Recent questions tagged theorem

$A manufacturer of small motors is concerned with three major types of defects. If $A$ is the event that the shaft size is too large, $B$ is the event that the windings are improper, and $C$$

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A manufacturer of small motors is concerned with three major types of defects. If $A$ is the event that the shaft size is too large, $B$ is the event that the windings are improper, and $C$

asked Jun 17 in Data Science & Statistics by ♦Pieter Diamond (40,719 points) | 9 views

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In each of the following situations, should your value be near the average or an outlier? If outlier, should it be too large or too small?

asked Jun 17 in Data Science & Statistics by ♦Pieter Diamond (40,719 points) | 10 views

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Find the remainder when $7^{103}$ is divided by 25

asked Jun 14 in Mathematics by ♦MathsGee Platinum (122,736 points) | 36 views

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What does the sigmoid function state?

asked Jun 8 in Mathematics by ♦MathsGee Platinum (122,736 points) | 19 views

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Factor $x^{4}-256$ completely

asked Jun 4 in Mathematics by ♦Pieter Diamond (40,719 points) | 35 views

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If i have 32 numbers but the 1st combo can only be 1 or 2 the 2nd poss 3 or 4, etc...what r the combos?

asked Jun 3 in Mathematics by ♦Pieter Diamond (40,719 points) | 14 views

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If $x$ is too small so that terms of $x^{3}$ and higher can be ignored, show that: \[ \left(\frac{1}{2}+x\right)(1+x)^{4}=\frac{1}{2}+3 x+7 x^{2} \text {. } \]

asked May 31 in Mathematics by ♦Pieter Diamond (40,719 points) | 42 views

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If $x$ is too small so that terms of $x^{3}$ and higher can be ignored, show that \[ (4-x)(1-2 x)^{6}=4-49 x+252 x^{2} \]

asked May 31 in Mathematics by ♦Pieter Diamond (40,719 points) | 31 views

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The functions $x^{4}+b x^{3}-3 x^{2}-4 x-5$ and $3 x^{3}-8 x^{2}-2 x-13$, have the same remainder when divided by $(\mathrm{x}-2)$. What is the value of $\mathrm{b}$ ?

asked May 31 in Mathematics by ♦Pieter Diamond (40,719 points) | 39 views

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The expression, $2 x^{3}+a x^{2}+b$, has a remainder of 9 when divided by $(x-1)$ and a remainder of $-3$ when divided by $(x+2)$. Find the values of $a$ and $b$.

asked May 31 in Mathematics by ♦Pieter Diamond (40,719 points) | 44 views

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The functions $x^{3}-7 x-4$ and $3 x^{3}-3 x^{2}+b x+14$, have the same remainder when divided by $(x-3)$. What is the value of $b$ ?

asked May 31 in Mathematics by ♦Pieter Diamond (40,719 points) | 37 views

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The expression, $x^{3}+a x^{2}-2 x-4$, is divisible exactly by $(x+1)$. Find the value of $a$ and the remainder when the expression is divided by $(x+2)$.

asked May 31 in Mathematics by ♦Pieter Diamond (40,719 points) | 48 views

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The function $f(x)=a x^{2}+x-7$ has a remainder of 3 when divided by $(x-2)$. Find the value of $a$.

asked May 31 in Mathematics by ♦Pieter Diamond (40,719 points) | 47 views

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Find the remainder when $x^{2}-2 x-3$ is divided by $x+1$ using the Remainder Theorem.

asked May 31 in Mathematics by ♦Pieter Diamond (40,719 points) | 37 views

$$O$ is the centre of the circle with tangent $B A$ and secant $B C E$. $O D=D E=D C$ and $A O E$ is a straight line.$

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$O$ is the centre of the circle with tangent $B A$ and secant $B C E$. $O D=D E=D C$ and $A O E$ is a straight line.

asked Apr 17 in Mathematics by ♦Pieter Diamond (40,719 points) | 174 views

$$O$ is the centre of circle with tangents $K I$ and $I T . O E I$ is a straight line.$

