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.)
A coin is flipped two times and the number of heads is counted. Which of the following is a valid assignment
of probabilities for the number of heads observed in two flips?
8.
Number of heads
Probability
0
1/10
1
5/10
2
4/10
b.
Number of heads
0
1
2
Probability
1/4
2/4
1/4
C.
0
1
Number of heads
Probability
2
1/3
1/3
1/3
d. All answer options are correct
Answer:
5/10, 1, 2/4,
Step-by-step explanation:
Help meeeeeeeeeeeeeeeee
Answer:
x-3
Step-by-step explanation:
the inverse is x-3
this is the answer
[tex]-4\sqrt{28x}[/tex] times [tex]\sqrt{7x^3}[/tex]
Answer:
[tex] {56x}^{2} [/tex]
Step-by-step explanation:
[tex] - 4 \sqrt{28x} \times \sqrt{ {7x}^{3} } [/tex]
[tex] = -4 \times 2 \sqrt{7x} \times \sqrt{7x} [/tex]
[tex] = - 4 \times 2 \times 7x \times x[/tex]
[tex] = {56x}^{2} [/tex]
Find the coordinates of the point 7/10 of the way from A to B A -3,-7 B 11,4
9514 1404 393
Answer:
(6.8, 0.7)
Step-by-step explanation:
That point is ...
A + (7/10)(B -A)
= (-3, -7) +(7/10)(11 -(-3), 4 -(-7)) = (-3, -7) +7/10(14, 11)
= (-3, -7) +(9.8, 7.7) = (6.8, 0.7)
The point 7/10 from A to B is (6.8, 0.7).
One number exceeds another by 12 and their sum is 44 find the two numbers you
Answer:
Step-by-step explanation:
x - first
x + 12 - second
x + (x + 12) = 44
2x=44-12
x=16
first number is 16
second number is 16+12=28
two numbers are 16 and 28
16 and 28 are the required two numbers when one number exceeds another by 12 and their sum is 44
One number exceeds another by 12 and their sum is 44
We need to find the two numbers
What is equation?Two expressions with equal sign is called equation.
Let x be the first number
x + 12 be the second number
x + (x + 12) = 44
2x=44-12
x=16
Therefore first number is 16
second number is 16+12=28
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12. A jet stream can move a particle of air
11 miles in 5 minutes. At this rate, how far
will the particle move in 1 hour?
(5 minutes = 1 hour) (Example 1)
Answer:
132 particles
Step-by-step explanation:
5 minutes = 11 miles
1 hour (60 minutes)
11*x = 11 x 60 = 660
11x = 660/5=132
The distance of a jet stream can move a particle of air 132 miles in 1 hour.
Here,
A jet stream can move a particle of air 11 miles in 5 minutes.
We have to find, The distance of particles move in 1 hour.
What is distance?
The length along a line or line segment between two points on the line or line segment.
Now,
A jet stream can move a particle of air 11 miles in 5 minutes.
5 minutes = 11 miles
Then, for 1 minute a jet stream can move a particle of air = 11 / 5 miles
Hence, In 1 hour ( 60 minutes) a jet stream can move a particle of air;
⇒ [tex]\frac{11}{5} * 60 = 132[/tex]
So, The distance of a jet stream can move a particle of air 132 miles in 1 hour.
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Combine like terms and write the simplified
Answer:
4x-3 16t-4
Step-by-step explanation:
Answer:
1. 8x-4x=4x
5-2=3
so the answer will be
4x+3
2.9t-7t+12-8=2t+4.
3.i have no idea
4. 18x^2+12x^2+16x-11x-17+19=30x^2+5x-36.
In ΔPQR, sin P = 0.2, sin R = 0.2 and r = 12. Find the length of p.
9514 1404 393
Answer:
p = 12
Step-by-step explanation:
The sines of the opposite angles are the same, so the lengths of the sides are the same.
p = 12
_____
The law of sines tells you ...
p/sin(P) = r/sin(R)
p/0.2 = 12/0.2 . . . . . . substitute given values
Multiply by 0.2 to get ...
p(0.2/0.2) = 12(0.2/0.2)
p = 12
Need help!!
What is the equation of the quadratic functions shown in the graph?
