Answer:
271
Step-by-step explanation:
An open box with a square base is to have a volume of 18 ft^3.
(a) Find a function that models the surface area A of the box in terms of the length of one side of the base x.
(b) Find the box dimensions that minimize the amount of material used. (Round your answers to two decimal places.)
Answer:
2.29 ft of side length and 1.14 height
Step-by-step explanation:
a) Volume V = x2h, where x is side of square base and h is hite.
Then surface area S = x2 + 4xh because box is open.
b) From V = x2h = 6 we have h = 6/x2.
Substitude in formula for surface area: S = x2 + 4x·6/x2, S = x2 + 24/x.
We get S as function of one variable x. To get minimum we have to find derivative S' = 2x - 24/x2 = 0, from here 2x3 - 24 = 0, x3 = 12, x = (12)1/3 ≅ 2.29 ft.
Then h = 6/(12)2/3 = (12)1/3/2 ≅ 1.14 ft.
To prove that we have minimum let get second derivative: S'' = 2 + 48/x3, S''(121/3) = 2 + 48/12 = 6 > 0.
And because by second derivative test we have minimum: Smin = (12)2/3 + 4(12)1/3(12)1/3/2 = 3(12)2/3 ≅ 15.72 ft2
The box dimensions that minimize the amount of material used are; side length of base = 3.30 ft and height = 1.65 ft
How to minimize area?a) We know that a box has length, width and height and so volume of a box is;
V = L × W × H
Now, we are told the base of the box is square and if we label it x, then we have to function that models the volume as;
V = x²h
where x is side of square base and h is height.
Thus surface area function is;
S = x² + 4xh
b) We are told that the volume is 18 ft³ and so;
x²h = 18
Thus;
h = 18/x².
Put 18/x² for h in the surface area function to get: S = x² + 4x(18/x²)
S = x² + 72/x.
To get minimum, we have to find derivative of S. Thus;
S' = 2x - 72/x² = 0,
Thus;
2x³ = 72
x³ = 72/2
x³ = 36
x = 3.3 ft
Thus;
h = 18/3.3²
h = 1.65 ft
Read more about minimizing area at; https://brainly.com/question/17219343
4. Write an equation in slope-intercept form for the following linear relationship.
х
y
1
12
2
15
3
18
4
21
PLSSSS HELP I NEED THIS BY TOMORROW OR THE DAY AFTER PLS
Answer:
equation: y = 3x + 9
Step-by-step explanation:
first take two coordinates: ( 1 , 12 ) , ( 2 , 15 )
find slope: [tex]\frac{y2-y1}{x2-x1}[/tex]
: [tex]\frac{15-12}{2-1}[/tex]
: 3 ...........this is our slope, m
use the formula to solve or equation: y - y1 = m( x - x1 )
y - 12 = 3 ( x - 1 )
y = 3x - 3 + 12
y = 3x + 9
Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: $5,000, annual interest: 8%, interest periods: 2, number of years: 19
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$5000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &19 \end{cases} \\\\\\ A=5000\left(1+\frac{0.08}{2}\right)^{2\cdot 19}\implies A\approx 22194.067 \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$5000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &19 \end{cases} \\\\\\ A=5000\left(1+\frac{0.08}{1}\right)^{1\cdot 19}\implies A\approx 21578.505[/tex]
It takes light from the Sun 3.25 minutes to reach Mercury. How far away is the planet from the Sun (in km)? The speed of light, c, is 3 ✕ 105 km/s.
Answer:
66528 km
Step-by-step explanation:
1 sec = 3*105
60 sec = 1 min = 3*60*105 km
3.25 min-?
3 .25×60×105
The distance of Mercury from sun will be 585,000,000 km.
It is given that it takes 3.25 minutes to light to reach from sun to mercury.
If speed of light is 3 × [tex]10^{5}[/tex] km/sec , then calculate the distance from sun to mercury.
What will be the value of (2 × [tex]x^{2}[/tex] ) ÷ 2 ?
The value will be [tex]x^{2}[/tex] .
Distance travelled by light in 1 seconds = 3 × [tex]10^{5}[/tex] km
∵ 1 minute = 60 seconds
⇒ Distance travelled by light in 1 minute will be ;
= 60 × 3 × [tex]10^{5}[/tex] km
⇒ Distance travelled by light in 3.25 minutes will be ;
= 3.25 × 60 × 3 × [tex]10^{5}[/tex] km
= 585,000,000 km
Thus , distance of Mercury from sun will be 585,000,000 km.