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$O$ is the centre of circle with tangents $K I$ and $I T . O E I$ is a straight line.

asked Apr 17 in Mathematics by ♦Pieter Diamond (40,719 points) | 88 views

$Prove the theorem of Pythagoras $T P^{2}=P R^{2}+T R^{2}$$

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Prove the theorem of Pythagoras $T P^{2}=P R^{2}+T R^{2}$

asked Apr 17 in Mathematics by ♦Pieter Diamond (40,719 points) | 68 views

$In the diagram below $A D\|E F\| B C$. Prove that $A F \cdot B D=A C \cdot D F$.$

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In the diagram below $A D\|E F\| B C$. Prove that $A F \cdot B D=A C \cdot D F$.

asked Apr 17 in Mathematics by ♦Pieter Diamond (40,719 points) | 103 views

$In circle $O, R Q \perp P M, O Q=Q N$ and $x=\frac{M R}{M P}$. Calculate $x$$

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In circle $O, R Q \perp P M, O Q=Q N$ and $x=\frac{M R}{M P}$. Calculate $x$

asked Apr 17 in Mathematics by ♦Pieter Diamond (40,719 points) | 120 views

$Prove that $A B D E$ is a cyclic quadrilateral given $\hat{E}_{2}=x$.$

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Prove that $A B D E$ is a cyclic quadrilateral given $\hat{E}_{2}=x$.

asked Apr 17 in Mathematics by ♦MathsGee Platinum (122,736 points) | 123 views

$$T R N$ is a tangent at $R$ and $S R=R Q$. If $\hat{R}_{1}=x$, find five angles equal to $x$.$

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$T R N$ is a tangent at $R$ and $S R=R Q$. If $\hat{R}_{1}=x$, find five angles equal to $x$.

asked Apr 17 in Mathematics by ♦MathsGee Platinum (122,736 points) | 150 views

$Given that the angle between a tangent to a circle and a chord drawn from the point of contact is equal to an angle in the alternate segment. Prove that $\hat{A}_{1}=\hat{C}_{2}$$

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Given that the angle between a tangent to a circle and a chord drawn from the point of contact is equal to an angle in the alternate segment. Prove that $\hat{A}_{1}=\hat{C}_{2}$

asked Apr 17 in Mathematics by ♦MathsGee Platinum (122,736 points) | 138 views

$Given that two tangents drawn to a circle from the same point outside the circle are equal in length and tangents $T P K$ and $S R K$ to circle centre $O$, prove that $PK=RK$$

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Given that two tangents drawn to a circle from the same point outside the circle are equal in length and tangents $T P K$ and $S R K$ to circle centre $O$, prove that $PK=RK$

asked Apr 17 in Mathematics by ♦MathsGee Platinum (122,736 points) | 96 views

$Given that two tangents drawn to a circle from the same point outside the circle are equal in length and tangents $T P K$ and $S R K$ to circle centre $O$.Prove that $PK=RK$$

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Given that two tangents drawn to a circle from the same point outside the circle are equal in length and tangents $T P K$ and $S R K$ to circle centre $O$.Prove that $PK=RK$

asked Apr 17 in Mathematics by ♦MathsGee Platinum (122,736 points) | 181 views

$$A B C D$ is a parallelogram and $B \hat{A} D=\hat{F}_{1}$. Prove that $C E F G$ is a cyclic quad.$

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$A B C D$ is a parallelogram and $B \hat{A} D=\hat{F}_{1}$. Prove that $C E F G$ is a cyclic quad.

asked Apr 17 in Mathematics by ♦MathsGee Platinum (122,736 points) | 83 views

$Given that the opposite angles of a cyclic quadrilateral are supplementary and Circle centre $C$ with quad $QUAD$, prove that $\hat{Q}+\hat{A}=180^{\circ}$$

