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2 years ago

The volume of a rectangular prism is given by the following function:

1 answer:

8 0

$v(x) = wlh \\ 2x {}^{3} + {x}^{2} - 16 x- 15 =(2x + 5)(x - 3)h \\ h = \frac{2x {}^{3} + x {}^{2} - 16x - 15 }{2x {}^{2} - x - 15 } \\ using \: long \: divison \\ h = x + 1$

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Two fraternities, Sig Ep and Ep Sig, plan to raise money jointly to benefit homeless people on Long Island. They will sell Yoda

WINSTONCH [101]

Answer:

a. Based on this information, construct a linear demand equation for Yoda vs. Alien T-shirts, and hence obtain the weekly revenue R as a function of the unit price x.

y = 640 - 80x ⇒ demand equation
xy = - 80x² + 640x ⇒ weekly revenue

b. The university administration charges the fraternities a weekly fee of $500 for use of the Student Center. Write down the monthly profit P as a function of the unit price x, and hence determine how much the fraternities should charge to obtain the largest possible weekly profit. What is the largest possible weekly profit?

$780

Step-by-step explanation:

first, we must determine the slope = (400 - 240) / (3 - 5) = 160 / -2 = -80

the demand equation:

y - 240 = -80 (x - 5)

y = -80x + 400 + 240

y = 640 - 80x

total weekly revenue:

xy = -80x² + 640x

xy - 500 = -80x² + 640x - 500

max. profit ⇒ x = -640 / (2 x -80) = -640 / -160 = 4

maximum weekly profit = -80($4²) + 640($4) - $500 = -$1,280 + $2,560 - $500 = $780

7 0

3 years ago

Hurry I'm almost out of time !!!!

stich3 [128]

Answer:

v= 7*6/2 *8 (The last one)

Step-by-step explanation:

To find the volume you have to multiply the base and the height which is 7 and 6 and divide it by 2. Then you multiply the 8.

8 0

3 years ago

Read 2 more answers

All 6 members of a family work. Their hourly wages (in dollars) are the following.37, 38, 39, 40, 39, 11Assuming that these wage

tiny-mole [99]

We have a sample that in fact represents the population.

We have to calculate the standard deviation of this population.

The difference between the standard deviation of a population comparing it to the calculation of the standard deviation of a sample is that we divide by the population side n instead of (n-1).

We have to start by calculating the mean of the population first:

$\begin{gathered} \mu=\dfrac{1}{n}\sum ^n_{i=1}\, x_i \\ \mu=\dfrac{1}{6}(37+38+39+40+39+11) \\ \mu=\dfrac{204}{6} \\ \mu=34 \end{gathered}$

Now, we can calculate the standard deviation as:

$\sigma=\sqrt[]{\dfrac{1}{n}\sum^n_{i=1}\, (x_i-\mu)^2}$ $\begin{gathered} \sigma=\sqrt[]{\dfrac{1}{6}((37-34)^2+(38-34)^2+(39-34)^2+(40-34)^2+(39-34)^2+(11-34)^2)} \\ \sigma=\sqrt[]{\frac{1}{6}(3^2+4^2+5^2+6^2+5^2+(-23)^2)} \\ \sigma=\sqrt[]{\frac{1}{6}(9+16+25+36+25+529)} \\ \sigma=\sqrt[]{\frac{1}{6}(640)} \\ \sigma\approx\sqrt[]{106.67} \\ \sigma\approx10.33 \end{gathered}$

Answer: the standard deviation of this population is approximately 10.33

3 0

2 years ago

Polygon XYZW is dilated by a scale factor of 2 with point T as the center of dilation, resulting in the image X′Y′Z′W′. If point

Anettt [7]

Since the whole figure including all the points is enlarged at the same time, the dilated figure will still have the same slope and that includes the fact that point T is still in line Y'Z'. The slope or shape does not change, only the size alters.The center of dilation is still at Point T in this case.

5 0

4 years ago

Read 2 more answers

Please help and Please write real equation for the answer thank you

Sidana [21]

Answer:

f(x) = (3x -12)/(x² -7x +12)

Step-by-step explanation:

The equation for a rational function can be written from the clues offered by the horizontal and vertical asymptotes, the y-intercept, and any "holes" in the function graph. Here, those clues are ...

horizontal asymptote: y = 0
vertical asymptote: x = 3
hole: (x, y) = (4, 3)
y-intercept: (0, -1)

The horizontal asymptote at y=0 tells you the denominator is of higher degree than the numerator. The vertical asymptote at x=3 tells you (x-3) is a factor of the denominator. The hole at x=4 tells you there is a factor of (x-4) in both numerator and denominator.

At this point, the function is tentatively ...

$f(x)=a\dfrac{x-4}{(x-3)(x-4)}$

Evaluating this at the y-intercept, x=0, gives ...

f(0) = -1 = a/(0 -3) = -a/3

a = 3 . . . . . multiply by -3

Then our rational function, consistent with all of the features of the graph, is ...

$f(x)=\dfrac{3(x -4)}{(x -3)(x -4)}\\\\\boxed{f(x)=\dfrac{3x-12}{x^2-7x+12}}$

4 0

3 years ago