We want to find the rate of change of the surface for a cube of increasing volume.
When the side length is equal to 20 inches, the surface area is increasing at a rate of 439.29 in^2 per minute.
We know that for a cube of side length S, the volume is:
V = S^3
And the surface area is:
A = 6*S^2
Here we know that the volume increases at a rate of 12in^3/min.
Because the volume depends on the side length cubed, we can say that the side length increases at a rate of:
∛(12in^3)/min = 2.29 in/min
Then, as a function of time t in minutes, we can write the side length as:
S(t) = (2.29 in/min)*t
Then the surface area equation is:
A(t) = 6*((2.29 in/min)*t)*((2.29 in/min)*t)
A(t) = (31.46 in^2/min^2)*t^2
The rate of change is given by direct differentiation, we get:
A'(t) = 2*(31.46 in^2/min^2)*t
Now we need to evaluate this in the value of t such that the side length is equal to 20 in:
S(t) = 20in = (2.29 in/min)*t
(20in)/(2.29 in/min) = t = 8.73 min
Then we will get:
A'(8.73min) = 2*(31.46 in^2/min^2)*8.73min = 439.29 in^2/min
This means that when the side length is equal to 20 inches, the surface area is increasing at a rate of 439.29 in^2 per minute.
If you want to learn more, you can read:
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add 3 3/5 + 6 3/10 tyyyyy
[tex] = 9 \frac{9}{10} \\ \\ in \: \: alternate \: \: forms \\ \\ \frac{99}{10} \: \: \: and \: \: 9.9 \\ \\ hope \: it \: \: helps[/tex]
see the attachment!m
+ 4 = 7
Step One:
Step Two:
Step Three:
Step Four:
ma9
m/3+4+4+7+4
m/3-7
m=21
m/3+4-47-4
m/3*3+4=743
m/3-3
ma17
m/3+4-3=7-3
m/3*3=3*3
m/3+7=4
m=3
m/3+8=11
m/314-4=7
m+4=21
Answer:
9
Step-by-step explanation:
1. m/3+4-4=7-4
2. m/3=3
3. m/3*3 = 3*3
4. m=9
Answer:
m=9
Step-by-step explanation:
m/3+4-4=7-4
m/3=3
m/3*3=3*3
m=9
5/6 x 15 in simplest form
Answer:
25/2
Step-by-step explanation:
5/6 x 15=12.5
12.5 in simplest form is 25/2
Evaluate 8r-rs when r=6 and s=5 ?
100 Points. Help solve.
Answer:
Step-by-step explanation:
[tex]\frac{8}{x} =cos 60\\\frac{8}{x} =\frac{1}{2} \\x=8 \times2=16\\\frac{y}{x} =sin60\\\frac{y}{16} =\frac{1}{\sqrt{2}} \\y=\frac{16}{\sqrt{2}} \\y=\frac{16}{\sqrt{2}} \times\frac{\sqrt{2}}{\sqrt{2}} \\y=\frac{16\sqrt{2}}{2} =8\sqrt{2}[/tex]
Answer:
the second option/x = 4, y = 8√3
Step-by-step explanation:
out of the tree options, the second one makes sense
What is the one thing?
Answer:
.. what ? can you be more specific & show a pic or sum ?
Please help with question got stuck
Answer:
y=4x
Step-by-step explanation:
Evaluate 5 - (4 + 2)^2. Show the steps
Answer:
-31
Step-by-step explanation:
1. Simplify 4+2 to 6
5-6^2
2.Simplify 6^2 to 36
5-36
3.Simplify
-31
Hope this helps :)
5 - (4+2)^2
add what is inside of the parentheses
4 + 2 = 6
then do the exponent, which would be 6 times itself
5 - 6^2
6(6)
then subtract 36 from 5, which gives the answer of -31.
5 - 36 = -31
the answer is -31, hope this helps!
A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean = 87 and standard deviation = 25. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.)
(a) x is more than 60
(b) x is less than 110
(c) x is between 60 and 110
(d) x is greater than 125 (borderline diabetes starts at 125)
Using the normal distribution, it is found that:
a) 0.8599 = 85.99% probability that x is more than 60.
b) 0.1788 = 17.88% probability that x is less than 110.
c) 0.6811 = 68.11% probability that x is between 60 and 110.
d) 0.0643 = 6.43% probability that x is greater than 125.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
The mean is of 87, thus [tex]\mu = 87[/tex].The standard deviation is of 25, thus [tex]\sigma = 25[/tex].Item a:
This probability is 1 subtracted by the p-value of Z when X = 60, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{60 - 87}{25}[/tex]
[tex]Z = -1.08[/tex]
[tex]Z = -1.08[/tex] has a p-value of 0.1401.
1 - 0.1401 = 0.8599
0.8599 = 85.99% probability that x is more than 60.
