suppose the functions u and w are defined as follows u(x)=x+9 w(x)=the square root of x+8 find the following (wou)(8)= (uow)(8)=

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.)

Answer:

(M-5rt^2)/(-2r) =v

Step-by-step explanation:

M = 5rt^2- 2rv

Subtract  5rt^2 from each side

M-5rt^2 = 5rt^2- 2rv -5rt^2

M-5rt^2 = - 2rv

Divide each side by -2r

(M-5rt^2)/(-2r) =- 2rv / (-2r)

(M-5rt^2)/(-2r) =v

Answer:

[tex]v = -\frac{M-5rt^2}{2r}[/tex]

Step-by-step explanation:

[tex]M = 5rt^2 - 2rv[/tex]

Switch sides

[tex]5rt^2-2rv=M[/tex]

Subtract [tex]5rt^2[/tex] from both sides

[tex]5rt^2 - 2rv-5rt^2= M -5rt^2[/tex]

Simplify

[tex]-2rv = M - 5rt^2[/tex]

Divide both sides by [tex]-2r[/tex]

[tex]\frac{-2rv}{-2r} =\frac{M}{-2r} -\frac{5rt^2}{-2r}[/tex]

Simplify

[tex]-\frac{M-5rt^2}{2r}[/tex]

Answer:

12000

Step-by-step explanation:

8000+4000=12000

The range of the exponential function is: B. [tex]g(x)>-6[/tex]

Recall:

Range of any function includes all possible values of y (output)

Domain of any function includes all possible values of x (input).

Thus:

The values of y in the exponential function greater than -6 on the y-axis as shown in the graph given.

Therefore:

Range of the exponential function given in the graph is: B. [tex]g(x)>-6[/tex].

Learn more about exponential function here:

https://brainly.com/question/19554225

Step-by-step explanation:

hopefully it makes sense and is visible

:)

After a small search, I've found that we want to find the inverses of both functions. We will find that E(x) does not have an inverse function, and the inverse function of T(x) is h(x) = x/6 - 1/6

Here we have a piecewise function:

T(x) = 6(x-3) + 25  if x > 3

E(x) = 25    if 0 ≤ x ≤ 3

First, remember that two functions f(x) and g(x) are inverses if:

f(g(x)) = x

g(f(x)) = x

From that definition we can see that E(x) does not have an inverse, because for any function g(x), we will have:

E(g(x)) = 25

So E(x) can't meet the condition.

Now let's analyze the function T(x)

T(x) = 6(x-3) + 25  

We can rewrite it as:

T(x) = 6x - 6×3 + 25

T(x) = 6x + 1

Note that T(x) is a linear equation, so the inverse will also be a linear equation. Let's assume that the inverse is h(x) = ax + b

We will have:

T(h(x)) = 6×h(x) + 1 = 6(ax + b) + 1  

Now, if these are inverses, we have:

6(ax + b) + 1 = x

6ax + 6b + 1 = x

Then we must have:

6b + 1 = 0

6ax = x

From the first equation, we can get:

6b + 1 = 0

6b = -1

b = -1/6

From the second equation we have:

6ax = x

6a = 1

a = 1/6

Then:

h(x) = x/6 - 1/6

And this is the inverse function of T(x)

If you want to learn more, you can read:

https://brainly.com/question/10300045

Answer:

1/18

Step-by-step explanation:

Probability of spinning red=2/6=1/3

Probability of spinning green=1/6

probability of spinning green and then red=(1/6)*(1/3)=1/18

Answer:

B. 3.09-3.10-3.2-3.5 is the answer

Answer:

Step-by-step explanation:

You will have to interpret the question with the aid of a diagram and make out the relevant angles and either make use of cosine rule,sine rule etc....Your knowledge on angles should be sound

Answer:

−2(y+1)

Step-by-step explanation:

factor ..................

9514 1404 393

Answer:

  C. The order in which numbers are added does not affect the sum.

Step-by-step explanation:

In symbols, the commutative property of addition is ...

  a +b = b +a

The order in which numbers are added does not affect the sum.

hi <3

just form a quick equation:

3/4p = 18

divide both sides by 3/4 to get your answer:

p = 24

hope this helps :)

Answer:

Step-by-step explanation:

The financial statement performed by Snell Corporation shows how the revenue recognition provides financial statement users(i.e. the client that uses Snell Co. service in May, June, and July) with relevant information regarding the services associated with revenue from customer contracts.

