HURRYYY

If <img src="https://tex.z-dn.net/?f=%20300cm%5E%7B2%7D%20" id="TexFormula1" title=" 300cm^{2} " alt=" 300cm^{2} " align="absmid

Artist 52 [7]

Check the picture below. Recall, is an open-top box, so, the top is not part of the surface area, of the 300 cm². Also, recall, the base is a square, thus, length = width = x.

$\bf \textit{volume of a rectangular prism}\\\\
V=lwh\quad 
\begin{cases}
l = length\\
w=width\\
h=height\\
-----\\
w=l=x
\end{cases}\implies V=xxh\implies \boxed{V=x^2h}\\\\
-------------------------------\\\\
\textit{surface area}\\\\
S=4xh+x^2\implies 300=4xh+x^2\implies \cfrac{300-x^2}{4x}=h
\\\\\\
\boxed{\cfrac{75}{x}-\cfrac{x}{4}=h}\\\\
-------------------------------\\\\
V=x^2\left( \cfrac{75}{x}-\cfrac{x}{4} \right)\implies V(x)=75x-\cfrac{1}{4}x^3$

so.. that'd be the V(x) for such box, now, where is the maximum point at?

$\bf V(x)=75x-\cfrac{1}{4}x^3\implies \cfrac{dV}{dx}=75-\cfrac{3}{4}x^2\implies 0=75-\cfrac{3}{4}x^2
\\\\\\
\cfrac{3}{4}x^2=75\implies 3x^2=300\implies x^2=\cfrac{300}{3}\implies x^2=100
\\\\\\
x=\pm10\impliedby \textit{is a length unit, so we can dismiss -10}\qquad \boxed{x=10}$

now, let's check if it's a maximum point at 10, by doing a first-derivative test on it. Check the second picture below.

so, the volume will then be at $\bf V(10)=75(10)-\cfrac{1}{4}(10)^3\implies V(10)=500 \ cm^3$

6 0

3 years ago

If Gabe's Soccer Ball Company is able, due to competitive pressure, to charge $60 for a new soccer ball, while one soccer ball c

Brums [2.3K]

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

Selling price= $60

Unitary variable cost= $28

Fixed costs= $15,000

First, we need to calculate the average total cost:

Average cost= total cost / number of units

For example, for 1 unit and 10,000 units:

1 unit:

Average cost= 15,028/1 = 15,028

10,000 units:

Average cost= (15,000 + 28*10,000) / 10,000

Average cost= $29.5

Now, we can calculate the break-even point in units:

0= (60*x) - (28*x) - 15,000

x= number of units to break-even

0= 32x - 15,000

15,000/32= x

468.75=x

break-even point in units= 469

For the desired profit of $10,000:

10,000 = (60*x) - (28*x) - 15,000

25,000= 32x

781.25= x

Break-even point= 782 units

Finally, fixed costs dropped by $8,000:

0= 32x - 7,000

x= 7,000/32

x= 218.75

Break-even point= 219

Difference= 250 units

5 0

3 years ago

A recursive rule for a sequence is given. Find the first four terms of the sequence.

tigry1 [53]

Answer:

So...

a0 = -2

a1 = (a0)2 - 4 = 4 - 4 = 0

a2 = (a1)2 - 4 = ((a0)2-4)2 - 4 =...= 02 - 4 = -4

For an+1, you may use the previous term (an) if you have just calculated it, rather than calculating it recursively again

a3 = (-4)2 - 4 = 12

The first four terms in the sequence are -2, 0, -4, 12.

Step-by-step explanation:

This recursive sequence is defined as follows:

a0 = -2 [the first term]

an+1 = an2 - 4 [for all other terms, n≥0; note that you cannot find a0 using this line]

Note that this is not "BASE" for a number base, but it is "SUB" for subscript, indicating the term. Sometimes, sequences are written with the first term being a1 and sometimes sequences are written with the first term being a0. This is because there are situations that make one or the other more convenient (for example, starting with elapsed time t=0 makes sense).

To find the value of later terms, a recursive definition requires that you find the value of the previous term, which requires that you find the value of the previous term, which requires that you find the value of the previous term, which requires that you find the value of the previous term, ... which requires that use the value of the first term.

That's why (joke) that the dictionary definition of "recursive" is "see recursive."

4 0

3 years ago

Please help!! See the attachment, please!

topjm [15]

Answer:

$946$

Step-by-step explanation:

we know that

The formula to find the sum is equal to

$S=(a1+an)n/2$

where

a1 is the first term

an is the last term

n is the number of terms

In this problem we have

$n=11$

$a1=(98-2(1))=96$

$an=(98-2(11))=76$

substitute the values in the formula

$S=(96+76)(11/2)=946$

5 0

3 years ago

Slope = 1, y-intercept = -4 ??

dalvyx [7]

Slope (m) = 1
Y-intercept (b) = -4

Formula: y = mx + b
To put it in the y=mx+b formula, you just have to plug it in so the answer would be...

y = 1x + -4

Hope that helped

8 0

3 years ago

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