i hang a 15 cm length spring in the classroom. the spring has a spring constant of 99 N/m. i the. attach a mass of 439 g to the spring. based on the information provided, use hookes law to predict the new length of the spring. (answer in cm)

0.19 m

Explanation:

Spring constant (k) = 99 N/m

Length of spring hung = 15cm = 0.15m

Mass attached to the spring = 498g

The new length of spring :

F = kdx

F = mass (m) * acceleration due to gravity (g)

g = 9.8 m/s²

dx = L2 - L1 (Change in length)

m = 439 / 1000 = 0.439kg

L2 = new length

L1 = initial length

mg = k(L2 - L1)

0.439 * 9.8 = 99(L2 - 0.15)

4.3022 = 99(L2 - 0.15)

4.3022 = 99L2 - 14.85

4.3022 + 14.85 = 99L2

19.1522 = 99L2

L2 = 19.1522 / 99

L2 = 0.1934565

L2 = 0.19 m

New length of spring = 0.19 m

emily ruth's annual premium is $1058.50

step-by-step explanation:

emily ruth is a female of 27 years age purchasing 20 year endowment insurance with face value $25000.

from the given table,

for females, the age of a male 3 years younger should be used.

so, we have to check for 24 year male for 20 year endowment.

it is 42.34 for every $1000 face value.

for a face value of $25000,

it is 25 * 42.34 = $1058.50

∴ emily ruth's annual premium is $1058.50

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .