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3 years ago

Justin's dog eats 3/4 a cup of food a day Mason's puppy eats 1/3 of a cup of food a day how much more food does Justin's dog eat

Mathematics

2 answers:

crimeas [40]3 years ago

8 0

Justins dog eats 5/4 of a cup more then masons dog

Nina [5.8K]3 years ago

3 0

5/12 you can work it out on a scientific calculator or take away the 2 fractions

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How do I differentiate this?

disa [49]

Answer:

$\frac{8}{\left(-x+2\right)^2}$ & $x = 1, x = 3$

Step-by-step explanation:

I'm sure you are familiar with the product rule,

If y = u*v => dy/dx = u * dv/dx + v * dy/dx <----- product rule

In this case:

$u=3x+2,\:v=\left(2-x\right)^{-1},\\=>\frac{d}{dx}\left(3x+2\right)\left(2-x\right)^{-1}+\frac{d}{dx}\left(\left(2-x\right)^{-1}\right)\left(3x+2\right)$

Now remember the sum rule:

$\frac{d}{dx}\left(3x+2\right) = \frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(2\right),\\\frac{d}{dx}\left(3x\right) = 3,\\\frac{d}{dx}\left(2\right) = 0\\\frac{d}{dx}\left(3x+2\right) = 3$

For this second bit we apply the chain rule:

$\frac{d}{dx}\left(\left(2-x\right)^{-1}\right) = -\frac{1}{\left(2-x\right)^2}\frac{d}{dx}\left(2-x\right),\\\frac{d}{dx}\left(2-x\right) = -1,\\\\=> -\frac{1}{\left(2-x\right)^2}\left(-1\right)\\=> \frac{1}{\left(2-x\right)^2}$

If we substitute these values back into the expression... $\frac{d}{dx}\left(3x+2\right)\left(2-x\right)^{-1}+\frac{d}{dx}\left(\left(2-x\right)^{-1}\right)\left(3x+2\right)$

...we get the following:

$3\left(2-x\right)^{-1}+\frac{1}{\left(2-x\right)^2}\left(3x+2\right)$

The rest is just pure simplification:

$3\left(2-x\right)^{-1}+\frac{1}{\left(2-x\right)^2}\left(3x+2\right)\\= \frac{3}{-x+2}+\frac{3x+2}{\left(-x+2\right)^2}\\= \frac{3\left(-x+2\right)}{\left(-x+2\right)^2}+\frac{3x+2}{\left(-x+2\right)^2}\\\\= \frac{3\left(-x+2\right)+3x+2}{\left(-x+2\right)^2}\\\\= \frac{8}{\left(-x+2\right)^2}$

Now let's equate this to equal 8 for the second bit and solve for x:

$\frac{8}{\left(-x+2\right)^2}=8,\\\frac{8}{\left(-x+2\right)^2}\left(-x+2\right)^2=8\left(-x+2\right)^2,\\8=8\left(-x+2\right)^2,\\\left(-x+2\right)^2=1,\\x = 1, x = 3$

4 0

2 years ago

Apply the rules for order of operations to simplify 2+3-4+(5X4)

katovenus [111]

The answer should be 21 hope it helps

5 0

2 years ago

Read 2 more answers

lame 《 Solve & Share A flash drive costs $24, including tax. A customer purchases 3 flash drives and pays the cashier $80. H

lbvjy [14]

Answer:

Step-by-step explanation:

1 flashdrive = $24

3 flash drives x $24 = $7

$80 - $72 = $8

3 0

3 years ago

Which of the following can be represented by the equation y = 2x?

KatRina [158]

Answer:

B) Graph B only.

Step-by-step explanation:

Table A is not correct, because:

In Y = 2X, replacing each row:
3 =/= 2 x 2
6 =/= 2 x 4
9 =/= 2 * 6

Table B is correct, because:
When Y is 2, X is 1 which is equal to 2x1.
When Y is 4, X is 2 which is equal to 2x2.

3 0

1 year ago

If f(x) = _4x _ 1, find f(_2)

tia_tia [17]

The answer is 7

f(x) = -4x - 1
f(-2) = ?

Since f(x) = f(-2), then x = -2. Now just substitute x in the function:
f(-2) = (-4) * (-2) - 1
f(-2) = 8 - 1
f(-2) = 7

8 0

3 years ago