Find the surface area of a pyramid

Mathematics

1 answer:

Cerrena [4.2K]3 years ago

7 0

Answer:

$A=lw+l\sqrt{(\frac{1}{2}w) ^{2} +h^{2} } +w\sqrt{(\frac{1}{2}l) ^{2} +h^{2} }$

Step-by-step explanation:

The formula for the surface area of a pyramid is $A=lw+l\sqrt{(\frac{1}{2}w) ^{2} +h^{2} } +w\sqrt{(\frac{1}{2}l) ^{2} +h^{2} }$

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Find the general solution of the given higher-order differential equation. d3u dt3 + d2u dt2 − 2u = 0

STALIN [3.7K]

$\dfrac{\mathrm d^3u}{\mathrm dt^3}+\dfrac{\mathrm d^2u}{\mathrm dt^2}-2u=0$

This ODE has characteristic equation

$r^3+r^2-2=(r^3-r)+(r^2+r-2)=r(r^2-1)+(r+2)(r-1)$

$=(r(r+1)+(r+2))(r-1)=(r^2+2r+2)(r-1)=0$

which has roots at $r=1,-1\pm i$ . Then the characteristic solution to the ODE is

$u(t)=C_1e^t+C_2e^{(-1+i)t}+C_3e^{(-1-i)t}$

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3 years ago

Given y=-3/4x-2. What is the equation of the line that is perpendicular and has the point (-4,1)? Write answer in slope intercep

raketka [301]

Answer:

y=4/3+19/3

Step-by-step explanation:

When it asks for perpendicular it means your focusing on the slope.

Perpendicular means opposite of the current slope, so flip it and change the sign (-3/4 changes to 4/3). Next you will use the equation (y-y1)=m(x-x1)

y1=the y value given

x1=the x value given

m=your slope

(y-1)=4/3(x+4) Since the x point is minus a negative we get to change the sign to a positive. Next distribute the 4/3 to each term in the parenthesis.

y-1=4/3(x)+4/3(4)

y-1=4/3x+16/3 Now we add the one to both sides.

+1 +1 The one isn't in teh correct format to just add so first imagine it as 1/1. Now to get the bottom to have a 3 like in 16/3 we just multiply the top and bottom by 3.

$\frac{1}{1} x\frac{3}{3}=\frac{3}{3}$ Now we can add this to the 16/3