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Mathematics gr10
Arithmetic mean is given by the sum of numbers divided by the count of the numbers. Thus, the arithmetic mean of 12 and 34 is given by $\dfrac{12+34}{2}=\dfrac{46}{2}=23$.
Arithmetic mean is given by the sum of numbers divided by the count of the numbers.
Thus, the arithmetic mean of 12 and 34 is given by .
See lessArithmetic means
Arithmetic mean is given by the sum of numbers divided by the count of the numbers. Thus, the arithmetic mean of 2 and 32 is given by $\dfrac{2+32}{2}=\dfrac{34}{2}=17$.
Arithmetic mean is given by the sum of numbers divided by the count of the numbers.
Thus, the arithmetic mean of 2 and 32 is given by .
See lessArithmetic mean
Arithmetic mean is given by the sum of numbers divided by the count of the numbers. Thus, the arithmetic mean of 10, 18, and 32 is given by $\dfrac{10+18+32}{3}=\dfrac{60}{3}=20$.
Arithmetic mean is given by the sum of numbers divided by the count of the numbers.
Thus, the arithmetic mean of 10, 18, and 32 is given by .
See lessProblem solving
Let the tens digit be $a$ and the ones digit be $b$, then the number is given by $10a+b$. The sum of the digits is 12 means that $a+b=12$ . . . . . (1) Reversing the digits, we have the number $10b+a$. Thus, "reversing the digits decreases the value by 36" means $10a+b-36=10b+a\Rightarrow10a-a+b-10bRead more
Let the tens digit be and the ones digit be , then the number is given by .
The sum of the digits is 12 means that . . . . . (1)
Reversing the digits, we have the number .
Thus, “reversing the digits decreases the value by 36” means . . . . . (2)
From (1), , which when substituted into (2) gives .
Dividing both sides by -18, we have and .
Therefore, the number is .
See lessFind the derivative
Given $=(x+2)^2\Rightarrow y=(x+2)(x+2)$. Let $U=x+2$, then $\dfrac{dU}{dx}=1$, also let $V=x+2$, then $\dfrac{dV}{dx}=1$. Then, $y=UV\Rightarrow\dfrac{dy}{dx}=U\dfrac{dV}{dx}+V\dfrac{dU}{dx}=(x+2)\cdot1+(x+2)\cdot1$ $\Rightarrow\dfrac{dy}{dx}=x+2+x+2=2x+4$.
Given .
Let , then , also let , then .
Then,
.
See lessWhat is Sohcahtoa
SOHCAHTOA is a mnemonic for the right triangle trigonometry. If we have a right with an angle, $\theta\ne90^o$, and the legs opposite and adjacent $\theta$. Then, SOH means $\sin\theta=\dfrac{\text{opposite}}{\text{hypotenuse}}$. CAH means $\cos\theta=\dfrac{\text{adjacent}}{\text{hypotenuse}}$. TOARead more
SOHCAHTOA is a mnemonic for the right triangle trigonometry.
If we have a right with an angle, , and the legs opposite and adjacent .
Then, SOH means .
CAH means .
TOA means .
See lessPermutation with Repetition
RETREAT has 7 letters where R, E, and T appear twice. Thus, the number of ways that RETREAT can be arranged is given by $\dfrac{7!}{2!\times2!\times2!}=\dfrac{7\times6\times5\times4\times3\times2\times1}{2\times1\times2\times1\times2\times1}$ $=7\times6\times5\times3=630$ ways.
RETREAT has 7 letters where R, E, and T appear twice.
Thus, the number of ways that RETREAT can be arranged is given by
ways.
See lessProblem Solving
If a quadratic equation, $ax^2+bx+c=0$ has two unequal real roots then, $b^2-4ac>0$. Thus given that $6x^2 + 5x + k = 0$ has two unequal roots, then $5^2-4\times6\timesk>0\Rightarrow25-24k>0\Rightarrow24k<25\Rightarrow k<\dfrac{25}{24}$
If a quadratic equation, has two unequal real roots then, .
Thus given that has two unequal roots, then
See lessSolve the following
Given $\dfrac{4}{x}+3y=8$, multiplying through by $x$ gives $4+3xy=8x\Rightarrow8x-3xy=4\Rightarrow x(8-3y)=4\Rightarrow x=\dfrac{4}{8-3y}$. Substituting $x=\dfrac{4}{8-3y}$ into the second equation, $\dfrac{6}{x}-4y=-5$, we have $\dfrac{6}{\frac{4}{8-3y}}-4y=-5\Rightarrow\dfrac{6(8-3y)}{4}-4y=-5\RiRead more
Given , multiplying through by gives .
Substituting into the second equation, , we have
.
Substituting into , we have
Therefore, and .
See lessSolve the following
The $y$-intercept of a line is the value of $y$ when $x$ is equal to 0. Thus, given $-4x+6y=-12$, setting $x=0$, we have $-4(0)+6y=-12\Rightarrow6y=-12$. Dividing both sides by 6 gives $\dfrac{6y}{6}=\dfrac{-12}{6}\Rightarrow y=-2$. Thus, the $y$-intercept is (0, -2).
The -intercept of a line is the value of when is equal to 0.
Thus, given , setting , we have .
Dividing both sides by 6 gives .
Thus, the -intercept is (0, -2).
See less