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krek1111 [17]
3 years ago
11

Two lines L1 and L2 pass through the point of intersection of 2y=x-13 and 3y+x+12=0. L1 passes through P(-4,-7) and L2 is perpen

dicular to 2x-5y=4.find the acute angle between L1 andL2
Mathematics
1 answer:
alexgriva [62]3 years ago
6 0

Answer:

84°

Step-by-step explanation:

1. <u>point of intersection of 2y=x-13 and 3y+x+12=0</u>

x = 2y + 13   ==> 3y + (2y+13) + 12 = 0   ==>  5y + 25 = 0  ==> y = -5

x = 2*(-5) +13 = 3

point of intersection: (3 , -5)        L1: pass (3 , -5) and (-4 , -7)

slope of L1 = (-7 - -5)/(-4-3) = -2 / -7 = 2/7

L2 pass (3 , -5) perpendicular to 2x-5y=4

2x-5y=4  ==> y = 2/5 x - 4  slope = 2/5  

so slope of L2 = -5/2

angle Θ between two slopes: tan Θ = | (m2-m1) / (1 + m1*m2)|

==> = | (-5/2 - 2/7) / (1 + -5/2*2/7) | = |(-39/14) / (4/14) | = |- 39/4| = 39/4 = 9.75

Θ = 84°

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A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the number of cakes sold per
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The total revenue is TR=580x-10x^2.

The marginal revenue is MR=580-20x.

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The marginal cost function is MC=50x+300.

Step-by-step explanation:

The Total Revenue (TR) received from the sale of x goods at price p is given by

                                                         TR=p\cdot x

The Marginal Revenue (MR) is the derivative of total revenue with respect to demand and is given by

                                                       MR=\frac{d(TR)}{dx}

From the information given we know that the price they can sell cakes is given by the function p=580-10x, where x is the number of cakes sold per day.

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TR=(580-10x)\cdot x\\TR=580x-10x^2

And the marginal revenue is

MR=\frac{d}{dx}(580x-10x^2) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\MR=\frac{d}{dx}\left(580x\right)-\frac{d}{dx}\left(10x^2\right)\\\\MR=580-20x

The Fixed Cost (FC) is the amount of money you have to spend regardless of how many items you produce.

The Marginal Cost (MC) function is the derivative of the cost function and is given by

                                                   MC=\frac{d(TC)}{dx}

We know that the total cost function of the company is given by C=(30+5x)^2, which it is equal to

\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a+b\right)^2=a^2+2ab+b^2\\a=30,\:\:b=5x\\\\\left(30+5x\right)^2=30^2+2\cdot \:30\cdot \:5x+\left(5x\right)^2=25x^2+300x+900\\\\C=25x^2+300x+900

From the total cost function and applying the definition of fixed cost, the fixed cost is $900.

And the marginal cost function is

MC=\frac{d}{\:dx}\left(25x^2+300x+900\right)\\\\MC=\frac{d}{dx}\left(25x^2\right)+\frac{d}{dx}\left(300x\right)+\frac{d}{dx}\left(900\right)\\\\MC=50x+300+0=50x+300

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