If the arithmetic mean of two unequal positive real number 'a' and 'b’, (a > b), be twice as great as their geometric mean, show that a : b = = (2 + V3) : (2 – V3)

Q: A 50-foot ladder leans against a wall so that it is 40 feet high at the top. The ladder is moved so…

A: We have to find the height where top of ladder is higher from base.

Q: The product of two positive integers is 30, and their sum is 17. What are the integers?

A:

Q: Is the statement true or false? If an odd number is less than 15, then it is prime. False Give a…

A: We have to check

Q: Is there a real number whose square is –1? a. Is there a real number x such that _? such that x =…

A: In general, there does not exist any such real number whose square is a negative real number. Hence,…

Q: Express the interval shown on the number line in interval notation. -8 4 8. 10 12 -12 -10 -4 -2 () U…

A:

Q: The sum of any two integers of the from 4k+ is always: a) prime b) zero c) Even

A:

Q: Find and show on the real number line the solutions set of the in equality. 1. l 7 - 4x l ≤ 9 2. l…

A: Since you have posted two questions, we will solve first question for you. To get another question…

Q: 15) The product of two consecutive odd integers is 143. Find all this condition.

A:

Q: 15. Find the solution set, graph it on a number line, and express it in interval notation. |r +5-1<2…

A: We have to find the solution set, solution set graph on number line and we have to express the…

Q: What two positive real numbers whose product is 19have the smallest possible​ sum?

A: We want to find the two positive real numbers whose product is 19 and the smallest possible sum.

Q: A company pays $20 per hour for up to 5 hours of work, and $30 per hour for overtime hours (hours…

A: The Expression for overtime hours is  =  x-5   The Expression for Total earning in overtime hours is…

Q: A ball is dropped from a height of 128 feet. After each bounce it will rebound to a height that is…

A:

Q: Prove that given any set of eight integers, there is a pair among them whose sum or difference is…

A: Let n1,n2,n3,n4,n5,n6,n7,n8 be the 8 integers. Let ni≡rimod12 where 0≤ri&lt;12 Suppose, no two of…

Q: A piece of land is to be fenced and subdivided as shown so that each rectangle has the same…

A: Since each rectangle has same dimension so each of them has width=3x+1 and height =x

Q: Is any real number exactly 1 less than its cube?

A: Is any real number exactly 1 less than its cube?

Q: A 50-foot ladder leans against a wall so that it is 40 feet high at the top. The ladder is moved so…

A:

Q: Find three consecutive integers Such thate Hour times the sauare Of theo third less three times the…

A: Let consecutive integers are x-1,x,x+1

Q: A student has scores of 78, 77.25, and 81.75 on his first three tests. He needs an average of at…

A:

Q: Find two non-negative numbers such that the sum of two times the first and three times the second s…

A:

Q: What two nonnegative real numbers with a sum of 23 have thelargest possible product?

A: we have to find the two non negative real number with a sum of 23 which will have largest possible…

Q: O INTENATUNAL SCHUUL Find the condition for 2x² +3kx + 4c to be positive for all real values of .

A: To find the condition for 2x2+3kx+4c  to be positive for all real values of x.

Q: Express the interval shown on the number line in interval notation. -12 -10 -8 -6 -4 -2 0 2 4 6 8 10…

A: In this question we have to define the interval shown on the number line in interval notation.

Q: Use direct proof to show that product of two consecutive integers is even.

A:

Q: What two nonnegative real numbers with a sum of 34 have the largest possible product?

A:

Q: It is possible to rewrite the expression 4. 2 In(x) – In(ax) as In(kx) where k is a constant.…

A:

Q: A hot air balloon descends at a rate of 4ft per minute for 6 minutes, then rises at a rate of 2ft…

A: Given Data: The descending rate of the balloon is: D'=-4 ft per minute The time till the balloon…

Q: Show that the sum of a positive number and its reciprocal is at least 2.

A:

Q: Find two positive real numbers such that the sum of the first number squared and the second number…

A: Here we use application of derivatives.

Q: Prove: “The sum of two even integers is even.”

A: To prove: The sum of two even integers is even. n is an even number if it can be expressed as n =…

Q: Leonhard Euler approached negative numbers by describing how they "ought to" behave arithmetically…

A:

Q: A manufacturer of an anti-inflammatory drug claims that the drug will be effective for 8 hours. An…

A: A manufacturer of an anti-inflammatory drug claims that the drug will be effective for 8 hours. An…

Q: Solve the inequality for real x:  3x – 7 &gt; 5x – 1

A: Given inequality:

Q: A 50-foot ladder leans against a wall so that it is 30 feet high at the top. The ladder is moved so…

A:

Q: Find two positive integers such that the sum of the first number and four times the second number is…

A: Given: The sum of first number and four times the second number is 1000. The product of two numbers…

Q: Solve the inequality for real x:  4x + 3 &lt; 5x + 7

A:

Q: Express the following using factorials: 10 x 9 x 8 x 7

A: Meaning of factorial of a natural number : Suppose n is a natural number then meaning of n! is…

Q: Show that every odd integer is the sum of two consecutive integers

A:

Q: 4. ( it as linear combination of both numbers. Find the greatest common divisor of the numbers 1520…

A:

Q: One more than five times a number is less than or equal toten. Find all such numbers.

A: We can the numbers as below

Q: A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster,…

A: Let the speed of the train be x km per hour and time taken be y hours.Then

Q: Is the sum of two irrational numbers always an irrationalnumber?

A:

Q: other than the real root 2o , find the other 7 the equaton z 3 -용 +i and- 号- and 2 C. 늘 +i and 수 -…

A: Solution

Q: A bouncy ball is dropped such that the height of its first bounce is 7 feet and each successive…

A: The bounces of the ball represents a geometric sequence with First term=a=7Common ratio=r=67100=0.67

Q: How can I show that there exists at least one solution in the set of real numbers for x5-x3+3x=5…

A:

Q: Find and show on the real number line the solutions set of the in equality. 1. l 3x - 2 l ≥ 4

A: Concept |x| 1 . When absolute value is positive |x| will be x 2. When absolute value is negative |x|…

Q: Show that the equation has exactly one real root. 25 + 6x + 7x^5 + 4x^7

A: Given equation is    25+6x+7x5+4x7   First if we look at the limits of our function we see, that:…

Q: A(n) ______ number is a real number that cannot be expressed as a ratio of two integers

A: