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Drupady [299]
3 years ago
15

Why do you think we see phases of the Moon?

Mathematics
1 answer:
spin [16.1K]3 years ago
5 0

We only see the Moon because sunlight reflects back to us from its surface. But the the lit side does not always face the Earth. As the moon circles the Earth, the amount of the lit side we see changes.

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1. Find the derivative of <img src="https://tex.z-dn.net/?f=f%28x%29%3D6%2Fx" id="TexFormula1" title="f(x)=6/x" alt="f(x)=6/x" a
Slav-nsk [51]

1) Answer: -\frac{3}{2}

<u>Step-by-step explanation:</u>

f(x) = 6x⁻¹

f'(x) = -6x⁻²

     = \frac{-6}{x^{2}}

f'(-2) = \frac{-6}{(-2)^{2}}

        = -\frac{6}{4}

        = -\frac{3}{2}

*****************************************************

2) Answer: \frac{1}{4}

<u>Step-by-step explanation:</u>

f(x) = -9x⁻¹

f'(x) = 9x⁻²

     = \frac{9}{x^{2}}

f'(6) = \frac{9}{(6)^{2}}

        = \frac{9}{36}

        = \frac{1}{4}

8 0
2 years ago
Find a quadratic equation that models the decline in physical recorded music revenue​ (not digital). Let x number of years since
den301095 [7]

The rate of decrease in the revenue reduces each year, resulting in an

approximate quadratic equation model that is concave upwards.

\mathrm{The \ quadratic \ equation \ models   \ is}; \ \underline{y = 76.5 \cdot x^2 - 2264.8 \overline 3 \cdot x + 18769. \overline 6}

The difference between the actual and predicted values are;

\begin{array}{|c|c|c|c|}\underline{Year}& \underline{Difference \ in \ Values}\\2008&0\\2009&-143.\overline 6\\2010&-118.\overline 3\\2011&0\\2012& 62.\overline 3\\2013&71.\overline 6\\2014&0\end{array}\right]

Reasons:

The variables are;

x = Number of years since 2,000

y = Revenue for  physically recorded music in millions of dollars

Required:

To model the decline using a quadratic equation.

Solution:

The general form of the quadratic equation is; y = a·x² + b·x + c

When y = 5547, x = 8

We get;

5547 = a·8² + b·8 + c = 64·a + 8·b + c

5547 = 64·a + 8·b + c...(1)

When y = 3113, x = 11

We get;

3113 = a·11² + b·11 + c = 121·a + 11·b + c

3113 = 121·a + 11·b + c...(2)

When y = 2056, x = 14

We get;

2056 = a·14² + b·14 + c = 196·a + 14·b + c

2056 = 196·a + 14·b + c...(3)

Subtracting equation (2) from equation (1) gives;

5547 - 3113 = 64·a + 8·b + c - (121·a + 11·b + c) = -57·a - 3·b

2434 =  -57·a - 3·b...(4)

Subtracting equation (3) from equation (2) gives;

3113 - 2056 = 121·a + 11·b + c - (196·a + 14·b + c) = -75·a - 3·b

1057 = -75·a - 3·b...(5)

Subtracting equation (5) from equation (4) gives;

2434 - 1057 = -57·a - 3·b - (-75·a - 3·b) = 18·a

1377 = 18·a

a = \dfrac{1377}{18} = 76.5

a = 76.5

From, equation (4), 2434 =  -57·a - 3·b, we have;

2434 =  -57 × 76.5  - 3·b

Therefore;

b = \dfrac{2434 + 57 \times 76.5}{-3} = -\dfrac{13589}{6} = -2264.8 \overline{3}

b = -2264.8\mathbf{\overline 3}

From equation (1), we get;

5547 = 64 × 76.5 + 8×(-2264.8\overline 3) + c

Therefore;

c = 5547 - (64 × 76.5 + 8×(-2264.8\overline 3)) = 18769.\overline 6

c = 18769.\mathbf{\overline 6}

Therefore, the quadratic model is; \underline{y = 76.5 \cdot x^2 - 2264.8 \overline 3 \cdot x + 18769. \overline 6}

Verifying, we have in year 2012, x = 12

y = 76.5×12² - 2264.8\overline 3×12 + 18769.\overline 6 = 2607.74

The completed table and comparison of the predicted physical revenue

and actual values is presented as follows;

\begin{array}{|c|c|c|c|}Year&Actual \ Revenue&Predicted \ Revenue& Difference \\2008&5547&5547&0\\2009&4439&4582.\overline 6&-143.\overline 6\\2010&3653&3771.\overline 3&-118.\overline 3\\2011&3113&3113&0\\2012&2670&2607. \overline 6 & 62.\overline 3\\2013&2327&2255.\overline 3&71.\overline 6\\2014&2056&2056&0\end{array}\right]

Learn more here:

brainly.com/question/11826603

7 0
2 years ago
If a kilowatt-hour of energy costs 75 cents, how much does it cost to leave a 40-watt light bulb on for the entire month of May
spin [16.1K]
May has 31 days
31 x 24 = 744 hours in may
744 x 40 = 29760 watt hours
29760 watt hours = 29.76 kwh 
29.76 x 75 = 2232 cents
2232 cents = $22.32
8 0
3 years ago
eduardo has 4 1/2 yard of rope light. Exactly how many more yard does he need to finish the car's ceiling
Over [174]

Answer:

2 1/6

Step-by-step explanation:

Because the denominators are different, and there are whole numbers involved, then first make the fractions improper.

4 1/2 -> 9/2

6 2/3 -> 20/3

Next, make the denominators the same by multiplying each fraction by the denominator of the other.

9/2 * 3 = 27/6

20/3 * 2 = 40/6

Then you can subtract the numerators because the denominators are the same:

40/6-27/6= 13/6

Then you can convert to a mixed fraction if need be.

3 0
2 years ago
Jenny is trimming the edge of pillows with lace. Each pillow requires 15 inches of lace. She has one piece of lace that is 3 fee
Anna71 [15]

Answer:

I think Jenny will be able to do 9 pillows with the lace trim.

4 0
3 years ago
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