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3 years ago

Finding a Segment Length

Mathematics

1 answer:

Allushta [10]3 years ago

8 0

Answer:

x = 6.6

length of DE = 16.2

Step-by-step explanation:

edge 2020

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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

If g(x) =x^2 + 1, find g(4)

Papessa [141]

Answer:

Step-by-step explanation:

Since we are evaluating g(x) for g(4), we would substitute x in the equation with 4.

x² + 1

(4)²+ 1

16 + 1

I hope this helps

4 0

3 years ago

Choose the missing step in the given solution to the inequality ?x ? 3 < 13 + 3x. (1 point) ?x ? 3 < 13 + 3x _____________

SSSSS [86.1K]

Answer:

Step-by-step explanation:

4x=542

7 0

4 years ago

Need help with school work

vichka [17]

15^2 + 36^2 = 39^2

Your answer is 39

3 0

3 years ago

Read 2 more answers

Noelle and Micah went to the bank to open new checking accounts. The equation C=0.2n+1.20 represents the monthly cost, C, in dol

Kaylis [27]

Answer:

C = $2.40

n = 6

Step-by-step explanation:

For Noelle,

Equation that represents the monthly cost 'C',

C = 0.2n + 1.20

Here, n = number of checks written in a month

For Micah,

Monthly cost for writing checks 'C' = $1.20

Number of checks 'n' = 3

Since, Cost of writing checks ∝ Number of checks written

C' ∝ n

C' = kn

k = $\frac{C'}{n}$

Here, k = proportionality constant

For C' = 1.2 and n = 3

k = $\frac{1.2}{3}$

k = 0.4

Equation will be,

C' = 0.4n

For any month C = C'

Therefore, 0.2n + 1.20 = 0.4n

0.4n - 0.2n = 1.20

0.2n = 1.20

n = 6

Number of checks written by Noelle and Micah = 6

For n = 6,

C = 0.2(6) + 1.20

C = $2.40

Cost of writing checks = $2.40

7 0

3 years ago