Prove the transitivity of similarity: If △ ???~ △ ??? and △ ???~ △ ??? then △ ???~ △ ???. Write this proof in the numbered statements and reasons style.and also a picture of triangles.

A. In the following parts, consider the function f(x) =1/3x^3+3/2x^2−4x+ 7

(a)Find the intervals on which f is increasing/decreasing and identify any local extrema.

(b) Find the intervals on which f is concave up/down and find any inflection points.

B. Consider the function f(x) = sin(x) + cos(x). Find the absolute minimum and absolute maximum on the interval [−π,π].

A pilot on a heading of 320^o with an air speed of 240 km/h. Her actual ground velocity is 250 km/h at a bearing of 318^o. Calculate the speed and direction of the wind.

Please include the equation we are trying to solve values for as I get confused easily! Thank you in advance.

Find the Fourier cosine and sine series of f(t) = t^2 ,0 < t < π

An airplane is flying at an air speed of 420 km/h on a heading of 210^o. A 45 km/h wind is blowing from a bearing of 50^o. Determine the bearing and ground velocity of the airplane using geometric vectors.

Please include what equation we are trying to solve for, thank you in advance~!

Find point PP that belongs to the line and direction vector vv of the line. Express vv in component form. Find the distance from the origin to line L. 251. x=1+t,y=3+t,z=5+4t,x=1+t,y=3+t,z=5+4t, t∈R answers are

a- P=(1,3,5) V=<1,1,4> b. Square root of 3

I want all work shown please. I do not understand how to get root 3

Jeannie makes flower arrangements. she has 13 different cut flowers and plans to use 5 of them. how many different selections of the 5 flowers are possible?

Let Vector_1=[Column (1 &-2&1)],Vector_2=[Column(2&-1&1)],Vector_3=[Column(-2&... Let Vector_1=[Column (1 &-2&1)],Vector_2=[Column(2&-1&1)],Vector_3=[Column(-2&-2&0)],Vector_4=[Column(1&-2&-2)]. Show that S={Vector_1,Vector_2,Vector_3,Vector_4} is linearly dependent.

Show that Vector_3 can be written as a linear combination of Vector_1,Vector_2 and Vector_4.

Show that T={Vector_1,Vector_2,Vector_4} is linearly independent.

Show that the set of all linear combinations of vectors from S is the same as the set of all linear combinations of vectors from T.

3. a) Consider the vector field F(x, y, z) = (2xy2 z, 2x 2 yz, x2 y 2 ) and the curve r(t) = (sin t,sin t cost, cost) on the interval [ π 4 , 3π 4 ]. Calculate R C F · dr using the definition of the line integral. [5] b) Find a function f : R 3 → R so that F = ∇f. [5] c) Verify your answer from (a) using (b) and the Fundamental Theorem for Line Integrals. [5]

1. Find p and graph the parabola y+12x−2x^2=16

2. Find e, d and determine which conic that has the equation r= 4 / 5 - 4sin(theta)

Please show steps. Thanks a lot.

The demand function for a particular product is given by D(x)=3x2−7x+110‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√D(x)=3x2−7x+110 dollars, where x is the number of units sold. What is the marginal revenue when 44 items are sold? Round your answer to 2 decimal places.

D(x)=3x2−7x+110‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√t

thats a suqare root over the numbers

Find a polynomial function P of the lowest possible​ degree, having real​ coefficients, a leading coefficient of​ 1, and with the given zeros. 1+3i​, -1​, and 2?

Find all zeros of the polynomial function. Use the Rational Zero​ Theorem, Descartes's Rule of​ Signs, and possibly the graph of the polynomial function shown by a graphing utility as an aid in obtaining the first zero or the first root.

f(x)=2x⁴-17x³+13x²+53x+21

The zeros of the function are?

A company manufactures x units of Product A and y units of Product B, on two machines, I and II. It has been determined that the company will realize a profit of $2/unit of Product A and a profit of $6/unit of Product B. To manufacture a unit of Product A requires 6 min on Machine I and 5 min on Machine II. To manufacture a unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of machine time available on Machine I and 3 hr of machine time available on Machine II in each work shift. How many units of each product should be produced in each shift to maximize the company's profit?