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kherson [118]
3 years ago
15

The faucet drips 6 ¾ gallons of water in 4 hours what is the unit rate?

Mathematics
1 answer:
Finger [1]3 years ago
6 0

Answer:

1.6875 gallons per hour

Step-by-step explanation:

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Xe^(-x^2/128) absolute max and absolute min
adoni [48]
f(x)=xe^{-x^2/128}
\implies f'(x)=e^{-x^2/128}+x\left(-\dfrac{2x}{128}\right)e^{-x^2/128}=\left(1-\dfrac1{64}x^2\right)e^{-x^2/128}

Extrema can occur when the derivative is zero or undefined.

\left(1-\dfrac1{64}x^2\right)e^{-x^2/128}=0\implies 1-\dfrac1{64}x^2=0\implies x^2=64\implies x=\pm8

Maxima occur where the first derivative is zero and the second derivative is negative; minima where the second derivative is positive. You have

f''(x)=-\dfrac1{32}xe^{-x^2/128}+\left(1-\dfrac1{64}x^2\right)\left(-\dfrac{2x}{128}\right)e^{-x^2/128}=\left(-\dfrac3{64}x+\dfrac1{4096}x^3\right)e^{-x^2/128}

At the critical points, you get

f''(-8)=\dfrac1{4\sqrt e}>0
f''(8)=-\dfrac1{4\sqrt e}

So you have a minimum at \left(-8,-\dfrac8{\sqrt e}\right) and a maximum at \left(8,\dfrac8{\sqrt e}\right).

Meanwhile, as x\to\pm\infty, it's clear that f(x)\to0, so these extrema are absolute on the function's domain.
6 0
3 years ago
True or False? In an isosceles trapezoid the diagonals are congruent.
Ainat [17]
It is true, they are congruent by doing a proof. You have to divide the trapezoid into 2 equal triangles. Then you can prove it. They are congruent since corresponding parts of congruent triangles are congruent.
3 0
3 years ago
What is the sum of the fractions? Use the number line to help find the answer.
natali 33 [55]
Answer is - 4 over 5
4 0
3 years ago
My family was excited to begin our vacation on Saturday. We all woke up early and then ate a big breakfast. After that, we put o
kirill [66]

Answer:

B) Cause and effect

8 0
3 years ago
Read 2 more answers
Find the equation of the line between the points (10, – 5) and ( - 2,0).
Natali5045456 [20]

Answer <u>(assuming it can be in slope-intercept form)</u>:

y = -\frac{5}{12} x-\frac{5}{6}  

Step-by-step explanation:

1) First, find the slope of the line between the two points by using the slope formula, m  = \frac{y_2-y_1}{x_2-x_1}. Substitute the x and y values of the given points into the formula and solve:

m = \frac{(0)-(-5)}{(-2)-(10)} \\m = \frac{0+5}{-2-10} \\m=\frac{5}{-12}

Thus, the slope of the line is -\frac{5}{12}.

2) Next, use the point-slope formula y-y_1 = m (x-x_1) to write the equation of the line in point-slope form. Substitute values for m, x_1, and y_1 in the formula.

Since m represents the slope, substitute -\frac{5}{12} in its place. Since x_1 and y_1 represent the x and y values of one point the line intersects, choose any of the given points (it doesn't matter which one, it will equal the same thing) and substitute its x and y values into the formula as well. (I chose (-2,0), as seen below.) Then, isolate y and expand the right side in the resulting equation to find the equation of the line in slope-intercept form:

y-(0)=-\frac{5}{12} (x-(-2))\\y-0 = -\frac{5}{12} (x+2)\\y = -\frac{5}{12} x-\frac{5}{6}

3 0
2 years ago
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