So here we use the pythagorean theorem which is a2 + b2 = c2 (“a” squared times “b” squared equals “c” squared) the length from calvins house to the intersection is “a” and the length from phoebes house to the intersection is “b” so in order to find out the length of “c” (calvins house to phoebes house) we need to use the pythagorean theorem

a2 275x275=75,625

b2 113x113 = 12,769

so now that we have figured out what a2 and b2 are let’s add them

75,625 + 12,769 = 88,394

now since we only need to find out the length and not the area we need to find the square root of 88,394

the square root of 88,394 is 297.311 (i cut off the decimal after three places)

the direct length from phoebes house to calvins is 297.311 meters

5 0

2 years ago

∠ABD and ∠BDE are supplementary. Find the measures of both angles.

Gnom [1K]

Supplementary means that the angles have to add up to 180, so you have your equation.

180=5x+17x-18

198=22x

x=9

Then to find the measures of the angles, you plug x back in.

m∠ABD=5(9)=45 degrees

m∠BDE=17(9)-18=153-18=135 degrees

5 0

3 years ago

d^2y/dx^2=sqrt(1+(dy/dx)^2 state the order of the given ordinary differential equation. Determine whether the equation is linear

Georgia [21]

This is a second-order ODE since the highest order derivative is 2 (from $\dfrac{\mathrm d^2y}{\mathrm dx^2}$ ).

It's not linear because it doesn't take the form

$F\left(\dfrac{\mathrm d^2y}{\mathrm dx^2},\dfrac{\mathrm dy}{\mathrm dx},y,x\right)=0\iff f_2(x)\dfrac{\mathrm d^2y}{\mathrm dx^2}+f_1(x)\dfrac{\mathrm dy}{\mathrm dx}+f_0(x)y+g(x)=0$

and it's not possible to rewrite it as such.

5 0

2 years ago