Mrs. Lindsay doesn't have a cat crate and needs to take her cats to the vet. She's
going to make a box out of a 8 foot by 8 foot piece of cardboard. How many feet
should Mrs. Lindsay cut from the corners to have the maximum amount of space
inside the box?

Answers

Answer 1

Answer:

The amount to remove from each corner is a square, 4/3 ft by 4/3 ft.

Step-by-step explanation:

The piece of cardboard measures 8 ft by 8 ft.

Each corner will be cut to create the sides of the box.

Let the square cut from each corner measure x by x ft.

The base of the box will measure 8 - 2x by 8 - 2x, and the height of the box will be x.

V = (8 - 2x)^2 * x

V = 64x - 32x^2 + 4x^3

Now we differentiate and set the derivative equal to zero to find a maximum value.

64 - 64x + 12x^2 = 0

3x^2 - 16x + 16 = 0

(3x - 4)(x - 4) = 0

3x - 4 = 0  or  x - 4 = 0

3x = 4   or   x = 4

x = 4/3  or  x = 4

The solution x = 4 must be discarded since 8 - 2x = 8 - 8 = 0, and the sides would have 0 length.

The amount to remove from each corner is a square, 4/3 ft by 4/3 ft.


Related Questions

A jar contains 30 red marbles, 50 blue marbles, and 20 white marbles. You pick one at random. Find
the given probabilities:

Type a full reduced fraction. Ex. 1/4
P(red)=
P(blue)=
P(not white)=

Answers

Answer:

P(blue)=1/2 50 marbles are blue

Plz solve this question

Answers

7). 1/(√7-√11)

= 1×(√7+√11)/(√7-√11)(√7+√11)

= √7+√11 / (√7)² - (√11)²

= √7 + √11 / 7 - 11

= √7 + √11 / (-4)

EXPLAINATION:

to rationalize the denominator we multiply the numerator and the denominator by the denominator, but with the opposite sign.

For example - in the first question we multiplied 1 and 7 - 11 by 7 + 11 .

I need help I will give brainliest.

Answers

Answer:

C

Step-by-step explanation:

Answer: 12

Explanation: QT = x +4
Use proportions: x +4/ 4 = 9/3
Cross Multiply: 3(x+4) = 36
Solve 3x+12 = 36
x=8

Plug back into equation: 8 +4 = 12

what is the slope of the line?

Answers

Answer:

y = 2x - 3

Step-by-step explanation:

Since the line is going 2 down and 1 left. The slope is 2.

The line crosses the y-intercept at -3.

y = 2x - 3

Answer:

m = 2

Step-by-step explanation:

You have to use the slope formula and insert your points into the formula. Your formula should have turned into 0 - (-3)/1.5 - 0. If you simplfy your equation your get m(slope)=2.

Hope this helps! :D

-Luna

help solve this please

Answers

Answer:

f² - 11f - 12

Step-by-step explanation:

(f-12)(f+1) = f² + 1f - 12f - 12

answer choices for number one:

x<4
x>4
x<0
x<-4

answer choices for number two:

x<-3
x>-3
x<9
x>9

Answers

Answer:

Question 1. x>4

Question 2.  x<9

Phoebe has 72 roses that she is putting into 5 vases. If she puts the same number of roses in each vase, how many roses are left over?

Answers

Answer:

2 roses left over

Step-by-step explanation:

72/ 5 = 14.4

so we know for sure that we can put 14 roses on each vase  but no mor than 14 on each vase  Some will be  left left over

14x5 = 70

  72-70 = 2  (2 roses left over)

The rectangle ABCD is reflected across the y-axis. What are the
coordinates of the vertex A'?

Answers

The answer would be (-2,5), this is because when we reflect on the Y axis the Y stays the same and X changes and vise versa for the X axis. Then the amount of units away from the y axis is the amount of units more that it’s going to travel. Hope this helps

The model below has an area of 16 square units which expression represents the side length of the model in units /64 /4 /16 /8

Answers

Answer:

4

Step-by-step explanation:

the area of a square = length²

16 = length²

find the square root of both sides of the equation

length = 4

4x – 5 + 2(x – 3) = 12x + 7
X=

Answers

Answer:

-3

Step-by-step explanation:

