3. If the area of a rectangle is expressed as x* - 9y? then the product of the length and the width of the rectangle could be expressed as. 1) (х- Зу)/(х + Зу) Зу) 2) (x² - 3y)(x² + 3y) 3) (x2 - Зу(x2- 3у) 4) (x*+ у(х -9у)
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- Note: For the First Order Equations-Linear Nonhomogeneous How can you slove without method of Intergating Factor1. A farmer wants to fence off a rectangular field and use a well as one side. He has500 meters of fencing. What are the dimensions of the field that has the largestarea? 2.Two cars, one going due West at the rate of 100 km/hr and the other goingNorth at the rate of 70 km/hr, are traveling toward the intersection of the tworoads. At what rate are the cars approaching each other at the instant when thefirst car is0.3 km and the second car is 0.2 km from the intersection?I need general solution for 1, disregard the y denominator in the 1st term Topic: variable separable and homogenous DE
- a.) A wire of length 34 m is divided into two pieces and each piece is bent into a square. How should this be done in order to minimize the sum of the areas of the two squares? (Give your answer in the form of a comma separated list of the lengths of the two pieces.) the lengths of the pieces:Suppose that the population of whales in world’s oceans increasesby 20 % per year in the absence of external factors. If there are originally 1000 whalesand scientists are allowed to capture 150 whales per year, derive an IVP that gives thenumber of whales present in any year and solve itA rectangle field is to be watered by a rotating sprinkler head with a range of 25 feet. The sprinkler is to be placed in the middle of the field and the water set to just reach the corners of the field. If the area of the field is 1000 square feet, what are the dimensions of the field?
- You wish to cross the 11 m x 10 m courtyard without being detected by the two guards and escape through a door located on the western wall. Guard 1 is located in a tower at the northeast corner of the yard and Guard 2 is located in the yard, in the southwest corner, as shown in the figure below. Guard 1 can hear you if anything more than 1/36 of the footstep sound energy reaches them; similarly Guard 2 can hear you if anything more than 1/16 of the footstep sound energy reaches them (Guard 1 can hear more due to his elevated height in the tower). Assume for now that both guards are fixed at these locations and cannot move unless they detect you. Based on this information, answer the following questions. 1. determine if it exists, the safe distance between the two hearing zones of the guards for you to pass through undetected? (Hint: use Pythagorean Theorem or distance formula) Distance between two red dots is:________________ . (5 pts) We know that the radius of the hearing zones are:…You wish to cross the 11 m x 10 m courtyard without being detected by the two guards and escape through a door located on the western wall. Guard 1 is located in a tower at the northeast corner of the yard and Guard 2 is located in the yard, in the southwest corner, as shown in the figure below. Guard 1 can hear you if anything more than 1/36 of the footstep sound energy reaches them; similarly Guard 2 can hear you if anything more than 1/16 of the footstep sound energy reaches them (Guard 1 can hear more due to his elevated height in the tower). Assume for now that both guards are fixed at these locations and cannot move unless they detect you. Now assume that Guard 2 is on patrol. He walks a straight patrol route up and down along the dotted line always remaining 3 m from the western wall. Determine the new maximum safe distance between the two hearing zones of the guards for you to pass undetected? (Hint: use Pythagorean Theorem or distance formula) Where is the Guard 2 located for…You wish to cross the 11 m x 10 m courtyard without being detected by the two guards and escape through a door located on the western wall. Guard 1 is located in a tower at the northeast corner of the yard and Guard 2 is located in the yard, in the southwest corner, as shown in the figure below. Guard 1 can hear you if anything more than 1/36 of the footstep sound energy reaches them; similarly Guard 2 can hear you if anything more than 1/16 of the footstep sound energy reaches them (Guard 1 can hear more due to his elevated height in the tower). Assume for now that both guards are fixed at these locations and cannot move unless they detect you. Now assume that Guard 2 is on patrol. He walks a straight patrol route up and down along the dotted line always remaining 3 m from the western wall. Determine the new maximum safe distance between the two hearing zones of the guards for you to pass undetected? (Hint: use Pythagorean Theorem or distance formula) Where is the Guard 2 located for…
- 7. The rectangular bird sanctuary with one side along a straight river is to be constructed so that it contains 8km2 of area. Find the dimensions of the rectangle to minimize the amount of fence necessary to enclose theremaining three sides.An open box is to be formed out of a rectangular piece of cardboard whose length is 8 cm longer than its width. To form the box, a square of side 4 cm will be removed from each corner of the cardboard. Then the edges of the remaining cardboard will be turned up.A rectangular box without a lid must be made at a cost of $15 for stuff. If the material for the base costs $0.20 per square inch and material for the sides costs $0.35 per square inch, find the dimensions of the largest volume box that can be made.