Connections between tan theta and tan(90 + theta)

1 answer:

7 0

Tan(90+ theta) = (tan90 + tantheta)/(1-tan90tantheta)

= ( sin90costheta + sintheta cos 90) / (cos90costheta - sin90sintheta))
= sin(90 + theta)/ cos(90+ theta) = costheta/-sintheta = - 1/tantheta

tan(90 + theta ) = -1/tantheta

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If Tom, George and Mario work together, they can paint a 600 ft2 room in 4 hours. When only George and Mario work together, it t

WINSTONCH [101]

We call:

T = Tom's paiting rate $( \frac{ ft^{2} }{h} )$
G = George's paiting rate $( \frac{ ft^{2} }{h} )$
M = Mario's paiting rate $( \frac{ ft^{2} }{h} )$

As the first statement says that they can work together, then:

T + G + M = Painting rate working together, that is the surface area they paint per hour.

Since the problem says that they last four hours painting a $600ft^{2}$ room, then we need to multiply the amount of hours times the painting rate that is equal the surface area of the room, so:

4(T + G + M) = 600

Applying a similar reasoning, the George and Mario's painting rate is:

0 + G + M
Note that 0 implies that Tom didn't work in this case.

As they last eight hours painting the room, then:

8(0 + G + M) = 600

The same reasoning is applied to Tom and George working together. In this case 0 implies that Mario didn't work, so:

6(T + G + 0) = 600

We have a system of linear equations in three variables T, G, M:

4(T+G+M)=600
8(0+G+M)=600
6(T+G+0)=600

Solving:

(1) T + G + M = 150
(2) G + M = 75
(3) T + G = 100

Substitute (3) in (1):
100 + M = 150 ∴ M = 50

Replace M in (2):
G + 50 = 75 ∴ G = 25

Substitute G in (3)
T + 25 = 100 ∴ T = 75

Then, the painting rates are:
Tom = 75 $( \frac{ ft^{2} }{h} )$
George = 25 $( \frac{ ft^{2} }{h} )$
Mario = 50 $( \frac{ ft^{2} }{h} )$

Solving for Time to determine how long it would take Tom to paint the room alone:

Painted Area = Painting Rate×Time, so:

 $Time Tom = \frac{Painted Area}{Painting Rate (T)}$
$Time Tom = \frac{600}{75} = 8 hours$

6 0

3 years ago

Read 2 more answers

Area of a circle how do you do this

Katena32 [7]

Answer:

See below.

Step-by-step explanation:

The area of the circle is given by the formula:

$A=\pi r^2$