4x - 5 + 2(x - 3) = 12x + 7

4x - 5 + 2x - 6 = 12x + 7

4x + 2x - 5 - 6 = 12x + 7

6x - 11 = 12x + 7

collect like terms

6x - 12x = 7 + 11

-6x = 18

-x = 3

x = -3

Can someone please help me find the area of this semi circle plz

Answers

Answer: I think it is 39.25

Step-by-step explanation:

10/2=5

5^2=25

25*3.14=78.5

78.5/2=39.25

!!!!!!!PLEASE HELP I DNT UNDERSTAND!!!!!! WILL GIVE BRAINLYIEST

Answers

Answer:

11. 8/30

Step-by-step explanation:

add all the marbles

you get 30 marbles

then the probability of yellow being taken out is 8

3/5 pencils sold in the morning. 1/4 of the remainder in the afternoon. If 200 more pencils were sold in the morning than afternoon, how many pencils did they start with

Answers

Answer:

x = total pencils = 400 pencils

Step-by-step explanation:

Let

x = total pencils

Pencils sold in the morning = 3/5x

Remaining pencil = x - 3/5x

= 5x-3x/5

= 2/5x

Pencils sold in the afternoon = 1/4 of the remainder

= 1/4 * 2/5x

= 2/20x

= 1/10x

Pencils sold in the afternoon = 1/10x

3/5x + 200 = 1/10x

3/5x - 1/10x = 200

(6x-x)/10 = 200

5/10x = 200

1/2x = 200

x = 200 ÷ 1/2

= 200 × 2/1

x = 400 pencils

x = total pencils = 400 pencils

Can someone please help me

Answers

Answer: I'm not to sure about this question its kind of confusing.

Step-by-step explanation:

A bag contains 4 white, 3 blue, and 3 red marbles. Find the probability of choosing a red marble, then a white marble if the marbles are not replaced

Answers

Answer: 2 / 15

Step-by-step explanation:

3 red / 10 total

4 white / 9 total

3/10 * 4/9 = 12/90 = 2/15

A point at (-7, -6) is reflected over the x-axis. What is the distance between the point and its reflection?

6 units
7 units
12 units
14 units

Answers

Answer:

It Would be 14 units.

Step-by-step explanation:

Have a Great Day.

:)

Will accept Brainliest

Which of the following statement is false?​

Answers

Answer:

D.) rational numbers are associative under subtraction

Step-by-step explanation:

rational numbers are closed under subtraction

↳ TRUE

zero is the identity for addition of rational numbers

↳ TRUE

subtraction is the inverse of the addition

↳ TRUE

rational numbers are associative under subtraction

↳ FALSE

PLEASE NEED HELP FAST!!

Buying one item at regular price and buying a second identical item for 50% off is the same as buying both items for 25% off.
If the regular price of an item is x dollars, which equation illustrates this relationship?
O A x+0.5x = 2(0.25.x)
B. X-0.5.x = 2(0.25.x)
O C. 1-0.5x = 2(0.75.8)
D. X+0.5.x = 2(0.75.x)


Answers

Answer:

b

Step-by-step explanation:

Answer:

ok

Step-by-step explanation

part b


Do not give me any types of links.
Find the surface area of a sphere with radius 5 using the formula SA=4pir2
Leave answer in terms of n
A. 75 pi units squared
B. 100 pi units squared

Answers

Answer:

B. 100 pi units squared

Step-by-step explanation:

Find the surface area of a sphere with radius 5 using the formula SA=4pir²

Leave answer in terms of π = pi

From the question

The formula for the Surface Area if a square = 4 × pi × r²

r = 5

Hence,

Surface Area of a Sphere = 4 × pi × 5²

= 100 pi units squared

Option B is the correct option

Please help, due soon. Find the length of each arc. Use exact answer

Answers

Answer:

C

Step-by-step explanation:

The arc length is calculated as

arc = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{285}{360}[/tex]

    = 2π × 18 × [tex]\frac{19}{24}[/tex]

    = 36π × [tex]\frac{19}{24}[/tex] ( cancel 36 and 24 by 12 )

    = 3π × [tex]\frac{19}{2}[/tex]

    = [tex]\frac{57\pi }{2}[/tex] → C

(6, - 3, 1) and (8,9,-11) find the angle between the vector​

Answers

Answer:

The angle between the two vectors is 84.813°.

Step-by-step explanation:

Statement is incomplete. Complete form is presented below:

Let be (6,-3, 1) and (8, 9, -11) vector with same origin. Find the angle between the two vectors.

