Allie used 14.5 m3 of cement to make a square patio. If the thickness of the patio is 25 cm, the length of the patio must be
To find the length of the patio, we need to first calculate the volume of the patio.
The volume of the patio can be calculated using the formula:
Volume = Length x Width x Height
Since the patio is square, the length and width will be the same.
Let's assume the length of the patio is L.
The width of the patio will also be L.
Given that the thickness of the patio is 25 cm, which is equivalent to 0.25 meters, we can calculate the height of the patio:
Height = thickness = 0.25 m
The volume of the patio can now be calculated as:
Volume = L x L x 0.25
Given that the volume of cement used is 14.5 m^3, we can set up the following equation:
14.5 = L x L x 0.25
Simplifying the equation:
14.5 = 0.25L^2
Dividing both sides of the equation by 0.25:
14.5 / 0.25 = L^2
58 = L^2
Taking the square root of both sides of the equation:
L = √58
L ≈ 7.62
Therefore, the length of the patio must be approximately 7.62 meters.
The restriction on x in the expression square root of 4 x minus 2 end root can be written as:
The expression is square root of (4x - 2), and we want to find the restriction on x, meaning the values of x that make the expression valid.
For the expression to be valid, the value inside the square root (4x - 2) must be greater than or equal to zero, since we cannot take the square root of a negative number.
Therefore, we can write the restriction as:
4x - 2 ≥ 0
To solve this inequality, we can add 2 to both sides:
4x ≥ 2
Then, divide both sides by 4:
x ≥ 1/2
So, the restriction on x is x ≥ 1/2.
When you simplify 3 square root of 6 left parenthesis 2 square root of 3 minus 18 right parenthesis completely, it can be written in the form a square root of b minus c square root of d.
The values of a, b, c and are as follows:
To simplify the expression, let's start by distributing the 3 to both terms inside the parentheses:
3 * √6 * (2 * √3 - 18)
Simplifying further:
6 * √3 - 54 * √6
Now, let's identify the parts of the expression that can be written in the form a * √b:
a = 6
b = 3
c = 54
d = 6
So, the simplified expression can be written as:
6 * √3 - 54 * √6
Thus, a = 6, b = 3, c = 54, and d = 6.
A rectangle has an area of 3 square root of 5 plus 2 square root of 2 space c m squared and a side length of 2 square root of 3 space c m. Determine the width of this rectangle in simplified form (remember the denominator of any fraction cannot contain a radical).
The simplified width will take on the form fraction numerator a square root of b plus c square root of d over denominator e end fraction.
To find the width of the rectangle, we can use the formula for the area of a rectangle: A = length * width.
Given that the area is "3√5 + 2√2 c square meters" and the length is "2√3 c meters", we can set up the equation:
2√3 c * width = 3√5 + 2√2 c
To solve for the width, we need to isolate it on one side of the equation. Dividing both sides by 2√3 c:
width = (3√5 + 2√2 c) / (2√3 c)
Next, we need to simplify the expression to the desired form of (a√b + c√d) / e.
Let's simplify the numerator first:
3√5 + 2√2 c = 3√5 + 2√2 * √(c^2) = 3√5 + 2√(2c^2)
Now, let's rewrite the denominator as a product of rationalized form:
2√3 c = 2 * √3 * √(c^2) = 2√(3c^2)
Plugging these simplified forms back into the equation for the width:
width = (3√5 + 2√(2c^2)) / (2√(3c^2))
So, in simplified form, the width of the rectangle is:
(3√5 + 2√(2c^2)) / (2√(3c^2))
At a paper cup factory they use 300 cm2 of paper to make the lateral surface of a cup with a radius of 5 cm. What is the height of this cup to the nearest cm?
SA equals πr square root of straight r squared plus straight h squared end root, where r is the radius of the cylinder and h is the height of the cylinder.
We are given that the lateral surface area of the cup is 300 cm^2 and that the radius of the cup is 5 cm.
Let's use the formula for the lateral surface area of a cylinder:
SA = 2πrh
Plugging in the given values:
300 = 2π(5)h
To solve for the height, divide both sides of the equation by 2π(5):
300 / (2π(5)) = h
Approximating the value of π to 3.14:
300 / (2(3.14)(5)) ≈ h
300 / (31.4) ≈ h
h ≈ 9.55
Therefore, the height of the cup is approximately 9.55 cm. Rounded to the nearest cm, the height is 10 cm.
To calculate the length of the patio, we can start by finding the volume of the patio. The volume of a rectangular object is given by the formula V = l × w × h, where V is the volume, l is the length, w is the width, and h is the height.
In this case, we know that the thickness of the patio is 25 cm, which is equal to 0.25 meters. Let's assume the length and width of the patio are the same (since it is a square). So, the volume of the patio is:
V = l × l × 0.25
Now, we have to find the length of the patio. We know that Allie used 14.5 m³ of cement, which is equal to the volume of the patio. So, we can equate the volume of the patio to 14.5:
14.5 = l² × 0.25
To find the length, we need to solve this equation for l. We can do this by multiplying both sides of the equation by 4 (to eliminate the denominator):
14.5 × 4 = l² × 0.25 × 4
58 = l²
Now, we take the square root of both sides of the equation to find the length:
l = √58
l ≈ 7.62 meters
Therefore, the length of the square patio is approximately 7.62 meters.