Answer with explanation:
The Normalization Principle states that

Given
Thus solving the integral we get

The integral shall be solved using chain rule initially and finally we shall apply the limits as shown below

Applying the limits and solving for A we get
![I=\frac{1}{k}[\frac{1}{e^{kx}}-\frac{x}{e^{kx}}]_{0}^{+\infty }\\\\I=-\frac{1}{k}\\\\\therefore A=-k](https://tex.z-dn.net/?f=I%3D%5Cfrac%7B1%7D%7Bk%7D%5B%5Cfrac%7B1%7D%7Be%5E%7Bkx%7D%7D-%5Cfrac%7Bx%7D%7Be%5E%7Bkx%7D%7D%5D_%7B0%7D%5E%7B%2B%5Cinfty%20%7D%5C%5C%5C%5CI%3D-%5Cfrac%7B1%7D%7Bk%7D%5C%5C%5C%5C%5Ctherefore%20A%3D-k)
Answer:
1. Density = 1200[kg/m^3]; 2. Volume= 0.005775[m^3], mass= 15.59[kg]
Explanation:
1. We know that the density is defined by the following expression.
![Density = \frac{mass}{volume} \\where:\\mass=90[kg]\\volume=0.075[m^{3} ]\\density=\frac{90}{0.075} \\density=1200[\frac{kg}{m^{3} }]](https://tex.z-dn.net/?f=Density%20%3D%20%5Cfrac%7Bmass%7D%7Bvolume%7D%20%5C%5Cwhere%3A%5C%5Cmass%3D90%5Bkg%5D%5C%5Cvolume%3D0.075%5Bm%5E%7B3%7D%20%5D%5C%5Cdensity%3D%5Cfrac%7B90%7D%7B0.075%7D%20%5C%5Cdensity%3D1200%5B%5Cfrac%7Bkg%7D%7Bm%5E%7B3%7D%20%7D%5D)
2. First we need to convert the units to meters.
wide = 35[cm] = 35/100 = 0.35[m]
long = 11 [dm] = 11 decimeters = 11/10 = 1.1[m]
Thick = 15[mm] = 15/1000 = 0.015[m]
Now we can find the density using the expression for the density.
![density= \frac{mass}{volume} \\where:\\volume = wide*long*thick\\volume=0.35*1.1*0.015 = 0.005775[m^3]\\\\mass= density*volume = 2700*0.005775 = 15.59[kg]](https://tex.z-dn.net/?f=density%3D%20%5Cfrac%7Bmass%7D%7Bvolume%7D%20%5C%5Cwhere%3A%5C%5Cvolume%20%3D%20wide%2Along%2Athick%5C%5Cvolume%3D0.35%2A1.1%2A0.015%20%3D%200.005775%5Bm%5E3%5D%5C%5C%5C%5Cmass%3D%20density%2Avolume%20%3D%202700%2A0.005775%20%3D%2015.59%5Bkg%5D)
I think the correct answer from the choices listed above is the third option. The magnetic quantum number of an electron (m) designates the orientation in space of the orbital (electron cloud). <span>This number divides the subshell into individual orbitals which hold the electrons; there are 2l+1 orbitals in each subshell. </span>
Answer:
1. In general, the best shields will be able to block a spectrum of radiation. Aboard the space station, the use of hydrogen-rich shielding such as polyethylene in the most frequently occupied locations, such as the sleeping quarters and the galley, has reduced the crew's exposure to space radiation.
2. It absorbs harmful ultraviolet radiation from the sun, helps keep Earth's surface warm via the greenhouse effect, and reduces temperature extremes between day and night. ... So, thanks to gravity, although some of Earth's atmosphere is escaping to space, most is staying here.
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The mantle<span> is heated in the core, where it is hotter it is more buoyant, whereas in areas where it is cooler it is less buoyant. This results in</span>convection<span> cells in the </span>mantle<span>, and produces horizontal motion of </span>mantle<span> material close to the Earth surface.</span>