I've been stuck on this problem forever now!
provide reasons for the proof.
given: angle 2=4
and 2 and 3 are supplementary
prove: angle 1=3
statement: reason
1. 2=4 1. given
2. m2=m4 2. angle congruence postulate
3. angles 2 and 3 are supplementary 3. given
4. m2+m3=180 4. definition of supplementary angles
5. angles 1 and 4 are supplementary 5. fill in blank
6. m1+m4=180 6. definition of supplementary angles
7. m1+m4=m2+m3 7. fill in blank
8. m1+m4=m4+m3 8. fill in blank
9. m1=m3 9. fill in blank
10. 1=3 10. fill in blank

The input to the function is x and the output is y. write the function such that x can be a vector (use element-by-element operations). a) use the function to calculate y(-1.5) and y(5). b) use the function to make a plot of the function y(x) for -2 ≤ x ≤ 6.

Nthe opening scene of the movie raiders of the lost ark, indiana jones replaces a golden statue with a bag of sand. the platform on which the statue is placed is designed to detect the mass of the statue. if the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues. the density of gold is about 20\text{ g/cm}^320 g/cm 3 20, space, g, slash, c, m, start superscript, 3, end superscript. the density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm 3 2, point, 5, space, g, slash, c, m, start superscript, 3, end superscript. the gold statue can be modeled as a cylinder with height 25\text{ cm}25 cm25, space, c, m and radius 8\text{ cm}8 cm8, space, c, m. in terms of \piπpi, what is the mass of sand indiana jones needs to avoid triggering the mechanism?

Awavelength of 610 nm was found to be the most intense wavelength emitted by copper. answer the following questions about this wavelength of light. a) what is this wavelength in cm? b) what is the frequency that corresponds to this wavelength? c) what is the energy of light of this wavelength? d) what is the wavenumber corresponding to this wavelength?