I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least 600 pounds more than each of her trucks, but no more than 1/3 of the total load her four trucks combined can carry. Based on these facts, what is the greatest load I can be sure that my large truck can carry, in pounds?

The load the large truck can carry  is 2400 pounds

Step-by-step explanation:

Let the load the large truck can carry  = X

Let the  load each of the four trucks owned by the neighbor can carry = Y

The given parameters are;

The load the large truck can carry X = 600 + Y(1)

The number trucks owned by the neighbor = 4

The load the large truck can carry X ≤ 1/3 × 4 × Y

Therefore, X ≤ 4/3 × Y

At maximum capacity, we have;

X = 4/3 × Y

Substituting the value of X into equation (1), we have;

4/3 × Y = 600 + Y

600 = 4/3 × Y - Y = 1/3·Y

Y = 3 × 300 = 1800 pounds

Y =  = 1800 pounds

Therefore, the load the neighbors truck can carry = 1800 pounds

X = 600 + Y gives;

X = 600 + 1800 = 2400 pounds

∴ The load the large truck can carry  = 2400 pounds

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)

d

step-by-step explanation: