The specifications for the dimensions of a new cardboard container are shown. If the volume of the container is modeled by V(h) = 2h^3 - 9h^2 + 4h and it will hold 45 cubic inches of merchandise, what are the containers dimensions?
Answers
Solving a cubic equation, it is found that the dimensions of the container are of 1 inch, 9 inches and 5 inches.
The volume of the cubic container is given by the following equation:
[tex]V(h) = 2h^3 - 9h^2 + 4h[/tex]
Since it holds 45 cubic inches of merchandise, we have that [tex]V(h) = 45[/tex], then:
[tex]V(h) = 2h^3 - 9h^2 + 4h[/tex]
[tex]45 = 2h^3 - 9h^2 + 4h[/tex]
[tex]2h^3 - 9h^2 + 4h - 45 = 0[/tex]
Using a cubic equation calculator, the real solution is [tex]h = 5[/tex], thus, the dimensions are:
[tex]h = 5[/tex]
[tex]h - 4 = 5 - 4 = 1[/tex]
[tex]2h - 1 = 2(5) - 1 = 10 - 1 = 9[/tex]
The dimensions of the container are of 1 inch, 9 inches and 5 inches.
A similar problem is given at https://brainly.com/question/16606259
Related Questions
 RST is a right triangle with RS = 12,
RT = 20, and ST = 16. What is sin R?
Answers
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\\ \sf\longmapsto sinR=\dfrac{ST}{RT}[/tex]
[tex]\\ \sf\longmapsto sinR=\dfrac{16}{20}[/tex]
Option B
The points (-6, 4) and (-4, r) lie on a line with slope 3. Find the missing coordinate r.
Answers
[tex]\\ \sf\longmapsto m=3[/tex]
(-6,4)(-4,r)[tex]\\ \sf\longmapsto \dfrac{r-4}{-4+6}=3[/tex]
[tex]\\ \sf\longmapsto \dfrac{r-4}{2}=3[/tex]
[tex]\\ \sf\longmapsto r-4=6[/tex]
[tex]\\ \sf\longmapsto r=6+4[/tex]
[tex]\\ \sf\longmapsto r=10[/tex]
8+4 =17+5
identify and explain the error made by the leaner
Answers
Answer:
let the value of x
Step-by-step explanation:
x=8+4=17+5
x=12=22x=22/12
x=1.8334
Mr.E.Terry, an engineer, runs a small business. The accounts for the firm are:
* Bank Automobile HST Payable Miscellaneous Expense
* A/R—Various Equipment E. Terry, Capital Rent Expense
* Office Supplies A/P—Various E. Terry, Drawings Telephone Expense
* Office Furniture HST Recoverable Fees Earned
* Journalize the following transactions, using the general journal page below. Calculate and add the HST on any transactions that need it. The rate for HST is 13%. Do not provide explanations.
Jul. 3 Cheque Copy
No. 105, Chambers Bros., payment for monthly rent $450 plus HST of $58.50,
total $508.50.
5 Purchase Invoice
From Glen Printing, $86.50 for office supplies plus HST
8 Sales Invoice
No. 50 to J. Greenley, $250 for services performed, plus taxes.
10 Cash Receipt
From R. Grieve, $200 payment on account.
18 Cash Sales Slip
No. 100 to E. Webb, $85.50 plus taxes.
20 Cheque Copy
No. 106 to E. Terry, $490 for personal use.
24 Bank Debit Memo
Bank deducted $25.00 for a bank service charge.
29 Cheque Copy
No. 107 to Star Blueprinting, $500 on account.
29 Cheque Copy
No. 108 to Municipal Telephone for payment of telephone bill, $200 plus HST of
$26, total $226.
31 Cheque Copy
The balances in the HST accounts for the previous period were: HST Recoverable
$890 and HST Payable $1410. Cheque 109 was written to the Receiver General
for $520 to clear the accounts for that period.
Journalizing these transactions.
Answers
Journalizing the transactions in the accounts of Mr. E. Terry's firm are as follows:
Debit Rent Expense $450
Debit HST Recoverable $58.50
Credit Cash $508.50
Debit Supplies $76.55
Debit HST Recoverable $9.95
Credit Accounts Payable (Glen Printing) $86.50
Debit Accounts Receivable (J. Greenley) $250
Credit Service Revenue $221.24
Credit HST Payable $28.76
Debit Cash $200
Credit Accounts Receivable (R. Grieve) $200
Debit Cash $85.50
Credit Service Revenue $76.66
Credit HST $9.84
Debit Drawings, Terry $490
Credit Cash $490
Debit Bank Charges $25
Credit Cash $25
Debit Accounts Payable (Star Blueprinting) $500
Credit Cash $500
Debit Utilities Expense $200
Debit HST Recoverable $26
Credit Cash $226
Debit HST Payable $1,410
Credit HST Recoverable $890
Credit Cash $520
Data Analysis:
a. Rent Expense $450 HST Recoverable $58.50 Cash $508.50
b. Supplies $76.55 HST Recoverable $9.95 Accounts Payable (Glen Printing) $86.50
c. Accounts Receivable (J. Greenley) $250 Service Revenue $221.24 HST Payable $28.76
d. Cash $200 Accounts Receivable (R. Grieve) $200
e. Cash $85.50 Service Revenue $76.66 HST $9.84
f. Drawings, Terry $490 Cash $490
g. Bank Charges $25 Cash $25
h. Accounts Payable (Star Blueprinting) $500 Cash $500
i. Utilities Expense $200 HST Recoverable $26 Cash $226
j. HST Payable $1,410 HST Recoverable $890 Cash $520
Learn more: https://brainly.com/question/16889477
someoneplz help me plzzzzzzzzzzzz
Answers
Answer:
Whats the question ???
