the volume of a cube is increasing at the rate of 12 in^3/min. how fast is the surface area increasing in square inches per minute, when the length of an edge is 20in.?
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.
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10. A stockbroker charges his customers $30 to open an account and
$15 per month to manage the account. Write an equation to represent the
number of months, n, an account has been open if the total cost is $360.
Answer:
the answer is 22
the equation is 30 + 15n
Step-by-step explanation:
15n as it increases each month and 30 as it never changes and will always be a value of 30
Answer:
15n+30=360
Step-by-step explanation:
$15 per month is being charged
The flat fee is $30
The Total cost is 360
15n+30=360
Evaluate the expression 6^2-(8–4^2+7
Answer
11
you can confirm from by yourself or tell
please mark this answer as brainlist
Find the measure of the angle with the red dot (NOT X.)
Picture Included. Thank you!
Step-by-step explanation:
I can't see picture very well but as I see first angle is
-4x+5 and second is -13x+39 ( if it isn't, correct me)
sum of this angles is 180° because they are inner angles
(-4x+5) + (-13x+39) = 180
-4x+5 -13x+39=180
-17x+44=180
-17x = 180-44
-17x= 136
x= -8
angle -4x+5 will be:
-4*-8 + 5= 32+5= 37°
I NEED HELP WITH THIS ASAP
Answer:
4
Step-by-step explanation:
( 5x - 6 ) and ( 3x + 2 ) are alternate interior angles.
Alternate interior angles are equal,
So,
5x - 6 = 3x + 2
5x - 3x = 2 + 6
2x = 8
x = 8 / 2
x = 4
Needs to show work.
Find the X intercept and the Y intercept for 2x-6y=12
Answer:
x: (6,0)
y: (0,-2)
Step-by-step explanation:
To find the x-intercept, substitute in 0 for y and solve for x . To find the y intercept, substitute in 0 for x and solve for y .
Ex -
X : 2x -6(0)=12
2x=12
2 cancels out with 2
12/2 = 6
Y: 2(0 )- 6y =12
-6y=12
negative 6 times negative 6 cancels
12/-6 = -2
Answer:
See Below
Step-by-step explanation:
Given: 2x-6y=12
Plug 0 in the equation for y:
y is zero
2x-6(0)=12
2x=12
The x-intercept: (6,0)
Plug 0 in the equation for x:
x is zero
2(0)-6y=12
−6y=12
The y-intercept: (0,−2)
write an equivalent expression for x^4 over 4
help
please
Answer:
1/4 · x⁴
Step-by-step explanation:
Which equation describes the sum of the vectors plotted below?
6
A. r 38 27
B. 2x+y
C. r 38 1 27
O Dr 3x Ý
Answer: [tex]A) \ 3\vec{x} -2\vec{y}[/tex]
Step-by-step explanation:
The resultant can be calculated using triangular law of vector addition as :
[tex]\rm \vec{r}=\vec{AB} +\vec{AC}=2x+y+x-3y=\boxed{3x-2y }[/tex]
Michael wants to save $46,000.00 for a down payment on a home. How much will he need to invest in an account with 6.1% APR, compounding daily, in order to reach his goal in 7 years? Round the answer to the nearest cent
Step-by-step explanation:
Simple Interest
Discussing interest starts with the principal, or amount your account starts with. This could be a starting investment, or the starting amount of a loan. Interest, in its most simple form, is calculated as a percent of the principal. For example, if you borrowed $100 from a friend and agree to repay it with 5% interest, then the amount of interest you would pay would just be 5% of 100: $100(0.05) = $5. The total amount you would repay would be $105, the original principal plus the interest.
four rolled-up dollar bills seeming to grow out of dirt, with a miniature rake lying in between them
SIMPLE ONE-TIME INTEREST
I
=
P
0
r
A
=
P
0
+
I
=
P
0
+
P
0
r
=
P
0
(
1
+
r
)
I is the interest
A is the end amount: principal plus interest
P
0
is the principal (starting amount)
r is the interest rate (in decimal form. Example: 5% = 0.05)
EXAMPLES
A friend asks to borrow $300 and agrees to repay it in 30 days with 3% interest. How much interest will you earn?
Show Solution
The following video works through this example in detail.
One-time simple interest is only common for extremely short-term loans. For longer term loans, it is common for interest to be paid on a daily, monthly, quarterly, or annual basis. In that case, interest would be earned regularly.
