Solve the system of equations. 2y-y=5 and 3x+2y=4

If 2y=x³ + 2x², find dy/dx when x=2.

scZoUnD [109]

Answer:

10

Step-by-step explanation:

$\boxed{\textsf{If }y=x^n,\: \textsf{then }\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}}$

Given equation:

$2y=x^3+2x^2$

Isolate y by dividing both sides by 2:

$\implies y=\dfrac{1}{2}x^3+x^2$

Differentiate with respect to x:

$\implies \dfrac{\text{d}y}{\text{d}x}=3 \cdot \dfrac{1}{2}x^{3-1}+2 \cdot x^{2-1}$

$\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{3}{2}x^2+2x$

Finally, substitute x = 2 into the differentiated equation:

$\begin{aligned} \implies \dfrac{\text{d}y}{\text{d}x} & =\dfrac{3}{2}(2)^2+2(2)\\\\ & = \dfrac{3}{2}(4)+4\\\\ & = \dfrac{12}{2}+4\\\\ & = 6+4\\\\ & = 10\end{aligned}$

Learn more about differentiation here:

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5 0

2 years ago

A parking lot has seventy-eight parking spaces numbered from 1 to 78. There are no cars in the parking lot when Jillian pulls in

polet [3.4K]

Answer:

49/78

Step-by-step explanation:

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.

probability that the number on the parking space where she parks is greater than or equal to 30 = numbers greater than or equal to 30 / total numbers

49 / 78

6 0

3 years ago

PLEASE HELP what is the next term what is A in the sequence and what is the common ratio for 2 4 8 16 32

mel-nik [20]

Answer:

The next term is 64, a is 2, and the common ratio is 2.

Step-by-step explanation:

Look at what's happening from each number to the next. What do you need to do to get from 2 to 4, or 4 to 8? Multiply by 2. That's your common ratio. To get the next number in the sequence, multiply the last number by the common ratio of 2. 32 x 2 = 64, so the next number in the sequence is 64. "a" is just the very first term, meaning it's 2.

5 0

3 years ago

How would you answer this question?

grigory [225]

Answer: Choice B

If you lower your rates by 6% you will increase the number of occupancies by 12%

========================================================

Explanation:

Price Elasticity of Demand is found by dividing the percent change of demand over the percent change in price

$\text{Price Elasticity of Demand} = \frac{\% \text{ change in demand}}{\% \text{ change in price}}$

If the price drops 6% leads to a 12% increase in demand, then we get this elasticity

$\text{Price Elasticity of Demand} = \frac{\% \text{ change in demand}}{\% \text{ change in price}}\\\\\text{Price Elasticity of Demand} = \frac{12\% \text{ increase in demand}}{6\% \text{ drop in price}}\\\\\text{Price Elasticity of Demand} = \frac{12\%}{-6\%}\\\\\text{Price Elasticity of Demand} = \frac{0.12}{-0.06}\\\\\text{Price Elasticity of Demand} = -2\\\\$

The absolute value of that result is 2. We work backwards going from 2 to see the relationship between the 12% and 6%.

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Side notes:

Choice A is incorrect as a price elasticity of demand larger than 2 means we have elastic (rather than inelastic) demand.
Choice C is incorrect because while raising rates does bring in more money in certain situations, there's a limit to how much the price goes up before people stop showing up. The prices can't go up forever. Also, the fact we have an elastic product means people are either forgoing this hotel or finding a substitute.
Choice D is incorrect. Products with high demand elasticity usually have substitutes. Any slight change in the price leads people to seek cheaper options. Unless we're dealing with a small town there are usually multiple hotels to choose from.

5 0

4 years ago

Express 2x^2+3x/(2x+3)(x-2) - 6/x^2-x-2 As a single fraction in its simplest form.

Dmitry [639]

Answer:

(x + 3)/(x + 1) .

Step-by-step explanation:

2x^2 + 3x/(2x + 3)(x - 2) - 6 /x^2 - x - 2

= 2x^2 + 3x/(2x + 3)(x - 2) - 6 / (x - 2)(x + 1)

The LCM is (2x + 3)(x - 2)(x + 1) so we have

(2x^2 + 3x)(x + 1) - 6(2x + 3) x( 2x + 3)(x + 1) - 6(2x + 3)

--------------------------------------- = ------------------------------------

(2x + 3)(x - 2)(x + 1) (2x + 3)(x - 2)(x + 1)

(2x + 3)(x(x + 1) - 6) (2x + 3)(x - 2)(x + 3)

= ---------------------------- = --------------------------- = (x + 3)/(x + 1)

(2x + 3)(x - 2)(x + 1) (2x + 3)(x - 2)(x + 1)

7 0

4 years ago