In the given case, the Snell Co. service charge was hiked in May since the entire service income must be accounted for in May. The amount owed from a client is seen as a current asset on the balance sheet, and once the amount is received from a client, it is removed off from the current asset. Thus it is added to the zero dollars ($0) company's cash balance. In this case, the cash collected in June and July is not recorded as revenue.

We can conclude that the monthly revenue recorded from Snell Co. performance and services for the client in May, June, and July for this service is as follows:

Months                               Revenue

May                                     $1000

June                                       0

July                                         0

Learn more about revenue here:

https://brainly.com/question/19682087?referrer=searchResults

Revenue is only earned after the required obligation (goods delivered or service rendered) has been fulfilled. From the question, we noted that Snell Co. performs and completes services for a client in May hence the revenue was earned in May irrespective of when money was received for the service rendered.

As such revenue earned in;

May is $1,000

June is $0

July is $0

for the service rendered

Answer:

15.2

[tex] {c }^{2} = {a}^{2} + {b}^{2} \: \\ {c}^{2} ={6}^{2} + {14}^{2} \\ {c}^{2} = 36 + 196 \\ {c}^{2} = 232 \\ \sqrt{c } = \sqrt{232} \\ c = 15.23154621[/tex]

Answer:

90,000+9,000+700+60+3

Answer:

90,000 + 9,000 + 700 + 60 + 3 I hope this helped

Answer:

12 meters far.

Step-by-step explanation:

The question translates to 10+2. The word problem states that the height of the platform is 10 meters. That means we can say that he'd have already traveled 10 meters down when he dived. And the problem also states that the diver goes two meters under the water, meaning that he had traveled 2 meters, in addition to the 10 meters. And so, we add the 10 and 2 to get 12 meters in total.

Answer:

going up in even numbers

Step-by-step explanation:

its like the two times table, and it goes up in even numbers

Answer:

any number you can take

Step-by-step explanation:

like 4'6'8''12

[tex]\boxed{\sf \:\begin{cases}\\\begin{gathered} {\underline{{ \sf {\blue{\Large\bf \underbrace{ {\rm {\purple{\begin{array}{r | l}\large\rm{\red{ 5}}&\underline{315,420,525}\\\large\rm{\red{ 3}}& \underline{63,84,105}\\\large\rm{\red{3}}&\underline{21,28,35}\\\large\rm{\red{ 7}}&\underline{7,28,35}\\\large\rm{\red{2}}&\underline{1,4,5}\\\large\rm{\red{2}}&\underline{1,2,5}\\\large\rm{\red{5}}&\underline{1,1,5}\\&1,1,1\end{array}}}}} }}}}}\end{gathered}\\\end{cases}}[/tex]

LCM = 5 × 3 × 3 × 7 × 2 × 2 × 5

LCM = 6300

Hence, the LCM of 315 , 420 , 525 is 6300

Answer:

Step-by-step explanation:

Prime factors of given numbers:

The LCM is:

p ∧ q (i.e. "p and q") is true only if both p and q are true. This is the case for the first two rows, but not the third.

Similarly, (p ∧ q) ∧ r is true only if both p ∧ q and r are true. We know when p ∧ q is true, so (p ∧ q) ∧ r is true only when all three of p, q, and r are true. This happens only in the first row.

All other cases are false.

The table should look like this:

[tex]\begin{array}{c|c|c|c|c}p&q&r&p\land q&(p\land q)\land r) \\---&---&---&---&--- \\T&T&T&\boxed T&\boxed T\\&&&&\\T&T&F&\boxed T&\boxed F\\&&&&\\T&F&T&\boxed F&\boxed F\end{array}[/tex]

Answer:

2/3 can be wrtten in three ways

Step-by-step explanation:

1: 6/9

2. 4/6

3.20/30

Answer:

4y

Step-by-step explanation:

Answer:

perimeter=4y

Step-by-step explanation:

y+y+y+y=4y

..........

Answer:

50cm

Step-by-step explanation:

oh apdiya I just wanted to let you

Answer:

22

Step-by-step explanation:

All thats need to do in this problem is add both line lengths to find the length of FH.

8 + 14 = 22

Best of Luck!