Step-by-step explanation:
Let the dimension of the box be x, y and z.
Volume of the box V = xyz
Since the box is a rectangular box, the base will be a square of equal length.
V = x²h where h is the height of the box
If the sum of the length, width, and height equals 180, then x+x+h = 180
2x+h = 180
h = 180-2x
Substitute h = 180-2x into the volume of the box
V = x²(180-2x)
V = 180x²-2x³
The box has its maximum volume when [tex]\frac{dV}{dx} = 0[/tex]
[tex]\frac{dV}{dx} = 360x-6x^{2}[/tex]
[tex]360x-6x^{2} = 0\\360x = 6x^2\\360 = 6x\\6x = 360\\x = \frac{360}{6}\\ x = 60[/tex]
Since 2x+h = 180
Substitute x = 60 into the equation ang get the height h
2(60)+h = 180
120+h = 180
h = 180-120
h = 60
Hence the dimension of the rectangular box is 60 by 60 by 60
The dimensions of the rectangular box of maximum volume are;
Length = 60
Length = 60Width = 60
Length = 60Width = 60Height = 60
Let the dimensions of the rectangular box be;
Length = x
Width = y
Height = h
Volume of a rectangular box is given by;
V = length × width × height
Thus;
Volume of this box in question is;
V = xyz
The box is called a rectangular box because it's sides are rectangular in shape but it's base will be square in shape.
Thus;
width = x and so;
V = x²h
We are given the sum of the length, width, and height of the rectangular box to be equal to 180.
Thus; x + x + h = 180
2x + h = 180
h = 180-2x
Put 180 - 2x for h in the equation for volume;
V = x²(180 - 2x)
V = 180x² - 2x³
The maximum volume will occur at the dimensions when dV/dx = 0. Thus;
dV/dx = 360x - 6x²
At dV/dx = 0, we have;
360x - 6x² = 0
6x² = 360x
x = 60
Recall that; h = 180 - 2x, thus;
h = 180 - 2(60)
h = 60
Read more at;https://brainly.com/question/19053087
The list shows numbers in order from least to greatest. Negative 15, negative 3 and four-fifths, negative 1.5, blank, 2.3, 5 and two-thirds Which is an integer that can be inserted on the blank line in the list? A. –2 B. Negative 1 and one-third C. 0 D. 1.2
Answer:
The correct option is option C
Step-by-step explanation:
Here we want an integer that can be inserted into the blank.
We have:
-15 , -3 4/5 , -1.5 , blank , 2.3 , 5 2/3
The integer that must be inserted into the blank should have a value between -1.5 and 2.3
What this means is that it should be greater than -1.5 but less than 2.3
Option A is incorrect since -2 itself is less than -1.5
option B is incorrect as it not an integer ( integer are whole numbers)
option C is correct
D. option D is incorrect since it is not an integer
Answer:
C
Step-by-step explanation:
what is the sale tax on a $14,500 truck if the tax rate is 9%
Answer:
$15, 805.00
Step-by-step explanation:
Tax is based on the state you live in.
Find the value of x. PLEASE HELP - test tomorrow
The answer is 39.
I need to show my work.
THANK YOU!!!!!
Answer:
39
Step-by-step explanation:
b+25+296=360
b+321=360
b=360-321
b=39
translation: 4 units left and 4 units up
J(−1, −2), A(−1, 0), N(3, −3)
Answer:
J(-5,2), A(-5,4), and N(-1,1)
Step-by-step explanation:
A.Name a constant
B.Name the coefficients
Answer:
7 & 13 are constants
8 & 3 are coefficients
Step-by-step explanation:
uestion 1:
Damon wants to sell his motorcycle that he paid $4,000 for 3 years ago. The motorcycle depreciated (decreased in value) at a constant rate each month over a 3-year period. If x represents the monthly depreciation amount, write an expression that shows how much Damon can sell his motorcycle for today.
Answer:
4,000 -x3
Step-by-step explanation:
x times 3 is equal to the decrease so therefore you take the decrease away form 4/oo
Answer:
3y-x=4,000
Step-by-step explanation:
James has $36.42 if he can only spend 1/6 of his money, how much money can he spend? 6 1
Answer:6.07
Step-by-step explanation:
Answer:
$6.07
Step-by-step explanation:
36 / 6 = 6
.42 / 6 = 7
6.07
bc we skip two decimal spaces to put it before the 0, there for the answer is $6.07!
