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Solve the equation $\frac{x-8}{\sqrt{25+(8-x)^{2}}}+\frac{x}{\sqrt{x^{2}+16}}=0$
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What strategy can be used to complete the square for any equation of the form $x^{2}+a x+b=0$
1 answer 64 views
What strategy can be used to complete the square for any equation of the form $x^{2}+a x+b=0$What strategy can be used to complete the square for any equation of the form $x^{2}+a x+b=0$ ...
by Pieter SIlver Status
(17,439 points)
asked in Mathematics Jun 11, 2021
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What are the Sum-Difference identities in trigonometry?
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What are the Sum-Difference identities in trigonometry?What are the Sum-Difference identities in trigonometry? ...
by Pieter SIlver Status
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asked in Mathematics Jun 11, 2021
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Factorize $x^{3}+4 x^{2}+3 x+12$
1 answer 42 views
Factorize $x^{3}+4 x^{2}+3 x+12$Factorize $x^{3}+4 x^{2}+3 x+12$ ...
by Pieter SIlver Status
(17,439 points)
asked in Mathematics Jun 11, 2021
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Prove Wilson's Theorem
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Prove Wilson's TheoremProve Wilson's Theorem ...
by MathsGee Platinum
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asked in Mathematics Jun 4, 2021
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Prove the following
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Prove the followingLet $n,k \in  \mathbb{R}^+ $ such that $ k =(p-1)q +r, 0 \leq r \leq p$ Prove that $ n^k \equiv n^r \ (mod \ p)$ ...
by Claudia Wooden
(4,756 points)
asked in Mathematics Jun 1, 2021
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Given a real value $x$ such that $0 \leq x \leq 1$, show that $$ \frac{x^{2}}{x+1}+\frac{(1-x)^{2}}{2-x} \geq \frac{1}{3} $$
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Prove that if the product of $n$ positive real numbers is 1, then their sum is at least $n$
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Prove that if the product of $n$ positive real numbers is 1, then their sum is at least $n$Prove that if the product of $n$ positive real numbers is 1, then their sum is at least $n$ ...
by MathsGee Platinum
(102,810 points)
asked in Mathematics May 31, 2021
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Find the number of real solutions to the equation: $$ \left(16 x^{200}+1\right)\left(y^{200}+1\right)=16(x y)^{100} $$
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Use the central limit theorem to provide an approximation to this probability.
1 answer 74 views
Use the central limit theorem to provide an approximation to this probability.$N$ independent trials are to be conducted, each with "success" probability $p .$ Let $X_{i}=1$ if trial $i$ is a success and $X_{i}=0$ if i ...
by MathsGee Platinum
(102,810 points)
asked in Data Science & Statistics May 30, 2021
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What is the value of $t$ such that $Q(t)=4 ?$
0 answers 38 views
What is the value of $t$ such that $Q(t)=4 ?$$$ \begin{array}{c} \frac{d Q}{d t}=6(5-Q(t)) \\ Q(0)=0 \end{array} $$ The function $Q(t)$ satisfies the differential equation shown above. What is th ...
by MathsGee Platinum
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asked in Mathematics May 30, 2021
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Given the following center-radius form of the equation for a circle, find the center of the circle. $$ (x-3)^{2}+(y+2)^{2}=16 $$
1 answer 91 views
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Prove that a positive integer $n$ is a prime number if no prime number less than or equal to $\sqrt{n}$ divides $n$.
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Prove the trigonometric identity
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Prove the trigonometric identityProve that $$\cos 2 \alpha=\left\{\begin{array}{l}\cos ^{2} \alpha-\sin ^{2} \alpha \\ 1-2 \sin ^{2} \alpha \\ 2 \cos ^{2} \alpha-1\end{array}\right ...
by MathsGee Platinum
(102,810 points)
asked in Mathematics May 26, 2021
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Find the Maclaurin series for $\ln (1+x)$.
1 answer 53 views
Find the Maclaurin series for $\ln (1+x)$.(a) Find the Maclaurin series for $\ln (1+x)$. (b) Use the alternating series estimation theorem to prove that $x-\frac{x^{2}}{2} \leq \ln (1+x) \leq ...
by Student SIlver Status
(10,386 points)
asked in Mathematics May 24, 2021
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By using a suitable Maclaurin series given in the text find the sum to infinity of the following infinite series:
1 answer 146 views
By using a suitable Maclaurin series given in the text find the sum to infinity of the following infinite series:By using a suitable Maclaurin series given in the text find the sum to infinity of the following infinite series: (a) $\pi-\frac{\pi^{3}}{3 !}+\frac{ ...
by Student SIlver Status
(10,386 points)
asked in Mathematics May 23, 2021
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Using the axioms of probability, prove the following:
1 answer 361 views
Using the axioms of probability, prove the following:Using the axioms of probability, prove the following: a. For any event $A, P\left(A^{c}\right)=1-P(A)$. b. The probability of the empty set is zero, ...
by Pieter SIlver Status
(17,439 points)
asked in Data Science & Statistics May 22, 2021
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