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3 years ago

In △ABC, m∠CAB=30° and M is the midpoint of AB so that AB=2CM. Find the angles of the triangle. Find AB if BC=7 ft.

Mathematics

2 answers:

elena55 [62]3 years ago

7 0

angle ACB = 90 degrees

angle B = 60 degrees

AB = 14ft.

topjm [15]3 years ago

4 0

Answer:

hypotenuse side AB is twice than BC, i.e. 14 ft.

Step-by-step explanation:

Given data:

angle CAB = 30 degree

M is mid point of AB and AB = 2 times of CM

We can say that, |MA| = |MB| = |MC|. and point A, B, and C are equidistant from M. It signifies that the point M is act as center of the circle which circumscribed around the given triangle ABC.

Therefore AB is diameter of circle and angle ACB is leaning on diameter AB.

It signifies that the angle ACB is 90 degree angle and the triangle ABC is right-angled triangle.

Since the angle CAB is 30 degree, therefore the other acute angle is 90-30 = 60 degree.

Thus the triangle ABC is (30 - 60 - 90) degree triangle.

Since side BC opposite to 30 degree is given as 7 ft, therefore hypotenuse side AB is twice than BC, i.e. 14 ft.

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HACTEHA [7]

Answer:

A) Revenue function = R(x) = (580x - 10x²)

Marginal Revenue function = (580 - 20x)

B) Fixed Cost = 900

Marginal Cost function = (300 + 50x)

C) Profit function = P(x) = (-35x² + 280x - 900)

D) The quantity that maximizes profit = 4

Step-by-step explanation:

Given,

The Price function for the cake = p = 580 - 10x

where x = number of cakes sold per day.

The total cost function is given as

C = (30 + 5x)² = (900 + 300x + 25x²)

where x = number of cakes sold per day.

Please note that all the calculations and functions obtained are done on a per day basis.

A) Find the revenue and marginal revenue functions [Hint: revenue is price multiplied by quantity i.e. revenue = price × quantity]

Revenue = R(x) = price × quantity = p × x

= (580 - 10x) × x = (580x - 10x²)

Marginal Revenue = (dR/dx)

= (d/dx) (580x - 10x²)

= (580 - 20x)

B) Find the fixed cost and marginal cost function [Hint: fixed cost does not change with quantity produced]

The total cost function is given as

C = (30 + 5x)² = (900 + 300x + 25x²)

The total cost function is a sum of the fixed cost and the variable cost.

The fixed cost is the unchanging part of the total cost function with changing levels of production (quantity produced), which is the term independent of x.

C(x) = 900 + 300x + 25x²

The only term independent of x is 900.

Hence, the fixed cost = 900

Marginal Cost function = (dC/dx)

= (d/dx) (900 + 300x + 25x²)

= (300 + 50x)

C) Find the profit function [Hint: profit is revenue minus total cost]

Profit = Revenue - Total Cost

Revenue = (580x - 10x²)

Total Cost = (900 + 300x + 25x²)

Profit = P(x)

= (580x - 10x²) - (900 + 300x + 25x²)

= 580x - 10x² - 900 - 300x - 25x²

= 280x - 35x² - 900

= (-35x² + 280x - 900)

D) Find the quantity that maximizes profit

To obtain this, we use differentiation analysis to obtain the maximum point of the Profit function.

At maximum point, (dP/dx) = 0 and (d²P/dx²) < 0

P(x) = (-35x² + 280x - 900)

(dP/dx) = -70x + 280 = 0

70x = 280

x = (280/70) = 4

(d²P/dx²) = -70 < 0

Hence, the point obtained truly corresponds to a maximum point of the profit function, P(x).

This quantity demanded obtained, is the quantity demanded that maximises the Profit function.

Hope this Helps!!!

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Answer:

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sertanlavr [38]

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lapo4ka [179]

Answer:

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