A rectangular box with open top and has a square base is a school project of two senior high school students. However, they are wondering what would be the minimum dimensions of their box if it will have a fixed volume of 62.5 cm³. Steps 1. Draw a diagram. List what is asked on the problem and label the diagram with relevant data. 2. Write the constraint and the optimization equations. 3. Substitute the constraint equations, to the corresponding length, width and height of the optimization equation. 4. Simplify and take its first derivative. 5. Set the equation to zero and solve for the x value (critical point). 6. If there are two critical values, we have to check which one will give a sensible answer by substituting them to the volume equation. 7. Test the x value. Substitute it to the second derivative and check whether the answer is less than or greater than zero. 8. Substitute the maximum x value to the simplified constraint equation to solve for I and w. 9. Solve for the dimensions. Solution Constraint equation: Optimization equation: height= length width=

Solve for x: 4(2х - 6) 3D 10х- 6 O 5 O -7 O -9 10

The picture shows Leo's garden divided into two sections. 4 ft E3 ft+ 5 ft Leo wants to find the area of the whole garden. Create two different equations Leo can use to model the total area of the garden Enter each equation on a separate line.

A row of grassed seating at an amphitheater has been marked out to define 25 spaces of equal width that can be booked for an event, the row is 20m long. If s represents the width in metres of one space, express this as an algebraic equation, do not simplify your equation, use whole numbers in the equation. Observe algebraic conventions, do not include brackets or units in your equation: Use your algebraic equation to find the width of each space, s. Your answer should be a numerical value to 2 decimal places, give your answer in the same units used in the question, include units and no spaces in your answer: S=

Solve completely

Please help me with this. Show all your work. Please I am not understand what to do

pLEASE HELP ME SOLVE AND SHOW ALL STEPS TO COMPLETE THIS QUESTION   SEE PIC ATTACHED

Can you please help me find the answer to this math problem?

See the illustration below. The formula m + M V = (2gh)!/2 gives the velocity (in ft/sec) of a bullet with weight m fired into a block with weight M, that raises the height of the block h feet after the collision. The letter g represents the constant, 32. Find the velocity of the bullet to the nearest ft/sec, if m = 0.0624, M = 6, and h 0.9. V = ft/sec m lb M lb I h ft

4) The time a basketball player spends in the air when shooting a basket is called the​ "hang time." The vertical leap L measured in feet is related to the hang time t measured in seconds by the equation L=4t2. Suppose that a basketball player has a vertical leap of 3 feet 7 inches. Find the hang time for this leap.