Choose the formula in which TWO instances of the variable "x" are free:  a) ((∀x)Gx -> (Fx -> Hx)) b) ((Fx ᐱ Gx) -> Hx) c) ((Ǝx)(Fx ᐱ Gx) -> Hx) d) (∀x)(Fx -> Gx)

Q: What two positive real numbers whose product is 72 have the smallest possible sum?

A: let two real numbers are a and b then according to question ab=72..........(I) let sum is S then…

Q: Apply u-substitution

A: We have to find the integration using u-substitution: ∫4ln1xxdx Rewriting the integration using…

Q: h0-60 |--²-1²-₁-²

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Q: serves conv 1, then its a

A: Concept:

Q: नैग,ु गात्म की ए D) フー X- २० मर्तकीर अा X- C. 2. =ां 2. X- 8 पट-ट' + ८ 7 से रा र त्यतिज 2हि (ए X2-…

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Q: The numbers 1, 2, ... 10 are written in a row. Is it possible to put signs - and + between them so…

A: We know that the sum of all the numbers from 1 to 10 is 55

Q: A chemical manufacturer wants to lease a fleet of 28 railroad tank cars with a combined carrying…

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Q: The 24th term of an AP is twice its 10th term .Show that its 72th term is 4 times its 15th term

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Q: To receive Grade ‘A’ in a course, one must obtain an average of 90 marks ormore in five examinations…

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Q: There are 5 types to solve linear diff. eq. of first order * True False

A: Given that , Linear differential equation-A linear differential equation is defined by the linear…

Q: symmetri

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Q: Phythagoras was the one who formulated one of the earliest theorems known to ancient civilizations…

A: Yes the given statement is true  Because approx 2000years ago a theorem is granted named as ancient…

Q: Find proj, u and scalyu by inspection without using formulas. 10- projyu = 6- 4- 2- -10-8-6-4 2 -2-…

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Q: What is seC 6. sec(-) O 2/3 3 O 2/3 3 O 2 O -2

A: The objective is to find the trigonometric value.

Q: For each positive integer n, find the number of positive integers that are less than 210n which are…

A: ANSWER :

Q: , x); R = [0, -) D) D = (-, x); R = [-10, -)

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Q: A line segment partitioned by a ratio of 2:5 can be though of as having how many congruent parts

A: The given ratio is 2:5 So total parts = 2+5 = 7

Q: 2, then the conju

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Q: lHans, , Chenl exprcss 240° <0and sec -400°

A: A). 240°    Reference angle = 240°-180° =160°   B). -400°   Reference angle  = -400°+360° = -40°

Q: How many women use at most one brand? How many women do not use any of the 2 brands?

A: here given  Forty women were asked regarding 2 known brands of llipstick, it was found out that: 15…

Q: A man is 6 feet tall and his shadow measures 5 feet. If the shadow of a tree near the man measures…

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Q: witness to a hit-and-run accident told the police that the license number contained the letters RQLH…

A: Answer:72 Explanation: First digit=2 No.of digits=10 ie, (0,1,2,3,4,5,6,7,8,9) Now possibilities…

Q: For Theorem 2.8 and it corollary give a simplified and short example in order to explain it very…

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Q: The height of 10 plants is measured in inches and found to be 12,6,15,3,12,621,15,18 and 12. Verify…

A: We know that, Mean, X bar = (summation Xi)/m Here n= 10 X bar = (12+6+15+3+12+6+21+15+18+12)/10 = 12

Q: 6) The product of two numbers is equal to 192. Find values for these numbers such that the sum is…

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Q: A dining hall had a total of 25 tables, some long rectangular tables and some round ones.  Long…

A: x = 20 y = 5

Q: Find x so that x,x+2 and (x+3) are threee consecutive terms of GP

A: When a, b, c are in gp then b^2=ac.

Q: Solve the IVP: X' = AX, where --() 3 1 0 2 -1 0 0 A = 3 and X(0) = -1 2

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Q: If Xo and X, are two numbers with Xo < X, then the true one is

A: Answer:-  Option D is the correct answer.

Q: Which of these will prove the 10th step and the reason ?

A: Given : To find : The statement 3 and give the reason.

Q: Suppose that x, y and z are three positive numbers whose sum is 100 If P denotes the product of the…

A: Given,           Suppose that x,y and z are three positive numbers whose sum is 100.           Also,…

Q: Suppose a = {„",}- L,".]. Find the value of a.

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Q: Find numbers a and b such that ax + by =(9, -1, 10), where x =(3, -1, 0) and y =(0, 1, 5). Is there…

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Q: The doctor orders 300mls of a drug to be given through a tube ( intra-venous), over a period of 1…

A:

Q: 19. The sum of 3 real numbers is known to be zero. If the sum of their cubes is e™, what is their…

A: Solve #19

Q: What are all of the natural numbers divisible by 8 whose sum of digits is less than 10 and the…

A: Given the requirements

Q: A can do a piece of work in 80 days . He works at it for 10 days and then B alone finishes the…

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Q: Express in the form a+ bi. -21

A: Our Aim is to express 51+2i-(i) in the form a+bi

Q: Find two concecutive odd integers such that when the smaller is added to twice the larger, the…

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Q: Express in terms of i. V- 4

A: -4=-1×4=-1×4=i×(2)=2i

Q: A farmer has 180 yd of fencing material and wants to enclose three rectangular pens. Suppose that r…

A: Given, A farmer has 180 yards of fencing material,

Q: Use different ways to show all possible combination in this situations

A: Here use different ways of representing a total possibilities Here use listing , table, and tree and…

Q: State the theorem that justifies the statement &lt;6= &lt;7.

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

A: Given x is the total hours worked. And beyond 5 hours it will be overtime hours.

Q: If x is a n-700 as a. always b. real number Sometimes never such that 1x11, then x" -> -0

A: We want to find correct answer.

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: The technique of boxing in a triangle and determing its area by using rectangle and right triangle…

A: Let ABC is triangle with vertices, Ax1,y1,Bx2,y2,Cx3,y3. WhereDx1,0, Ex2,0, Fx3,0 are points on…

Q: How do I solve for A in (4-Ax3=7-Ax6)

A: Add Ax^6 to both sides.

Q: Prove that equation x^2 + y^3 = 60 does not have any positive integer solution. Prove by…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.