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2 years ago

8.54 as a place value

Mathematics

1 answer:

alexandr402 [8]2 years ago

7 0

Eight and fifty four hundredths

8 . 5 4
Ones Tenths Hundredths

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Equation for motion

AlexFokin [52]

v=at+v^0 is the equation

7 0

2 years ago

Differentiate x^2 e^x logx

zimovet [89]

Product rule:

$\dfrac{\mathrm d}{\mathrm dx}(x^2e^x\log x)$

$=\dfrac{\mathrm d(x^2)}{\mathrm dx}e^x\log x+x^2\dfrac{\mathrm d(e^x)}{\mathrm dx}\log x+x^2e^x\dfrac{\mathrm d(\log x)}{\mathrm dx}$

Power rule:

$\dfrac{\mathrm d(x^2)}{\mathrm dx}=2x$

The exponential function is its own derivative:

$\dfrac{\mathrm d(e^x)}{\mathrm dx}=e^x$

Assuming the base of $\log x$ is $e$ , its derivative is

$\dfrac{\mathrm d(\log x)}{\mathrm dx}=\dfrac1x$

But if you mean a logarithm of arbitrary base $b$ , we have

$y=\log_bx\implies x=b^y=e^{y\ln b}\implies1=e^{y\ln b}\ln b\dfrac{\mathrm dy}{\mathrm dx}$

$\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{e^{-y\ln b}}{\ln b}=\dfrac1{b^y\ln b}$

$\implies\dfrac{\mathrm d(\log_bx)}{\mathrm dx}=\dfrac1{x\ln b}$

So we end up with

$2xe^x\log x+x^2e^x\log x+\dfrac{x^2e^x}x$

$=xe^x(2\log x+x\log x+1)$

8 0

2 years ago

HELP!!! Lucas deposits $250,000 into two investment accounts. Over a year, the first account

prohojiy [21]

The amount deposited in the account that earns 3.6% interest is $57,600 and the amount deposited in the account that earns 2.1% interest is $192,400

The first step is to determine the amount of interest he earned in total over a year

Interest = Amount in the account - amount deposited

$256,114 - $250,000 = $6,114

The second step is to formulate two set of equations and use simultaneous equation to solve the question

a + b = $250,000 equation 1

0.036a + 0.021b = $6,114 equation 2

Where a represent amount deposited in the account that earns 3.6% interest

b represent amount deposited in the account that earns 2,1% interest

Multiply equation 1 by 0.036

0.036a + 0.036b = 9000 equation 3

Subtract equation 2 from 3

2886 = 0.015b

divide both sides of the equation by 0.015

b = $192,400

Substitute for b in equation 1

a + 192,400 = 250,000

a = 250,000 - 192400

a = $57,600

To learn more about simultaneous equations, please check: brainly.com/question/23589883?referrer=searchResults

6 0

2 years ago

Mariah builds a tabletop using square tiles, There are 12 rows of tiles and 30 tiles in each row. How many tiles does Mariah use

kiruha [24]

360 tiles because you have to multiply 12x30.

4 0

2 years ago

Find the distance between<br> (-1, - 3) and (8, – 3).

dimaraw [331]

Answer: d (A,B) = 9

Step-by-step explanation: d(A,B) = √(xB - xA)^2 + (yB - yA)^2

d(A,B) = √(8-(-1))^2 + (-3 - (-3))^2

d(A,B) = √81 + 0

d(A,B) = 9

5 0

2 years ago