i) Given that q =ť + 6t + 5 , express q in the form (t + a)´ + b where e :(t+ 3)" - 4 ] and b are integers to be determined. ii) Hence or otherwise, state: a) the minimum value of q and 4 b) the minimum value of a. ( how to lve 7

Q: A piece of wire 40 cm long is to be cut into two pieces . One piece wil bent to form a circle, the…

A: The total length of the wire is 40 cm and one piece is to be formed into a circle and another one is…

Q: Among all pairs of numbers whose difference is 14, find a pair whose product is as small as…

A: As per our guidelines, we are allowed to answer only one question. Since you have asked multiple…

Q: truck travelling west at 100km/h is 250km due east of a sports car going north at 120km/h.…

A: At t = 1.04 hour, they are closests to each other. Minimum distance between them is 192.07 km.

Q: find An eignuector of the matix 12 17 2 VZ V3 19 2 J3 -VIT -2 Ji

A:

Q: 3. The square of a certain number exceeds twice the square of another mumber 5 Find possible pairs…

A:

Q: A closed rectangular box to contain 16 ft³ is to be made of three kinds of materials. The cost of…

A: Let's find dimension for minimum cost of given rectangular box.

Q: 4. The bottom of the legs of a three-legged table are the vertices of an isosceles triangle with…

A: In the question 4 it is asked to calculate the minimum wire length required to make a brace of of…

Q: Among all pairs of numbers whose difference is 14, find a pair whose product is as small as…

A:

Q: An architect is attempting to fit a rectangular closet of maximal volume into a chopped-off corner…

A: Given : x+2y+3z=24--(1) We have to find the maximum volume of the rectangular closet. Let x, y, z be…

Q: How.S You Are to ConSÅruct an afen rectangular boxfro4- 12 t? of material what dimensions w resuttin…

A: Given an open rectangular box from 12 ft2

Q: 10. A wire of length 20m is cut into two parts, one of which is bent into a circle and the other…

A:

Q: A company has determined that when x hundred dulcimers are​ built, the average cost per dulcimer can…

A: The average cost per duclimer  can be estimated by the following function…

Q: A wire of length 10 is to be cut into two pieces, one being bent to form a square and the other to…

A:

Q: A piece of 1m wire is cut into two parts, one bent into the shape of a circle and the other into the…

A:

Q: Show that the interval [0,1) does not have a maximum element; that is, there is no largest number…

A:

Q: 3. The sides of the base of a rectangular cardboard shoe box are 3x and 2x cm respectively. The…

A: Let's find.

Q: Among all pairs of numbers whose difference is 18, find a pair whose product is as small as…

A:

Q: A closed rectangular box to contain 16 ft³ is to be made of three kinds of materials. The cost of…

A: Easy to handle two variables rather than three variables, so i substitute by a variables by other…

Q: 6. Find the maximum area of a rectangle in the first quadrant where one side of the rectangle lies…

A:

Q: Two nonnegative numbers whose product is 36a? (where a > 0) and whose sum is a minimum, are

A: Now we will solve the problem.

Q: What is the minimum value of x^2+100/x on a horizontal span of 1 to 5?

A: The given expression is x2+100x;1,2,3,4,5. Let us use the graph to analyze the above function for…

Q: A wire of length 10 is to be cut into two pieces, one being bent to form a square and the other to…

A: It is given that a wire of length 10 units to be cut into two pieces. Let one piece of wire be x…

Q: Find the minimum value of y = 240 - x on the horizontal span from 0 to 5. (Enter the minimum value…

A: we have to figure out the minimum value of y=f(x)= 240-x^3 for the values of x  x less than equal to…

Q: an I ask how the maximum and mininmum points were obtained?

A: We need to find max and min points.

Q: Among all pairs of numbers whose difference is 16, find a pair whose product is as small as…

A: The difference of two numbers is 16. We have to find a pair whose product is as small as possible.…

Q: Let A be a positive real number. If the absolute minimum value of f(x) = Ax³ – 40x³ on 0, 00) occurs…

A: fx=Ax5-40x3 Differentiating with respect to x, we get f'x=A·5x4-40·3x2=5Ax4-120x2 Now to find…

Q: Among all pairs of numbers whose difference is 10, find a pair whose product is as small as…

A:

Q: (a) The minimum UGPA that would still place a student in the top 5% of UGPAS is. (Round to two…

A: u = 3.28 sigma =0.19

Q: rectangular field is to have an area of This is to be enclosed and divided into three equal lots…

A: Minimize

Q: Let f (x) be the square of the distance from the point (2, 1) to a point (x, 3x + 2) on the line y =…

A: The square of the distance between two points (a, b) and (c, d) = (c - a)2 + (d - b)2

Q: In open topped glass aquarium with a square base is designed to hold 62.5 cubic feet of water. What…

A:

Q: 1. A 12-meter wire is cut into two pieces so that x meters will be used to form a circle and the…

A:

Q: A wire of length L is cut into pieces, one being bent to form a square and the other form an…

A: Assuming that the wire is cut in 2 pieces of length x and L-x where the first is used to make a…

Q: Prove that if A has n as a minimum then B = {x ∈ R | ∃a ∈ A, x = −3a} has −3n as a maximum

A:

Q: An offshore oil well located at a point W that is 5 km from the closest point A on a straight…

A: Make a diagram using the given statements Now we find the cost function   cost of laying…

Q: A wire b is cut into two pieces. One piece is bent into an equilateral triangle and the other is…

A:

Q: Let a be a real number and a and B the roots of x'- 2a'x+1= 0. Show that attains a' a minimum…

A:

Q: 6) A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of…

A:

Q: )A wire of length L is cut into pieces, one being bent to form a square and the other o form an…

A: Given problem is :

Q: What is the absolute minimum value of q(x) = 2x -1 over -2, 5?

A: We have to find the absolute minimum value of q(x) = 2x2 - 1 over [-2, 5].

Q: 2) Prove by using the pigeonhole principle that among any 17 points in a square of side one there is…

A: Given: A square of side one contains 17 points. To show: There is at least a pair whose distance is…

Q: The head of a groundwater aquifer is described in Cartesian coordinates by 1 h(x, y) = 1+x2 + y2 + x…

A: The head of a ground water aquifer is described in Cartesian coordinates by, hx,y=11+x2+y2+x+xy

Q: You and your friends are hosting a round pizza party, and you are tasked in determining what size…

A:

Q: Find two positive numbers that satisfy the glven requirements. The second number Is the redlprocal…

A:

Q: A piece of wire 40 cm long is to be cut into two pieces. One piece will be bent to form a circle,…

A:

Q: is the total cost of production for a 7-hour day, where x machines are used to produce jackets and y…

A: The Extreme value theorem states that if a function is continuous on a closed interval a, b, then…

Q: In the article "Do Dogs Know Calculus?" the author Timothy Pennings explained how he noticed that…

A: Given: Speed on the sand = 6.2 m/s Speed on the water = 0.94 m/s To find: The distance x from C so…

Q: Suppose the product of x and y is 49 and both x and y are positive. What is the minimum possible sum…

A:

Q: Your school has contracted a choir group to perform at the school. The school has guaranteed an…

A: Let x be the number of students and y be the number of nonstudents who attended the choir.

Q: A rectangular field is to have an area of 900 sq. m. This is to be enclosed and divided into three…

A: Let's find.