If it took carlos 30 minutes to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 miles? (note: 1 mile = 5,280 feet)
(1) the average speed at which carlos cycled from his house to the library yesterday was greater than 16 feet per second.
(2) the average speed at which carlos cycled from his house to the library yesterday was less than 18 feet per second.

1) No

2) Yes

Step-by-step explanation:

Given : If it took Carlos 30 minutes to cycle from his house to the library yesterday.

To find : Was the distance that he cycled greater than 6 miles?

Solution :

The relation between speed , distance and time is

1) The average speed at which Carlos cycled from his house to the library yesterday was greater than 16 feet per second.

Speed = 16 feet per second

Converting into miles,

Time = 30 minute

Converting into seconds,

The distance he covered is

No, the distance that he cycled is not greater than 6 miles.

2) The average speed at which Carlos cycled from his house to the library yesterday was less than 18 feet per second.

Speed = 18 feet per second

Converting into miles,

Time = 30 minute

Converting into seconds,

The distance he covered is

Yes, the distance that he cycled is greater than 6 miles.

sec ф = 5/3 (quadrant 4)

let x = base

y = perp

z = hypotenuse

sec ф = hypotenuse/base = 5/3

⇒ z = 5 and x = 3

finding y:

z² = x² + y²

5² = 3² + y²

y² = 25-9

y² = 16

y = 4

now finding all other geometric functions of theta:

sin ф = y/z = 4/5

sin ф = -4/5 (sin is negative in the 4th quadrant)

cos ф = x/z = 3/5

cos ф = 3/5 (cos is positive in 4th quadrant)

tan ф = y/x = 4/3

tan ф = -4/3 (tan is negative in 4th quadrant)

cosec ф = z/y = 5/4

cosec ф = -5/4 (cosec is negative in the 4th quadrant)

cot ф = x/y = 3/4

tan ф = -3/4 (tan is negative in 4th quadrant)

step-by-step explanation: