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3 years ago

Find the solution to the system of equations. x+y+z=23 y+z=14 z=9

1 answer:

3 0

A) x+y+z=23
B) y+z=14
C) z=9
Since z = 9 then
A) x + y = 14
B) y = 5
A) x + y+ z=23
A) x + 5 + 9 = 23
A) x = 9

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Read 2 more answers

A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materi

blondinia [14]

Answer:

The required function is: $P(x)=-3x^2+78x-360$

The price for each feeder to maximize profit should be $13.

The maximum weekly profit is $147

Step-by-step explanation:

Consider the provided information.

Part (A)

The materials for each feeder cost $6, and the society sells an average of 30 per week at a price of $10 each.

Let x be the price per feeder.

Profit = Revenue - cost

So the profit per feeder is $x-6$

If we increase then for every dollar increase, it loses 3 sales per week.

This can be written as:

$30-3(x-10)$

$30-3x+30$

$-3x+60$

Where x-10 represents the increase in price and 3 represents the decrease in sales per week.

Thus the profit will be:

$P(x)=(x-6)(-3x+60)$

$P(x)=-3x^2+78x-360$

Hence, the required function is: $P(x)=-3x^2+78x-360$

Part (B) What price should the society charge for each feeder to maximize profits? What is the maximum weekly profit?

The above function is a downward parabola so the maximum will occur at vertex.

The x coordinate of the vertex of parabola is: $x=\frac{-b}{2a}$

Substitute a=-3, b=78 and c=-360 in above.

$x=\frac{-78}{2(-3)}=13$

Hence, the price for each feeder to maximize profit should be $13.

Now substitute the value of x in $P(x)=-3x^2+78x-360$

$P(x)=-3(13)^2+78(13)-360=$147$

Hence, the maximum weekly profit is $147

5 0

3 years ago

Use the formula for the cosine of the difference of two angles to find the exact value of the following expression.

Zolol [24]

Answer:

Exact value of Cos(45° - 60°) is 0.96 using difference of two angles.

Step-by-step explanation:

Given:

Cos(45° - 60°)

We have to apply the formula of cosine for difference of the two angles.

Formula:

$cos(a-b)=cos(a)\ cos(b)+sin(a)\ sin(b)$

Plugging the values.

⇒ $cos(45-60)=cos(45)\ cos(60) + sin(45)\ sin(60)$

We know that the values :

$sin(45) =cos(45) = \frac{1}{\sqrt{2} }$

$sin(60)=\frac{\sqrt{3} }{2}$ and $cos(60)=\frac{1}{2}$

So,

⇒ $cos(45-60)=(\frac{1}{\sqrt{2} } \times \frac{1}{2} ) + (\frac{1}{\sqrt{2} } \times \frac{\sqrt{3} }{2})$

⇒ $cos(45-60)=(\frac{1}{2\sqrt{2} } + \frac{\sqrt{3} }{2\sqrt{2} })$

⇒ $cos(45-60)=(\frac{1+\sqrt{3} }{2\sqrt{2} } )$

⇒ $cos(45-60)=(\frac{1+\sqrt{3} }{2\sqrt{2} } )\times \frac{2\sqrt{2} }{2\sqrt{2} }$ ...rationalizing

⇒ $cos(45-60)=\frac{2\sqrt{2} +2\sqrt{6} }{ 8}$

⇒ $cos(45-60)=\frac{2(\sqrt{2}+\sqrt{6})}{8}$ ...taking 2 as a common factor

⇒ $cos(45-60)=\frac{(\sqrt{2}+\sqrt{6})}{4}$

To find the exact values we have to put the values of sq-rt .

As, $\sqrt{2}=1.41$ and $\sqrt{6} =2.44$

Then

⇒ $cos(45-60)=\frac{( 1.41+2.44)}{4}$

⇒ $cos(45-60)=\frac{( 3.85)}{4}$

⇒ $cos(45-60)=0.96$

So the exact value of Cos(45° - 60°) is 0.96 using difference of two angles.

3 0

3 years ago