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3 years ago

Convert to scientific notation

Mathematics

2 answers:

Ainat [17]3 years ago

4 0

Answer:

5.7* 10 to the power of 4

Elodia [21]3 years ago

4 0

Answer:

Step-by-step explanation:

$\text{The scientific notation}:\\\\a\times10^k\\\\\text{where}\\\\1\leq a$

$57,000=5.7\times10000=5.7\times10^4\\\\-----------------------\\\\57000=5\underbrace{7000}_{\leftarrow4}=5\times10^4$

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3 years ago

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The wholesale price for a shirt is $5.50. A certain department store marks up the wholesale price by 40%. Find the price of the

Kazeer [188]

Answer:

$7.7

Step-by-step explanation:

Hello, I can help you with this

you can solve this by using a simple rule of three.

Step 1

define

if the wholesale price for a shirt is $5.50,it is 100 percent

$5.50⇔100%

the new price(x) is 40% more than the original, it means 140%

x ⇔ 140%

the relation is

$\frac{5.5}{100}= \frac{x}{140}\\$

Step 2

solve for x(isolate x)

$\frac{5.5}{100}= \frac{x}{140}\\x=\frac{5.5*140}{100}\\x=7.7$

the price of the shirt in the department store is $7.7

Have a nice day.

7 0

3 years ago

1. Express <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%282x%2B3%29%20%7D" id="TexFormula1" title="\frac{1}{x(2x+3) }" a

katovenus [111]

1. Let a and b be coefficients such that

$\dfrac1{x(2x+3)} = \dfrac ax + \dfrac b{2x+3}$

Combining the fractions on the right gives

$\dfrac1{x(2x+3)} = \dfrac{a(2x+3) + bx}{x(2x+3)}$

$\implies 1 = (2a+b)x + 3a$

$\implies \begin{cases}3a=1 \\ 2a+b=0\end{cases} \implies a=\dfrac13, b = -\dfrac23$

so that

$\dfrac1{x(2x+3)} = \boxed{\dfrac13 \left(\dfrac1x - \dfrac2{2x+3}\right)}$

2. a. The given ODE is separable as

$x(2x+3) \dfrac{dy}dx} = y \implies \dfrac{dy}y = \dfrac{dx}{x(2x+3)}$

Using the result of part (1), integrating both sides gives

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + C$

Given that y = 1 when x = 1, we find

$\ln|1| = \dfrac13 \left(\ln|1| - \ln|5|\right) + C \implies C = \dfrac13\ln(5)$

so the particular solution to the ODE is

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + \dfrac13\ln(5)$

We can solve this explicitly for y :

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3| + \ln(5)\right)$

$\ln|y| = \dfrac13 \ln\left|\dfrac{5x}{2x+3}\right|$

$\ln|y| = \ln\left|\sqrt[3]{\dfrac{5x}{2x+3}}\right|$

$\boxed{y = \sqrt[3]{\dfrac{5x}{2x+3}}}$

2. b. When x = 9, we get

$y = \sqrt[3]{\dfrac{45}{21}} = \sqrt[3]{\dfrac{15}7} \approx \boxed{1.29}$

8 0

2 years ago

Convert to scientific notation ​

Convert to scientific notation