Answer:
F(x)= (x+1)(X-3)
Step-by-step explanation:
Plug in the Zeros of the equation
HELP PLS!! PLS BRO LOLOLOLOL
Answer and Step-by-step explanation:
An easy way of doing this is to first square root the numerator and the denominator.
[tex]\sqrt{\frac{36}{81} } =\frac{\sqrt{36}}{\sqrt{81} } =[/tex] ±[tex]\frac{6}{9} =[/tex] ±[tex]\frac{2}{3}[/tex] <- This is the answer.
#teamtrees #PAW (Plant And Water)
I hope this helps!
HELP ME PLEASEEEEEEEE
Answer:
c
Step-by-step explanation:
i search it up
19. The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is (a) 20 (b) 23 (c) 169 (d) None of these
Answer:
B
Step-by-step explanation:
Let the two numbers be a and b.
The product of the two is 120 and their sum of their squares is 289. In other words:
[tex]\displaystyle ab = 120 \text{ and } a^2 + b^2 = 289[/tex]
And we want to find the sum of the two numbers.
We can use the perfect square trinomial. Recall that:
[tex]a^2 + 2ab + b^2 = (a+b)^2[/tex]
From the first equation, multiply by two:
[tex]2ab = 240[/tex]
Add the two equations together:
[tex](a^2+b^2)+(2ab) = (289)+(240)[/tex]
Simplify and rewrite:
[tex]a^2+2ab+b^2 = 529[/tex]
Factor using the perfect square trinomial pattern:
[tex](a+b)^2 = 529[/tex]
And take the square root of both sides:
[tex]\displaystyle a + b = \pm\sqrt{529} = \pm23[/tex]
Hence, the sum of the two numbers is 23 or -23.
In conclusion, our answer is B.
express
[tex](4 - x) {}^{ \frac{1}{2} } [/tex]
in ascending power of x up to term x²
Answer:
Step-by-step explanation:
Remember:
[tex]\boxed{(1+y)^{\frac{1}{2} }= 1+\dfrac{y}{2} -\dfrac{y^2}{2*4} +\dfrac{1*3*y^3}{2*4*6} +K\ with -1 < y \leq 1 }\\\\\\Let\ say\ 4-x=1+y\ or\ y=3-x\\\\\\(4-x)^{\frac{1}{2} }=1+\dfrac{3-x}{2} -\dfrac{(3-x)^2}{2*4} +K\ with\ 2\leq x <4\\\\=\dfrac{29}{8} -\dfrac{5x}{4} +\dfrac{x^2}{8} +K\\[/tex]
PLS HELP :( i’ve been trying to understand this but i cant. please explain this if you know how to do it pleaseee
Answer:
[tex]\huge\boxed{\sf x = 17}[/tex]
Step-by-step explanation:
Since m is a straight line, its measure is 180 degrees.
So,
2x + 5 + 8x + 5 = 180
2x + 8x + 5 + 5 = 180
10x + 10 = 180
10x = 180 - 10
10x = 170
Divide both sides by 10
x = 17
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Peace!What is the quotient of 7.584 x 10^9 and 7.9 x 10^ 2 expressed in scientific notation?
Answer:
9.6 × 10 6
Step-by-step explanation:
(7.584 × ) ÷ (7.9 × 10²)
This gives;
× = 0.96 ×
Simplifying further gives;
9.6 × = 9.6 ×
simplify square root of 3/8
please give steps!!
Step-by-step explanation:
Write the expression
[tex] \sqrt{ \frac{3}{8} } [/tex]
Let make the denominator a perfect square that is a multiple of 8. 16 is a multiple of 8 and a perfect square so
[tex] \sqrt{ \frac{3}{8} } = \sqrt{ \frac{6}{16} } [/tex]
Know that
[tex] \sqrt{ \frac{x}{y} } = \frac{ \sqrt{x} }{ \sqrt{y} } [/tex]
So
[tex] \sqrt{ \frac{6}{16} } = \frac{ \sqrt{6} }{4} [/tex]
The simplified form of the square root of 3/8 is (√6) / 4.
To simplify the square root of 3/8, we can simplify the numerator and denominator separately.
For the numerator, we take the square root of 3:
√3
For the denominator, we take the square root of 8:
√8
Now, let's simplify each of them:
√3 cannot be simplified further because 3 is a prime number.
