A​ sparkling-water distributor wants to make up 200 gal of sparkling water to sell for $5.00 per gallon. She wishes to mix three grades of water selling for

$99​.00, ​$22​.00, and​ $4.50 per​ gallon, respectively. She must use twice as much of the​ $4.50 water as the $2.00, water. How many gallons of each should she​ use?

The number of bacteria after ? hours in a controlled laboratory experiment is ? = ?(?).

a. Describe the meaning of ?′(4) and include right units.

b. If the supply of nutrients is limited, which value do you think is larger ?′(4) or ?′(15)?

A water trough is 8 m long and has a cross-section in the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 80 cm wide at the top, and has height 50 cm. If the trough is being filled with water at the rate of 0.1 m³/min how fast is the water level rising when the water is 40 cm deep?

A quadratic function f is given.

f(x) = x² + 6x + 8

(a) Express f in standard form.

(b) Find the vertex and x- and y-intercepts of f. (If an answer does not exist, enter DNE.)

(d) Find the domain and range of f. (Enter your answers using interval notation.)

A bakery makes Jumbo biscuits and Regular biscuits. The bakery is limited to: a. The oven can bake at most 150 biscuits per day. b. Each jumbo biscuit requires 2oz of flour and each regular biscuit requires 1oz of flour. The bakery has 200oz of flour available per day. c. Due to cooking time constraints, the total number of regular biscuits cannot exceed 130 d. Due to cooking time constraints, the total number of jumbo biscuits cannot exceed 70. The revenue from each jumbo biscuit sold is $1, and the revenue from each regular biscuit sold is $0.65. The cost to make each jumbo biscuit is $0.20, and the cost to make each regular biscuit is $0.15. A. Let x be the number of Regular biscuits and y the number of Jumbo biscuits. Write an inequality for the limitations a, b, c, and d. a. b. c. d. B. The bakery cannot produce less than zero of either type of biscuit either. Write an inequality for each type of biscuit that describes the minimum number of each type of biscuit. e. f. C. Can the bakery produce 20 regular biscuits and 80 jumbo biscuits? If not, explain which limitations are violated. D. Can the bakery produce 124 regular biscuits and 32 jumbo biscuits? If not, explain which limitations are violated. E. Can the bakery produce 80 regular biscuits and 50 jumbo biscuits? If not, explain which limitations are violated. F. Can the bakery produce 115 regular biscuits and 61 jumbo biscuits? If not, explain which limitations are violated. G. Graph the system of 6 inequalities (from questions 1 and 2 above) and shade the area that shows the “feasible solutions”, that is, the possible combinations of Regular and Jumbo biscuits. The maximum and minimum profit will occur at one of the intersections bordering the feasible zone. H. Find all the feasible intersections of limitations as ordered pairs. I. Write an equation for the profit for the two types of biscuits and find the combination of Regular and Jumbo biscuits that produces the maximum profit. a. Profit Equation: b. Maximum Profit is:

An air traffic controller spots two airplanes at the same altitude converging to a point as they fly at right angles to each other. One airplane is 120 miles from the point and has a speed of 480 miles per hour. The other is 160 miles from the point and has a speed of 640 miles per hour.

(a)At what rate is the distance between the planes changing? In MPH

(b)How much time does the controller have to get one of the airplanes on a different flight path? in MIN

The cleaning process of a certain industrial tank consists of 2 phases:
• Phase 1: It begins by placing 2,000 L of water in the tank together with 100 kg of a certain chemical cleaner (soluble in water).
• Phase 2: 40 L / min of water containing 2 kg of the cleaner per liter are poured into the tank. At the same time, the well mixed solution is pumped out of the tank at a rate of 45 L / min.
a) Find the quantity Q of the cleaner at any instant of time.
b) How many kilograms of the cleaner are present in the tank after 50 minutes?
c) If the cleaning process ends when the chemical cleaner is completely removed from the tank, how long does that process take?

{sinx, 2cosx, 3sinx+cosx} find the wronskian solution.

Create a function f(x) of at least degree 3 that has at least three terms. For that function, use derivatives to find the following information:

1. The function needs to have at least one maximum or minimum value.   

2.        Find the domain of f(x)

3.       Find the y-intercept f(x)

4.        End behavior: Find the limit of the f(x) as x approaches both ∞ and -∞

5. Find the increasing and decreasing interval(s) of f(x)

6.        Find the interval(s) of concavity

7.        Find any maximum points, minimum points, or points of inflection

8.       Graph f(x) to verify that if the above answers are correct or accurate.

a) Let D be the disk of radius 4 in the xy-plane centered at the origin. Find the biggest and the smallest values of the function f(x, y) = x 2 + y 2 + 2x − 4y on D.

b) Let R be the triangle in the xy-plane with vertices at (0, 0),(10, 0) and (0, 20) (R includes the sides as well as the inside of the triangle). Find the biggest and the smallest values of the function g(x, y) = xy(20 − 2x − y) on R.

Suppose that a cup of soup cooled from 90C to 60C after 15 minutes in a room whose temperatures was 20C. Use Newton's law of cooling to answer the following questions.

a. How much longer would it take the soup to cool to 40C?

b. Instead of being left to stand in the room, the cup of 90C soup is put in the freezer whose temperature is -15C. How long will it take the soup to cool from 90C to 40C?

Find the work done by the force field F(x,y,z) =8x^2yzi+5zj-4xyk

r(t)=ti+t^2j+t^3k (0

Find volume of D enclosed by surfaces
z = x² + 3y² and z = 8 - x² - y²