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3 years ago

Please help me with this question!

Mathematics

1 answer:

Alina [70]3 years ago

4 0

Answer:

see explanation

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°, thus

∠1 = 180° - (72 + 57)° = 180° - 129° = 51°

The right angle at the left vertex is composed of 72° and ∠2, thus

∠2 = 90° - 72° = 18°

57° and ∠3 form a straight angle and are supplementary, thus

∠3 = 180° - 57° = 123°

∠4 = 180° - (∠2 + ∠3 ) ← sum of angles in a triangle

∠4 = 180° - (18 + 123)° = 180° - 141° = 39°

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The management of Ditton Industries has determined that the daily marginal revenue function associated with selling x units of t

barxatty [35]

Answer:

(a) The daily total revenue realized from the sale of 210 units of the toaster oven is $6,195.

(b) The additional revenue realized when the production (and sales) level is increased from 210 to 310 units is $1,400.

Step-by-step explanation:

The marginal revenue gives the actual revenue realized from the sale of an additional unit of the commodity given that sales are already at a certain level. The derivative R' of the function R measures the rate of change of the revenue function.

We know that the daily marginal revenue function is given by

$R'(x) = -0.1x+40$

(a) To find the the daily total revenue you must:

Integrate the daily marginal revenue function,

$\int R'(x)dx = \int(-0.1x+40)dx\\\\R(x)=-\int \:0.1xdx+\int \:40dx\\\\R(x)=-0.05x^2+40x+C$ ,

where C is a constant.

Find the value of C, using the fact that if you sell 0 units your daily revenue is $0.

$0=-0.05(0)^2+40(0)+C\\C=0$

$R(x)=-0.05x^2+40x$

The daily total revenue realized from the sale of 210 units of the toaster oven is

x = 210 units

$R(210)=-0.05(210)^2+40(210)\\R(210)=-210^2\cdot \:0.05+8400\\R(210)=-2205+8400\\R(210)=6195$

(b) To find the additional revenue realized when the production (and sales) level is increased from 210 to 310 units you must:

Find the daily total revenue realized from the sale of 310 units

$R(310)=-0.05(310)^2+40(310)\\R(310)=-310^2\cdot \:0.05+12400\\R(310)=-4805+12400\\R(310)=7595$

The additional revenue realized when the production (and sales) level is increased from 210 to 310 units is

$R(310)-R(210)=7595-6195=1400$

3 0

4 years ago

Q2. Calculate the area of the shaded region in the figure shown. 40° 12m 10m

Anvisha [2.4K]

Answer:

Area of the shaded area = 60 m^2

Step-by-step explanation:

Remark

I don't think you need the 40 degrees for anything.

Formula

Area of Shaded part = area of the rectangle - area of the triangle

Solution

Area of the Rectangle

L = 12 meters

W = 10 meters

Area = 12 * 10

Area = 120 m^2

Area of the triangle

Area = 1/2 b * h

b = 12

h = 10

Area = 1/2 * 12 * 10

Area = 120/2 = 60

Area of the shaded area

120 - 60 = 60

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