А<br> С<br> If AB = 3 and BC = 7, AC = [?]

box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the box (in cm) that minimize the am

Naya [18.7K]

Answer:

Hence the width, length is 20 cm and height is 10 cm

Step-by-step explanation:

Since the box has a square base, let length = width = x. Also, let the height = y, therefore:

The volume of box = width * length * height

4000 = x * x * y

4000 = x²y

y=4000/x²

The surface area (SA) = area of the base + sum of the area of each side

SA = x² + xy + xy + xy + xy

SA = x² + 4xy

substitute y = 4000/x²

SA = x² + 4x(4000/x²)

SA = x² + 16000/x

Taking the derivative:

SA' = 2x - 16000/x²

making SA' = 0:

0 = 2x - 16000/x²

2x = 16000/x²

2x³ = 16000

x³ = 8000

x = 20 cm

y = 4000 / x² = 4000 / 20² = 10 cm

Hence the width, length is 20 cm and height is 10 cm

6 0

2 years ago

Kim purchased white vases, red vases, and flowers to create centerpieces for an event. The flowers cost a total of $336 and each

laiz [17]

Option A:

I and III only the answers.

Solution:

Let white vases be "w" and red vases be "r".

Cost of total flower = $336

Cost of each vase = $11

Total cost of the centerpieces

= Cost of (white vases + red vases) + Cost of flowers

= 11(w + r) + 336

= 11w + 11r + 336

Total cost of the centerpieces = 11w + 11r + 336 = 11(w + r) + 336

Therefore I and III only the answers.

Option A is the correct answer.

4 0

2 years ago

Jamal is making two paintings using canvases that are similar rectangles. The length of the smaller canvas is 3 ft and the width

Alex787 [66]

Let's start with what we know:

Smaller canvas:
Length ( $L_{1}$ ) = 3ft
Width ( $W_{1}$ ) = 5ft

Larger canvas:
Length ( $L_{2}$ ) = ?
Width ( $W_{2}$ ) = 10ft

Since these are similar rectangles, we can cross-multiply to calculate the missing length. Here's that formula:

$\frac{ L_{1} }{ L_{2} } = \frac{ W_{1} }{ W_{2} }$
So let's plug it all in from above:

$\frac{ 3 }{ L_{2} } = \frac{ 5 }{ 10 }$
Now we cross multiply by multiplying the top-left by the bottom-right and vice versa:

$(3)(10) = (5)(L_{2})$
$30 = 5L_{2}$
Now divide each side by 5 to isolate $L_{2}$

$\frac{30}{5} = \frac{ 5L_{2}}{5}$
The 5s on the right cancel out, leaving us with:

$6 = L_{2}$

So the length of the larger canvas is 6 ft

4 0

3 years ago

Read 2 more answers

Six times a number is two hundred and forty what is The number

butalik [34]

240/6=x
x=40

the number is 40

4 0

3 years ago

Read 2 more answers

Jimmy’s dad gave him $100 on his birthday, which is January 1. Jimmy deposited the $100 in his savings account the same day. At

aliya0001 [1]

$300 every month beginning Feb 1st until the month of June = $1800