Answer:
2.47 feet
Step-by-step explanation:
Let l, b, and h be the length, width, and height of the box.
As the length is twice the width, so l=2b ...(i)
The volume of the box is 20 cubic feet, so
lbh=20
(2b)bh=20 [by using (i)]
[tex]h=\frac {20}{2b^2} \\\\h= \frac {10}{b^2} ...(ii)[/tex]
The material required= surface area, S, of the open box
S= lb+2bh+2lh
By using equation (i) and (ii), we have
[tex]S= 2b(b)+2b\times \frac {10}{b^2} +2(2b)\times \frac {10}{b^2}[/tex]
[tex]S= 2b^2+ \frac {20}{b} + \frac {40}{b} \\\\S= 2b^2+ \frac {60}{b} \cdots(i)[/tex]
Now, we have the surface area, S, as the function of width, b.
Differentiate S with respect to b then equate it to zero to get the extremum values, as
[tex]\frac {dS}{db}=0 \\\\\frac {d}{db}(2b^2 +60/b)=0 \\\\4b-\frac{-60}{b^2}=0 \\\\4b=\frac{60}{b^2} \\\\b^3=\frac{60}{4} \\\\b=(15)^{1/3}[/tex]
b=2.47 feet.
Now, by second differentiation, checking the nature of extremum value.
[tex]\frac {d^2S}{db^2}=4+\frac {120}{b^3}[/tex]
For [tex]b>0, \frac {d^2S}{db^2} >0[/tex]
So, the width of the box, b=2.47, is the minima for the area, S(b).
Hence, the width of the box that can be produced using the minimum amount of material is 2.47 feet.
Which equations represent functions?
2x + 3y = 10
4x = 16
2x − 3 = 14
3y = 18
14.6 = 2x
Answer:
e represent a fraction happy to help
dhsshdhjdjdjdjdndjcixhxbxnxxxi
Answer:
(3x + 4)²Step-by-step explanation:
1) Your number = x
2) Multiply it by 3 = 3x
3) Add 4 = 3x + 4
4) Square the result (quantity square) = (3x + 4)²
I hope this helps! I would really appreciate it if you would please mark me brainliest! Have a blessed day!
Ella invested $2,700 in an account paying an interest rate of 5.4% compounded
monthly. Assuming no deposits or withdrawals are made, how long would it take, to
the nearest year, for the value of the account to reach $4,020?
Answer:
7.4 years
Step-by-step explanation:
This is a compound interest question, from the question, we know we are to find the time.
The formula for Time in compound interest =
t = ln(A/P) / n[ln(1 + r/n)]
Where:
A = Amount after time t = $4,020
P = Principle = Initial amount invested = $2700
r = Interest rate = 5.4% = 0.054
t = ??
n = compounding frequency = monthly = 12
t = ln(A/P) / n[ln(1 + r/n)]
t = In(4020/2700)/12[In(1 + 0.054/12)]
t = 7.388 years
Approximately = 7.4 years
Find the value of each variable
Answer:
x = 17[tex]\sqrt{3}[/tex]
y = 17
Step-by-step explanation:
You would need to use the following trigonometric functions cosine and sin. Sin is used for the y-variable to get the answer and cosine is used for the x-variable to get the answer. For this case, you would need to do 34 sin 30 for y and 34 cos 30 for x. You should get 17 for y and 17 root 3 for x when you put it in the calculator.
The value of each variable are,
x = 17√3
y = 17
We have to give that,
A triangle is shown in the image.
Now, from the triangle we get;
cos 30° = x/34
Solve for x,
√3/2 = x/34
Cross multiply,
34√3 = 2 × x
2x = 34√3
x = 17√3
And, We get;
⇒ sin 30° = y/34
⇒ 1/2 = y/34
Cross multiply,
⇒ 34 = 2y
⇒ y = 17
Hence, the value of each variable is,
x = 17√3
y = 17
To learn more about the triangle visit;
brainly.com/question/1058720
#SPJ6
Jazmine can run 4 5/6 miles in 2/3 of an hour. How many miles can she run in 1 hour?
Answer: she can run [tex]6\dfrac54[/tex] mile sin 1 hour.
Step-by-step explanation:
Given : Distance run by Jasmine in [tex]\dfrac23[/tex] of an hour = [tex]4\dfrac56\text{ miles}=\dfrac{24+5}{6}\text{ miles}[/tex]
[tex]=\dfrac{29}{6}[/tex] miles
Distance run by Jasmine in 1 hour = [tex]\dfrac{29}{6}\times\dfrac{3}{2}=\dfrac{29}{4}[/tex] miles.
[tex]=6\dfrac{5}{4}[/tex] miles.
Hence, she can run [tex]6\dfrac54[/tex] mile sin 1 hour.
Please help I’m in finals and I have to complete all my missing assignments
Answer:
Between 3 and 3.5
Step-by-step explanation:
more than 9 and less than 16. 9 is closer to 10 making it c.
