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leva [86]
3 years ago
13

Factor -3bk 2 + 9bk - 6b

Mathematics
1 answer:
satela [25.4K]3 years ago
8 0
First you do -3bk+9bk and that equals 6bk then since there are no more like terms the experssion would be simplified into 6bk+2-6b
    HOPE THAT HELPED!
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How to evaluate question number 4
ANTONII [103]

There are 2 ways that spring to mind.

One is to use the definition of the derivative at a point:

f'(c)=\displaystyle\lim_{x\to c}\frac{f(x)-f(c)}{x-c}

In this case, c=0 and f(x)=\sqrt{5-x}. Then

f'(x)=-\dfrac1{2\sqrt{5-x}}\implies f'(0)=\displaystyle\lim_{x\to0}\frac{\sqrt{5-x}-\sqrt5}x=-\dfrac1{2\sqrt5}

- - -

If you don't know about derivative yet (I would think you do, considering this is for a midterm in AP Calc, but I digress), the other way is to rely on algebraic manipulation. Multiply the numerator and denominator by the conjugate of the numerator to get

\dfrac{\sqrt{5-x}-\sqrt5}x\cdot\dfrac{\sqrt{5-x}+\sqrt5}{\sqrt{5-x}+\sqrt5}=\dfrac{\left(\sqrt{5-x}\right)^2-\left(\sqrt5\right)^2}{x\left(\sqrt{5-x}+\sqrt5\right)}=-\dfrac x{x\left(\sqrt{5-x}+\sqrt5\right)}=-\dfrac1{\sqrt{5-x}+\sqrt5}

This is continuous at x=0, so the limit is the value of the expression at x=0:

\displaystyle\lim_{x\to0}\frac{\sqrt{5-x}-\sqrt5}x=-\lim_{x\to0}\frac1{\sqrt{5-x}+\sqrt5}=-\frac1{2\sqrt5}

5 0
3 years ago
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faltersainse [42]
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6 0
3 years ago
From 1st principle find the derivative of log (ax+b)
OLga [1]

Answer:

Step-by-step explanation:

The parent function here is y = log x, where 10 is the base.

The derivative of y = log x is dy/dx = (ln x) / ln 10.

The derivative of y = log (ax+b) is found in that manner, but additional steps are necessary:  differentiate the argument ax + b:

The derivative with respect to 10 of log (ax + b) is:

dy/dx = [ 1 / (ax + b) ] / [ ln 10 ] *a, where a is the derivative of (ax + b).

Alternatively, we could express the answer as

dy/dx = [ a / (ax + b) ] / [ ln 10 ]

5 0
3 years ago
The larger of two number is 12 more than the smaller number.if the sum of the two numbers is 74, find the two numbers
Mars2501 [29]
<h3><u>The value of the smaller number is 31.</u></h3><h3><u>The value of the larger number is 43.</u></h3>

y = 12 + x

y + x = 74

Since we have a value for y, we can plug it into the second equation

12 + x + x = 74

Subtract 12 from both sides.

x + x = 62

Combine like terms.

2x = 62

Divide both sides by 2.

x = 31


Now that we have a value of x, we can plug it into the original equation to get a value for y.

y = 12 + 31

y = 43

3 0
3 years ago
point a has the coordinates(2,5) point B has the coordinates (6,17) how long is segment ab in simplified radical form
IRISSAK [1]

Answer:

4\sqrt{10}

Step-by-step explanation:

We have been given that point A has the coordinates(2,5) point B has the coordinates (6,17).

To find the length of segment AB we will use distance formula.

\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Upon substituting coordinates of point A and point B in distance formula we will get,

\text{Distance between point A and point B}=\sqrt{(6-2)^2+(17-5)^2}

\text{Distance between point A and point B}=\sqrt{(4)^2+(12)^2}

\text{Distance between point A and point B}=\sqrt{16+144}

\text{Distance between point A and point B}=\sqrt{160}

\text{Distance between point A and point B}=4\sqrt{10}

Therefore, the length of segment AB is 4\sqrt{10}.

3 0
3 years ago
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