I jus need confirmation to see if I got the correct answer. If it is wrong could you please help me with it.

A company has found that the daily demand x for its boxes of chocolates is inversely proportional to the price p. When the price

Amiraneli [1.4K]

Answer:

667 boxes

Step-by-step explanation:

-Given that x is the demand and p the price.

-Let k be the constant of proportionality. We then express the inverse relationship as:

$x=\frac{k}{p}\\\\k=xp=800\times 5=4000$

#We substitute for the new x value and the calculated k to solve for p:

$x=\frac{k}{p}\\\\p=\frac{k}{x}\\\\=\frac{4000}{6}\\\\=666.6667\\\\\approx 667\ boxes$

Hence, the demand at a price of $6 is approximately 667 boxes

3 0

3 years ago

Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = x^3 – 3x^2 + 2x

castortr0y [4]

Answer: The correct option is second, i.e. ,"2 times the integral from 0 to 1 of the quantity x cubed minus 3 times x squared plus 2 times x, dx".

Explanation:

The given equation is,

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

It can be written as,

$f(x)=x^3-3x^2+2x$

Find the zeros of the equation. Equation the function equal to 0.

$0=x^3-3x^2+2x$

$x(x^2-3x+2)=0$

$x(x^2-2x-x+2)=0$

$x(x-2)(x-1)=0$

So, the three zeros are 0, 1 and 2.

The graph of the equation is shown below.

From the given graph it is noticed that the enclosed by the curve and x- axis is lies between 0 to 2, but the area from 0 to 1 lies above the x-axis and area from 1 to 2 lies below the x-axis. So the function will be negative from 1 to 2.

The area enclosed by curve and x-axis is,

$A=\int_{0}^{1}f(x)dx+\int_{1}^{2}[-f(x)]dx$

$A=\int_{0}^{1}f(x)dx-\int_{1}^{2}f(x)dx$

From the graph it is noticed that the area from 0 to 1 is symmetric or same as area from 1 to 2. So the total area is the twice of area from 0 to 1.

$A=2\int_{0}^{1}f(x)dx$

$A=2\int_{0}^{1}[x^3-3x^2+2x]dx$

Therefore, The correct option is "2 times the integral from 0 to 1 of the quantity x cubed minus 3 times x squared plus 2 times x, dx".

3 0

3 years ago

If a bird is sitting 30m along the first wall and a cat is 34m along the top of the other wall, how far apart are the cat and th

Varvara68 [4.7K]

Draw a right triangle. The cat represents a side, the bird represents a side. Then just use the Pythagorean Theorem to find the hypotenuse. a^2 + b^2 = c^2. Let a = cat; b = bird; then solve for c.

6 0

4 years ago

Steve will roll a number cube, numbered 1-6, twice. What is the probability

Leni [432]

Answer:

25%

Step-by-step explanation:

First we calculate the probability of rolling a number greater than 3, that is, it can be 4, 5 or 6.

The probability of each number is 1/6, so:

P1 = (1/6) + (1/6) + (1/6) = 3/6 = 1/2

Then, we calculate the probability of rolling a prime number, that is, 2, 3 or 5.

As we have again 3 numbers, the probability P2 will also be 1/2

Then, the final probability is the product of both P1 and P2:

P = P1 * P2 = (1/2) * (1/2) = 1/4 = 25%

3 0

4 years ago

(x + 1)^7<br> Use Pascal's Triangle and Binomial.Theorem

KATRIN_1 [288]

Answer:

x⁷+7x⁶+21x⁵+35x⁴+35x³+21x²+7x+1

Step-by-step explanation:

(x + 1)⁷: Pascal's Triangle for (a+b)⁷

a₇+7a⁶b+21a⁵b²+35a⁴b³+... + 7a¹b⁶ + b⁷

x⁷+7x⁶+21x⁵+35x⁴+35x³+21x²+7x+1

8 0

3 years ago