The equation modeling the population growth of a small town is P(t)=30000(1.02)^t, where P represents the population, and t represents the years from now. What is the approximate population change that occurs between 2 years from now and 10 years from now.
Answer:
5358
Step-by-step explanation:
The equation modeling the population growth of a small town is given as:
P(t)=30000(1.02)^t
When t = 2
P(2) = 30000(1.02)^2
P(2) = 31212
When t = 10
P(10) = 30000(1.02)^10
P(10) = 36569.8326
The approximate population change that occurs between 2 years from now and 10 years from now is calculated as:
= P(10) - P(2)
= 36569.83259984272 − 31212
= 5357.8325998
Approximately ≈ 5358
PLEASEEEE please please help me with thissss ill luv u forever!!
Answer:
Hello,I don't think anyone can help you as your question is not there only the subquestions are. Kindly post the main question for assistance.
Regards
find the value of X in each of the following X/3-2=6
X/5+1 =5
please help me
Answer:
a) x = 24
b) x = 20
Step-by-step explanation:
a) x÷3 - 2 = 6
+2 +2
x÷3 = 8
×3 ×3
8 × 3 = 24
x = 24
b) x÷5 + 1 = 5
-1 -1
x÷5 = 4
×5 ×5
4 × 5 = 20
x = 24
A piano teacher gives lessons that are each Three-fourths hour long. How many piano lessons can the teacher fit into a 12-hour work day? Assume no breaks are taken in the 12 hour period.
Answer:
16 lessons
Step-by-step explanation:
12 divided by .75 = 16
Answer:
16
Step-by-step explanation:
How are the areas of triangles and parallelograms in the coordinate
plane calculated?
Answer:
___________________________________________________________
By finding the product of a point's x coordinate times the next point's y coordinate, then subtracting the y coordinate of the first point times the x coordinate of the second coordinate and dividing by two, you will find the area of the polygon.
___________________________________________________________
What value of x makes the equation true?
-7x-5=-10x-26
Please show work
Answer:
-7
Step-by-step explanation:
-7x-5= -10x-26
-7x= -10x-21
3x= -21
x=-7
What is the distance between -21 and 6 on a number line, in units?
Answer:
27 units
Step-by-step explanation: 21 +6 = 27 they are 27 units apart
What is a correct name for the angle shown?
Answer:
SRT
Step-by-step explanation:
Answer:
obtuse angle
Step-by-step explanation:
a L is a right angle, a right angle is 90 degrees. if the angle is more then 90 degrees and looks like its being stretched it is obtuse. and if it is smaller then 90% and looks like it is being squashed it an acute angle.
Ruffles Boutique brought a leather jacket from a wholesale distributor for $140. The story markup on this item is 220%. What is the selling price for the jacket?
Sell price = purchase price x Mark up
Sell price = 140 x 220%
Sell price = 140 x 2.2 = 308
Sell price = $308
I need help ASAPPPPPO
Answer:
3x²y==
Step-by-step explanation:
Multiple the number
help me find the answer lol
Answer:
First/Top graph.
Step-by-step explanation:
First, we need to solve the inequality for n:
-6n + 5 < 11 (Given)
-6n < 6 (Subtracted 5 on both sides)
n > -1 (Divided -6 on both sides)
NOTE: Whenever you multiply or divide by a negative number when dealing with inequalities, the sign switches.
Now that we know that n > -1, we need to look for a graph that has an open circle on the point -1 and goes in the right direction.
Therefore, the first graph is the correct answer.
Ernesto measured the height of a door frame as 6.35 feet, but the actual height was 6.5 feet. What is the percentage of error in Ernesto's measurement? (5 points)
a
2.31%
b
1.98%
c
2.36%
d
2.02%
Answer:
A or B
Step-by-step explanation:
sry if im wrong-happy new year!
Translate the sentence into an equation.
Eight more than the quotient of a number and 3 is 5.
This would help a lot
Simplify the midpoint of PR.
Q (2b, 2c)
R (2a+2b, 2c)
Pl(0,0)
S (2a, 0)
Answer:
The midpoint of PR is;
(a + b, c)
Step-by-step explanation:
Here, we want to get the coordinates of the midpoint of PR
To get these, we make use of the midpoint formula
Mathematically, that will be;
(x,y) = (x1+y1)/2, (x2+y2)/2
(x1,y1) = (0,0)
(x2,y2) = (2a+2b, 2c)
The midpoint is thus;
(2a+2b)/2 , 2c/2
= (a + b, c )
Answer:
(a+b, c)
Step-by-step explanation:
Smile because it's correct for Acellus
Help... with number 15 plz
Answer:
P
Step-by-step explanation:
p is the ans
The measure of one angle of a triangle is 105°. What do you know about the measures of the other two angles? Check all
that apply.
O Both angles are acute.