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Given that the opposite angles of a cyclic quadrilateral are supplementary and Circle centre $C$ with quad $QUAD$, prove that $\hat{Q}+\hat{A}=180^{\circ}$

asked Apr 17 in Mathematics by ♦MathsGee Platinum (122,736 points) | 94 views

$Given that the circle centre $N$ with arc $R T$ subtending $R \hat{P} T$ and $R \hat{M} T$ in the same segment. Prove that $R \hat{P} T=R \hat{M} T$$

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Given that the circle centre $N$ with arc $R T$ subtending $R \hat{P} T$ and $R \hat{M} T$ in the same segment. Prove that $R \hat{P} T=R \hat{M} T$

asked Apr 17 in Mathematics by ♦MathsGee Platinum (122,736 points) | 97 views

$Given that the perpendicular bisector of a chord passes through the centre of the circle and $R T=R P$ and $M R \perp T P$, prove that $M R$ goes through the centre of the circle.$

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Given that the perpendicular bisector of a chord passes through the centre of the circle and $R T=R P$ and $M R \perp T P$, prove that $M R$ goes through the centre of the circle.

asked Apr 17 in Mathematics by ♦MathsGee Platinum (122,736 points) | 73 views

$Given that a line drawn from the centre of a circle perpendicular to a chord bisects the chord. Prove that $NM=MP$$

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Given that a line drawn from the centre of a circle perpendicular to a chord bisects the chord. Prove that $NM=MP$

asked Apr 17 in Mathematics by ♦MathsGee Platinum (122,736 points) | 94 views

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What is 56 Divided by 2?

asked Mar 27 in Mathematics by ♦Pieter Diamond (40,719 points) | 76 views

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What is an asset in finance?

asked Mar 14 in Economics and Finance by ♦Pieter Diamond (40,719 points) | 80 views

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What is the equation of the normal to the curve $y=(3 x+10)^2$ at the point $(-3,1)$ ?

asked Mar 8 in Mathematics by ♦Pieter Diamond (40,719 points) | 245 views

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State the Implicit function theorem

asked Feb 20 in Mathematics by ♦MathsGee Platinum (122,736 points) | 85 views

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A function $f(x)$ is convex on $(a, b)$ if

asked Feb 20 in Mathematics by ♦MathsGee Platinum (122,736 points) | 103 views

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If $f(x) \in C^{n+1}[a, b]$, then

asked Feb 20 in Mathematics by ♦MathsGee Platinum (122,736 points) | 88 views

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What does the mean value theorem say?

asked Feb 20 in Mathematics by ♦MathsGee Platinum (122,736 points) | 92 views

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What does the binomial theorem state?

asked Feb 20 in Mathematics by ♦MathsGee Platinum (122,736 points) | 100 views

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How do I determine binomial coefficients?

asked Feb 20 in Mathematics by ♦MathsGee Platinum (122,736 points) | 61 views

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Complete the number sentence to make the statement true, by filling in <; > or =: 22101 _____ 22110

asked Feb 5 in Mathematics by ♦Pieter Diamond (40,719 points) | 107 views

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State the Extreme Value Theorem, clearly identifying any hypothesis and the conclusion.

asked Feb 4 in Mathematics by ♦Pieter Diamond (40,719 points) | 66 views

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State the Mean Value Theorem, clearly identifying any hypothesis and the conclusion.

asked Feb 4 in Mathematics by ♦Pieter Diamond (40,719 points) | 75 views

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State Fermat's Theorem, clearly identifying any hypothesis and the conclusion.

asked Feb 4 in Mathematics by ♦Pieter Diamond (40,719 points) | 75 views

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State the Squeeze Theorem, clearly identifying any hypothesis and the conclusion.

asked Feb 4 in Mathematics by ♦Pieter Diamond (40,719 points) | 83 views

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The Economist magazine reports from a study of $\underline{20}$ subscribers that the average income is $\$ 80,000$ USD with a standard deviation of the population is $\$ 15,000$ USD.

asked Feb 2 in Data Science & Statistics by ♦MathsGee Platinum (122,736 points) | 69 views

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