1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sergeu [11.5K]
3 years ago
8

Find the maximum volume of a box that can be made by cutting out squares from the corners of an 8-inch by 15-inch rectangular sh

eet of cardboard and folding up the sides.
Mathematics
1 answer:
Vedmedyk [2.9K]3 years ago
7 0
<span>Answers: V = (15-2x)(8-2x)x V = 120x -46x²+ 4x³ V' = 120 -92x + 12x² 0 = 120 -92x + 12x² x = (92±52)/24 x = 6 or 5/3 Pick x = 5/3 Volume = (15-2*5/3)(8-2*5/3)*5/3 = 90.74 in³ To justify x = 5/3 is the max V" = -92 + 24x V"(5/3) = -92 + 24(5/3) <0 negative. Volume V(5/3) is max because the function is concave down with V"<0.</span>
You might be interested in
To mix weed killer with water correctly, it is necessary to mix 30 teaspoons of weed killer with 5 gallons of water. Find how ma
nlexa [21]
Answer
6 Gallons



Each gallon of water needs 6 teaspoons because 30/5=6

Now we know that teaspoons/6=amount of gallons

36/6=6 gallons
7 0
2 years ago
One number is 9 more than another. if the sum of the two numbers is 171, find the two numbers
allochka39001 [22]
Let x be the 1st number
x + 9 be the second number

Equation:
x + x+9 = 171

Solution:
2x + 9 = 171
2x = 171 - 9
2x = 162
x = 81
x + 9 = 90

81 + 90 = 171
4 0
3 years ago
Find the least common multiple (LCM) of 8y^6+ 144y^5+ 640y^4 and 2y^4 + 40y^3 + 200y^2.
Mice21 [21]

Answer:

<em>LCM</em> = 8y^{4}(y+ 10)^{2}(y + 8)

Step-by-step explanation:

Making factors of 8y^{6}+ 144y^{5}+ 640y^{4}

Taking 8y^{4} common:

\Rightarrow 8y^{4} (y^{2}+ 18y+ 80)

Using <em>factorization</em> method:

\Rightarrow 8y^{4} (y^{2}+ 10y + 8y + 80)\\\Rightarrow 8y^{4} (y (y+ 10) + 8(y + 10))\\\Rightarrow 8y^{4} (y+ 10)(y + 8))\\\Rightarrow \underline{2y^{2}} \times  4y^{2} \underline{(y+ 10)}(y + 8)) ..... (1)

Now, Making factors of 2y^{4} + 40y^{3} + 200y^{2}

Taking 2y^{2} common:

\Rightarrow 2y^{2} (y^{2}+ 20y+ 100)

Using <em>factorization</em> method:

\Rightarrow 2y^{2} (y^{2}+ 10y+ 10y+ 100)\\\Rightarrow 2y^{2} (y (y+ 10) + 10(y + 10))\\\Rightarrow \underline {2y^{2} (y+ 10)}(y + 10)        ............ (2)

The underlined parts show the Highest Common Factor(HCF).

i.e. <em>HCF</em> is 2y^{2} (y+ 10).

We know the relation between <em>LCM, HCF</em> of the two numbers <em>'p' , 'q'</em> and the <em>numbers</em> themselves as:

HCF \times LCM = p \times q

Using equations <em>(1)</em> and <em>(2)</em>: \Rightarrow 2y^{2} (y+ 10) \times LCM = 2y^{2} \times  4y^{2}(y+ 10)(y + 8) \times 2y^{2} (y+ 10)(y + 10)\\\Rightarrow LCM = 2y^{2} \times  4y^{2}(y+ 10)(y + 8) \times (y + 10)\\\Rightarrow LCM = 8y^{4}(y+ 10)^{2}(y + 8)

Hence, <em>LCM</em> = 8y^{4}(y+ 10)^{2}(y + 8)

5 0
3 years ago
3.53 divided by 51<br> 24.2 divided by 42<br> 9.13 divided by 23<br> 79.2 divided by 39
patriot [66]

Answer:

1. 0.0692156863

2. 0.5761904762

3. 0.3969565217

4. 2.030769231

Step-by-step explanation:

5 0
3 years ago
Help pleaseeeeeee, I need help
Arlecino [84]

Answer:

15, 60, and 61

Step-by-step explanation:

First we have to find the 3rd side length from 2 side length chosen. So let’s pick 8 meters and 11 meters, to find the third side length we use the Pythagorean theorem: c^2 = a^2 + b^2

c = 11^2 + 8^2 = 121 + 64 = 185 = 13.6

13.6 isn’t one of the answers so we can’t pick 11 & 8. Let’s try 11 & 15:

c = 15^2 + 11^2 = 225 + 121 = 346 = 18.6

18.6 isn’t one of the answers either. Let’s try 15 & 60:

c = 60^2 + 15^2 = 3600 + 225 = 3825 = 61.85

61.85 might be it but let’s try one more just in case:

c = 60^2 + 61^2 = 3600 + 3721 = 7321 = 85.6

Nope! That means 15, 60, and 61 are the answer. I hope this is correct!

5 0
3 years ago
Other questions:
  • ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing. Show your work or give an explaination.
    8·2 answers
  • What is the 30th term of the linear sequence below? −4, −1, 2, 5, 8
    14·1 answer
  • Find the value of s.<br>1s + 14 = 26​
    14·2 answers
  • How do you write out -5 * (-4) in repeated addition
    9·1 answer
  • For every 9 miles lana jogged. Victor jogged 5 miles. If lana jogged 1 how many miles would Victor have jogged?
    9·1 answer
  • If f(x) = 1-x2 and g(x) = 1 - x which is the rule of function (f – g)(x)?
    6·1 answer
  • $0.25 per bottle water
    13·1 answer
  • If ava makes $15 in 2 hours, what is her rate of pay?
    11·2 answers
  • B<br> 45°<br> 71°<br> E<br> 27°<br> A<br> D<br> 11. What is mBAC
    8·1 answer
  • Which shows the image of quadrilateral ABCD after the transformation Ro, 90°?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!