Answer:
Part A)
[tex]\displaystyle R'(t) = (5000-240t)(120-t^2)+(5000t-120t^2)(-2t)[/tex]
Part B)
After three months, the revenue is increasing at a rate of $391,560 per month.
Step-by-step explanation:
A product is introduced into the market. The quantity per month q sold is given by the function:
[tex]q(t) = 5000t - 120t^2[/tex]
And the price p (in dollars) of the product is given by the function:
[tex]p(t) = 120-t^2[/tex]
Part A)
R(t), or the revenue, will be the product of the quantity sold and its respective price during the month. Hence:
[tex]\displaystyle R(t) = q(t)\cdot p(t)[/tex]
Substitute:
[tex]\displaystyle R(t) = \left(5000t-120t^2\right)\left(120-t^2\right)[/tex]
To find R'(t), take the derivative of both sides with respect to t:
[tex]\displaystyle R'(t) = \frac{d}{dt}\left[ \left(5000t-120t^2\right)\left(120-t^2\right)\right][/tex]
Since the function is a product of two expressions, we can consider using the Product Rule:
[tex]\displaystyle \frac{d}{dx} \left[uv\right] = u'v+uv'[/tex]
Hence:
[tex]\displaystyle R'(t) = \frac{d}{dt}\left[5000t-120t^2\right]\left(120-t^2\right) + \left(5000t-120t^2\right)\frac{d}{dt}\left[120-t^2\right][/tex]
Differentiate. Therefore:
[tex]\displaystyle R'(t) = (5000-240t)(120-t^2)+(5000t-120t^2)(-2t)[/tex]
(We may simplify if we desire, but this is not required by the problem.)
Part B)
To find the rate of change of revenue with respect to time three months after the introduction, we can evaluate R'(t) at t = 3. Hence:
[tex]\displaystyle R'(3) = (5000-240(3))(120-(3)^2)+(5000(3)-120(3)^2)(-2(3))[/tex]
Evaluate:
[tex]R'(3) = 391560\text{ dollars/month}[/tex]
In conclusion, after three months, the revenue is increasing at a rate of $391,560 per month.
(Note: it is increasing because the final value is positive.)
Problem 1.3
T
Use what you know about area to determine the area of
triangle T
Submit
5
3
Answer: it's supposed to be 60, check
Step-by-step explanation:
I have to factorise the following
Write the decimal expansion for 5/6 Choose the correct decimal notation. A. 0.83 B. 0.8 C. 0.6 D. 0.83
Answer: Choice A
Explanation:
If you use a calculator or long division, you should find that
5/6 = 0.8333333...
where the '3's go on forever. We shorten this down to [tex]0.8\overline{3}[/tex], the horizontal bar tells us which item goes on forever (just the 3 only).
The answer is A. I don't know how to explain.
No link answers please solve honestly
Answer:
y = 78
Step-by-step explanation:
66 + 4 = 70 + 4 = 74 + 4 = 78
-12 + 3 = -9 + 3 = -6 + 3 = -3
x = -3
y = 78
Find the simple interest.
Principal
Rate 11% principle 9000 time1 1/2 years what's the amount of simple interest earned is
Answer:
Here is your answer. Hope this helps you!
Answer:
Rate(R)= 11%
Times(T)=11/2
Principle(P)= 9000
We know that,
SI = P×T×R÷100
= 9000×11/2×11÷100
=9000×5.5×11÷100
= 544500÷100
=5445
Hence, the required simple interest is 5445.
Ans
If 1 lb = 2 cups what does 1/2 cups equal?
PLEASE HELP
Answer:
16 ounces equals one pound or two cups. Another way to look at the equivalent is that one cup weighs eight ounces and therefore two cups equal 16 ounces and this is the same weight of one pound--16 ounces.
Step-by-step explanation:
Express the ratio as a unit rate.
4.5 miles in 25 minutes
Answer:
10 mins
Step-by-step explanation:
This is a fraction equal to
25 minutes ÷ 2.5 4.5
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 2.5
25 minutes ÷ 2.5
2.5 4.5 ÷ 2.5
=
10 minutes
1 4.5
=
10 minutes
4.5
= 10 minutes per 4.5
Anyone know how to solve it?
Answer:
[4 -2 -19]
[-1 1 8]
Step-by-step explanation:
[ 2 5] * [a b c] = [3 1 2]
[ 1 3] ld e f] [1 1 5]
[2a+5d 2b+5e 2c+ 5f] = [3 1 2]
[a+3d b + 3e c + 3f] [1 1 5]
Solving systems of equations:
2a + 5d = 3
a + 3d = 1
2a + 6d = 2
Subtract -d = 1 so d = -1
and a = 1 - 3d = 1 - 3(-1) = 4
So d = -1 and a = -4.
In the same way we find that b = -2, e = 1, c = -19, f = 8.
Your average bi-weekly net pay is $489.00. What is 15% of your average monthly net pay? (1 point)
$146.70
$158.93
$160.13
Bi weekly means you get paid every 2 weeks so you would get two paychecks per month.