To learn more about unitary methods click here ;
https://brainly.com/question/1955459
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What is the median of this group of numbers?
25, 35, 35, 40, 41, 45, 100
o
39.5
o
40
o
40.5
o
41
Pls tell me the answer
Answer:
40
Step-by-step explanation:
40 is in the middle there are three numbers to either side
Answer:
40 because it is in the middle
Find the area of the triangle, attached picture below
Answer:
Step-by-step explanation:
area of the triangle=1/2×19×6=57 cm²
How many pieces of ribbon each 6cm long can be cut out from a roll of ribbon 24 cm long
Answer:
=4
Step-by-step explanation:
24/6
=4
so we can cut 4 pieces of each 6cm long from a roll of 24cm
mark me brainliest
what is the midpoint of a segment with These endpoints (-6,-9) and (16,5)
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{16}~,~\stackrel{y_2}{5}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 16 -6}{2}~~~ ,~~~ \cfrac{ 5 -9}{2} \right)\implies \left( \cfrac{10}{2}~~,~~\cfrac{-4}{2} \right)\implies (5~~,~-2)[/tex]
My dad paid 72% of the cost of my shoes and I paid the rest. If my dad paid $54.18, what was the total cost of my shoes?
Answer:
$93.19
Step-by-step explanation:
first we have to identify 72% as a decimal
72/100=0.72
then we have to multiply 0.72 by $54.18.
0.72 x $54.18 = $39.01
Your dad paid $39.01, but now we have to identify how much is the total.
$54.18 + $39.01 = $93.19
(Hope I could help!)
Answer:
$93.19
Step-by-step explanation:
54.18 x .72 = 39.0096 [Round] 39.01
54.18+39.01=93.19
Total cost of your shoes is $93.19
Help me plz AND PLZ NO LINKS
Answer:
5. 4.2
6. 100.7
7. 14.8
8. 0.1
9. 24.192
10. 0.0996
11. 213
12. 0.156
Step-by-step explanation:
The accountant charged $35 for the first hour of work and $23 for each hour after that. He earned a total of $127. How many hours did he work
Answer:
5 hours
Step-by-step explanation:
Subtract the amount the accountant charged for the 1st hour worked from the total earned:
127 - 35 = 92
Now divide 92 by 23 to find the number of hours he worked at the rate of $23 per hour:
92 ÷ 23 = 4 hours
Therefore, the account worked the 1st hour plus 4 more hours = 5 hours in total
what is the first derivative of:
sin(x)*cos(x)/(x^2-x)
Answer:
that's the answer
Step-by-step explanation:
for the next time, dont post you derivative questions on brainly, there is a lot of websites that can solve this for you with steps.
Fifteen ounces of paprika cost $1.87. Find the cost of 45 ounces.
Answer:
5.61
Step-by-step explanation:
Answer:
$5.61
Step-by-step explanation:
(1.87/15) x 45
=5.61
Thomas has a collection of 25 coins; some are dimes and some are quarters. If
the total value of all the coins is $5.05, how many kinds of coins are there
Answer:
17 quarters and 8 dimes
Step-by-step explanation:
10dimes +25*(25-dimes)=505
NEED THIS ASAP NO WORK SHOWN NEEDED
Answer:
35 degrees
Step-by-step explanation:
180 - 110 = 70 (TUW and UWT together)
70 / 2 = 35 (UWT)
Since the other part is congruent, we can assume it is also 35.
Answer:
m∠UWV = 35°
Step-by-step explanation:
Angle V is similar to Angle T
so angle V is 110°
---------------------------------------------------------------------------------------------
The triangle UVW is a isosceles triangle with two similar sides.
m∠UWV = ( 180° - 110° ) ÷ 2
= 35°
How can 1% of 800 be used to determine 28% of 800?
Enter your answers in the boxes to correctly complete the statement.
1% of 800 is
so 28% of 800 is
Answer:
3600
Step-by-step explanation:
Answer:
1% of 800 is 8
so 28% of 800 is 224
Step-by-step explanation:
Brainliest Please
please someone help me solve this question
Answer:
D. right 4, down 8
Step-by-step explanation:
The usual transformations applied to functions are ...
f(x) ⇒ f(x -h) . . . . translation right h units
f(x) ⇒ f(x) +k . . . . translation up k units
f(x) ⇒ k·f(x) . . . . . vertical scaling by a factor of k; reflection over x-axis when k < 0
f(x) ⇒ f(x/k) . . . . . horizontal scaling by a factor of k; reflection over y-axis when k < 0
In the above, "scaling" will be expansion when |k| > 1, compression when |k| < 1.
