Which percent is equivalent to 1 9/12

BOXES Simon will make a box without a top by cutting out corners of equal size from a 22 inch by 15 inch sheet of cardboard and

il63 [147K]

Answer:

Volume of box is $432 in^3$

Step-by-step explanation:

Let x be the side of square corner

Length of box after cutting corners =22-2x

Breadth of box after cutting corners =15-2x

Height =x

Volume of box = (22-2x)(15-2x)x

Volume of box = $4x^3-74x^2+330x$

Differentiate w.r.t x

$\frac{dV}{dx}=12x^2-148x+330$

Substitute derivative =0

$12x^2-148x+330=0\\x=\frac{37-\sqrt{379}}{6},\frac{37+\sqrt{379}}{6}\\\frac{d^2V}{dx^2}=24x-148$

at $x=\frac{37-\sqrt{379}}{6}$

$\frac{d^2V}{dx^2}=24x-148=24(\frac{37-\sqrt{379}}{6} )-148=-77.87 < 0$ hence maximum

at $x=\frac{37+\sqrt{379}}{6}$

$\frac{d^2V}{dx^2}=24x-148=24(\frac{37+\sqrt{379}}{6} )-148=77.87>0$ hence minimum

So,Volume of box = $4x^3-74x^2+330x=4(\frac{37-\sqrt{379}}{6} )^3-74(\frac{37-\sqrt{379}}{6} )^2+330(\frac{37-\sqrt{379}}{6} )=432.23 in^3$

Hence Volume of box is $432 in^3$

4 0

4 years ago

Use the point slope form of each equation to identify a point the line passes through and the slope of the line.

Alja [10]

Point slope form:
P(x₀,y₀)
slope=m

y-y₀=m(x-x₀)

1)
y-2=-3(x+6)
P(-6,2)
m=-3.

2)
y-5=7(x-14)
P(14,5)
m=7

3)
y+3.7=3.2(x-1.7)
P(1.7 , -3.7)
m=3.2

4)
y+1=11(x-1)
P(1 , -1).
m=11

5)
y+6=-4(x-8)
P(8 , -6)
m=-4

6)
y-7=4(x+3)
P(-3,7)
m=4

6 0

3 years ago

Points a b and c are collinear point b is between A and C solve for x AB = 3x BC = 2x -2 and AC =18

Anna35 [415]

<h3>Answer: x = 4</h3>

=====================================

Work Shown:

AB + BC = AC .... see diagram below

(3x)+(2x-2) = 18 ... plug in given expressions

5x-2 = 18

5x-2+2 = 18+2 ... add 2 to both sides

5x = 20

5x/5 = 20/5 ... divide both sides by 5

x = 4

6 0

4 years ago

4k+mn=n-3; solve for n

solong [7]

Since we are solving for n you have to isolate the n. Therefore, you want all the variables with an n in it on one side and all the variables without an n on the other side:) :
4k+3= -mn+n (There were a change in signs because for example you moved the -3 to the other side, therefore it can only be a negative on one side so now you have to change the sign to a positive:) hope you got that)
That would've been your answer because you cannot do anything else...Hope this helped :)

8 0

3 years ago

Help with just one Geometry question.

blondinia [14]

In the given problem we are given a pentagon.

A pentagon has 5 sides and 5 internal angles.

In order to find the required angle, we need to find the total sum of all angles of a a pentagon.

We know formula for the total sum of all angles of a a polygon is given by,

Angle sum = (n-2) *180, where n is the number of sides of the given polygon.

As we know, the given ploygon (pentagon) has 5 side, so the value of n=5.

Plugging n=5 in above formula.

(n-2)*180 = (5-2)*180.

Subtracting 5-2 first, we get 3.

Now, multiplying 3 * 180, we get 540.

So, the total sum of all angles of a Pentagon = 540°.

Given angles 131°, 108°, 107°, 110° and x.

Sum of all angles = 540

Adding angles,

131° + 108° + 107° + 110° + x = 540

456° + x = 540.

Subtractcing 456 from both sides,

456° + x - 456 = 540 - 456.

x=84°.

Therefore, required angle x=84°.

3 0

4 years ago