Volume of cuboid :
[tex]14 = x^2h\\\\h = \dfrac{14}{x^2}[/tex]
Surface area of this cuboid :
[tex]A = 2( x^2 + xh + xh )\\\\A = 2( x^2 + 2xh)[/tex]
Putting [tex]h = \dfrac{14}{x^2}[/tex] in above equation, we get :
[tex]A=2(x^2 + 2x\times \dfrac{14}{x^2})\\\\A = 2( x^2 + \dfrac{28}{x} )[/tex]
For minimum area, [tex]\dfrac{dA}{dx}=0[/tex] :
[tex]\dfrac{dA}{dx}=2( 2x -\dfrac{28}{x^2})\\\\\dfrac{dA}{dx }= 4(x - \dfrac{14}{x^2})\\\\x - \dfrac{14}{x^2}=0\\\\x=\sqrt[3] {14} = 2.41[/tex]
Therefore, value of x is 2.14 .
Hence, this is the required solution.
The dimension for which the volume is 14 and the surface area is as small as possible are 2.41 by 2.41 by 2.41
The formula for calculating the volume of the square box is expressed as:
[tex]V = x^2h[/tex]
Given that the volume of the box is 14, on substituting the value we will have:
[tex]14 =x^2h\\h=\frac{14}{x^2}[/tex]
The surface area of the box is expressed as:
[tex]S = 2(x^2+xh+xh)\\S=2(x^2+2xh)\\S = 2(x^2+2x(\frac{14}{x^2} ))\\S = 2(x^2+\frac{28}{x} )\\S=2x^2+\frac{56}{x}[/tex]
To get the surface area is as small as possible, then dS/dx = 0
[tex]\frac{dS}{dx} = 4x-\frac{56}{x^2}\\0 = 4x-\frac{56}{x^2}\\4x = \frac{56}{x^2}\\4x^3 = 56\\ x^3=14\\x=\sqrt[3]{14}\\x= 2.41[/tex]
Get the height of the box. Recall that;
[tex]h=\frac{14}{x^2}\\h=\frac{14}{(2.41)^2}\\h=\frac{14}{5.8081}\\h= 2.41[/tex]
Hence the dimension for which the volume is 14 and the surface area is as small as possible are 2.41 by 2.41 by 2.41
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Like a Quarter Pounder, I found her
She with a boy think it's Ned Flanders
She said that, really nice
With my ice, I drown her
I found her soul in the night
She's a Salamander
Cold blooded the type
passes through (6,-3) slope: -1/3 write in slope intercept form
Answer:
y = [tex]-\frac{1}{3}[/tex] x – 1 (see below)
Step-by-step explanation:
First, refer to the slope-intercept formula:
y = mx + b
The variable m represents the slope. The slope is the steepness of the line. The variable b represents the y-intercept. The y-intercept is the point where the line intersects the y-axis.
The slope is already given, so you can plug it in:
y = [tex]-\frac{1}{3}[/tex] x + b
To find the y-intercept, you will need a point on the line. Because there is already a point in which you are required to intersect, you might as well use that point. Also, keep in mind that it's the simplest way to get a line through that point.
First, plug in the point's values (6, –3) into your almost-complete formula:
y = [tex]-\frac{1}{3}[/tex] x + b
–3 = [tex]-\frac{1}{3}[/tex] (6) + b
–3 = –2 + b
–3 + 2 = b
b = –1
Now that you have your y-intercept, your equation is complete:
y = [tex]-\frac{1}{3}[/tex] x – 1
23 pointsPLEASE HELP QUICK Which of the following represents a function
7x=7x.This a illustration of which property
Answer:
i think it is identity property
Step-by-step explanation:
Answer: Reflexive Property of Equality
4. The time needed to complete the final exam in statistics at CAU is normally distributed with a mean of 90 minutes and a standard deviation of 10 minutes.What is the probability that the exam will be completed in one hour or less
Answer:
The value is [tex]P(X \le 60 ) = 0.00135[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 90 \ minutes[/tex]
The standard deviation is [tex]\sigma = 10[/tex]
Generally 1 hours = 60 minutes
Generally the probability that the exam will be completed in one hour or less is
[tex]P(X \le 60 ) = 1 - P(X > 60 )[/tex]
Here
[tex]P(X > 60 ) = P( \frac{ X - \mu }{ \sigma } > \frac{ 60 - 90 }{ 10 } )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
[tex]P(X > 60 ) = P( Z> -3 )[/tex]
From the z -distribution table the probability of ( Z> -3 )
[tex]P( Z> -3 ) = 0.99865[/tex]
[tex]P(X > 60 ) = 0.99865[/tex]
=> [tex]P(X \le 60 ) = 1 - 0.99865[/tex]
=> [tex]P(X \le 60 ) = 0.00135[/tex]
Please help please help
An artist uses 2 ounces of blue paint for every
7 ounces of yellow paint. The artist has 49
ounces of yellow paint. How many ounces of blue
paint will she need to add.