Step-by-step explanation:
What do you need help with?
A vector starts at point (-3, 4) and ends at point (6, -3). What is the magnitude of the vector? Answer to two decimal places.
Answers
Answer:
the magnitude of the vector is 11.40
Blanca is considering selling her blossoming art business, but is unsure what fair value would be. A friend in accounting told her she could help if she can calculate her EBIT. She has sold 120 art collages for $300. Her expenses are minimal since she usually uses recycled materials. She estimates it costs her about $4 per collage and she has created 200 collages this year. Help her calculate her EBIT. Annual Revenue Annual Expenses, and EBIT
Answers
Answer: 15x-4956
Step-by-step
this is
A) 52°
B) 78°
C) 96°
D) 39°
Answers
8x + 104 = 360
8x=256
x= 32
32 x 3 = 96
A pillar is fixed at one of the corners of a square meadow. The length of each edge of the meadow is 30m and the angle of elevation of the top of the pillar from the opposite comer is found 60°. Find the height of the pillar.
(A) 93.49 m (B) 83.48 m (C) 69.93 m (D) 73.48m
Answers
Answer:
D. 73.48 m.
Step-by-step explanation:
The diagonal distance across the meadow
= √(30^2+30^2)
= √1800
tan 60 = h / length of the diagonal (where h = height of the pillar).
h = √1800 * tan 60
= 73.48 m
The required height of the pillar if length of each edge of the meadow is 30m and the angle of elevation of 60 degrees is 73.48m
Angle of elevation and depressionThe angle situated below the pillar is known as the angle of elevation
Determine the diagonal distanceThe diagonal distance across the meadow is calculated using the Pythagoras theorem:
l = √(30^2+30^2)
l = √1800
tan 60 = h/l
where h = height of the pillar
h = √1800 * tan 60
h = 73.48 m
Hence the required height of the pillar if length of each edge of the meadow is 30m and the angle of elevation of the top of the pillar from the opposite comer of 60 degrees is 73.48m
Learn more on angle of elevation here: https://brainly.com/question/25748640
Explain how multiplying with 6 is like multiplying with 3.
Answers
Answer:
Step-by-step explanation:
lets say 6 times 6 =36
3 is a half of six so if you
6x6=36
3x6=18
solve pls brainliest
Answers
3. They each have a brother who
weighs 40 units. Whose brother
weighs 40 pounds, and whose
weighs 40 kilograms? Explain your
reasoning
Answers
Lin's brother weighs 40 pounds, and Elena's brother weighs 40 kilograms, because kilograms are heavier than pounds and Elena's brother is bigger.
How many solutions does this equation have?
–7c = –7c + 3
Answers
Answer:
0
Step-by-step explanation:
If you move like terms to one side you'll get
-7c + 7c = 3
0c =3
0 = 3
cannot be true, so there are zero solutions
PLEASE HELP ME WITH THIS PLEASE!!!!!
Answers
Answer:
9)x=-4
10)x=5
11)x=4
12)x=-9
13)x=-8
14)x=-3
Step-by-step explanation:
A triangle is 180º total so just add the numbers togeather and make an equation where they x+#s=180.
What methods do you know that can be used to solve a quadratic equation?
Answers
Answer: If the quadratic equation has real, rational solutions, the quickest way to solve it is often to factorise into the form (px + q)(mx + n), where m, n, p and q are integers. This is especially true where the coefficient of x2 is 1.
Example 1 - Solve x2+7x+12=0
Step-by-step explanation:
that's the only one I remember
Answer:
factoring, using the square roots, completing the square and the quadratic formula.
Step-by-step explanation:
X = 6(2+3[2{7-3)+(4+1)-3]}
Answers
(Modified ex que Two years ago, Kim Ean invested RMP in her account which earns r% simple interest. After 18 months, she noticed that the amount had become RM10,450 and today the amount is RM10,600. Find the value of P and R.
