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Bess [88]
4 years ago
6

Anna is in a cave 37 feet below the cave entrance. She descends 17 feet, then

Mathematics
1 answer:
ser-zykov [4K]4 years ago
7 0
H=(-37-17)+24
that is the numerical expression, while h being height.
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Find the solution of the given initial value problem in explicit form. y′=(1−5x)y2, y(0)=−12 Enclose numerators and denominators
Nata [24]

Answer:

The solution is y=-\frac{12}{12x-30x^2+1}.

Step-by-step explanation:

A first order differential equation y'=f(x,y) is called a separable equation if the function f(x,y) can be factored into the product of two functions of x and y:

f(x,y)=p(x)h(y)

where p(x) and h(y) are continuous functions.

We have the following differential equation

y'=(1-5x)y^2, \quad y(0)=-12

In the given case p(x)=1-5x and h(y)=y^2.

We divide the equation by h(y) and move dx to the right side:

\frac{1}{y^2}dy\:=(1-5x)dx

Next, integrate both sides:

\int \frac{1}{y^2}dy\:=\int(1-5x)dx\\\\-\frac{1}{y}=x-\frac{5x^2}{2}+C

Now, we solve for y

-\frac{1}{y}=x-\frac{5x^2}{2}+C\\-\frac{1}{y}\cdot \:2y=x\cdot \:2y-\frac{5x^2}{2}\cdot \:2y+C\cdot \:2y\\-2=2yx-5yx^2+2Cy\\y\left(2x-5x^2+2C\right)=-2\\\\y=-\frac{2}{2x-5x^2+2C}

We use the initial condition y(0)=-12 to find the value of C.

-12=-\frac{2}{2\left(0\right)-5\left(0\right)^2+2C}\\-12=-\frac{1}{c}\\c=\frac{1}{12}

Therefore,

y=-\frac{2}{2x-5x^2+2(\frac{1}{12})}\\y=-\frac{12}{12x-30x^2+1}

4 0
3 years ago
This is a statistics problem.
Irina18 [472]
<span>The point estimate of the mean percentage of reservations is the midpoint of the interval, which is 3.2%</span>
4 0
3 years ago
Can someone help me out with these two problems and show work please !!
lara [203]

Answer :

<em>( 6 y^4 + 3 y^2 -7) - (12 y^4 - y^2 + 5)</em>

Step-by-step explanation:

(6 y^4+ 3 y^2-7) - (12 y^4 - y^2 + 5 )

=6 y^4 +3 y ^2 - 7 - 12 y^4 + y^2 - 5

=6 y ^4 - 12 y ^4 +3 y ^2 + y ^2 - 7 -5

= -6 y ^4 + 4 y ^2- 12

Hope this helps!

8 0
2 years ago
Find f(3) 1 point Multiple choice + Graph!
lianna [129]

we know that

f(3) is the value of the function when x is equal to 3

so

For x=3

see in the graph

f(3)=6

see the attached figure

therefore

<u>the answer is</u>

f(3)=6

4 0
3 years ago
You have 4/6 cup of flower in your cupboard. A recipe for bread calls for 1/4 cup of flour. How much flour would you have left i
Keith_Richards [23]
3/2 I'm pretty sure idk if I'm right though but you'll do good!
6 0
3 years ago
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