Volume of the box = length ^ 3 = 5^3 = 125 cubic inches
Volume of rectangular prism = length x width x height = 3 x 4 x 18 = 216 cubic inches
Volume of entire sculpture = volume of box + volume of rectangular prism = 125 + 216 = 341 cubic inches.

4 0

3 years ago

Consider the differential equation y'' − y' − 30y = 0. Verify that the functions e−5x and e6x form a fundamental set of solution

Alex Ar [27]

Answer:

Step-by-step explanation:

We have to take the derivatives for both functions and replace in the differential equation. Hence

for y=e^{-5x}:

$y(x)=e^{-5x}\\y'(x)=-5e^{-5x}\\y''(x)=25e^{-5x}\\$

for y=e^{6x}:

$y(x)=e^{6x}\\y'(x)=6e^{6x}\\y''(x)=36e^{6x}\\$

Now we replace in the differential equation y'' − y' − 30y = 0

for y=e^{-5x}:

$25e^{-5x}+5e^{-5x}-30e^{-5x}=0\\25+5-30=0$

for y=e^{6x}:

$36e^{6x}-6e^{6x}-30=0\\36-6+30=0$

Now, to know if both function are linearly independent we calculate the Wronskian

$W(f,g)=fg'-f'g$

$W(e^{-5x},e^{6x})=(e^{-5x})(6e^{6x})-(-5e^{-5x})(e^{6x})\neq 0$

I hope this is useful for you

Best regard

7 0

3 years ago

If the height of the base is 15 and the width of the base is 8 what is the length of the hypotenuse

tino4ka555 [31]

Answer:

The length of the hypotenuse is 17.

Step-by-step explanation:

$15^2 + 8^2 = 17^2.$

I found this out by doing:

15 x 15 = 225

8 x 8 = 64

225 + 64 = 289

$\sqrt{289} = 17$

Hope this helps you! :)

7 0

3 years ago