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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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Howard is designing a chair swing ride. The swing ropes are 4 44 meters long, and in full swing they tilt in an angle of 2 3 ∘ 2

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Question:

Howard is designing a chair swing ride. The swing ropes are 4 meters long, and in full swing they tilt in an angle of 23°. Howard wants the chairs to be 3.5 meters above the ground in full swing. How tall should the pole of the swing ride be? Round your final answer to the nearest hundredth.

Answer:

7.18 meters

Step-by-step explanation:

Given:

Length of rope, L = 4 m

Angle = 23°

Height of chair, H= 3.5 m

In this question, we are to asked to find the height of the pole of the swing ride.

Let X represent the height of the pole of the swing ride.

Let's first find the length of pole from the top of the swing ride. Thus, we have:

$cos \theta = \frac{h}{L}$

Substituting figures, we have:

$cos(23) = \frac{h}{4}$

Let's make h subject of the formula.

$h = 4cos(23) = 3.68$

The length of pole from the top of the swing ride is 3.68 meters

To find the height of the pole of the swing ride, we have:

X = h + H

X = 3.68 + 3.5

X = 7.18

Height of the pole of the swing ride is 7.18 meters

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3 years ago

Ava bought a rectangular rug for her hallway. The rug is 23 yards wide and 234 yards long.

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Answer:

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Step-by-step explanation:

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3 years ago

The sum of two numbers is 30. the first number is twice the second number. what are the numbers?

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Let the numbers be x and y.

by the first statement of the question, we get , x + y = 30.,,..(1)

by the second satement, we get , x = y+ y => x=2y... (2)

from equation (2), let us put the value of x in equation (1),
x + y = 30
=> 2y + y = 30
=> 3y = 30
=> y =30/3
=> y = 10

and x=2y => x = 2*10 = 20

in short, the numbers are 10 and 20

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Answer:

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Answer:

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Step-by-step explanation:

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2 years ago