Jorge is asked to build a box in the shape of a rectangular prism. The maximum girth of the box is 20 cm. What is the width of the box that would yield the maximum volume? What is the maximum volume given a girth of 20 cm? Use a graphing calculator to determine the width that provides the maximum volume, round to the nearest tenth.
The width of the box is __________cm
The maximum volume is __________cm3
Answers
Answer:
The width of the box is 6.7 cm
The maximum volume is 148.1 cm³
Step-by-step explanation:
The given parameters of the box Jorge is asked to build are;
The maximum girth of the box = 20 cm
The nature of the sides of the box = 2 square sides and 4 rectangular sides
The side length of square side of the box = w
The length of the rectangular side of the box = l
Therefore, we have;
The girth = 2·w + 2·l = 20 cm
∴ w + l = 20/2 = 10
w + l = 10
l = 10 - w
The volume of the box, V = Area of square side × Length of rectangular side
∴ V = w × w × l = w × w × (10 - w)
V = 10·w² - w³
At the maximum volume, we have;
dV/dw = d(10·w² - w³)/dw = 0
∴ d(10·w² - w³)/dw = 2×10·w - 3·w² = 0
2×10·w - 3·w² = 20·w - 3·w² = 0
20·w - 3·w² = 0 at the maximum volume
w·(20 - 3·w) = 0
∴ w = 0 or w = 20/3 = 6.[tex]\overline 6[/tex]
Given that 6.[tex]\overline 6[/tex] > 0, we have;
At the maximum volume, the width of the block, w = 6.[tex]\overline 6[/tex] cm ≈ 6.7 cm
The maximum volume, [tex]V_{max}[/tex], is therefore given when w = 6.[tex]\overline 6[/tex] cm = 20/3 cm as follows;
V = 10·w² - w³
[tex]V_{max}[/tex] = 10·(20/3)² - (20/3)³ = 4000/27 = 148.[tex]\overline {148}[/tex]
The maximum volume, [tex]V_{max}[/tex] = 148.[tex]\overline {148}[/tex] cm³ ≈ 148.1 cm³
Using a graphing calculator, also, we have by finding the extremum of the function V = 10·w² - w³, the coordinate of the maximum point is (20/3, 4000/27)
The width of the box is;
6.7 cm
The maximum volume is;
148.1 cm³
Related Questions
whats is f (5) = 2x + 17
Answers
Answer:
f(5)=27
Step-by-step explanation:
The 5 in the f(5) just means thats what x is equal to, so using that information you can do 2(5)+17=27, so f(5)=27. (Sorry if its short)
Help me if your good with math I’ll give brainliest
Answers
Answer:
Step-by-step explanation:
x^3=27
x=sqrt27=3
x=3
Answer:
A) x=3
Step-by-step explanation:
you can type it in the calculator like this: [tex]\sqrt[3]{27} =3[/tex]
There are ten centimeters in one decimeter. How many decimeters are in thirty seven centimeters?
Answers
Answer: 3.7
Step-by-step explanation: In this case you're just multiplying by (10) usually this is done to make a decimal to a whole number
There are ten centimeters in one decimeter. How many decimeters are in thirty seven centimeters?
Divide 37/10=3.7
Another way is 3. 7*10=37
¿Cómo ubicas el sistema de ecuaciones en sistema de cocoodernadas?
Answers
Answer:
resolviendo para xey
Step-by-step explanation:
Espero que esto ayude amiga/o
Please help me all questions. Thank you very much :)
Answers
Answer:
a, c, d
Step-by-step explanation:
[tex]6:8 = 3:4[/tex]
[tex]9:15 = 3:5[/tex]
[tex]12:16 = 3:4[/tex]
[tex]15:20 = 3:4[/tex]
5.2x10^3 written in standard
Answers
Answer:
5200
Step-by-step explanation:
[tex]\huge {\red{5.2 \times {10}^{3}}} = \orange {5200} [/tex]
Can someone help find the solutions
Answers
Answer:
x = 3.5
Step-by-step explanation:
Given
[tex]3^{2x-5}[/tex] = 9 , that is
[tex]3^{2x-5}[/tex] = 3²
Since the bases on both sides are equal, both 3 , then equate the exponents
2x - 5 = 2 ( add 5 to both sides )
2x = 7 ( divide both sides by 2 )
x = 3.5
Find the percent change if the original is $300 and the new cost is $1,100?