Answers
Answer:
r= 3% P=10k
using formula S=P(1+rt)
substitute 2 diff range time and it will form 2 equation. To find r u need to divide those 2 equation. after finding r u can find P by substitute the value of r in either one of those equation. hope it can helps you
Can you help me on attached picture
Answers
3 times 3 is 9. And 5 times 3 is 15.
-1/3x-1/6=2/9 solution
Answers
Answer:
-1 1/6
Step-by-step explanation:
Use a common denominator first to convert all the fractions so they can be easily added or subtracted.
Common denominator is 18 since 3, 6, and 9 can all evenly divide into 18
1/3 = 6/18
1/6 = 3/18
2/9 = 4/18
So now you have
-6/18x - 3/18 = 4/18
add 6/18x to both sides so you can make the number with the variable positive
6/18x - 6/18x - 3/18 = 4/18 + 6/18x simplifies to - 3/18 = 4/18 + 6/18x
subtract 4/18 from both sides
- 3/18 - 4/18 = 4/18 - 4/18 + 6/18x simplifies to - 7/18 = 6/18x
Divide both sides by 6/18 so x is alone on the one side
( - 7/18) / ( 6/18) = ( 6/18x) / ( 6/18) simplifies to ( - 7/18) / ( 6/18) = x
When you divide a fraction by a fraction, the bottom fraction gets flipped over then you multiply the two new fractions straight across
so the new equation looks like this
- 7/18 times 18/6 and you multiply -7 x 18 = -126 and the bottom is 18 times 6 = 108 you now have -126/108
x = -126/108 which simplifies to - 1 18/108 which can still be simplified more to -1 1 / 6 since 108 can be divided by 18 that gives you 6.
What is 91835 rounded to the nearest Highest Place
Answers
Answer:
90,000
Step-by-step explanation:
Which table shows a proportional relationship between x and y?
A.
x y
2 4
3 6
4 9
B.
x y
3 4
9 16
15 20
C.
x y
4 12
5 15
6 18
D.
x y
1 4
2 8
3 15
Answers
Answer:
c is the answer
Step-by-step explanation:
(3 x 62) - 25 + n = 166
Answers
Answer:
n = 5
Step-by-step explanation:
186 - 25 + n = 166
n + 186 - 25 = 166
n + 161 = 166
(n + 161) + (-161) = 166 + (-161)
n + 161 - 161 = 166 - 161
n = 5
Rashawn read 25 pages of his book each day until he finished the book. his book was 400 pages long. which sketch represents this situation?
Answers
Answer:
It took 16 days
Step-by-step explanation:
400/25=16
NEDDDD ASAPPPPP!!!!!!!!!
Answers
Answer:
9
Step-by-step explanation:
4y + 6y = 90
10y =90
y = 90÷10
y = 9
50,000 is 20% of what?
Answers
Answer:
250000
Step-by-step explanation:
20% of x is 50000
----------------------------
50000=20x/100
50000= x/5
5(50000) = x
250000 = x
What is the value of 5 in 102,587?
Answers
Answer:
Value of 5 is 500
From right to left ones, tens, hundreds, thousands, ten thousands, hundred thousands
5 is in the hundredth place
HOPE THIS IS WORTH IT :)b. What is the number that is halfway between the two values?
7 and 11
Submit
Answers
Answer:
9
Step-by-step explanation:
It would be 9 because 7 +2 is 9 and 11 - 2 is 9.
Isn't way to hard.
Good luck on whatever you are doing.
9514 1404 393
Answer:
9
Step-by-step explanation:
The midpoint between two values is their average. The average is half their sum.
(7 +11)/2 = 18/2 = 9
The number 9 is halfway between 7 and 11.
_____
Check
The distance from 7 to 9 is 9-7 = 2. The distance from 9 to 11 is 11-9 = 2. The distances are the same, so 9 is halfway between 7 and 11.
help with question 4 please
Answers
Answer:
dont know
Step-by-step explanation:
sorry
100 POINTS IF YOU ANSWER ALL OF THESE AND NO LINKS!
Answers
Answer:
divide 8/3
8/3 = 2
and for -11/3 it = -4 because it would originally = to -3.66666666667 and u have to round it.
----------------------------------
for the second picture
make it into an improper fraction
-2 1/2 = -5/2
and for 6 1/2 it = to 13/2
now, to plot it on the line you have to divide
divide -5/2 = -2.5
and divide 13/2 = 6.5
------------------------------------
Hope this helps!
a
A map has a scale of 1cm : 3 km
On the map, the distance between two towns is 7cm.
What is the actual distance between the two towns?
Include units for your answer.
A map has a scale of 1cm : 4 kilometres.
The actual distance between two cities is 52 kilometres.
What is the distance between the cities on the map?
Answers
Answer:
7/3=2.3
1. the distance between the towns is 2.3 km
52/4=13
2. the distance between the cities on the map is 13 cm
Step-by-step explanation: