If a mass m is placed at the end of a spring, and if the mass is pulled downward and released, the mass-spring system will begin to oscillate. the displacement y of the mass from its resting position is given by a function of the form y(t)equalsc 1 cosine omega t plus c 2 sine omega t, where omega is a constant that depends on the spring and the mass. show that the set of all functions of this form (with omega fixed and c 1 and c 2 arbitrary) is a vector space.

89

step-by-step explanation:

we have the parent function given by,

1. the function is translated 5 units to the left.

so, we get,   becomes

2. the function is translated 5 units to the right.

so, we get,   becomes

3. the function is translated 5 units upwards.

so, we get,   becomes

4. the function is translated 5 units downwards.

so, we get,   becomes

5. the function is reflected across x-axis.

so, we get,   becomes

6. the function is reflected across y-axis.

so, we get,   becomes .

step-by-step explanation:

mark brainliest.

i need points

step-by-step explanation:

sorry bubs

part a: 1.08

part b: 27.59