O The sum of the measures of the two angles is 75°.
O The sum of the measures of the two angles is 155°.
OOne of the angles is a right angle.
O The measure of neither angle is more than 75°.
O The measures of the other angles must be 105° too.
D The measure of one of the other angles equals 75°.
O The measure of one of the other angles must be 45°.
Save and Exit
Submnit
Answer:
both angles are acute
Step-by-step explanation:
What is x if: x ÷ 0.6 = 1 2/3
Answer:
x = 1
Step-by-step explanation:
Rewrite the equation to get x/0.6 = 5/3, since the division sign is the same thing as a slash sign and that 1 2/3 is equivalent to 5/3. Multiply 0.6 on both sides to get 1 as your final answer.
Answer:
1
Step-by-step explanation:
0.6 times 1 2/3 is 1. in that case, 1 divided by 0.6 is 1.66666666667, also known as 1 2/3 making x = 1
Tom paid $2.50 for two pounds of boiled peanuts. Rose paid $9.50 for 8 pounds of boiled peanuts. Is the relationship between these two purchases proportional?
Hi! help is greatly appreciated!
Find the value of x.
A. 6
B. 2
C. 4
D. 3
Answer:
answer is 3
because first we add 4+2=6
the sum of the line is 6 then we will got
x+3=6
x=6-3
x=3
Step-by-step explanation:
hope my answer is helpful to you
plz mark me as brainlist
Helplsieedgoodgradeplspls
Answer:
He would need to walk the dog 6 more times because 8 times 11 is 88 and if he has already walked the dog 5 times you would subtract that from 11 to get 6. So the answer would be 6
Step-by-step explanation:
8·11= 88
11-5= 6
Corrado has 27 books in his room that he has already read. He wants to give them away to his 3 younger siblings. How many books will each of Corrado's siblings receive?
If b represents the number of books each sibling receives, which equation could be used to solve the problem?
Answer:
3b = 27
Step-by-step explanation:
They will each receive 9 books
Elwood invested $5,000 in a money market account and has been tracking its progress. He found that after 3 years, the account held $7,100 and after 8 years, the account held $10,350. Use this information to complete the statements. Over the first 3 years, the value of the account increased at ___ over the last 5 years. Over the entire 8 years, the value of the account increased at an average rate of approximately $___ annually.
Answer:
Given:
Principal= $5,000
After 3 years, Amount= $7,100
After 8 years, Amount= $10,350
Step-by-step explanation:
Interest after 3 years= $7,100- $5,000
=$2,100
Interest in last 5 years= $10,350- $7,100
=$ 3,250
Difference between first 3 years and last 5 years= $3,250- $2,100
=$1,150
Amount= Principal*[tex](1+r/100)^{t}[/tex]
10,350=5000[tex](1+r/100)^{8}[/tex]
[tex]\frac{10350}{5000}[/tex]=[tex](1+r/100)^{8}[/tex]
2.07=[tex](1+r/100)^{8}[/tex]
[tex]2.07^{1/8}[/tex]=1+[tex]\frac{r}{100}[/tex]
1.095-1=[tex]\frac{r}{100}[/tex]
0.095*100=r
r=9.5%
Average rate=[tex]\frac{5000*9.5*1}{100}[/tex]
=$475
Answer:
drop down 1 a slower rate per year
drop down 2 670
Step-by-step explanation:
as in three years you get $7100
you take that and subtract it by your starting amount (5000)
7100-5000= 2100
then divide 2100 by the number of years (3)
to get your annual rate of 700$
then you take the 8 year total and subtract it from your 3 year total
10350-7100= 3250
Then divide that by 5 because that how many years it has been
to get the annual rate of 650
making the 5 year rate slower.
The to find the average rate over all 8 year you take 10350 and subtract it from your starting number 5000
10350-5000= 5350
then take 5350 and divide it by the number of years (8)
you then get you average rate of 668.75
668.75=670
Hope this helps!
Mr. Thompson drew a rectangle on the chalkboard with a length to width ratio of 5 to 2. He asked students to draw a rectangle with the same ratio of length to width in their journals. Audrey plans to draw a rectangle with a width of 6 centimeters. What length should Audrey's rectangle have?
Answer:
15 centimeters
Step-by-step explanation:
Ratio of Mr. Thompson rectangle = length : width
= 5 : 2
Audrey plans to draw a rectangle with a width of 6 centimeters.
Ratio of Audrey rectangle = length : width
= x centimeters : 6 centimeters
Equate the two ratios to find the value of x
5 : 2 = x : 6
Cross product
5 * 6 = 2 * x
30 = 2x
Divide both sides by 2
x = 30 / 2
= 15
x = 15 centimeters
Audrey's rectangle should have a length of 15 centimeters
Answer:
15
Step-by-step explanation:
The product of a negative number and zero is?
Answer:
0
Step-by-step explanation:
Eg:
-5*0=0
-1*0=0