Answers
The percentage change from $300 to $1,100 is 266.67% increase
How?
1,100 - 300 ÷ 300 = 2.6667
2.6667 x 100 = 266.67%
^this is how you find the percent in change
(You could have just asked me to show my work instead of reporting me- that was a bit uncalled for)
Answer: $266.667% change
Step-by-step explanation:
(V2 - V3) (1100 - 300) 800
_______ x100 = ________ x 100 = ____ x 100= $2.66667% = $266.667%
V1 300 300 x 100 increase or change
Find the discount and sale price of a dresser whose original price is $280 and is discounted 15% off,
Answers
Answer:
Sale=238 Discount=42
Step-by-step explanation:
15% of 280 is 42...So 280 - 42 =238
Natalie walked 3/5 mile in 1/2 hour how fast did she walk in miles perhour
Answers
Answer:
Speed = Distance / Time
Speed = 3/5 ÷ 1/2
Speed = 3/5 * 2
Speed = 6/5 mph or 1.2 mph.
Step-by-step explanation:
HOPE IT HELPS, PLS MARK IT AS THE BRAINLIEST AND PLS
Find the greatest common factor 15y^2 and 6b^3
Answers
Hey there!
• 15y²: 1, 3, 5, 15, y, y
• 6b³: 1, 2, 3, 6, b, b, b
• They both share 1 & 3... the greatest out of those two is/are: 3
• Answer: 3 ☑️
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
Can somebody help and explain if you're able to. thank you
Answers
Answer:
6.5 or 6 1/2 miles per minute
Step-by-step explanation:
basically divide the amount of minutes by how many miles Jessica ran hence the minutes per mile.
Answer:
Step-by-step explanation: You divide the fractions. Start by making them a fraction instead of a mixed number then cross multiply keep the first flip the second and theres your answer :)
help me please I'm trying to get this donee
Answers
Answer:
The answer is 15.
Step-by-step explanation:
Plug in the numbers for the a and b values individually. For the numerator, 5(6) is the same thing as 5 * 6 = 30. For the denominator, 1/4^2 would equal to 1/16 and when you multiply it by 32, you will get 2.
To clear things up, the fraction should be 30/2 and your answer should be 15 as a result.
Step-by-step explanation:
so...the answer is 15
...........
Does anyone know why I only got 2/3 marks, and can you explain how to get 3 marks. Thank you :)
Answers
Answer:
The reason is likely because of an unit error of centimetres square (cm²) which is to be in metres square (m²)
Step-by-step explanation:
The units of the length is in meters, and the side length, S, of the cube is S = 0.7 m, therefore, the answer is to be given as follows;
The surface area of one face of the cube = S² = (0.7 m)² = 0.49 m²
The number of faces in a cube = 6, therefore, we have;
The surface area of the cube = 6 × The surface area of one face of the cube
The surface area of the cube = 6 × 0.49 m² = 2.94 m²
Therefore, the surface area of the cube is 2.94 m² (m² not cm²)
An item is regularly priced at $65. Abdul bought it at a discount of 95% off the regular price. Use the ALEKS calculator to find how much Abdul paid.
Answers
Answer:
$3.25
Step-by-step explanation:
An item is regularly priced at $65. Abdul bought it at a discount of 95% off the regular price. Use the ALEKS calculator to find how much Abdul paid.
Original price of item = $65
percent discount = 95%
discount price = 95% * 65
discount price = 0.95 * 65
discount price= $61.75
Amount abdul paid = Original price - discounted price
Amount abdul paid = $65 - $61.75
Amount abdul paid = $3.25
Hence abdul paid $3.25
solve the following equation by the trial and error method...
plzzzz fast ......
Answers
Answer:
the required answers are :
a) x = 4
b) x = 3
c) a = 7
d) x = -15
Step-by-step explanation:
the whole process is given in the solution in attached picture. okay
An arc subtends an angle of 72 degree at the circumference of a circle of radius 5 cm. calculate the length of the arc in terms of pie
Answers
Hope you understand the solution. Call my attention if you need any help
In a large urban high school, 68% of the students take public transportation to and from school. Annette takes a random sample of 75 students from this school. What is the probability that more than 70% of the students in the sample take public transportation to and from school?
