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2 years ago

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Gary works at a bakery, and he needs to select a rectangular cookie sheet with an area of 192 square inches. The area of the coo

kie sheet is represented by the expression given below.

1 answer:

True [87]2 years ago

3 0

Answer:

Can we see the expression please

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Cranberry juice costs $6.30 per quart and apple juice costs $3.60 per quart. Terrence wants to know how many quarts q of cranber

Korvikt [17]

We know that:

Cost (Cranberry Juice): 6.3 per quart

Cost (Apple Juice): 3.6 per quart

Quantity (Apple Juice): 4 quarts

Quantity (Cranberry Juice): q quarts

Further we know that Terrence wants the cost of the juice to be 4.5 per quart

Hence Total Cost = Cost per quart × Total Number of quarts = (Cost per quart for Apple Juice × Total Number of Apple Juice Quarts) + (Cost per quart for Cranberry Juice × Total Number of Cranberry Juice Quarts)

⇒ Total Cost = 4.5 × (q+4) = 6.3 × q + 3.6 × 4

⇒ 4.5(q+4) = 6.3q + 14.4, which matches with option D

Hence, the correct option is D

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3 years ago

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3 years ago

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Ludmilka [50]

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3 years ago

Solve the equation <img src="https://tex.z-dn.net/?f=%2835%20x%5E%7B4%7D%20y%2B14%20x%5E%7B5%7D%20y-2%20y%5E%7B3%7D-4x%20y%5E%7B

jeka94

$\underbrace{35x^4y+14x^5y-2y^3-4xy^3}_M\,\mathrm dx+\underbrace{7x^5-6xy^2}_N\,\mathrm dy=0$

$M_y=35x^4+14x^5-6y^2-12xy^2$
$N_x=35x^4-6y^2$

$\dfrac{N_x-M_y}N=\dfrac{-14x^5+12xy^2}{7x^5-6xy^2}=-2$

This suggests an integrating factor depending on $x$ only is possible, and given by

$\mu(x)=\exp\left(-\displaystyle\int\frac{N_x-M_y}N\,\mathrm dx\right)=e^{2x}$

Distributing across the ODE, we end up with

$\underbrace{(35x^4y+14x^5y-2y^3-4xy^3)e^{2x}}_{M^*}\,\mathrm dx+\underbrace{(7x^5-6xy^2)e^{2x}}_{N^*}\,\mathrm dy=0$

The equation is now exact, with

${M^*}_y={N^*}_x=(35x^4+14x^5-6y^2-12xy^2)e^{2x}$

Now we find the solution:

$F_x=M^*$
$F=\displaystyle\int(35x^4+14x^5-2y^3-4xy^3)e^{2x}\,\mathrm dx$
$F=(7x^5y-2xy^3)e^{2x}+f(y)$

$F_y=N^*$
$(7x^5-6xy^2)e^{2x}+f'(y)=(7x^5-6xy^2)e^{2x}$
$f'(y)=0$
$\implies f(y)=C$

The general solution is then

$F(x,y)=(7x^5y-2xy^3)e^{2x}=C$

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3 years ago

Cameron won a laptop in a school raffle. The diagonal of the laptop measures 26 inches. The length is 24 inches. How tall is the

Over [174]

I need help to with this

4 0

3 years ago