For example, bonds are essentially a loan made to the bond issuer (a company or government) by you, the bond holder. In return for the loan, the issuer agrees to pay interest, often annually. Bonds have a maturity date, at which time the issuer pays back the original bond value.
EXERCISES
Suppose your city is building a new park, and issues bonds to raise the money to build it. You obtain a $1,000 bond that pays 5% interest annually that matures in 5 years. How much interest will you earn?
Show Solution
Further explanation about solving this example can be seen here.
what is proportion mean
Answer:
a part, share, or number considered in comparative relation to a whole.
Step-by-step explanation:
hope it helps
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. The temperature fell 13°c on each of the first 2 days of the week. It rose 7°c on each of
the next 3 days and fell 9°c on each of the last 2 days. If the temperature was originally
34% what was the final temperature?
Answer:
The final temperature was 9 degrees.
Step-by-step explanation:
You can first multiply 13x2, 7x2, and 9x2. Then you subtract 26 and 18 from 34. then add 14
Please help me I only have 10 points left so ten points I’ll give please help thank you I’ll give brainless to the first person
Answer:
It would be g(x) = 2^-x
Step-by-step explanation:
Does anyone know how to do multiple in fractions like for a example 1/12•1/3? Please explain step by step
[tex] \frac{1}{12} \times \frac{1}{3} \\ = \frac{1 \times 1}{12 \times 3} \\ = \frac{1}{36} [/tex]
When you want to multiply 2 fractions, merge the fractions together & then multiply the numerator first & then the denominator. After that, simplify to the lowest form if possible.The Astronomical Telescope shop plans to introduce a new model based on the following information: Rent and utilities per period are $ {fixed}; variable cost per unit is $ 217; selling price per unit is $ 305; determine the break-even point in units if rent and utilities are increased to $ 5420.
Using the profit concept, it is found that the break-even point is of 61.6 units.
Profit is given by revenue subtracted by cost.The break-even point is when the revenue is the same as the cost, which means that the profit is zero.In this problem:
Variable cost per unit x of $217, fixed cost of $5,420, thus, the cost equation is given by:[tex]C(x) = 217x + 5420[/tex]
Selling price per unit of $305, thus, the revenue equation is given by:
[tex]R(x) = 305x[/tex]
The break-even point is the value of x for which:
[tex]R(x) = C(x)[/tex]
Then
[tex]305x = 217x + 5420[/tex]
[tex]88x = 5420[/tex]
[tex]x = \frac{5420}{88}[/tex]
[tex]x = 61.6[/tex]
The break-even point is of 61.6 units.
A similar problem is given at https://brainly.com/question/4001746
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Answer:c?
Step-by-step explanation: i think?
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.
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Michelle divided her birthday cake into sixteen pieces and gave one piece to each of her nine friends. Express the total number of pieces of cake she gave to her friends as a fraction.
Answer:
give me 1 min ill answer it
Step-by-step explanation:
pls help
which trend line properly describes the data relationship in the scatterplot?
Answer:
The 2nd one
Step-by-step explanation:
The trend line properly describes the data relationship in the scatterplot is plot A.
What is Trend line?A trend line is also known as a line of best fit, and it is used to illustrate the behaviour of a set of data to assess if it is in a given pattern. So, a trend line is an analytical technique that is frequently used in conjunction with a scatter plot to determine whether or not there is a relationship between two variables.
As, per the plots.
The scatter plot A have the points distributed symmetrically on the both side of line.
Also, straights lines are negatively correlated with scatter points.
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10 ft
8 ft
I
Find the area of this figure. Round your
answer to the nearest hundredth. Use
3.14 to approximate .
A = [? ] ft?
=
You have at most $20 to spend at an arcade. Arcade games cost $0.75 each, and snacks cost $2.25 each. Write an inequality that represents the numbers of games (x )you can play and snacks( y) you can buy.
The inequality is ??
Answer:
y ≤ -1/3x+80/9
Step-by-step explanation:
(1). 0.75(x)+2.25(y) ≤ 20
0.75 - Number of arcade games (X).
2.25 - Number of snacks (Y).
20 - The total.
(2). 0.75x+2.25y≤20
(After multiplying the x's and y's together, with the numbers).