Jayden's family watched 8 hours of TV last week. This week, they watchec
25% more than that. How many hours of TV did they watch this week? *
Answer:
I THINK that it is 10 hours
Step-by-step explanation:
(Sorry if I am wrong)
25% = 1/4 SO 8 divided by 4 = 2
Since they watched 25% MORE you add 2 to 8 and get 10
Use the drop down menus to complete the statement to match the information shown by the graph
Hasan travels
at the same speed asAnneliese because the
slopeof Hasan's graph is
equal tothat of Anneliese's graph.
The
slopeof the graph tells you the unit rate is in
meters per minutersI am even. The sum of my digits is sixteen. Who am I?
Answer:
2, 4, 6, 8, 10, 12, 14
Step-by-step explanation:
8+8=16
6+10=16
4+12=16
2+14=16
Find the perimeter of the figure if the following
is true:
a = x2
b = 4x + 8
c = 2x²
d = x
What is the slope and y-intercept of the linear equation y = 5x − 4?
m =
b =
Answer:
I got it right on edge 2020/2021
Step-by-step explanation:
m=5
b=-4
6 ≤ -3x + 12
can somone solve this for me *correctly* ill give u brainlest only if ur right
Answer:
x ≤ 2
Step-by-step explanation:
-3x+12≥6
-3x≥6
3x≤6
x ≤ 2
Answer:
x ≤ 2 is the correct answer!
Step-by-step explanation:
Hope this helps!
Each picture shows how a mapping, f, maps elements of a domain onto a range.
Which mapping, f, is NOT a function?
Domain
Range
Domain
Range
-6
2.
5
6 00
4
7
7
1
9
8
Domain
Range
Domain
Range
5
4
2
→8
7
2
Answer:
Top left
Step-by-step explanation:
If an x value (domain) leads to more than one y-value (range), it is not a function. In other words, if each input value leads to only one output value, it is a function. It's still a function if the y-value leads to multiple x-values.
The function h(x)=1/x^2+1 is the result of the composition f(g(x)). If g(x) = x^2+1,what is f(x)? A f(x)=1/square root x B f(x)=1/x C f(x)= 1/x+1 D f(x)=1/x^2+1
Answer:
Option B is correct
Step-by-step explanation:
Given: [tex]h(x)=\frac{1}{x^2+1}[/tex] is the result of the composition [tex]f(g(x))[/tex].
Also, [tex]g(x)=x^2+1[/tex]
To find: [tex]f(x)[/tex]
Solution:
Take [tex]f(x)=\frac{1}{x}[/tex]
Now check whether [tex]h(x)[/tex] is equal to [tex]f(g(x))[/tex] or not.
First find [tex]f(g(x))[/tex]
[tex]f(g(x))=f(x^2+1)=\frac{1}{x^2+1}[/tex]
Also, [tex]h(x)=\frac{1}{x^2+1}[/tex]
Therefore,
[tex]h(x)=f(g(x))[/tex]
So,
Option B is correct
Answer: B. f(x)=1/x
Step-by-step explanation:
Edge
Evaluate 12x−3y when x=−14 and y=3.
Answer:
-177
Step-by-step explanation:
12(-14) -3(3)
-168-9
-177
Answer:
-177
Step-by-step explanation:
Plug in -14 for x and 3 for y:
12(-14) - 3(3)
Note that when you multiply a positive and a negative number, your answer will be negative.
Multiply:
12 * -14 = -168
-3 * 3 = -9
Combine the terms:
-168 + (-9) = -168 - 9 = -177
-177 is your answer.
~
how many solutions does this equation have? 2x+7=2x
Answer:
no solution
Step-by-step explanation:
None of input and output table work for the rule.
Step-by-step explanation:
Start with the numbers given at A, B,C.
According to the rule you need to multiply by 666 to get the output.
A 000 * 666 = 0 (=NOT the output)
B 111 * 666 = 73926 (=NOT the output)
C 222 * 666 = 147852 (=NOT the output)
None of input and output table work for the rule.
Answer:
333 * 666
Step-by-step explanation:
56x + 40 = 48x + 104
Answer:
56x-48x=104-40
8x=24
X=3
Step-by-step explanation:
the answer is 8
]explanation subtract 56-48 and 104-40 you should get 8x=64
divide 8/8 and 64/8 and the answer is 8
LUCILLE'S PENCIL POUCH WOULD HOLD 3/8
OF THE 48 PENCILS THAT SHE PURCHASED AT
THE BEGINNING OF THE NEW SCHOOL YEAR. How many pencils will fit in her pouch
HOW MANY PENCILS WILL FIT IN HER POUCH?
