothing about probability. You will need to tell the class what each term , 1-5, is represented by in this particular example. Use correct grammar and punctuation.
In: Math
The two basic facts about the quantifiers you need to understand, and from which all of the logical properties of the quantifiers follow are:
Basic Fact 1: A universal quantifier (x) Fx is equivalent to an infinite conjunction: Fa & Fb & Fc & Fd & ........
where a, b, c, d, are the names of objects in the universe picked out by the 'x' in the universal quantifier '(x)'.
Basic Fact 2: An existential quantifier is equivalent to an infinite disjunction
Fa v Fb v Fc v Fd v ......
Expand in a two-element universe
(a) ~(x) ((Fx v Gy) v Ka)
In: Math
Water is flowing at the rate of 5m3/min into a tank in the form
of a cone of altitude 20 m and a base radius of 10 m, with its
vertex in the downward direction.
a) How fast is the water level rising when the water is 8m
deep?
b) If the tank has a leak at the bottom and the water level is
rising at 0.084 m/sec when the water is 8 m deep, how fast is the
water leaking?
In: Math
The quantity demanded of a certain electronic device is 1000 units when the price is $665. At a unit price of $640, demand increases to 1200 units. The manufacturer will not market any of the device at a price of $90 or less. However for each $50 increase in price above $100, the manufacturer will market an additional 1000 units. Assume that both the supply equation and the demand equation are linear.
(a) Find the supply equation.
(b) Find the demand equation
(c) Find the equilibrium price.
(d) Find the equilibrium quantity
In: Math
[10 pts] A model rocket is launched from a raised platform at a speed of 120 feet per second. Its height in feet is given by h(t) = -16t^2 +120 t + 32 where t represents seconds after launch.
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a. [3 pts] After how many second does the object reach its maximum height? Use the vertex formula. |
b. [2 pts] Use the previous result to find the maximum height reached by the rocket. |
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c. [5 pts] After how many second does the rocket hit the ground? |
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In: Math
1. For each, circle either True or False. please add an explanation to each one so i can understand the reasoning
(a) (1 point) A continuous function is always integrable. T/F
(b) (1 point) A differentiable function is always continuous. T/F
(c) (1 point) An integrable function is always differentiable. T/F
(d) (1 point) If c is a critical value of function f then f(c) is a relative maximum. T/F
(e) (1 point) If c is a relative minimum of function f then c is a critical value of f. T/F
(f) (1 point) If f is not differentiable at a then f(a) does not exist. T/F
(g) (1 point) f00(c) = 0 implies c is an infection point. T/F
(h) (1 point) A relative maximum is always an absolute maximum. T/F
In: Math
In: Math
a) ty’ −y/(1+T) = T,(T>0),y(1)=0
b) y′+(tanT)y=(cos(T))^2,y(0)=π2
Solve the above equations.
In: Math
In: Math
first of all thankuu and please
i dont need theory just clear my concept very clear so that i never have problems insolving such questions
give me a very brief explanation about volume of solid rotated about a line, x axis ,y axis using shell method washer method and disk method using visual representation of how to choose element area and then limits how we decide i dont need this for any assignments or anything submission type its for my understanding because seriously i have a very confusing regarding how to solve such questions type please its very help to me i will rate you definitely pleasee
teach me how to setup intergal using diagram in easy language
thanks, dont cut copy paste from anywhere
In: Math
The point ?(√6 cos ? , √3 sin ?) is on an ellipse.
a) Write down the equation of this ellipse in Cartesian form and find its foci.
b) A hyperbola has the same foci as this ellipse and one of the branches cuts the ?-axis at 1. What is the equation of the hyperbola?
In: Math