__
Your transformation is ...
x^2 ⇒ (x -4)^2 -8
f(x) ⇒ f(x -4) -8
This is translation with h=4 and k=-8. That is, it is translation right 4 units and down 8 units.
_____
Additional comment
Like much of math, it is all about matching patterns.
are 3/7and 10/21 proportionate
Answer:
NOT proportional.
Step-by-step explanation:
When both fractions have the same denominator, their numerators are different. Therefore, they are NOT proportional.
Answer:
[tex] \frac{3}{7} = \frac{10}{21} [/tex]
[tex]3 \times 21 = 7 \times 10[/tex]
[tex]63 = 70[/tex]
No, 3/7 and 10/21 are jot proportionate
Basketballs used in professional games must have a circumference of 29 inches.
What is the surface area of a basketball used in a professional game?
Answer: 841 / pi inches^2
Step-by-step explanation:
circumference of circle on the sphere = 2*pi*r
surface area of sphere = 4 * pi * r^2
29 inches = 2 * pi * r
r = 29 / (2 * pi) inches
surface area of sphere = 4 * pi * r^2
= (2 * pi * r) * 2 * r
= (29 inches) * 2 * (29 / (2 * pi) inches)
= (29 inches) * (29 / (pi) inches)
= 841 / pi
exact answer is 841 / pi inches^2
which is approximately 267.7 inches^2
4) Describe the different types of Semantics, when and how are they applied, what are the advantages or disadvantages to each type.
Answer:
Operational semantics are classified in two categories: structural operational semantics (or small-step semantics) formally describe how the individual steps of a computation take place in a computer-based system; by opposition natural semantics (or big-step semantics)
Determine whether each point lies on the graph of the equation.
y = |x − 2| + 3
(a)
(3, 4)
Yes, the point is on the graph.
No, the point is not on the graph.
(b)
(−2, 0)
Yes, the point is on the graph.
No, the point is not on the graph.
solve the problem and find the answer
Answer:
Step-by-step explanation:
im in elementary so i do not know
A chemist is using 344 milliliters of a solution of acid and water. If 17.2% of the solution is acid, how many milliliters of acid are there? Round your answer to the nearest tenth.
Espa Maya's chocolate bar is 29% cocoa. If the weight of the chocolate bar is 67 grams, how many grams of cocoa does it contain? Round your answer to the nearest tenth.
Answer:
19.4 g (rounded to the nearest tenth)
Step-by-step explanation:
Convert the percentage to a decimal by dividing by 100:
29% = 29/100 = 0.29
To find 29% of 67, multiply the decimal percentage by the total amount:
0.29 x 67 = 19.43
= 19.4 g (rounded to the nearest tenth)
At a college 60% of the undergraduates are female. If 1680 women attend the college, how many total undergraduates attend the college?
Answer:
1008
Step-by-step explanation:
A cell phone has 30% of its charge left. Which number line shows a point that represents 30%?
A.
B.
C.
D.
Answer:
C
(second to bottom)
since it has 3 out of 10 ticks marked
and 30% = 3/10
With counting how much do you have of squares?
Answer:
32 × 3
96 squares..........................
which linear equation best represents the data given in the table?
answers-
y=4x-3
y=3x+4
y=3x-4
y=4x+3
Can someone help me with a basic geometry question :c
A computer repair shop buys fan cables from two suppliers. A west coast supplier sells the cables for $4.39 each and charges $38 to ship the order. An east coast supplier sells the cables for $3.14 each and charges $63 for shipping. How many cables (
c
) must the repair shop purchase so the total cost from each supplier is the same?
1.
Step 2: What does the variable represent in this problem?
The variable
c
represents the number of fan cables purchased.
The variable
c
represents the cost for each fan cable.
The variable
c
represents the cost for all fan cables shipped.
The variable
c
represents the total cost to ship the fan cables ordered.
Answer:
20
Step-by-step explanation:
Let x be the number of cables.
Let y be the total cost.
Therefore,
West coast: y = 4.39x + 38
East coast: y = 3.14x + 63
if the total cost is the same, equate the equations and solve for x:
y = y
4.39x + 38 = 3.14x + 63
4.39x - 3.14x = 63 - 38
1.25x = 25
x = 25 ÷ 1.25 = 20
Therefore, the repair shop should purchase 20 cables for the total cost from each supplier to be the same.
