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mrs_skeptik [129]
3 years ago
9

Kade makes 5/6 cup salad dressing. He uses 2/3 cup dressing on a salad. How much salad dressing is left

Mathematics
1 answer:
Ronch [10]3 years ago
4 0
To solve \frac{5}{6} -  \frac{2}{3}, we need to find a common denominator. If we multiply \frac{2}{3} by \frac{2}{2}, we get \frac{4}{6}. The reason we can do this is because two over two is really just equivalent to 1, and multiplying a number times one equals the original number. So if you're subtracting  \frac{4}{6} from \frac{5}{6}, you have


\dfrac{5}{6} -  \dfrac{4}{6} =  \dfrac{5-4}{6} =  \dfrac{1}{6} \ cups.


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Hey there

the answer is

x=4

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What is the equation of the sinusoid shown in the graph?
ololo11 [35]

Answer:

<em>Answer: C</em>

Step-by-step explanation:

<u>The Cosine Function</u>

The graph of a cosine function is a sinusoid that starts at its maximum value of 1 at x=0 and takes x=2π radians to complete a full cycle. The function of the parent cosine function is:

y=\cos x

Both the amplitude A and the angular frequency w of a cosine can be modeled by the function

y=A\cos(\omega x)

The graph of the cosine function shown in the figure has an amplitude of A=3 and it completes a full cycle at x=π/2, thus:

\frac{\pi}{2}\omega =2\pi

Thus:

\omega = 4

Therefore, the equation of the sinusoid is:

y=3\cos (4x)

Answer: C

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the 4th one

Step-by-step explanation:

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All rhombuses are parallelograms, but not all parallelograms are rhombuses. What attribute does a rhombus have that a parallelog
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Determine whether the equation is exact. If it​ is, then solve it. e Superscript t Baseline (7 y minus 3 t )dt plus (2 plus 7 e
umka21 [38]

Answer:

F(t,y)=(2+7e^t)y+3(1-t)e^t +C

Step-by-step explanation:

You have the following differential equation:

e^t(7y-3t)dt+(2+7e^t)dy=0

This equation can be written as:

Mdt+Ndy=0

where

M=e^t(7y-3t)\\\\N=(2+7e^t)

If the differential equation is exact, it is necessary the following:

\frac{\partial M}{\partial y}=\frac{\partial N}{\partial t}

Then, you evaluate the partial derivatives:

\frac{\partial M}{\partial y}=\frac{\partial}{\partial t}e^t(7y-3t)\\\\\frac{\partial M}{\partial t}=7e^t\\\\\frac{\partial N}{\partial t}=\frac{\partial}{\partial t}(2+7e^t)\\\\\frac{\partial N}{\partial t}=7e^t\\\\\frac{\partial M}{\partial t} = \frac{\partial N}{\partial t}

The partial derivatives are equal, then, the differential equation is exact.

In order to obtain the solution of the equation you first integrate M or N:

F(t,y)=\int N \partial y = (2 +7e^t)y+g(t)        (1)

Next, you derive the last equation respect to t:

\frac{\partial F(t,y)}{\partial t}=7ye^t+g'(t)

however, the last derivative must be equal to M. From there you can calculate g(t):

\frac{\partial F(t,y)}{\partial t}=M=(7y-3t)e^t=7ye^t+g'(t)\\\\g'(t)=-3te^t\\\\g(t)=-3\int te^tdt=-3[te^t-\int e^tdt]=-3[te^t-e^t]

Hence, by replacing g(t) in the expression (1) for F(t,y) you obtain:

F(t,y)=(2+7e^t)y+3(1-t)e^t +C

where C is the constant of integration

8 0
3 years ago
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