All categories

2 years ago

Sabrina is building a rectangular raised flower bed. The boards

Mathematics

1 answer:

nlexa [21]2 years ago

8 0

Answer:

The outer dimensions of the flower bed would be 32 in × 14 in × 7 in

Step-by-step explanation:

The outer dimensions of the flower bed is given by:

L is the length of the longer boards

W is the length of the shorter boards

H is the height of the flower bed

As the two shorter sides are 6 inches thick and the two longer sides are 4 inches thick, the inner dimensions are:

L-12: is the inner dimension because there are two shorter boards

W-8: is the inner dimension because there are two longer boards

The boards to rise 4 inches above the level of the soil in the bed, then:

H-4 is the height of soil

The volume of soil is would be:

(L-12)×(W-8)×(H-4)= 3136

We also know that the outer length must be 4 times its height and the outer width must be 2 times its height, so:

L=4H

W=2H

We solve the equation:

(L-12)×(W-8)×(H-4)= 3136

(4H-12)×(2H-8)×(H-4)= 3136

(8H²-32H-24H+96)×(H-4)= 3136

(8H²-56H+96)×(H-4)= 3136

8H³-56H²+96H-32H²+224H-384= 3136

8H³-88H²+320H-384= 3136

8H³-88H²+320H-384-3136=0

8H³-88H²+320H-3520=0

We divide the equation by 8 in both members:

H³-11H²+40H-440=0

This equation has 1 real solution (H=11) and two complex solutions

The adecuate solution of the problem is H=11

Hence, the outer dimensions of the flower bed are:

L=4H=44 in

W=2H=22 in

Outer dimensions 44 in × 22 in × 11 in

You might be interested in

The table shows the ratio of cups of water to cups of juice needed for a certain number of servings. A 3-column table has 3 rows

SSSSS [86.1K]

Answer:

5:10

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Simon took out a zero-interest loan for $3,300 to buy a boat. He must pay $300 per month to pay off the total balance of the boa

Andru [333]

Answer:

After 3 months, Simon will be able to pay off his loan with the money he holds at his savings account.

Step-by-step explanation:

ending loan's principal balance = beginning loan's principal balance - number of months x $300

or we can simplify it: l₁ = l₀ - 300x ⇒ l₁ = 3,300 - 300x

l₁ = ending loan's principal balance

x = number of months

ending savings account balance = beginning savings account balance + number of months x $600

or we can simplify it: s₁ = s₀ + 600x ⇒ s₁ = 1,000 + 600x

s₁ = ending savings account balance

x = number of months

account balances for months

month 1 month 2 month 3 month 4

boat loan $3.000 $2,700 $2,400 $2,100

savings account $1,600 $2,200 $2,800 $3,400

4 0

2 years ago

Read 2 more answers

A sea turtle is 3 feet below the surface of the sea. If its position can be recorded as −3 feet, what would the position 0 repre

ArbitrLikvidat [17]

The turtle is 3 feet below the surface of the sea, if it rises 3 feet, it will be even with sea level. So, 0 can be represented as sea level.

7 0

2 years ago

a photo collage consists of seven equal sized square photo arranged in a row to form a rectangle if the total area of the colleg

Keith_Richards [23]

Answer:

Step-by-step explanation:

I have attached a written explanation to help :).

Let's say each side of the square = $x$

If we put 7 squares in a row to make the rectangle,

length of the rectangle = $7x$

Area of a rectangle = length multiplied by width

Area of rectangle = $7x$ multiplied by $x$ = $7x^2$

We are also told that the total area = 567

So $7x^2 = 567$

Now solve for $x$ .

Divide both sides by 7.

$\frac{7x^2}{7} = \frac{567}{7}$

$x^2 = 81$

Then square root both sides to find $x$

$x = \sqrt{81}$ = 9

Finally, the question asks to find the length of the collage which we said was $7x$ and we know $x = 9$

Length of collage = $7x = 7$ multiplied by $9$ = ?

7 0

2 years ago

Suppose a term of a geometric sequence is a4 = 121.5 and the common ratio is 3. write the formula for this sequence in the form

9966 [12]

The rule of the geometric sequence is $a* r^{n-1}$
a ⇒⇒⇒ the first term
r ⇒⇒⇒ common ratio

Given: the fourth term (a4) = 121.5 and the common ratio = 3 and n = 4

∴ $121.5 = a* 3^{4-1}$
∴ a = 121.5/3³ = 121.5/27 = 4.5

So, The formula for this sequence will be $4.5 * 3^{n-1}$

8 0

2 years ago

Read 2 more answers