Let [tex]\vec u = \langle 6, -3, 1 \rangle[/tex] and [tex]\vec v = \langle 8,9,-11 \rangle[/tex], the angle between the two vectors is determined from definition of dot product:

[tex]\theta = \cos^{-1} \left(\frac{\vec u \,\bullet \,\vec v}{\|\vec u\|\cdot \|\vec v\|} \right)[/tex] (1)

Where:

[tex]\vec u[/tex], [tex]\vec v[/tex] - Vectors.

[tex]\|\vec u\|[/tex], [tex]\|\vec v\|[/tex] - Norms of each vector.

Note: The norm of a vector in rectangular form can be determined by either the Pythagorean Theorem or definition of Dot Product.

If we know that [tex]\vec u = \langle 6,-3,1 \rangle[/tex] and [tex]\vec v = \langle 8, 9,-11 \rangle[/tex], then the angle between the two vectors is:

[tex]\theta = \cos^{-1}\left[\frac{(6)\cdot (8) + (-3)\cdot (9) + (1)\cdot (-11)}{\sqrt{6^{2}+(-3)^{2}+1^{2}}\cdot \sqrt{8^{2}+9^{2}+(-11)^{2}}} \right][/tex]

[tex]\theta \approx 84.813^{\circ}[/tex]

The angle between the two vectors is 84.813°.

Please help quick! last question on my hw.

Answers

Answer:

The answer in C

Step-by-step explanation:

if you add all the numbers and divide by 25 you get 17

30% of the 90 students in sixth grade are in the drama club. How many sixth graders are in the drama club?

Answers

Answer: 27 kids.
Explanation: Multiply 30%, or 0.3, by 90. That will find your answer. Hope this helps!

Answer:

27

Step-by-step explanation:

Multiply 90 by 0.3 and you have your answer

Solve 2 (x+3) = x - 4

Answers

Answer:

x=-10

Step-by-step explanation:

2(x+3)=x-4

2x+6=x-4

2x-x=-6-4

x=-10

Please mark me brainliest if it helped

2(x+3)=x-4

2x+6=x-4

-----------------

2x+6=x-4

2x+6=x-4-6

Subtract the numbers

2x=x-10

2x-x=x-10-x

Simplify

Combine like terms

Multiply by 1

Combine like terms

----->>> x= - 10

x equals -10

What value of x will make the equation below true?
7(4+x)=84

Answers

Answer:

x=8

Step-by-step explanation:

distribute 7(4+x)

28+7x=84

84-28=56

56/7=8

Determine how (if possible) the triangles can be proved similar.

AAA-
B.
SSS
COSAS
D. Not enough info/not similar

Answers

SSS sides are all 1.6 times bigger on one than the other. Also, when there are no markings for angles you can assume it won’t be an A answer

What fraction of the square is the green triangle?

Answers

Answer:

1/4

Step-by-step explanation:

Answer:

7/32

(btw thats the simplified version....look at the bottom for non-simplified if you didnt need it simplified)

Step-by-step explanation:

first count how many squares there are in total

its 8 by 8 so in total there are 64!

now there is the green triangle.....

count all the whole squares in it = 10

now count all the half squares (little triangles in it)= 8

Now if you put those little triangles together it would make one small unit square so it is 4 of all

10 + 4 = 14

So there is a Total of 14 unit squares in the green triangle

Fraction Time......

now lets take 14/64 and simplify it

that would be 7/32

We cant make it any more simplified now if you werent looking for the simplified version the your answser would be 14/64

I hope this was the answser you were looking for!! Mark Me Brainliest ;)

what goes in the highlighted box?

Answers

Answer: 11y

Step-by-step explanation:

When you add 6y and 5y that equals 11y <3

Answer:

11Y goes in the highlighted section.

Step-by-step explanation:

Since the Xs was crossed out you don't have to worry about the X going tin the highlighted area.

Then add the Ys together.

I can't really explain anymore, but i hope this helps!!!!

Then your final answer would be y=6. :)

How do you solve this proof?

Answers

Answer:

1) Given

2) Isosceles triangle's 2 sides are equal. Vertex angle is M. So, ML = MN

3) Given

4) T divided LN into to equal parts.

5) Common

6) SSS

A bag contains 96 marbles, some red and some green. The ratio of red marbles to green ones is
2:4. How many green marbles are there?

Answers

64 green marbles and there would be 32 red ones. 32:64 is the same ratio as 2:4.
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