(8.64 x 10^4)<br> (2.4 x 10^4)

jeka57 [31]

The volume prism refers to the number of cubic units that will exactly fill the figure. The volume of a rectangular prism can be found or calculate by using the formula V=Bh, where B represents to the area of the base or in other words the length and width of the rectangle.

In this exercise is given that the measurements of a prism are 5/2ft, 3/2ft, and 7/2ft; and it is asked to find its volume. In order to find the volume of the prism, you should substitute the given values into the previous mention formula.

V=Bh
V=(5/2 ft)(7/2 ft)(3/2 ft)
V=(35/4 ft²)(3/2 ft)
V=105/8ft³ or $13 \frac{1}{8}$ ft³

The volume of the rectangular prism is $13 \frac{1}{8}$ ft³.

5 0

3 years ago

Solve the following ODE's: c) y* - 9y' + 18y = t^2

Nastasia [14]

Answer:

y = $C_1e^{3t}+C_2e^{6t}$ + $\dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})$

Step-by-step explanation:

y''- 9 y' + 18 y = t²

solution of ordinary differential equation

using characteristics equation

m² - 9 m + 18 = 0

m² - 3 m - 6 m+ 18 = 0

(m-3)(m-6) = 0

m = 3,6

C.F. = $C_1e^{3t}+C_2e^{6t}$

now calculating P.I.

$P.I. = \frac{t^2}{D^2 - 9D +18}$

$P.I. = \dfrac{t^2}{(D-3)(D-6)}\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(1-\frac{D}{6})^{-1}(t^2)\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(1+\frac{D}{6}+\frac{D^2}{36}+....)(t^2)\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(t^2+\frac{2t}{6} + \frac{2}{36})\\P.I. =\dfrac{1}{18}(1+\frac{D}{3}+\frac{D^2}{9}+....)(t^2+\frac{2t}{6} + \frac{2}{36})\\P.I. =\dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})$