Answer:
The pouch would be able to hold 12.8 pencils :)
Step-by-step explanation:
because 3/8 is 37.5 and if you do that divided by 48 and add a decimal infront of the eight you will get your answer
State whether the given pair of sets are equal, equivalent, both, or neither. {0,9}; {8, 1)
Answer:
Equivalent
Step-by-step explanation:
A set is a well defined collection of objects.
Two sets are said to be equal if they have the same elements.
Two sets are said to be equivalent if they have the same number of elements.
Given sets are [tex]\{0,9\}\,,\,\{8,1\}[/tex]
These sets are not equal as both the sets have different elements.
Order of both the sets is 2 (number of elements in both sets is 2)
So,
these two sets are equivalent.
How do I solve for X?
Answer
50
Step-by-step explanation:
60 is supplementary to 120 so 60+70=130
and a triangle adds up to 180 so 180-130 would be 50
One package of blackberries costs $3. How many packages of blackberries can you buy for $15?
Answer:
5 packages
Step-by-step explanation:
One package of blackberries cost $3
Let x represent the number of packages that will cost $15
1 = $3
x= $15
3x= 15
Divide both sides by the coefficient of x which is 3
3x= 15/3
x= 5
Hence 5 packages of blackberries will cost $15
please help
Which values of k would cause this system of equations to have no solution? Check all that apply.
6x + 4y = 14,
3x + 2y = k
-2
5
7
10
21
Answer:
a , b , d , e
Step-by-step explanation:
Sub to SZ Lexrn if that does not show search up shiyo on vr and first vid is them please help out , thx bye . If you do it cmt and ill make a post for yall for 100 points, so my friends won't amke fun of me
Answer:
If it counts as a question, lol sure, I'd love to help
If a fuel efficient car can go 210 miles
on 4 gallons of fuel, how far can it go
on 12 gallons?
Answer:
The distance covered by the car in 12 gallons of fuel is 630 miles.
Step-by-step explanation:
Distance covered by car in 4 gallons of fuel = 210 miles.
Let us use unitary method to find distance covered by car in 1 gallon of fuel.
Distance covered by car in 1 gallon of fuel = 210/4 miles.
Let us use unitary method to find distance covered by car in 12 gallon of fuel.
Distance covered by car in 12 gallons of fuel = (210/4)*12 = 630 miles.
In the figure, <6 and <2 are
Answer:
d
Step-by-step explanation:
consecutive angles aren't a thing and the others there would have to be an angle on the other side.
In the figure, <6 and <3 are
Answer:B
Step-by-step explanation
Which proportion can be used to show that the slope of JL is equal to the slope of MP? (sorry for the horrible quality)
Answer:
The proportion can be used to show that the slope of JL is equal to the slope of MP is [tex]\frac{0-4}{-4-(-7)}[/tex] = [tex]\frac{-4-8}{-1-(-10)}[/tex] ⇒ G
Step-by-step explanation:
The rule of the slope of a line is [tex]m=\frac{y2-y1}{x2-x1}[/tex] , where (x1, y1) and (x2, y2) are two points on the line
∵ The coordinates of the point J are (-7, 4)
∵ The coordinates of the point L are (-4, 0)
∴ x1 = -7 and y1 = 4
∴ x2 = -4 and y2 = 0
→ Substitute them in the rule above to find the slope of LJ
∴ [tex]m_{JL}=\frac{0-4}{-4-(-7)}[/tex]
∵ The coordinates of the point M are (-10, 8)
∵ The coordinates of the point P are (-1, -4)
∴ x1 = -10 and y1 = 8
∴ x2 = -1 and y2 = -4
→ Substitute them in the rule above to find the slope of MP
∴ [tex]m_{MP}=\frac{-4-8}{-1-(-10)}[/tex]
∵ The slope of JL = the slope of MP
∴ [tex]\frac{0-4}{-4-(-7)}[/tex] = [tex]\frac{-4-8}{-1-(-10)}[/tex]
The proportion can be used to show that the slope of JL is equal to the slope of MP is [tex]\frac{0-4}{-4-(-7)}[/tex] = [tex]\frac{-4-8}{-1-(-10)}[/tex]
Which sequence can be defined by the recursive formula f (1) = 4, f (n + 1) = f (n) – 1.25 for n ≥ 1?
1, –0.25, –1.5, –2.75, –4, . . .
1, 2.25, 3.5, 4.75, 6, . . .
4, 2.75, 1.5, 0.25, –1, . . .
4, 5.25, 6.5, 7.75, 8, . . .
Answer:
4, 2.75, 1.5, 0.25, –1, . . .
Step-by-step explanation:
edge2020