Solve the equation we have that:
a. S = 3V²/ 4
b. S = 108 feet
<h3>How to solve the parameters?</h3>
We have the equation to be;
V = 2√3S
Where;
- V is the speed
- S is the length
Let's make S the subject from the formula, divide both sides by 2√2S = v/ 2. Take square of both sides:
Now we need to divide both sides by three:
S = 3V²/ 4
b. If v = 12miles per hour, substituting in the equation found earlier:
S = 3 (12²)/ 4
S= 432/ 4
S = 108 feet
Thus, the formula for the length is S = 3V²/ 4
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The dimensions and volume of the largest box formed by the 18 in. by 35 in. cardboard are;
- Width ≈ 8.89 in., length ≈ 24.89 in., height ≈ 4.55 in.
- Maximum volume of the box is approximately 1048.6 in.³
<h3>How can the dimensions and volume of the box be calculated?</h3>
The given dimensions of the cardboard are;
Width = 18 inches
Length = 35 inches
Let <em>x </em>represent the side lengths of the cut squares, we have;
Width of the box formed = 18 - 2•x
Length of the box = 35 - 2•x
Height of the box = x
Volume, <em>V</em>, of the box is therefore;
V = (18 - 2•x) × (35 - 2•x) × x = 4•x³ - 106•x² + 630•x
By differentiation, at the extreme locations, we have;
Which gives;
6•x² - 106•x + 315 = 0
Therefore;
x ≈ 4.55, or x ≈ -5.55
When x ≈ 4.55, we have;
V = 4•x³ - 106•x² + 630•x
Which gives;
V ≈ 1048.6
When x ≈ -5.55, we have;
V ≈ -7450.8
The dimensions of the box that gives the maximum volume are therefore;
- Width ≈ 18 - 2×4.55 in. = 8.89 in.
- Length of the box ≈ 35 - 2×4.55 in. = 24.89 in.
- The maximum volume of the box, <em>V </em><em> </em>≈ 1048.6 in.³
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Answer:
No
Step-by-step explanation:
Given: Angles of a triangle are equal to 90 degrees , 50 degrees, and 60 degrees
To check : if it possible to build a triangle with given angles
Solution:
According to angle sum property of a triangle, sum of angles of a triangle is equal to 
Here,
sum of given angles = 
Therefore, it is <u>not possible</u> to construct a triangle with given angles.
The domain is the set of allowed x inputs, or x coordinates of a function. In this case, any point on the curve has an x coordinate that is 4 or smaller.
Therefore, the domain is the set of numbers x such that 
To write this in interval notation, we would write ![(-\infty, 4]](https://tex.z-dn.net/?f=%28-%5Cinfty%2C%204%5D)
This interval starts at negative infinity and stops at 4. We exclude infinity with the curved parenthesis and include 4 with the square bracket.
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The range is the set of possible y outputs. Every point on this curve has a y coordinate that is either 0 or it is larger than 0.
The range is the set of y values such that 
In interval notation, it would be written as 
This time we start at 0 (including this endpoint) and "stop" at infinity
note: we always use curved parenthesis at positive or negative infinity because we cannot reach either infinity
9.) 3
10.) 1
11.) x-axis
12.) 4
13.) y-axis
