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3 years ago

What is the translation for the expression x-5

Mathematics

1 answer:

tamaranim1 [39]3 years ago

6 0

5 less than x
or
subtract 5 from x

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Because of their connection with secant lines, tangents, and instantaneous rates, limits of the form ModifyingBelow lim With h

Gre4nikov [31]

Answer:

$\dfrac{1}{2\sqrt{x}}$

Step-by-step explanation:

$f(x) = \sqrt{x} = x^{\frac{1}{2}}$

$f(x+h) = \sqrt{x+h} = (x+h)^{\frac{1}{2}}$

We use binomial expansion for $(x+h)^{\frac{1}{2}}$

This can be rewritten as

$[x(1+\dfrac{h}{x})]^{\frac{1}{2}}$

$x^{\frac{1}{2}}(1+\dfrac{h}{x})^{\frac{1}{2}}$

From the expansion

$(1+x)^n=1+nx+\dfrac{n(n-1)}{2!}+\ldots$

Setting $x=\dfrac{h}{x}$ and $n=\frac{1}{2}$ ,

$(1+\dfrac{h}{x})^{\frac{1}{2}}=1+(\dfrac{h}{x})(\dfrac{1}{2})+\dfrac{\frac{1}{2}(1-\frac{1}{2})}{2!}(\dfrac{h}{x})^2+\tldots$

$=1+\dfrac{h}{2x}-\dfrac{h^2}{8x^2}+\ldots$

Multiplying by $x^{\frac{1}{2}}$ ,

$x^{\frac{1}{2}}(1+\dfrac{h}{x})^{\frac{1}{2}}=x^{\frac{1}{2}}+\dfrac{h}{2x^{\frac{1}{2}}}-\dfrac{h^2}{8x^{\frac{3}{2}}}+\ldots$

$x^{\frac{1}{2}}(1+\dfrac{h}{x})^{\frac{1}{2}}-x^{\frac{1}{2}}=\dfrac{h}{2x^{\frac{1}{2}}}-\dfrac{h^2}{8x^{\frac{3}{2}}}+\ldots$

$\dfrac{x^{\frac{1}{2}}(1+\dfrac{h}{x})^{\frac{1}{2}}-x^{\frac{1}{2}}}{h}=\dfrac{1}{2x^{\frac{1}{2}}}-\dfrac{h}{8x^{\frac{3}{2}}}+\ldots$

The limit of this as $h\to 0$ is

$\lim_{h\to0} \dfrac{f(x+h)-f(x)}{h}=\dfrac{1}{2x^{\frac{1}{2}}}=\dfrac{1}{2\sqrt{x}}$ (since all the other terms involve $h$ and vanish to 0.)

8 0

3 years ago

Find the mean, median, mode, and range of the data set after you perform the given operation on each

agasfer [191]

Answer:

mean= 8.8

median= 9

mode= 9

range= 10

ANSWER: A

Step-by-step explanation:

6 0

3 years ago

Find the diamtere of a circle if its radius is 96.5cm

finlep [7]

$\huge \blue{\tt{Answer:}}$

$\sf {diameter = 2\times {radius}} = \sf{2\times{96.5}} = \sf{193~cm}$

4 0

2 years ago

How do u do stat edit

Svetlanka [38]

Answer:

The stat command has two options that allows you to customize the output according to your needs: -c, (--format="format") and --printf="format". The difference between these two options is that when two or more files are used as operants --format automatically adds a newline after each operand’s output.

Step-by-step explanation:

There you go!!!

6 0

3 years ago

Read 2 more answers

B/ 21 Marks

Serggg [28]

Answer:

y = 3x + 1.

Step-by-step explanation:

The slope is y2-y1/x2-x1

= 10/1/ 3-0

= 9/3

= 3.

Using the point-slope form for a straight line:

y-y1 = m(x-x1) (m = slope)

y - 10 = 3(x - 3)

y - 10 = 3x - 9

y = 3x - 9 + 10

y = 3x + 1 is the required equation.

5 0

2 years ago