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3 years ago

6

Shiloh is splitting a quart of mac n cheese with seven friends. If all 8 of them share the quart equally, how many cups will eac

h person get?
Can someone please help me

1 answer:

GalinKa [24]3 years ago

5 0

Answer:

0.125 quarts

Step-by-step explanation: One quart divided by 8

Can i be brainliest

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Consider the exponential function f ( x ) = 13 , 500 ⋅ 0.89^x, which models the value of Mikayla's scooter, where x represents t

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Step-by-step explanation:

To solve this, you can substitute 4 for x:

$f(x) = 13500*.89^4\\f(x) = 13500*0.6274\\f(x) = 8470$

Mikayla's scooter is worth around $8470 after 4 years.

It was originally worth 13,500 dollars and depreciated by 11% every year.

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3 years ago

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

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Answer: $\dfrac{2x^2-1}{x(x^2-1)}$

Step-by-step explanation:

The given function : $y=\ln(x(x^2 - 1)^{\frac{1}{2}})$

$\Rightarrow\ y=\ln x+\ln (x^2-1)^{\frac{1}{2}}$ [ $\because \ln(ab)=\ln a +\ln b$ ]

$\Rightarrow y=\ln x+\dfrac{1}{2}\ln (x^2-1)}$ [ $\because \ln(a)^n=n\ln a$ ]

Now , Differentiate both sides with respect to x , we will get

$\dfrac{dy}{dx}=\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})\dfrac{d}{dx}(x^2-1)$ (By Chain rule)

[Note : $\dfrac{d}{dx}(\ln x)=\dfrac{1}{x}$ ]

$\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})(2x-0)$

[ $\because \dfrac{d}{dx}(x^n)=nx^{n-1}$ ]

$=\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})(2x) = \dfrac{1}{x}+\dfrac{x}{x^2-1}\\\\\\=\dfrac{(x^2-1)+(x^2)}{x(x^2-1)}\\\\\\=\dfrac{2x^2-1}{x(x^2-1)}$

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You first need to find the LCD (lowest common denominator). You will need to find the smallest number that is a multiple of all numbers that is the denominator (2, 16, 8). Or, to say it another way, all the numbers in the denominator need to be a factor of this number.

You can find this by first checking if the largest number that is the denominator-- in this case 16-- is already the LCD, which means 16 is divisible by all the other numbers.

If this does not work, then multiply all the numbers together to get the LCD-- since you multiplied them together, you know that they will all be factors of the product.

However, you will be able to see that 16 is indeed the lowest common denominator:

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