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exis [7]
3 years ago
10

What is the rate of change of the function described in the

Mathematics
1 answer:
Debora [2.8K]3 years ago
5 0
5 because if you multiply the previous value by 5, you get the next answer
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Browns department store is having a 1/4 off sale. How much would a shirt that regularly sells for 36.00 cost during the sale?
nadya68 [22]
Since the shirt is 25 percent off your paying for 75 percent of the shirt. 0.75(36) is 27. The shirt will cost 27.00
4 0
2 years ago
If
Leno4ka [110]

Answer:

\frac{s^2-25}{(s^2+25)^2}

Step-by-step explanation:

Let's use the definition of the Laplace transform and the identity given:\mathcal{L}[t \cos 5t]=(-1)F'(s) with F(s)=\mathcal{L}[\cos 5t].

Now, F(s)=\int_0 ^{+ \infty}e^{-st}\cos(5t) dt. Using integration by parts with u=e^(-st) and dv=cos(5t), we obtain that F(s)=\frac{1}{5}\sin(5t)e^{-st} |_{0}^{+\infty}+\frac{s}{5}\int_0 ^{+ \infty}e^{-st}\sin(5t) dt=\int_0 ^{+ \infty}e^{-st}\sin(5t) dt.

Using integration by parts again with u=e^(-st) and dv=sin(5t), we obtain that

F(s)=\frac{s}{5}(\frac{-1}{5}\cos(5t)e^{-st} |_{0}^{+\infty}-\frac{s}{5}\int_0 ^{+ \infty}e^{-st}\sin(5t) dt)=\frac{s}{5}(\frac{1}{5}-\frac{s}{5}\int_0^{+ \infty}e^{-st}\sin(5t) dt)=\frac{s}{5}-\frac{s^2}{25}F(s).

Solving for F(s) on the last equation, F(s)=\frac{s}{s^2+25}, then the Laplace transform we were searching is -F'(s)=\frac{s^2-25}{(s^2+25)^2}

3 0
3 years ago
5. h(x)=0.5x - 1 with domain (-♾, 4) what is the range
Rudiy27

We have a domain of a function, that is, which x-es can we throw in. But we are asking which y-s will we get given that we can only throw x-es in (-\infty,4).

Let's try x=4 even though we are forbidden to put 4 inside h we are still able to do so.

So h(4)=0.5\cdot4-1=2-1=1 what we just got is the upper limit of the range. The lower limit is h(-\infty)=-\infty.

So the range is just (-\infty, 1).

Hope this helps :)

6 0
3 years ago
A manufacturer makes closed cubic containers from sheet metal. How many square centimeters of sheet metal will a 27,000 cm 3 con
dezoksy [38]

let's recall that a cube is just a rectangular prism with all equal sides, check picture below.

\bf \textit{volume of a cube}\\\\ V=s^3~~ \begin{cases} s=&length~of\\ &a~side\\ \cline{1-2} V=&27000 \end{cases}\implies 27000=s^3\implies \sqrt[3]{27000}=s\implies 30=s \\\\[-0.35em] ~\dotfill\\\\ \textit{surface area of a cube}\\\\ SA=6s~~\begin{cases} s=&length~of\\ &a~side\\ \cline{1-2} s=&30 \end{cases}\implies SA=6(30)\implies SA=180

6 0
3 years ago
Shows that usually cost $124.95 are on sale for $87.46. What percent off are they?
Ad libitum [116K]

Answer: They are 30% off


Step-by-step explanation:

$124.95 - 30% (37.485)

124.95-37.485= 87.465

4 0
3 years ago
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