How do you solve this question? Please solve with an explanation. A quartic polynomial [tex]P(x)[/tex] satisfies the following properties. (A) [tex]P(3)=32[/tex] (B) [tex]P(2x+1)=16P(x+1)[/tex] for all real [tex]x[/tex]. Then, find [tex]P(4)[/tex].
TakenName
Asked:
April 2023
Write an explanation along with the answer. I will report any spam answer at once. A problem inspired by JEE advanced 2020. Find the least value of the natural number [tex]n[/tex] such that [tex]f(1)+f(-2)+f(3)+f(-4)+\cdots+f\{(-1)^{n+1}n\}\geq21[/tex], if [tex]f(x)=\dfrac{4^{x}}{4^{x}+2}[/tex].
TakenName
Asked:
January 2023
A box contains 3, 2, and 4 balls of red, yellow, and green, respectively. What is the number of ways to arrange 6 chosen balls in order?
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January 2023
Reupload(2022 Feb 9th). Show that the inequality of the attachment is true.
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January 2023
[tex]\displaystyle\sum^{n}_{k=1}(2k-1)a_{k}=n(n+1)(4n-1)[/tex] Find [tex]a_{n}[/tex].
TakenName
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January 2023
2022-01-27 Suppose [tex]a_{n}[/tex] as the sum of the numbers in which the quotient and the remainder are equal when divided by [tex]n.[/tex] For example, [tex]a_{5}=6+12+18+24=60.[/tex] Find the least [tex]n[/tex] such that [tex]a_{n}\ \textgreater \ 500.[/tex]
TakenName
Asked:
December 2022
For consecutive two natural numbers , is satisfied. Let . Which is a correct option for ? 1. It is always even. 2. It is even or odd. 3. It is always odd. 4. It is rational or irrational. 5. It is always irrational. Show your reason!
TakenName
Asked:
December 2022
Challenge! Compare the area of the given triangles. Hint: Pythagorean theorem
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December 2022
Topic: Permutation and Combination Is the number of ways to color the diagram the same, or not? Please add your quality answer. Thanks for helping.
TakenName
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December 2022
Topic: Proof Can we prove is strictly increasing without derivative? Need quality answers. Don't spam here.
Topic: Trigonometry Can we evaluate trigonometric values such as [tex]\sin15^{\circ}[/tex], [tex]\cos5^{\circ}[/tex] and [tex]\tan3^{\circ}[/tex]? If yes, how?
TakenName
Asked:
December 2022
Help request(Spams are reported.) How would you solve this question? The answer is 415, but there's no explanation in the book. Topic: Floor Function What is the value of [tex]\left \lfloor{(\sqrt{3} +1})^6}\right \rfloor[/tex]? ([tex]\left \lfloor{n}\right \rfloor[/tex] means the greatest integer which isn't greater than [tex]n[/tex].)
Can we evaluate using concepts of probability?
TakenName
Asked:
December 2022
Math Quiz The words are engraved on someone's gravestone. "God gave him his boyhood one-sixth of his life, one-twelfth(1/12) more as a youth while whiskers grew rife; And then yet one-seventh after the marriage has begun; In five years there came a bouncing new son. Alas, the dear child of...
TakenName
Asked:
December 2022
A challenging problem Topic: Trigonometry If , find . Thanks for solving my problem, IdyllicAurora, Assingh, and others.
TakenName
Asked:
December 2022
Doubt: Permutation and Combination But in the second diagram, there is symmetry. So, is this true? Thanks, IdyllicAurora for solving my problem.
TakenName
Asked:
December 2022
How many possibilities are there that follow the conditions? 1. 5 colors are available. 2. The neighboring regions should be in a different color. Please send your quality answer. Thanks for solving my problem.
TakenName
Asked:
December 2022
Quiz: Series [tex]1+\dfrac{1}{2} +\dfrac{1}{3} +\dfrac{1}{4} +\dfrac{1}{5} +\dfrac{1}{6} +\dfrac{1}{7} +...[/tex] If we add the unit fractions, which numerator is 1, infinitely many times, does the result end in a number or infinity? Please add your quality answer. Thanks for answering.