(3). 0.75x (-0.75x) + 2.25y ≤ 20 (-0.75x)
(Subtract -0.75x to each side, which allows the equation to get closer to the answer).
(4). 2.25y -0.75x + 20
———— = ————
2.25 2.25
(Divide by 2.25 to each side).
(5). y ≤ -1/3x + 80/9
(The result and the inequality).
what is the inverse function of h(x)=-3/5x+1/2?
Answer:
h−1(x)=−5x/3+5/6
Step-by-step explanation:
your answer is the second one
Answer:
The answer is the third one
Step-by-step explanation:
I did the test
what is 100 divided by 5, (the answer) x 3 (the answer) x 79 (the answer) - 4
NO LINKS PLEASE! First to answer correct gets Branliest!!!
Answer:
4736
Step-by-step explanation:
1) 100 divided by 5 is 20
2) 20 times 3 is 60
3) 60 times 79 is 4740
4) 4740 subtract from 4 is 4736
5) Answer is 4736
Answer:
4736
Step-by-step explanation:
5*20 = 100
20*3 = 60
60*79 = 4740
4740 - 4 = 4736
The function y = 5.75 + 2.5(x - 2) can be used to determine cost in dollars to rent a house of x square feet. What is the rate of change of the cost in dollars with respect to the number of square feet?
The rate of change is given by the coefficient of x in the cost function. Hence, the rate of change of cost in the function is 2.5
Given the cost function :
y = 5.75 + 2.5(x - 2)Expanding the function and expressing in slope intercept form:
y = 5.75 + 2.5x - 5
y = 2.5x + 2.75
Therefore, the slope of the function is 2.5 ; which ubsthe rate of change of the cost function.
Learn more :https://brainly.com/question/18112348
2x=14−2
Find the value of x
Don't give wrong answer
Answer:
[tex]\sf\longmapsto \: x = 6[/tex]
Step-by-step explanation:
[tex]\sf\longmapsto \: 2x = 14 - 2[/tex]
[tex]\sf\longmapsto \: 2x = 12[/tex]
[tex]\sf\longmapsto \: x = \frac{12}{2} [/tex]
[tex]\sf\longmapsto \: x = 6[/tex]
Answer:
x = 6
Step-by-step explanation:
Hey there,
[tex]2x =14-2\\2x=12\\\frac{2x}{2}=\frac{12}{2} \\x = 6[/tex]
Hope this helps you.
Let me know if you have any other questions :-)
542+876-65+76×5444+556-77
Answer:
=415576
Step-by-step explanation:
=1418−65+(76)(5444)+556−77
=1353+(76)(5444)+556−77
=1353+413744+556−77
=415097+556−77
=415653−77
(01.02 HC) A jar contains 0.85 liter of strawberry juice and 0.50 liter of mango juice. Celina poured 0.15 liter of watermelon juice into the jar. She then drank 0.30 liter of the mixture.
Part A: Write an expression to represent the total amount of juice left in the jar.
Part B: Simplify the expression and identify which property is used in each step.
Part A:
GIVEN: Strawberry Juice = [tex]0.85[/tex] liters, Mango Juice = [tex]0.50[/tex] liters, Watermelon Juice = [tex]0.15[/tex] liters, Drank Juice = [tex]0.30[/tex] liters.
-------------------------------------------------------------------------------------------
· Find the expression
In this case, all of them have to be combined to find the expression
Thus,
Expressions in these queries are arithmetical statements that may be defined by the operator, and the following discussion could indeed define a minimum of 2 terms containing the numbers or the variables, or both.
strawberry juice = 0.85 liter
mango juice = 0.50 liter
watermelon juice= 0.15 liter
drank juice = 0.30 liter
solution:
0.85+0.5+0.15 = 1.5
if she drank 0.3, remove it from 1.5, then 1.3
this expression would be : (0.85+0.5+0.15) - 0.3 = 1.2
Find the slope of the line passing through the points (-7.6) and (-7.-2).
Answer:
Undefined
Step-by-step explanation:
the equation for slope is y2-y1/x2-x1
(-2-6)/(-7-(7))= -8/0
This would leave you with an undefined slope.
how do I determine what a function is for a line graph
Answer: Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
Step-by-step explanation:
Identify the graph that represents y=(x-1)^2+2
Step-by-step explanation:
i hope this is what you need
Label the figure.
20,24,114,702