Answer:
Height: 3/2 inches
Length: 12 inches
Width: 4 inches
Step-by-step explanation:
Let x is the side length of the square
The height of the box by cutting squares off :x
- The new length of the cardboard = 15 -2x (because we cut from 4 corners)
- The new width of the cardboard = 7 -2x (because we cut from 4 corners)
The new volume of it is:
V = (15 -2x) (7 -2x) x
<=> V = 
To maximum volume, we use the first derivative of the volume
<=> 
<=> 
<=> 2x -3 = 0 or 6x -35 = 0
<=> x = 3/2 or x = 35/6
To determine which value of x gives a maximum, we evaluate
= 24x -88
= 24(3/2) -88 = -52
= 24(35/6) -88 = 52
We choose x = 3/2 to have the maximum volume because the value of x that gives a negative value is maximum.
So the dimensions (in inches) of the box is:
Height: 3/2 inches
Length: 15-2(3/2) = 12 inches
Width: 7 - 2(3/2) = 4 inches
2x+12 would be the answer
Answer:
The measure of anle MNP is
Explanation:
The image attached shows the figure corresponding to this question.
The <em>angle MNP</em>, wich is also the angle LNP, is formed by the intersection of a secant and a tanget to a circle.
Then, you can use the theorem:
- the angle formed by a secant and a tangent to a circle that intersect outside the circle is half the difference of the major arc minus the minor arc.
The major arc formed is identified with the letter x and the minor arc is identified witht he letter y. Thus, the measure of the angle MNP is half the differenc x - y:
Answer:
hypotenuse:2 (AB)
adjacent side: 1 (AD)
opposite side:√3(BD)
Step-by-step explanation:
-->AB is hypotenuse cuz it's opposite to right angle (90°)
-->AD is adjacent,cuz it's adjacent to reference angle(60°)
-->BD is opposite side,cuz it's opposite to the reference angle(60°)
✌️:)
1/16=1,003, so
senior= 1003
infants=3009
children=6018
adults=6018
