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3 years ago

PQRS is a parallelogram with PQ=26cm and QR=20cm . If the distance between the longer-sides is 12.5cm , Find

Mathematics

1 answer:

Kay [80]3 years ago

6 0

Answer:

Below.

Step-by-step explanation:

I am guessing you want the area of the parallelogram.

Take the longer side to be the base.

Area = base * distance between base and opposite side

= 26 * 12.5

= 325 cm^2.

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You operate a gaming Web site, www.mudbeast.net, where users must pay a small fee to log on. When you charged $3 the demand was

Doss [256]

Answer:

A) The linear relation between price and demand is:

$d=-550x+2750$

The revenue R is:

$R=-550x^2+2750x$

B) The profit functionP is:

$P=-550x^2+2750x-30$

C) The largest monthly profit is obtained with a log-on fee of $2.5 per month. This corresponds to a profit of $3407.5.

Step-by-step explanation:

We have a site where the number of log-ons depends on our monthly fee. A linear relation is established between the price (log-on fee) and the number of log-ons.

We have two points for this linear relationship:

At price x=3, the demand is d=1100.
At price x=2.5, the demand is d=1375.

We will model the relation:

$d=mx+b$

We can calculate the slope m as:

$m=\dfrac{\Delta d}{\Delta x}=\dfrac{d_2-d_1}{x_2-x_1}=\dfrac{1375-1100}{2.5-3}\\\\\\m=\dfrac{275}{-0.5}=-550$

Then, replacing one point in the linear equation, we can calculate the intercept b:

$d_1=mx_1+b\\\\1100=(-550)\cdot 3+b\\\\1100=-1650+b\\\\b=1100+1650=2750$

Then, the linear relation between demand and price is:

$d=-550x+2750$

The revenue R can be expressed as the multiplication of the price and the demand:

$R=x\cdot d=x(-550x+2750)=-550x^2+2750x$

If we have a fixed cost of $30 per month, the profit P is:

$P=R-FC=-550x^2+2750x-30$

We can maximize the profit by deriving the profit function and making it equal to zero.

$\dfrac{dP}{dx}=0\\\\\\\dfrac{dP}{dx}=-550(2x)+2750(1)=0\\\\\\-1100x+2750=0\\\\x=\dfrac{2750}{1100}=2.5$

This corresponds to a profit of:

$P(2.5)=-550(2.5)^2+2750(2.5)-30\\\\P(2.5)=-550\cdot 6.25+6875-30\\\\P(2.5)=-3437.5+6875-30\\\\P(2.5)=3407.5$

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3 years ago

The product of 4x and 0 is

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Answer:

Step-by-step explanation:

any thing that is multiplied by 0 will be 0

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3 years ago

1 7/8 cups of ketchup times 3.

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Answer:

5 5/8 cups of ketchup

Step-by-step explanation:

1 7/8 x 3

15/8 x 3/1 = 45/8

45/8 = 5 5/8

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3 years ago

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What is the maximum number of possible extreme values for the function,

Liula [17]

Answer:

Step-by-step explanation:

We need to recur to the extreme value theorem, which states: "If a function is continuous on a closed interval, then that function has a maximum and a minimum inside that interval".

Basically, as the theorem states, if a dunction is continuous, then it has maxium or minium.

In this case, we have a quadratic function, which is a parabola. An important characteristic of parabolas is that they have a maximum or a minium, but they don't have both. When the quadratic term of the fuction is positive, then it has a minium at its vertex. When the quadratic term of the function is negative, then it has a maximum at its vertex.

So, the given function is $f(x)=x^{2} +4x^{2} -3x-18=5x^{2} -3x-18$ , where the quadratic term is positive, so the functions has a minimum at $V(h,k)$ , where $h=-\frac{b}{2a}$ and $k=f(h)$ , let's find that point

<h3> $h=-\frac{-3}{2(5)} =\frac{3}{10} =0.3$ </h3><h3> $k=f(0.3)=5(0.3)^{2} -3(0.3)-18=0.45-0.9-18=-18.45$ </h3><h3 /><h3>Therefore, the minium of the function is at (0.3, -18.45).</h3>

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3 years ago

PQRS is a parallelogram with PQ=26cm and QR=20cm . If the distance between the longer-sides is 12.5cm , Find​

PQRS is a parallelogram with PQ=26cm and QR=20cm . If the distance between the longer-sides is 12.5cm , Find