Proofs - practice problems
The proof is a convincing demonstration in mathematics that a statement is true under certain conditions.Instructions: Solve each problem carefully and provide a detailed solution for every item.
Number of problems found: 17
- The 5th
The 5th, 8th and 11th terms of a GP are a, b, c respectively. Show that a, b, c are in GP. - And or logic
If A and B are events with P(A)=0.3, P(A OR B)=0.76, and P(A AND B)=0.04, find P(B). Enter your answer in decimal form, rounded to one place. - Prove 2
Prove that the minimum number of straight single cuts/strokes needs to divide a given right-angled triangle or an obtuse-angled triangle into a collection of all acute-angled triangles is seven(7). - Isosceles triangle and cosine
Using the cosine theorem, prove that in an isosceles triangle ABC with base AB, c=2a cos α. - Cone semicircle proof
If the shell of a cone is a semicircle, then the diameter of the cone's base is equal to its side's length. Prove it. - Triangle angle bisector
In the triangle, ABC, the angles alpha and beta axes subtend the angle phi = R + gamma/2. R is a right angle of 90°. Verify. - Karel grade average
Charles has an average grade of exactly 1.12 from five-minute episodes. Prove that at least 22 of them have one. - Janice
Janice said that when you multiply a fraction less than 1 by a nonzero whole number, the product is always less than the whole number. Do you agree? Explain. - Triangle circle proof
Given is an acute-angled triangle ABC. On the half lines opposite to BA and CA lie successively the points D and E such that |BD| = |AC| and |CE| = |AB|. Prove that the center of the circle circumscribing triangle ADE lies on the circle circumscribing tri - Number power square
Find the smallest natural x such that 2x is the square and 3x is the third power of a natural number. - Triangle area proof
Squares are constructed above the overhangs and the transom. Connecting the outer vertices of adjacent squares creates three triangles. Prove that their areas are the same. - Bisector 2
ABC is an isosceles triangle. While AB=AC, AX is the bisector of the angle ∢BAC meeting side BC at X. Prove that X is the midpoint of BC. - Fraction and ratios
Fraction and ratios are different names for the same thing. - Simplify logarithm expr
Given that logxU + logxV =p and logxU - logxV =q Prove that U=x^½(p+q) - Division residue proof
If n is a natural number that gives a division of 2 or 3 when divided by 5, then n gives a residue of 4 when divided by 5. Prove directly - Divisibility indirect proof
Prove indirectly: No odd natural number is divisible by four. - Sequence decreasing proof
Prove that the sequence {3 - 4. n} from n = 1 to ∞ is decreasing.
Do you have unsolved math question and you need help? Ask a question, and we will try to solve it. We solve math question.
