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2 years ago

State when f(x) is increasing , decreasing , concave up , concave down .

Mathematics

1 answer:

Marizza181 [45]2 years ago

3 0

Answer:

f(x) = sec x. tan x

⇔ f(x) = 1/cosx . cosx/sinx

⇔ f(x) = sin x

+) when f(x) is increasing => sin x increases

=> x will increase

+) f(x) is decreasing => x will decrease

+) f(x) is concave up => x ∈ (-pi/2; 0)

+) f(x) concave down => x ∈ (0; pi/2)

Step-by-step explanation:

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2 years ago

Read 2 more answers

Arielle is building the wooden framework for the roof of a house. she needs the angle created by the vertical and horizontal boa

Brums [2.3K]

Answer:

Option A is correct

it is an acute triangle. about 0.8 foot needs to be removed from the 20-foot board to create a right triangle.

Step-by-step explanation:

She want to build a right angle frame

Then to proof it is right angle, we will apply Pythagoras theorem to the sides of the rectangle,

Since the vertical height of board is 12ft

And, the horizontal length of board is 15ft.

Then the beam that support the two beams which also form the hypotenuse is give as

(beam support)²=(horizontal board)²+(vertical board)²

x²=12²+15²

x²=144+225

x²=369

x=√369

x=19.2ft

Then the beam support is 19.2ft

To get the angle of the beam support to the horizontal

Applying trigonometric

Tanθ=opposite / adjacent

Tanθ= vertical / horizontal

Tanθ=12/15

Tanθ=0.8

θ=arctan(0.8)

θ=36.7°

This shows that it is an acute triangle.

We are told that the support beam is 20ft but this is not true because the support beam is calculated to be 19.2ft,

So, 0.8ft must be removed from the 20ft support beam to create the right angle.

Then, the best option is a

we need to cut the support beam by approx 0.8 feet to make right angle between vertical board and horizontal board.

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3 years ago