The length that a spring stretches varies directly with a weight placed at the end of the spring. When Sarah placed a 10lb watermelon on a hanging scale, the spring stretched 5in. Write an equation that relates the length L that the spring stretches to the weight w. How many pounds does a watermelon weigh if it stretch the spring 6in?

A watermelon weighs 12 lb if it stretches the spring 6in.

Step-by-step explanation:

If two variables are directly proportional, it means that an increase in the value of one variable would cause a corresponding increase in the other variable. Also, a decrease in the value of one variable would cause a corresponding decrease in the other variable.

Given that length, L varies directly with weight, W, if we introduce a constant of proportionality, k, the expression becomes

L = kW

When W = 10 and L = 5, then

5 = 10k

k = 5/10 = 0.5

Therefore, the equation that relates the length L that the spring stretches to the weight W is

L = 0.5W

Therefore, if L = 6 inch, then

6 = 0.5W

W = 6/0.5 = 12 lb

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)

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.