The volume of a cylinder can be determined using the formula pi*h*d^2/4, which leads us to V = pi*(39 mm)(39 mm)^2 / 4 = 46,589 mm^3. Dividing the mass of 1 kg by the volume of 46,589 mm^3 results in a density of 2.1464 x 10^-5 kg/mm^3. Typically, density is expressed in kg/m^3, so we convert this by multiplying by 1x10^9, yielding a density of 21,464 kg/m^3.
The telescope’s cost is $91
4.55 divided by 5% (0.05) equals 91.
Response:
The equation of the linear function can be represented as:
H(S) = 960 - 3.2*S
The behavior of the spring can be described using either a sine or cosine function. The spring's maximum displacement is 6 inches, occurring at t=0, which we will define as the positive peak. Therefore, we can express the function as:
6sin(at+B). The spring's period is 4 minutes, which means the time factor in the equation must complete a cycle (2π) in 4 minutes. This gives us the equation 4min*a=2π, leading to a=π/2. Generally, a=2π/T where a is the coefficient and T is the period. For B, since sin(π/2)=1, we determine B=π/2 because at t=0, the equation becomes 6sin(B)=6. Therefore, we substitute to form f(t)=6sin(πt/2+π/2)=6cos(πt/2)
due to trigonometric relations.
