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3 years ago

14

George enjoys skydiving. He jumped from a helicopter at 8000 feet above sea level. He then landed on a mountain at 5000 feet abo

ve sea level. How many feet did George descend?

1 answer:

UkoKoshka [18]3 years ago

7 0

George descended 3,000 feet above sea level

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Solving separable differential equation DY over DX equals xy+3x-y-3/xy-2x+4y-8

Ivanshal [37]

It looks like the differential equation is

$\dfrac{dy}{dx} = \dfrac{xy + 3x - y - 3}{xy - 2x + 4y - 8}$

Factorize the right side by grouping.

$xy + 3x - y - 3 = x (y + 3) - (y + 3) = (x - 1) (y + 3)$

$xy - 2x + 4y - 8 = x (y - 2) + 4 (y - 2) = (x + 4) (y - 2)$

Now we can separate variables as

$\dfrac{dy}{dx} = \dfrac{(x-1)(y+3)}{(x+4)(y-2)} \implies \dfrac{y-2}{y+3} \, dy = \dfrac{x-1}{x+4} \, dx$

Integrate both sides.

$\displaystyle \int \frac{y-2}{y+3} \, dy = \int \frac{x-1}{x+4} \, dx$

$\displaystyle \int \left(1 - \frac5{y+3}\right) \, dy = \int \left(1 - \frac5{x + 4}\right) \, dx$

$\implies \boxed{y - 5 \ln|y + 3| = x - 5 \ln|x + 4| + C}$

You could go on to solve for $y$ explicitly as a function of $x$ , but that involves a special function called the "product logarithm" or "Lambert W" function, which is probably beyond your scope.

8 0

2 years ago

A submarine rises a vertical distance of 200 m to the surface. The distance measured along the submarine's path is 500 m.

postnew [5]

Answer:

24°

Step-by-step explanation:

Oh, okay. So this is like (kinda?) the opposite of what I did in the last one. This time, instead of finding the side length of the imaginary triangle, you are trying to find the angle of elevation (that's what I call it)

sin θ = 200/500

θ = sin^-1 (200/500)

θ = 23.578...

Rounded:

θ = 24°

5 0

3 years ago

Gracie, Mary, and Nancy each have a small collection of seashells. Gracie has 5 more than 1 1/4 times the number of shells Mary

Zolol [24]

G = 1.25m + 5
n = 1.50n + 1
g = n

1.25m + 5 = 1.50m + 1 <== ur equation
5 - 1 = 1.50m - 1.25m
4 = 0.25m
4 / 0.25 = m
16 = m <== mary has 16 <==

g = 1.25m + 5....g = 1.25(16) + 5....g = 25 <==Gracie has 25 <==
n = 1.50m + 1...n = 1.50(16) + 1.....n = 25 <==Nancy has 25 <==

8 0

4 years ago

A triangular pyramid has a base with an area of 43 cm squared and lateral faces with bases of 10 cm and heights of 8.6 cm. What

Jet001 [13]

Answer:

The total surface area of triangular pyramid is 172 cm squared

Step-by-step explanation:

Triangular pyramid:

Number of faces 4.
Number of vertices of a triangular pyramid is 6.
The volume is $\frac13 AH$ . A= area of the pyramid's base and H= height of the pyramid.

The surface area of triangular pyramid B+L. B= area of base, L= area of lateral surface.

Given that, the area of the base is 43 cm squared. Lateral faces with bases of 10 cm and heights 8.6 cm.

The 3 sides of the triangular pyramid is triangle in shape.

The area of triangle is $\frac12 \times base \times height$ .

The lateral surface area of the triangular pyramid is

$=3(\frac12 \times base \times height)$

$=3(\frac12\times 10\times8.6)$ cm squared

=129 cm squared

The total surface area of triangular pyramid is

=Area of the base + lateral surface area

=(43+129) cm squared

=172 cm squared

8 0

4 years ago

The probability that it rains in London on any particular day is 0.3.

SpyIntel [72]

Answer:

It is 14.45 percent .

Step-by-step explanation:

Explanation:

The first day is independent from the day before. Therefore the first day probability (of rain) is 20 percent.

The second day (depends on the previous day) rainfall probability is 85 percent.

Finally, the third day (it must be rainy to satisfy the total probability) rainfall probability is 85 percent.

The probability of having three consecutive days which are rainy:

P(all rainy)

=

0.20

×

0.85

×

0.85

=

0.1445

or 14.45 percent.

6 0

3 years ago

Read 2 more answers