Monthly net pay = 489.00 x 2 = $968.00
Multiply monthly by 15%
968 x 0.15 = $146.70
Answer: $146.70
If Your average bi-weekly net pay is $489.00. Your average monthly net pay is:$146.70.
Average monthly net payFirst step
Monthly net pay=$489.00×2
Monthly net pay=$968
Second step
Average monthly net pay:
Average monthly net pay=$968×15%
Average monthly net pay=$146.70
Therefore your average monthly net pay is:$146.70.
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Find the area of a square with sides 11 feet long.
Answer:
the area of square is
the area of square is side*side
therefore ,area= 11*11= 121 feet square
2x-3y=6 and x+3y=3
help me I cannot understand it please in substitution method
Answer:
[tex]thank \: you[/tex]
Answer:
Take 2x- 3y= 6 as equation 1
And
x+ 3y= 3 as equation 2
Now add both equation
2x - 3y = 6
x + 3y = 3
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
3x 0 = 9
We can also write 3x 0= 9 as 3x = 9
Now we have to solve 3x =9
3x = 9
x = 9/3
x= 3
I hope this will help you
brainiest to whoever right
Answer:
Area of a triangle
Step-by-step explanation:
1/2bh is used to find the area for a triangle
Help please! Find the area of the shape below. (Show work)
9514 1404 393
Answer:
292 yd²
Step-by-step explanation:
We can find the area of the remaining L shape by subtracting the area of the 21×22 rectangle at lower left from the 26×29 overall rectangle.
shape area = (26 yd)(29 yd) -(21 yd)(22 yd) = 754 yd² -462 yd²
shape area = 292 yd²
__
Additional comment
The area of a rectangle is the product of its length and width.
There are many ways the area of this shape can be calculated. The area can be divided into two rectangles, two trapezoids, three rectangles, and other ways.
If you cut up the given shape into smaller pieces, you will generally need to know the widths of the arms of the L. One of those is shown as 7 yd. The other is 26-21 = 5 yd.
Using the method we did, we only needed the dimensions shown on the figure.
Solve for d when t = 0, t = 3, t = 5 d =2t
Answer:
When t = 0, d = 0When t = 3, d = 6When t = 5, d = 10Concept:
Here, we need to understand the idea of evaluation.
When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.
Solve:
PART ONE: Find d when t = 0
Given expression
d = 2t
Substitute value into the expression
d = 2 (0)
d = 0PART TWO: Find d when t = 3
Given expression
d = 2t
Substitute value into the expression
d = 2 (3)
d = 6PART THREE: Find d when t = 5
Given expression
d = 2t
Substitute value into the expression
d = 2 (5)
d = 10Hope this helps!! :)
Please let me know if you have any questions
What is the volume of a cone with a height of 9.5 inches and a radius of 8 inches? Cone V = 1 3 Bh 1. Rewrite the formula for the base area: V = 1 3 πr2h
2. Substitute the values into the formula: V = 1 3 π(82)(9.5)
3.Evaluate the power:V = 1 3 π(64)(9.5)
4.Simplify using multiplication: V = 1 3 π(608)
The cone has a volume of?
Answer:
608/3
Step-by-step explanation:
I got it correct
what is the symbol for line
Answer:
the symbol is ↔
HURRY QUICK PLEASE HELP!!
Which expression is equivalent to 10V5?
A.V500
B. V105
C. V50
D. V15
Answer:
A
Step-by-step explanation:
Answer:
Answer: A. √500
Step-by-step explanation:
[tex]10 \sqrt{5} \\ = (\sqrt{ {10}^{2} } ) \times ( \sqrt{5} ) \\ = \sqrt{100} \times \sqrt{5} \\ = \sqrt{500} [/tex]
in class of 80 student debre berhan university ,45 are good in mathematics,15 are good in both mathematics and in english,13 are good in both mathematics and psychology,16 are good in both english and psychology only,20 are good in psychology and 9 are good in both of three courses.how many students are not good in any of three courses ?
We want to find the number of students that are not good in any of the courses.
There are 80 students.
45 are good in mathematics
15 are good in both, mathematics and in English
13 are good in both, mathematics and psychology
16 are good in both English and psychology
20 are good in psychology
9 are good in all of the courses.
First, we know that we have:
45 good in math + 20 good in psychology = 65 students good in something.
But we know that:
13 are good in both, mathematics and psychology
This means that there are 13 students that are being counted twice, so we need to subtract 13.
45 + 20 - 13 = 52 students good in something.
Now we know that:
15 are good in both, mathematics and in English
16 are good in both English and psychology
9 are good in all of the courses.
So one would want to also count these students, but notice that these are already good in mathematics or in psychology, so these are already counted.
And we can't see the number of students that are only good with English, so we can conclude that
52 students are good in something.
then 28 students are not good at any of the 3 courses.