0.356
0.371
0.488
0.644
Answers
Answer:
0.488
Step-by-step explanation:
Answer:
0.356
Step-by-step explanation:
took the quiz
Two shops, Tisco and Azda, sell the same brand of baked beans with the following deals.
Calculate the price per item for each shop.
Write the shop which is the best value for money in the comment box.
Tisco - 4 for £1.84
Azda - 5 for £2.40
Answers
Answer:
The shop with the best value is Tisco with .46 per can.
Step-by-step explanation:
So you need to divide 1.84 by 4 which you get .46. Next you do 2.40 divided by 5 and you get .48. Finally you can tell that .48 is greater than .46.
Hope this helps!
two angles of an isosceles triangle are x and x+10.find two possible value of x
Answers
Recall two important facts:
- An isosceles triangle always has two identical angles
- The interior angles always add up to 180 degrees
Armed with this info, we can set up two different equations to solve for x, depending on which angle we treat as being one of the pair of identical angles.
If we assume that the identical angles are x, then:
180 = 2x + x + 10
170 = 3x
56[tex]\frac{2}{3}[/tex] = x
Alternately, we can assume that the identical angles are x+10. In this case:
180 = 2(x + 10) + x
180 = 2x + 20 + x
160 = 3x
53[tex]\frac{1}{3}[/tex] = x
On Monday, 243 students went on a field trip to the zoo. All 5 buses were filled and 8 students had to ride in a car. How many students were on each bus?
Answers
Answer:
47 students in each bus
Step-by-step explanation:
243-8= 235
235/5=47
An algebra I student solved the following inequality.if their work is correct draw a smiley face.if not, circle the error and explain your reasoning
Answers
Answer:
step 3
Step-by-step explanation:
^ i’m pretty sure that’s right
Sophie pays m dollars to rent a car for the weekend. On the drive home, she buys $25 worth of gasoline. Her friend Melody pays for one-half the cost of the car rental only. Choose an expression you could use to determine how much Sophie spent. A. m + 25 B. m + 25 –12 C. 12(m + 25) D. 12m + 25
Answers
Answer:
D. 1/2m + 25
Step-by-step explanation:
Sophie pays m dollars to rent a car for the weekend.
On the drive home, she buys $25 worth of gasoline.
From the above question, we are told that:
Her friend Melody pays for one-half the cost of the car rental only.
= m - 1/2m
= 1/2m
Hence, the cost of the rental that sophie is paying for is 1/2m dollars
She buys $25 of gasoline
Let the amount sophie spent be represented by A
The expression you could use to determine how much Sophie spent is given as:
A = 1/2m + 25
Answer:
1/2 + 25
Step-by-step explanation:
Don't feel like explaining. :)
If the simple interest on $6,000 for 6 years is $1,800, then what is the interest rate?
Answers
Answer:
10%
Step-by-step explanation:
1800/3 = 600
600/6000 = 10%
Writing each fraction of mixed number by a decimal.
Problem: What is 0.23 ?
Answers
2. Simplify the following fraction:
*
23
4
Answers
6 x ? x 3 = 90 pls help I’m to lazy to do it
Answers
Step-by-step explanation:
let the unknown number be x
6 * x * 3 = 90
18 x = 90
x = 90/ 18
x = 5
Hope it will help :)
Answer: 5
Step-by-step explanation:
30 divided by 6 is 5, so 6 x 5 x 3=90
Read again and write T (true ) or F (false
The assessment was last week.
The patient is not on any medication.
The patient should rest and avoid any
physical activity
a Sierching is important to his recovery.
e The doctor asks the patient to come in for
another appointment.
Answers
Answer:
t
Step-by-step explanation:
Find the measure of angle x in the figure.
129
133
127
130
133
125
Note: Angles not drawn to scale.
Angle x measures
Answers
130 feet
-I hope this helps! Enjoy the rest of your day
Describe the effect of reflecting EFGH over the x-axis to E’F’G’H’
Answers
Answer:
the sign of each y value changed
Step-by-step explanation: