Answer:
2.67 inches.
Step-by-step explanation:
Assuming that we represent the size of the squares with the letter y, such that after the squares are being cut from each corner, the rectangular length of the box that is formed can now be ( 23 - 2y), the width to be (13 - 2y) and the height be (x).
The formula for a rectangular box = L × B × W
= (23 -2y)(13-2y) (y)
= (299 - 46y - 26y + 4y²)y
= 299y - 72y² + 4y³
Now for the maximum volume:
dV/dy = 0
This implies that:
299y - 72y² + 4y³ = 299 - 144y + 12y² = 0
By using the quadratic formula; we have :
where;
a = 12; b = -144 and c = 299
Since the width is 13 inches., it can't be possible for the size of the square to be cut to be 9.33
Thus, the size of the square to be cut out from each corner to obtain the maximum volume is 2.67 inches.
Using relations in a right triangle, it is found that:
sin(x) = cos(y) = 0.6.
Since angles x and y are complementary, we have that sin(x) = cos(y), that is, the ratio is of 1.
<h3>What are the relations in a right triangle?</h3>
The relations in a right triangle are given as follows:
- The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.
- The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.
- The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.
Applying the Pythagorean Theorem, the hypotenuse is given by:
h² = 3² + 4²
h² = 25
h = 25.
Hence, applying the definitions:
Since angles x and y are complementary, we have that sin(x) = cos(y), that is, the ratio is of 1.
More can be learned about relations in a right triangle at brainly.com/question/26396675
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Answer:
Frank is 56 years old
Millie is 44 years old
Step-by-step explanation:
Since three times Millie's age is 132, you can figure out her age by dividing 132 by 3. Since Frank's age is 12 years older than Millie's, add 12 to 132 divided by 3.
Millie's age equation:
x = 132/3
x = 44 years old
Frank's age equation:
x = (132/3) + 12
x = (44) + 12
x = 56 years old
Answer:
An acute angle is an angle that is less than 90 degrees.
An obtuse angle is an angle that is over 90 degrees, but less that 180 degrees.
A right angle is an angle that is exactly 90 degrees.
A straight line has an angle of 180 degrees.
Hope this helps ^-^
Answer:
You would do $1.75 x 1,000. That would be 1$,750. Then, you would take away that $95 because they spent buying the box of tea bags, and their total would be $1,750 - $95 = $1,655.