Ask question

Ask question

All categories

1 year ago

12

A jet plane traveling at 400 mph overtakes a propeller plane traveling at 250 mph that had a 2-hour head start. How far from th

e starting point are the planes?

1 answer:

kotegsom [21]1 year ago

7 0

Answer:

I think they're 800miles from starting point

Step-by-step explanation:

You might be interested in

Solve the given initial-value problem. x^2y'' + xy' + y = 0, y(1) = 1, y'(1) = 8

Kitty [74]

Substitute $z=\ln x$ , so that

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dz}\cdot\dfrac{\mathrm dz}{\mathrm dx}=\dfrac1x\dfrac{\mathrm dy}{\mathrm dz}$

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1x\dfrac{\mathrm dy}{\mathrm dz}\right]=-\dfrac1{x^2}\dfrac{\mathrm dy}{\mathrm dz}+\dfrac1x\left(\dfrac1x\dfrac{\mathrm d^2y}{\mathrm dz^2}\right)=\dfrac1{x^2}\left(\dfrac{\mathrm d^2y}{\mathrm dz^2}-\dfrac{\mathrm dy}{\mathrm dz}\right)$

Then the ODE becomes

$x^2\dfrac{\mathrm d^2y}{\mathrm dx^2}+x\dfrac{\mathrm dy}{\mathrm dx}+y=0\implies\left(\dfrac{\mathrm d^2y}{\mathrm dz^2}-\dfrac{\mathrm dy}{\mathrm dz}\right)+\dfrac{\mathrm dy}{\mathrm dz}+y=0$
$\implies\dfrac{\mathrm d^2y}{\mathrm dz^2}+y=0$

which has the characteristic equation $r^2+1=0$ with roots at $r=\pm i$ . This means the characteristic solution for $y(z)$ is

$y_C(z)=C_1\cos z+C_2\sin z$

and in terms of $y(x)$ , this is

$y_C(x)=C_1\cos(\ln x)+C_2\sin(\ln x)$

From the given initial conditions, we find

$y(1)=1\implies 1=C_1\cos0+C_2\sin0\implies C_1=1$
$y'(1)=8\implies 8=-C_1\dfrac{\sin0}1+C_2\dfrac{\cos0}1\implies C_2=8$

so the particular solution to the IVP is

$y(x)=\cos(\ln x)+8\sin(\ln x)$

4 0

3 years ago

A glass box shaped like a rectangular prism has width 7 inches, length 9 inches, and height 12 inches. It is being shipped in a

Nadusha1986 [10]

Answer:

744 in³

Step-by-step explanation:

Since you are filling the larger box with both rectangular prism and Styrofoam peanuts, you need to find the overall volume of the larger box and subtract the volume of the glass box to find the amount of space that the Styrofoam peanuts need to take up.

Volume (prism) = Bh, where B = area of the base, h = height

Larger Box: V = 10 x 10 x 15 = 1500 in³

Glass Box: V = 7 x 9 x 12 = 756 in³

1500 - 756 = 744 in³ of Styrofoam peanuts

8 0

3 years ago

What is the answer for X+8

Alina [70]

Answer: the answer is x+8= 1

6 0

2 years ago

Starting with $800 and losing 5% each? is it linear or exponential growth or decay. also solve

kati45 [8]

Answer:

Decay

Step-by-step explanation:

The money is being lost, so it is decaying

5 0

3 years ago

A submarine descends 45 1/2 feet from the ocean surface, clinbs 39 ft, and then descends an additional 18 3/4 ft. What must the

tekilochka [14]

The answer is fill its tanks with air so it floats to the top, but I will solve for the distance since I am nice

so we do
decent means negative
cimb=positive
add

decends 45 and 1/2
-45 and 1/2

climbs 39
+39

decedns 18 and 3/4
-18 and 3/4

add
-45 and 1/2+39-18 and 3/4
add
convert 1/2 to 2/4
gropu negatives
-45 and 2/4-18 and 3/4+39
add
-63 and 5/4+39
-64 and 1/4+39
-25 and 1/4
that is how far dow the submarine is
so the submarine needs to gu 25 and 1/4 ft up to reach the csurface

7 0

3 years ago