√8 can be simplified by factoring out the perfect square:
√8 = √(4 × 2)
Since 4 is a perfect square (2² = 4), we can take it out of the square root:
√8 = 2√2
Now, let's put the simplified numerator and denominator together:
√3/8 = √3 / (2√2)
To rationalize the denominator, we multiply the expression by the conjugate of the denominator:
(√3 / (2√2)) × (√2 / √2) = (√3√2) / (2√2√2)
Simplifying the denominator:
(√3√2) / (2√4) = (√6) / (2 × 2)
Simplifying further:
(√6) / (2×2) = (√6) / 4
Therefore, the simplified form of the square root of 3/8 is (√6) / 4.
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Subtract. Write your answer in simplest form.
5/- 10/5
Answer:
-1/10
Step-by-step explanation:
(5/(-10))/5 = -(5/10)/5 = 1/10
(Hopefully this helped you out!)
Consider the sequence of numbers 50,48,46,44….
(A) What are the next three numbers in this sequence?
(B) Using n to represent the position of a number in this sequence, write an expression that allows you to calculate the nth number.
(C) use your expression to find the 100th number in this sequence
Step-by-step explanation:
(A) 42,40
(B) T(n) = 50 + (n-1)(-2)
= 50+2-2n
= 52-2n
(C) T(100) = 52 - 2(100)
= 52- 200
= - 148
How is the expression 3 x 1/10 written as a decimal
A)3
B).3
C).03
D).003
Answer:
B)
Step-by-step explanation:
3.0 / .1 = 0.3
Answer:
3×1/10=0.3 in decimals.
Step-by-step explanation:
3×1÷10
3÷10
0.3
Which describes the relationship between the distance and the difference?
Answer:
Which describes the relationship between the distance and the difference? The distance is always the opposite of the difference. ... The distance is the absolute value of the difference.
Use the rule for order of operations to simplify the expression as much as possible:
22−2(9⋅2−8)
What is this number sentence equal to?
If you could help, thank you so much!
Answer:
18.63
Step-by-step explanation:
[tex] \frac{6}{10} = 0.6 \\ \frac{3}{100} = 0.03[/tex]
[tex]10 + 8 + 0.6 + 0.03 = 18.63[/tex]
[tex]-7+1[3+8(2^2-8)][/tex]-7+1[3+8(2^2-8)]
Answer:
-36
Step-by-step explanation:
-7+1[3-32]
= -7-29
= -36
Given f(x) = x − 7 and g(x) = x2 .
Find g(f(4)).
g(f(4)) =
]
9514 1404 393
Answer:
g(f(4)) = 9
Step-by-step explanation:
Put the argument value where the variable is and do the arithmetic.
g(f(4)) = g(4 -7) = g(-3) = (-3)^2
g(f(4)) = 9
Order the numbers from least to greatest
Answer:
B
Step-by-step explanation:
It just is
How many different sets of answers are possible on a true-false test that has 11
questions?
A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 8
Blue 8
Green 3
Yellow 7
Purple 16
Based on these results, express the probability that the next spin will land on red or green or purple as a decimal to the nearest hundredth.
Step-by-step explanation:
The probability is the number of desired observations (red, green, blue) divided by total number of observed outcomes.
if (a°+10°)and (a°+20°)are supplementry angles ,find them
Step-by-step explanation:
a°+10°+a°+20°=180
becasue sum of angle of suplimentary angles is 180.
2a+30=180
2a=180-30
2a=150
a=75
Write the number in standard form.
ninety-two billion, seventy thousand,
one hundred eight
92.000.070.108
Step-by-step explanation:
Thousand has 3 zeros, a million has 6 and a billion has 9.
So for ninety-two billion, you take 92 and add 9 zeros behind it because a billion has 9 zeros
(92.000.000.000)
Determine the range of the following graph:
y
12
11
10
9
8
7
2
1
-12-11-10-9-8-7-6-5-4-3-2-11
1 2 3 4 5 6 7 8 9 10 11 12
- 2
-3
-4
-8
-9
-10
-11
-12
Answer:
r = (-4,9]
Step-by-step explanation:
hope this will help
Answer:
-4<y≤2
Step-by-step explanation:
The range of a graph is the range of the y values.