Answer:
14
Step-by-step explanation:
simplify (q+8)2 please help, thank you
q^2 +16q+64
All you have to do is substitute the exponent two.
Q by itself is q squared: q^2
Q times 8 is 8q, and because of exponent you have to double it, which gives you 16q.
And 8 times itself is 64.
Hope this helps
↓What is the least common denominator for the fractions 5/6 and 3/8?®
A. 14
B. 18
C. 24
D. 48
Please show how too! GIVING OUT BRAINLLEST!!!
Answer:
C
Step-by-step explanation:
the multiples of 6 are (6,12,18,24,30...)
and the multiples of 8 are (8,16,24,32,49...)
the common number here is 24
and it represents the the least therefore the Least Common denominator is 24
whats 10293 x 384? Its really hard!
Answer:
3,952,512
Step-by-step explanation:
What is m∠PTS? Enter your answer in the box. ° A horizontal line segment S R intersects with line segment P Q at their midpoint T. The upward-left and downward-right angles made by these lines are acute. The upward-left acute angle is labeled left square bracket 11 left parenthesis y minus 10 right parenthesis right square bracket degrees. The downward-right acute angle is labeled left parenthesis 4 y minus 5 right parenthesis degrees.
Answer:
m /_PTS = 55°
Step-by-step explanation:
Just took the quiz..
The measure of angle m∠PTS from the given figure is 55°.
From the given figure, the two angles are 11(y-10)° and (4y-5)°.
What is vertical angle theorem?Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.
Now, 11(y-10)° = (4y-5)°
⇒ 11y-110 = 4y-5
⇒ 11y-4y = -5+110
⇒ 7y = 105
⇒ y = 15
So, m∠PTS = 11(15-10)
= 55°
Therefore, the measure of angle m∠PTS from the given figure is 55°.
To learn more about the vertical angle theorem visit:
brainly.com/question/8119520.
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2. Simplify the expression: 5 x 6 + 6 = 6 - 12 x 2
c. 6
a. 4
b. 5
d. 7
Answer:
6
Step-by-step explanation:
5x6+6=6-12x2
collect like terms
5x6=6-6+12x2
5x6= +12x2
30=+24
collect like terms
30-24
=6
plz mark brainlest5-b<18 solve the question
Answer:
b>13
Step-by-step explanation:
Answer:
5-b<18 : [solution: b>-13]
[interval notation: (-13, \infinity/)
Step-by-step explanation:
I thought it was 120, guess not! I need help ASAP ughh
Answer: I dont know it but if you need a little help I never understood it but your supposed to break it into a triangle and a rectangle
Step-by-step explanation:
Answer:
feeling like
Step-by-step explanation:
what is th expression
-4^2+4*2
Answer:
−8
Step-by-step explanation:
=−16+(4)(2)
=−16+8
=−8
There are 360 calories in 9 bags of chips.How many calories are in 5 bags of those chips?
Answer:
200 calories
Step-by-step explanation:
360 ÷ 9 = 40
40 X 5 = 200
Answer:
there are 200 calories in 5 bags of chips
Step-by-step explanation:
divide 360÷9=40 and then multiply 40 times five equ3ald 200
If 3+2=5 then 5=3+2
is this an example of Symmetric property?
Answer:
d
Step-by-step explanation:
The ratio of people who have dogs to people who have cats is 4 to 2. If there are 24 people, how many have cats?
Answer:
8
Step-by-step explanation:
What number would you multiply the following equation by to eliminate the fractions?
1/2x+5/6−1/12=3/2
Answer:
With the largest denominator which is 12
Step-by-step explanation:
A cheetah's top speed is about 96 km/h.
A zebra's top speed is about 64 km/h.
If the animals both maintain their top speed for the entire race,
How much of a head start
would a zebra need to tie
a cheetah in a 5 km race?
Answer:
The zebra needs 1.66 Km of a head start to tie the cheetah in the race.
Step-by-step explanation:
The top speed of the cheetah is 96 Km/h.
If the cheetah ran for 5 Km, it would need
5 / 96 hours
The top speed of a zebra is 64 Km/h.
Running the same time, the zebra would travel a distance of:
5 / 96 * 64 = 3.33 Km
It would need an additional distance to tie the cheetah of 5 - 3.33 = 1.66 Km
The zebra needs 1.66 Km of a head start to tie the cheetah in the race.
A real-valued function f is said to be periodic with period T ≠ 0 if f(x + T) = f(x) for all x in the domain of f. If T is the smallest positive value for which f(x + T) = f(x) holds, then T is called the fundamental period of f. Determine the fundamental period T of the given function. f(x) = cos(2πx)
Answer:
f(x) = cos 2πx
Thus the fundamental period T = 1
Step-by-step explanation:
From the information given:
The periodic function f(x + T) = f(x) T ≠ 0 provided that T is the smallest positive value for which f(x + T) = f(x) holds, then T is called the fundamental period of f.