Item b:
This probability is the p-value of Z when X = 110, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{110 - 87}{25}[/tex]
[tex]Z = 0.92[/tex]
[tex]Z = 0.92[/tex] has a p-value of 0.8212.
1 - 0.8212 = 0.1788.
0.1788 = 17.88% probability that x is less than 110.
Item c:
This probability is the p-value of Z when X = 110 subtracted by the p-value of Z when X = 60.
From the previous two items, 0.8212 - 0.1401 = 0.6811.
0.6811 = 68.11% probability that x is between 60 and 110.
Item d:
This probability is 1 subtracted by the p-value of Z when X = 125, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{125 - 87}{25}[/tex]
[tex]Z = 1.52[/tex]
[tex]Z = 1.52[/tex] has a p-value of 0.9357.
1 - 0.9357 = 0.0643.
0.0643 = 6.43% probability that x is greater than 125.
A similar problem is given at https://brainly.com/question/24863330
Write a compound inequality for the graph shown below
Use x for your variable
State the domain and range and determine if the relation is a function
Answer:
DOMAIN = {3, 4, 5, 6, 7}, RANGE = {2, 1, 9, 12}, the relation is a function.
Step-by-step explanation:
The domain of the relation is the set of points in A which have a tail connected to it. That is {3, 4, 5, 6, 7}.
The range of the relation is the set of points in B which have a tip connected to it. That is {2, 1, 9, 12}.
Since each element of the domain of the relation is associated with exactly one element of the range, the relation is a function.
PLS HELppppppppppppppp
Answer: B
Step-by-step explanation:
Oki so I know this becaue I study to much and because if there was an answer saying this : y=6x+3 it would be wrong because it is adding to the constant
So y=6x is proportinal because it is allways constant. I forgot this was an example sorry.
Answer:
B. since x can equal anything, but nine is in front therefore, it can be what you want, so it is B.
i rlly need help help me out pls
Answer:
San francisco
Step-by-step explanation:
once you divide the distance by time then multiply the answer by the longest amount of time (aka 4)
San francisco = 2556
Minot = 1826
Phoenix = 2252
Solve for y in the equation x -4y = -4
Answer:
y = x/4 + 1
Step-by-step explanation:
x - 4y = -4
x + 4 = 4y
y = x/4 + 1
Answer:
1
Step-by-step explanation:
change to y=mx+b -> 4y=-x+4
divide 4 one the right side
y=4x+1
put zero one place of x
y=4(0)+1
y=0+1
y=1
A wire 18 cm long is cut into two pieces. The longer piece is 6 cm longer than the shorter piece. Find the length of the shorter piece of wire
Answer:
shorter piece = 6. longer piece = 12
Step-by-step explanation:
short piece = s
long piece = l
l+s= 18
l= 6+s , substitute
6+s+s = 18
6+2s= 18
2s= 18-6
2s= 12
s=12/2
s= 6= shorter piece
l= 6+s
l= 6+6= 12 = longer piece
Use the associative property to simplify the expression 50 + 20 + 37
Answer:
(50+20) +37=70+37=107
Help!!!!!! I'll give you brainliest!!!
A credit card company offers an annual 2% cash-back rebate on all gasoline
purchases. If a family spent $5,650 on gasoline purchases over the course of a year,
what was the family's rebate (in dollars) at the end of the year?|
$4,350 x 0.02 = $87
$360 - $87 = $273
Interest $270 no rebate
so $273 - $270 = $3
The family's rebate at the end of the year is $113.
What is a rebate?A rebate is a form of buying discount and is an amount paid by way of reduction, return, or refund that is paid retrospectively. It is a type of sales promotion that marketers use primarily as incentives or supplements to product sales.
Given that, a credit card company offers an annual 2% cash-back rebate on all gasoline purchases.
A family spent $5,650 on gasoline purchases over the course of a year.
Now, rebate =2% of 5650
= 2/100 ×5650
= 0.02×5650
= $113
Therefore, the family's rebate at the end of the year is $113.
Learn more about the rebate here:
https://brainly.com/question/15516502.
#SPJ2
answer I'll give brainliest to first one
10 points
Answer:
Have a splendiferous day...
Step-by-step explanation:
3÷12=¼
6÷10=⅗
7÷14=½
10÷11=⅚
2÷4=½
4÷16=¼
3÷24=⅛
18÷54=⅓
Answer:
1) 3÷12=[tex]\frac{1}{4}[/tex]
2) 6÷10=[tex]\frac{3}{5}[/tex]
3) 7÷14=[tex]\frac{1}{2}[/tex]
4) 10÷12=[tex]\frac{5}{6}[/tex]
5) 2÷4=[tex]\frac{1}{2}[/tex]
6) 4÷16=[tex]\frac{1}4[/tex]
7) 3÷24=[tex]\frac{1}{8}[/tex]
8) 18÷54=[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Hope this helps have a great day ahead! Have a great Halloween :) Tell me if im wrong please <3
PLEASE HELP ME WITH THESE ASAP
i'll give brainlist
Answer:
5/288
Step-by-step explanation:
can anyone heelp me pls
Lotion - liquid
Suspension- semisolid
Capsule- Solid
Hope this helps :)
how do i solve this step by step? i dont know how to set up this equation.
