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3 years ago

2/5;0.5 tell whether each pair shows equivalent number

Mathematics

1 answer:

Georgia [21]3 years ago

4 0

2/5= 40%, so no, they are not equivalent numbers,<span />

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Use the definition of the derivative to differentiate f(x)= In x

WINSTONCH [101]

By def. of the derivative, we have for y = ln(x),

$\displaystyle \frac{dy}{dx} = \lim_{h\to0} \frac{\ln(x+h)-\ln(x)}{h}$

$\displaystyle \frac{dy}{dx} = \lim_{h\to0} \frac1h \ln\left(\frac{x+h}{x}\right)$

$\displaystyle \frac{dy}{dx} = \lim_{h\to0} \ln\left(1+\frac hx\right)^{\frac1h}$

Substitute y = h/x, so that as h approaches 0, so does y. We then rewrite the limit as

$\displaystyle \frac{dy}{dx} = \lim_{y\to0} \ln\left(1+y\right)^{\frac1{xy}}$

$\displaystyle \frac{dy}{dx} = \frac1x \lim_{y\to0} \ln\left(1+y\right)^{\frac1y}$

Recall that the constant e is defined by the limit,

$\displaystyle e = \lim_{y\to0} \left(1+y\right)^{\frac1y}$

Then in our limit, we end up with

$\displaystyle \frac{dy}{dx} = \frac1x \ln(e) = \boxed{\frac1x}$

In Mathematica, use

D[Log[x], x]

5 0

3 years ago

The volume of a cone with a radius of 7 cm is 147 pi cubic centimeters. Which expression can be used to find h, the height of th

Aleks04 [339]

volume(V)=147cm^3

also,

v=1/3×3.14×7^2×h

or, 147×3=3.14×49×h

or, (441)/(3.14×49)=h

or, h=2.87cm

3 0

3 years ago

Read 2 more answers

Triangle inequalities? Write >, <, =, or NC?

lord [1]

_Award brainliest if helped!
ST > MN
BA > BC
m<a > m<f
m<L < m<R

6 0

3 years ago

(-18x^2+12x-2)*(x^3+12x^2+48x+64)

prohojiy [21]

<h2>Answer:</h2>

-18x^5-204x^4-722x^3-600x^2+672x-128

<h2>Explanation:</h2>

$( - 18 {x}^{2} + 12x - 2)$

$( {x}^{3} + 12 {x}^{2} + 48x + 64)$

There are multiple ways to solve this for example the foil method or the box method. I prefer to do the box method.

First we are going to set it up

After we set it up we have to solve it so first we are going to multiply

${x}^{3} \times - 18 {x}^{2} = - 18 {x}^{5}$

We have to add the exponent

$- 18 {x}^{2} \times 12 {x}^{2} = - 216 {x}^{4}$

$- 18 {x}^{2} \times 48x = - 864 {x}^{3 } \\ - 18{x}^{2} \times 64 = - 1152 {x}^{2} \\ 12x \times {x}^{3} = 12 {x}^{4} \\ 12x \times 12 {x}^{2} = 144 {x}^{3}$

$12x \times 48x = 576 {x}^{2} \\ 12x \times 64 = 768x$

$- 2 \times {x}^{3} = - 2 {x}^{3} \\ - 2 \times 12 {x}^{2} = - 24 {x}^{2} \\ - 2 \times 48x = - 96x \\ - 2 \times 64 = - 128$

Now we have to add them

-18x^5 stays because there is nothing to add to

Now we add the rest

$-216 {x}^{4} + 12 {x}^{4} = - 204 {x}^{4}$

$- 864 {x}^{3} + 144 {x}^{3} + - 2 {x}^{3} = - 722 {x}^{3}$

$768x - 96x = 672x$

And -128 stays the same

$- 1152 {x}^{2} + 576 {x}^{2} - 24 {x}^{2} = - 600 {x}^{2}$

The answer is

-18x^5-204x^4-722x^3-600x^2+672x-128

5 0

4 years ago

Help me guys this is 7th grade math

VMariaS [17]

The correct answer would be 2,656.25 because you take the 8.5% and move the decimal 2 places to the left.

Now multiply the total (250,000) by .085% and you get $21,250

You will now take 21,250 and divide it by 8 giving you the answer.

8 0

3 years ago