Find the largest area (sq. units) of the rectangle whose base is on the x-axis and its other two vertices above the x-axis and lying on the parabola y=8-x^2.

Q: Find two positive numbers whose product is 179 and whose sum is a minimum.

A: Let one number is = x Another number is = y

Q: What is the area of triangle bounded by the x-axis, the y-axis, and the line y=−4x+4?

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Q: Find three positive numbers whose sum is 300 and whose product is a maximum.

A: Let x ,y,z are 3 positive numbers such that x+y+z = 300 and xyz is maximumThe problem formed…

Q: Find the two positive numbers, whose product is 100 and sum is maximum.

A: We have to find the two positive numbers, whose product is 100 and sum is maximum.

Q: A closed box, whose length is twice its width, is to have a surface area of 192 sq. inches. Find the…

A: It's a closed box, so it has a top Let ? be the width of the box. Then its length is 2?. And the top…

Q: A page of 216 square inches is to have margins of 1 inch on either side and 1.5 inches at the top…

A: According to the question, Let x is the width of a the book page. Area given=216 square inches, Area…

Q: Find three positive numbers whose sum is 310 and whose product is a maximum.

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Q: Find the dimensions of the rectangle of maximum area that can be inscribed in an equilateral…

A: Use property of equilateral triangle and rectangle to solve this

Q: A rectangle has a length which is twice that of its width. Also, it's area is twice that of its…

A: This question is related to area and perimeter of rectangle, we will solve it using the given…

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Q: A piece of wire 60 cm long is to be folded into a rectangle.what should be the dimensions so that…

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Q: According to postal regulations, a carton is classified as “oversized” if the sum of its height and…

A: Assume a be the side length of the square base,h be the height of the carton and V be the volume of…

Q: Find three positive numbers whose sum is 100 and whose product is a maximum.

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Q: Find two positive numbers whose sum is 676 and the sum of whose squares is a minimum.

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Q: Mang Toti has a rectangular lot with one side against the wall. If he has 160m of fencing materials,…

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Q: An open box is to be made from a 6 ft by 16 ft reetangulas card board by cutting out equaL squares…

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Q: Find two numbers whose sum is a if the product of the square of one by the cube of the other is to…

A: Consider the first number be 'x'. The second number be 'y'. The sum of the numbers is given by a.…

Q: Find two positive numbers such that the sum of the first plus 7 times the second is 2,800 and their…

A: here also given that product is maximum. let; The first number is =x and second number= y According…

Q: Find two positive numbers whose sum is 12 so that the product of the square of one and 4th power of…

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Q: Find three positive numbers whose sum is 90 and whose product is a maximum.

A: Second derivative test: For critical points, fx=0 fy=0 A function f(x,y) has a local maximum value…

Q: Find the length and width of a rectangle that has perimeter 64 meters and a maximum area.

A: Given perimeter of rectangle is 64 meters. Let length of rectangle be x. Perimeter of…

Q: Find two positive numbers whose sum is 24 so that the product of the square of the first number and…

A: Given, Sum of numbers =24 Let numbers are x and y. x+y=24 P(x)=x2y4 is maximum.

Q: Find two positive numbers whose sum is 100 and whose product as largest as possible.

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Q: What positive number exceeds its cube by the maximum amount?

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Q: A rope of 40cm long is bent into the shape of a rectangle. Find the maximum rectangle area that can…

A: Let the length and breath of rectangle be l and b respectively. If a rope of length 40cm is bent in…

Q: Find the two numbers whose sum is 15 if the product of the square of one by the cube of the other is…

A: Let us consider one of the numbers to be x. So, the other number will be 15-x. Now, the function…

Q: Find three positive numbers whose sum is 3 and whose product is a maximum.

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Q: Find the dimensions of the right circular cylinder of greatest volum that can be inscribed in a…

A: Given query is to find the dimensions of a right circular cylinder that can be fit inside a sphere…

Q: The sum of the length and girth (perimeter of a cross-section) of a rectangular carried by a…

A: Look at the figure for the required package.

Q: You have to cut four equal squares from each corner of the 8.5" x 11" paper in order to make an open…

A: The volume of a cuboid is given by the formula V=l×w×h. Here, l is the length of the box, w is the…

Q: An open-top box is to be made from a 37 in. by 27 in. piece of cardboard by removing a square from…

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Q: A farmer has 1800 m of fencing to make two equal rectangular pens that share a common side.…

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Q: Find a number whose difference from its square root is least

A: Explanation of the answer is as follows

Q: Find the dimensions of a rectangle with area 1000m2 whose perimeter is as small as possible.

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Q: Mr. Raymundo has enough materials to fence 90 meters. What are the dimensions of the rectangular lot…

A: Let the length and width of the rectangle be x and y. Then the perimeter of the rectangle is = 2x+y…

Q: In your own words, describe the process of completing the square of a quadratic function. Explain…

A: It is required to describe the process of completing the square of the quadratic function and to…

Q: Find the dimensions of a rectangle with a perimeter of 200 feet that has the maximum area.

A: Given that the perimeter of the rectangle is 200 feet.   Suppose that the length of the rectangle x…

Q: The maximum area of the parabola inscribed in a right circular cone having a diameter of 24cm is…

A: Figure of right circular cone and inscribed parabola.

Q: Find two positive numbers whose sum equals 90 and who maximize the square root of their product.

A: Given that , Sum of two numbers are 90. find the numbers.

Q: A 27-inch by 72-inch piece of cardboard is used to make an open-top box by removing a square from…

A: The numerical is interpreted as shown in the drawing below;

Q: How many square units is the area of the region bounded by a parabola y = 4x - x^2 and the lines x =…

A: The equation of the curves are given by C1 : y = 4x-x2 C2 : y = 4 C3 : x =-2 To evaluate : The area…

Q: Find three positive numbers whose sum is 400 and whose product is a maximum.

A: Let 3 numbers be x, y, z Sum of these numbers is 400 x+y+z = 400          z= 400-x-y Product = P(x,…

Q: A rectangular garden whose length is 4ft longer than its width has an area of 65 sqft. Find the…

A: Given:Area of the rectangular garden is 65 square feet.

Q: The area of a paper that will be used to print a photo is 192 square inches. If a margin of 1 inch…

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Q: A piece of wire, 100 cm long, needs to be bent to form a rectangle. Determine the dimensions of a…

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Q: Find two positive numbers whose sum is 32 and the sum of their square roots is maximum.

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Q: Find two numbers whose sum is 11 and product is a maximum?

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Q: Find a non-negative number whose difference from its square is a maximum.

A: non-negative number whose difference from its square is a maximum.  Let the no is x

Q: A rancher has 1500 feet of fencing to enclose two adjacent rectangular corrals. What dimensions will…

A: Refer to the questionLet the common sides of two rectangular corrals be x then the sketch for the…