Now, for the given function f(x) = cos(2πx)
suppose T = 1/4 since T ≠ 0
Then:
f(x+ 1/4) = cos(2π (x + 1/4) )
f(x+ 1/4) = cos (2πx + π/2)
f(x+ 1/4) = -sin 2πx (Not satisfied)
suppose T = 1/2 since T ≠ 0
Then:
f(x+ 1/2) = cos(2π (x + 1/2) )
f(x+ 1/2) = cos (2πx + π)
f(x+ 1/2) = -cos 2πx (Not satisfied)
suppose T = 1 since T ≠ 0
Then:
f(x+ 1) = cos(2π (x + 1) )
f(x+ 1) = cos (2πx + 2π)
f(x+ 1) = cos 2πx
f(x+ 1) = f(x)
f(x) = cos 2πx
Therefore, the fundamental period T = 1 since f(x) = cos 2πx
russell did 36 push ups in 1 minute. will did 54 pushups in 1.5 minutes. did they do push ups ate the same rate.
Answer:
Yes
Step-by-step explanation:
If you convert these numbers to push ups per minute, It gives you the same amount per minute.
A water pump can produce 280 gallons in 24 hours
Answer: um is this suppose to be scientific notation if it is 11.6666667 but i dont know if this is a fact because it doesn't sound like a question
Step-by-step explanation:
Victor runs three laps around the track every five minutes to complete the table to show the relationship between the number of laps and time spent running. write your answers in the blank
Answer:
Step-by-step explanation:
Since, Victor takes 5 minutes to cover number of laps = 3
Relation between the time (t) and number of laps (l) covered shows a proportional relationship.
l ∝ t
l = kt
k = [tex]\frac{l}{t}[/tex]
where k = proportionality constant
For t = 5 minutes and l = 3 laps,
k = [tex]\frac{3}{5}[/tex] = 0.6
Therefore, equation will be,
l = 0.6t
For t = 1 min,
l = 0.6 laps
For l = [tex]1\frac{1}{5}[/tex] ≈ 1.2 laps
1.2 = 0.6t
t = 2
For t = 6 min,
l = 0.6(6)
l = 3.6 laps
Therefore, table will be,
Laps 0.6 [tex]1\frac{1}{5}[/tex] 3.6
Time (min) 1 2 6
Please help me idk what to do *GEOMETRY finding angles*
Answer:
69
Step-by-step explanation:
First, find the angle FCB by subtracting 70 and 41 from 180. You should get 69. Then, because it says AD paralell EG, you could use the transversal FC to locate some angles. Fortunately, GFC and FCB are opposite interior angles, meaning they are equal in angle measure.
why the factor 1.5 is broken into two numbers in the model.
A store had 776 more diet sodas than regular. The ratio of diet sodas to regular sodas was 8:4. How many total sodas were there?
Answer:
1114 sodas
Step-by-step explanation:
If you simplify 8:4, you will get 2:1. Given that information, since there are twice as many diet sodas as regular sodas, all you have to do is divide 776 by 2. You should get 338. All you have to do now is add 776 and 338 to get 1114.
The management of a forestry company estimates that acres of forest available for logging will increase at a rate given by R(t) = 56/root t + 7 for 0 leq t leq 20, where R(t) is the rate of new acreage becoming available in thousands of acres per year, t years after the current year. How many acres of forest, Q(t), will become available for logging over the first five years?
A. 46 thousand acres.
B. 148 thousand acres.
C. 296 thousand acres.
D. 92 thousand acres.
Answer:
Step-by-step explanation:
If the acres of forest available for logging will increase at a rate given by
R(t) = 56/√t + 7
In order to determine the acre of forest that become available after 5 years, we will substitute t = 5 into the formula.
R(5) = 56/√5 + 7
R(5) = 56/2.236 + 7
R(5) = 25.044 + 7
R(5) = 32.044
The amount that will be available over the first five years is 32 thousand acres
I need help !! I don’t understand it
Answer:
B
Step-by-step explanation:
subtract both sides by 2B and divide both sides by P to get h = S-2B / P
a popular roller coaster ride lasts 10 minutes. there are 20 people on average on the roller coaster during peak time. how many people are stepping into the roller coaster
Answer:
Flow rate is 2 people per minute
Step-by-step explanation:
The computation of the number of people stepping into the roller coaster is shown below:
Here we use the little law
As we know that
Inventory or number of jobs = throughput or flow rate × flow time
20 = throughput or flow rate × 10
Therefore
Flow rate is 2 people per minute
We simply applied the above formula