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SCORPION-xisa [38]
3 years ago
13

A tablet sells for $375 at both Kade's Craft Corner and Annie's Art Shack.

Mathematics
1 answer:
vovangra [49]3 years ago
4 0
At Kates craft corner the tablet will cost $300 because 375×20% equals 75 then you must subtract 75 from 375 to get your discount price

At Annie’s art shack the tablet will cost $337.50 because 375×10% equals 37.5 then you subtract 37.5 from 375 which will give you $337.5.
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y=c1e^x+c2e^−x is a two-parameter family of solutions of the second order differential equation y′′−y=0. Find a solution of the
vagabundo [1.1K]

The general form of a solution of the differential equation is already provided for us:

y(x) = c_1 \textrm{e}^x + c_2\textrm{e}^{-x},

where c_1, c_2 \in \mathbb{R}. We now want to find a solution y such that y(-1)=3 and y'(-1)=-3. Therefore, all we need to do is find the constants c_1 and c_2 that satisfy the initial conditions. For the first condition, we have:y(-1)=3 \iff c_1 \textrm{e}^{-1} + c_2 \textrm{e}^{-(-1)} = 3 \iff c_1\textrm{e}^{-1} + c_2\textrm{e} = 3.

For the second condition, we need to find the derivative y' first. In this case, we have:

y'(x) = \left(c_1\textrm{e}^x + c_2\textrm{e}^{-x}\right)' = c_1\textrm{e}^x - c_2\textrm{e}^{-x}.

Therefore:

y'(-1) = -3 \iff c_1\textrm{e}^{-1} - c_2\textrm{e}^{-(-1)} = -3 \iff c_1\textrm{e}^{-1} - c_2\textrm{e} = -3.

This means that we must solve the following system of equations:

\begin{cases}c_1\textrm{e}^{-1} + c_2\textrm{e} = 3 \\ c_1\textrm{e}^{-1} - c_2\textrm{e} = -3\end{cases}.

If we add the equations above, we get:

\left(c_1\textrm{e}^{-1} + c_2\textrm{e}\right) + \left(c_1\textrm{e}^{-1} - c_2\textrm{e}  \right) = 3-3 \iff 2c_1\textrm{e}^{-1} = 0 \iff c_1 = 0.

If we now substitute c_1 = 0 into either of the equations in the system, we get:

c_2 \textrm{e} = 3 \iff c_2 = \dfrac{3}{\textrm{e}} = 3\textrm{e}^{-1.}

This means that the solution obeying the initial conditions is:

\boxed{y(x) = 3\textrm{e}^{-1} \times \textrm{e}^{-x} = 3\textrm{e}^{-x-1}}.

Indeed, we can see that:

y(-1) = 3\textrm{e}^{-(-1) -1} = 3\textrm{e}^{1-1} = 3\textrm{e}^0 = 3

y'(x) =-3\textrm{e}^{-x-1} \implies y'(-1) = -3\textrm{e}^{-(-1)-1} = -3\textrm{e}^{1-1} = -3\textrm{e}^0 = -3,

which do correspond to the desired initial conditions.

3 0
3 years ago
FIND THE AREA OF ABC. <br><br>ROUND final answer to nearest hundredth if it's a decimal​
In-s [12.5K]
Hello! Your answer will be 6 square units. If you need an explanation let me know! Have a nice day :)!
4 0
3 years ago
Read 2 more answers
Which expressions are equivalent to 3x + 2(x-1) - 4?
Oduvanchick [21]
3x+2(x-1)-4
=3x+2x-2-4
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5 0
3 years ago
Help pls I’m super confused
sveta [45]
The answer is (-160) because you need to plug in the numbers for the equation 6 times
6 0
3 years ago
The use of logic, making empirical observations, and performing dissections were all part of the scientific studies by
lesya692 [45]

Answer:

Aristotle

Step-by-step explanation:

Aristotle is widely known as a Greek philosopher. His works cover a wide range of topics and subjects, including subjects relating to science, arts, and finance.

Throughout his lifetime as a philosopher he was known to utilize logic, preparing empirical observations, and performing dissections as all part of his scientific studies.

Hence, in this case, the correct answer is ARISTOTLE

7 0
2 years ago
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