Question 1

a. cos Ѳ =-24/25, Ѳ in quadrant 3, find sin Ѳ

b. sin Ѳ=12/13, Ѳ in quadrant 2, find cos Ѳ

c.cos Ѳ =12/13,270 degrees<Ѳ <360 degrees, find sin Ѳ

d.find the reference angle for 279 degrees

Geometric Nets

Suppose you could split open and flatten an ice cream cone.

Before doing so, you measure the circumference around the top of the cone and find it is 9.4 inches.

What is the radius of the opening of the cone approximated to the nearest tenth of an inch?Explain your answer.

Draw a picture of the flattened cone.

Explain how the circumference of the cone translates to the shape of your drawing.

A thermometer is taken from a room where the temperature is 23oC to the outdoors, where the temperature is −1oC. After one minute the thermometer reads 15oC.
(a) What will the reading on the thermometer be after 5 more minutes?

(b) When will the thermometer read 0oC? ________ minutes after it was taken to the outdoors.

A tank contains 220 L of pure water. Solution that contains 0.08 kg of sugar per liter enters the tank at the rate 8 L/min, and is thoroughly mixed into it. The new solution drains out of the tank at the same rate.
(a) How much sugar is in the tank at the begining? y(0)=___ kg

(b) Find the amount of sugar after t minutes. y(t)=___ kg

(c) As t becomes large, what value is y(t) approaching ? In other words, calculate the following limit. limt→∞y(t)=____ kg

A farmer is going to divide her 60 acre farm between two crops. Seed for crop A costs $20 per acre. Seed for crop B costs $40 per acre. The farmer can spend at most $2200 on seed.

If crop B brings in a profit of $320 per acre, and crop A brings in a profit of $140 per acre, how many acres of each crop should the farmer plant to maximize her profit?

1. Determine los extremos relativos de las siguientes funciones. Determine the relative extremes of the following functions

1. f(x,y)=9-(x^₂+y²-2x+1)^1/2  
2. f(x,y)=y⁴-4y³+2x²+8xy

1. triple integral... first form 0 to pi, second from 0 to pi/3, third to sec(phi) to 2 of p^2*sin(phi) dp d(phi) d(theta)

2. triple integral... first form 0 to pi, second from -sqrt(3) to sqrt(3), third to 1 to sqrt(4-r^2) of r dz dr d(theta)

3. triple integral... first form 0 to pi/2, second from 0 to sqrt(3), third to 1 to sqrt(4-r^2) of r dz dr d(theta)

4. triple integral... first form 0 to pi, second from 0 to sqrt(3), third to 1 to sqrt(4-r^2) of r dz dr d(theta)

5. triple integral... first form 0 to pi, second from 0 to pi/3, third to 1 to 2 of p^2*sin(phi) dp d(phi) d(theta)

6. triple integral... first form 0 to pi/2, second from 0 to pi/6, third to sec(phi) to 2 of p^2*sin(phi) dp d(phi) d(theta)

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?