If you want to learn more, you can read:
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Help me with the e or how many you can
Please afsp
Answer:
(a)
sin²A×cos²A+sin⁴A
we will take sin²A as an common factor
so it become
sin²A×(cos²A+sin²A)
sin²A+cos²A=1
sin²A×1=sin²A
(c)
sinA×cotA
cotA= cosA/sinA
sinA×cosA/sinA=cosA
(e)
(1+sinA)²-(1-sinA)²
(a+b)²=a²+b²+2×a×b
(a-b)²=a²+b²-2×a×b
1²+sin²A+2×1×sinA-(1²+sin²A-2×1×sinA)
1+sin²A+2sinA-1-sin²A+2sinA=4sinA
(g)
(cosec²A-1)/cosec²A
cosecA=1/sinA
1/sin²A-1/1/sin²A
(1/sin²A-1)×sin²A
1-sin²A
1=sin²A+cos²A
sin²A+cos²A-sin²A=cos²A
(i)
sqrt(1+tan²A)×sqrt(1-cos²A)
1+tan²A=
1+sin²A/cos²A=
sin²A+cos²A/cos²A
sin²A+cos²A=1
=1/cos²A
1-cos²A
1=sin²A+cos²A
sin²A+cos²A-cos²=sin²A
sqrt(1/cos²A)×sqrt(sin²A)
1/cosA×sinA=sinA/cosA=tanA
have a great day
Need help ASAP PLEASE!!!
Answer:
x=1
Step-by-step explanation:
3/2+1/2x=2x
or,3*1+1*1x/2=2x
or,4x/2=2x
or,4x-2x=2
or,x=2/2
so,x=1
A bakery sells 12 gourmet orange-zest cupcakes for $36.00. Select all the statements that are true.
Answer:
wut are the statements?
Step-by-step explanation:
Name the place value to which each number was rounded 16.932 to 20
Hi :)
Rounded to the tenth place value.
16 to 20
Rounding to the nearest whole number means converting a number to an approximate value that is easier to use and remember. The place value to which 16.932 was rounded is 17.
What do you mean by nearest whole number?Rounding to the nearest whole number means converting a number to an approximate value that is easier to use and remember. Usually, decimal numbers and fractions are rounded to the nearest whole number with the help of the appropriate rules.
To round 16.932 to the nearest whole number consider the tenths’ value of 16.932, which is 9 and equal or more than 5. Therefore, we have to round up the whole number part of 16.932, 16, increases by 1 to 17, and the decimal point and all digits (.932) are removed.
16.932 rounded to the nearest whole number = 17
Therefore, The table ahead contains starting numbers close to 16.932 rounded to the nearest basic counting number.
Hence, the place value to which 16.932 was rounded is 17.
Learn more about Rounding off Number here:
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6 + 5 - 4x = 1 - 4x
Pls hurry STEP BY STEP
Answer:
There are no solutions
Step-by-step explanation:
6+5−4x=1−4x
6+5+−4x=1+−4x
(−4x)+(6+5)=−4x+1
−4x+11=−4x+1
−4x+11=−4x+1
−4x+11+4x=−4x+1+4x
11=1
11−11=1−11
0 = −10
Answer:
10 = 0
Step-by-step explanation:
6 + 5 - 4x = 1 - 4x
11 - 4x = 1 - 4x
11 -1 = -4x +4x
10 = 0
Roast beef has 25 g of protein and 11 g of calcium per serving. A serving of mashed potatoes has 2 g of protein and 25 g of calcium. Set up and solve a system to show how many servings of each are needed to supply exactly 29g of protein and 61 g of calcium.
Step-by-step explanation:
your answer
mark me a brainlistEvaluate (solve) the expression 4x + 8 when x = 2
Hi ;-)
[tex]x=2\\\\4x+8=4\cdot2+8=8+8=\boxed{16}[/tex]
Step-by-step explanation:
4x + 8
4 × 2 + 8
8 + 8
16
Therefore its 16.
Solve the problem please
Answer:
x = 9±sqrt(7)
Step-by-step explanation:
3(x-9)^2 =21
Divide each side by 3
3/3(x-9)^2 =21/3
(x-9)^2 =7
Take the square root of each side
sqrt((x-9)^2) =±sqrt(7)
x-9 =±sqrt(7)
Add 9 to each side
x = 9±sqrt(7)
I need help ASAP!!! Thanks
WILL GIVE BRAINLIEST IF FAST!!!!
The store for select the poi was coming in 2010, the population was tot 30 million people in the
tering this feat
Trechts by trong this time
Enter your soxandre
Get More Help
Cear
CA
Help Me Shive This
View an Example
Answer:
can you please type that question
The picture above circled one
Write a formula for the number of subsets of any set; identify any symbols use
Please help me!!
Mark brainliest!!
Formula-
If a set has “n” elements, then the number of subset of the given set is 2n and the number of proper subsets of the given subset is given by 2n-1. Consider an example, If set A has the elements, A = {a, b}, then the proper subset of the given subset are { }, {a}, and {b}
Symbol that can be used-
The symbol "⊆" means "is a subset of". The symbol "⊂" means "is a proper subset of".
Hope it helps you... pls mark brainliest if it helped you.
What is the surface area of the rectangular prism formed from this net?
O A. 10.5 in.2
B. 16 in.2
C. 16.5 in.2
Ο Ο Ο
OD. 18 in.2
E 32.5 in.2