Answer:
Step-by-step explanation:
The two long sides on the left and right and bisected into two equal parts each
That means that since there is an angle in common to the top little triangle and the whole diagram, the little triangle on top and the whole triangle are similar.
The ratio of similarity is 1/2
10/(5x + 5) = 1/2 Cross multiply
(5x + 5)*1 = 10*2
5x + 5 = 20 Subtract 5 from both sides
5x = 20 - 5 Combine
5x = 15 Divide by 5
5x/5 = 15/5
x = 3
WHYYY ARE BOTS ON HERE HM HM?!
Answer:
Well it's because they want children to click there links for either tracking IP address's or just using it to bring you to another site.
Step-by-step explanation:
12. Una notaría cobra $3500 por elaborar un título de propiedad y $2000 por el acta constitu-
tiva de una empresa. En un mes realizó un total de 22 operaciones, entre títulos y actas que
representaron un ingreso total de $53000. ¿Cuántos títulos y actas se elaboraron?
Usando un sistema de ecuaciones, hay que se elaboraron 6 títulos y 16 actas.
Para el sistema, hay que:
x es el número de títulos elaborados.y es el número de actas elaboradas.Total de 22 operaciones, o sea:
[tex]x + y = 22[/tex]
$3500 por elaborar un título de propiedad y $2000 por el acta constitutiva de una empresa. Ingreso total de $53000, o sea:
[tex]3500x + 2000y = 53000[/tex]
De el primer ecuación:
[tex]y = 22 - x[/tex]
Reemplazando en la segunda:
[tex]3500x + 2000y = 53000[/tex]
[tex]3500x + 2000(22 - x) = 53000[/tex]
[tex]1500x = 9000[/tex]
[tex]x = \frac{9000}{1500}[/tex]
[tex]x = 6[/tex]
[tex]y = 22 - x = 22 - 6 = 16[/tex]
Se elaboraron 6 títulos y 16 actas.
Un problema similar es dado en https://brainly.com/question/24646137
Scarlett has 14 gallons of gas in her car at the beginning of a trip. Every hour Scarlett drives, she uses 2.5 gallons of gas. Answer the questions below regarding the relationship between the gallons of gas remaining in the tank and the total hours driven.
Answer:N(5)=1.5
Step-by-step explanation:The independent variable x represents the Number of hours driven and the dependent variable is the gallons of gas remaining, because the gallons of gas remaining depends on the number of hours driven.
A function relating these variables is Nx=14-2.5
So N(5)=1.5 meaning 5 hours of driving will result in 1.5 gallons left in the tank.
wHaT iS tHe AnWsEr?????????????
2,000 +300000000000000000000000000000000000
Answer:
3.0 E35
Step-by-step explanation:
Thanks.
Find the value of a that satisfies the following
P(Z>a)=0.9207
Answer:
-1.409
Step-by-step explanation:
I’m assuming this a z-score for stats. You would just go into your calculator, in my case a Casio. Then, you’d press on the stats module, click F5 (DIST), F1 (NORM), F3 (InvN). You would change the data to variable, then put in tail right, area .9207, SD 1, mean of 0. Then hit execute and you’ll get the answer of -1.4097958. Round it if needed.
Find the area of this figure. Round your answer to the nearest hundredth. Use 3.14 to approximate
Thank you!
Answer:
104 ft²
Step-by-step explanation:
The area of the rectangle is represented by the following:
8ft x 10 ft = 80 ft
The area of the triangle is represented by the following:
(6ft x 8ft) divided by 2 = 24
By combining the values, you get 104 square feet.
How can you represent a rate with 100 as the whole?
Since, 100 is a positive integer and is a counting number. Hence, it is considered to be a whole number.
If you want someone to do your homework assignments for you (math, English) for a cheap price lmk
Answer:
I do lol
Step-by-step explanation:
Answer:
why would you wanna do someone's homework on Math and English?
Step-by-step explanation:
they wouldn't learn anything if they make you do their homework, besides what's the point of the homework if they don't learn anything? I know homework's are hard, but they give it for you to understand more of the lesson.
and you will also make yourself tired doing someone's homework what about your responsibilities?
It'll be only beneficial for you but not for them yeah you'll get money but its best if you let them do their homework. I mean homework's aren't that bad.
They just think they can't do it cause their lazy, and they think they wouldn't know the answer. Besides they can't just lay around all day because they paid you for doing their homework, they won't even know if your scamming them.