4

Mathematics

1 answer:

Bezzdna [24]3 years ago

4 0

9514 1404 393

Answer:

y = 750 -100x

Step-by-step explanation:

The initial remaining balance is 750. The balance decreases by 100 per month, so is reduced by 100x. The equation describing this is ...

y = 750 -100x

You might be interested in

Adjust the number into correct standard form. 4381 × 10 3

ZanzabumX [31]

Answer:

the standard form of the given number is 4.381 x 10⁶

Step-by-step explanation:

Given number = 4381 x 10³

The above number can also be written as; 4381.0 x 10³

In standard form, the decimal point will be moved three steps backward to the first digit (4) and the resulting is multiplied by 1000, as shown in the number below;

4381.0 x 10³ = 4.381 x 10³ x 1000

= 4.381 x 10⁶

Thus, the standard form of the given number is 4.381 x 10⁶

3 0

3 years ago

Find a solution to the initial value problem, y′′+18x=0,y(0)=5,y′(0)=1.

Serga [27]

We want to find a solution to the initial value problem:

$y'' + 18x = 0 \qquad,\qquad y(0) = 5 \qquad,\qquad y'(0)=1.$

We can start by integrating the equation once:

$\dfrac{\textrm{d}^2 y}{\textrm{d}x^2} + 18 x = 0 \iff \dfrac{\textrm{d}^2 y}{\textrm{d}x^2} = -18 x \iff\\\\\iff \dfrac{\textrm{d}y}{\textrm{d}x} = -18\displaystyle\int x\textrm{ d}x \iff \dfrac{\textrm{d}y}{\textrm{d}x}=-18\dfrac{x^2}{2} + C \iff\\\\\iff \dfrac{\textrm{d}y}{\textrm{d}x} = -9x^2 + C.$

Using the initial condition $y'(0) = 1$ , we can determine the integration constant $C$ :

$\dfrac{\textrm{d}y}{\textrm{d}x}\Big\vert_{x= 0} = 1 \iff -9 \times 0^2 + C = 1 \iff C = 1.$

Therefore, we have:

$\dfrac{\textrm{d}y}{\textrm{d}x} = -9x^2 + 1$

We can now integrate again:

$y(x) = \displaystyle\int\dfrac{\textrm{d}y}{\textrm{d}x}\textrm{ d}x = \int\left(-9x^2+1\right)\textrm{d}x = -9\int x^2\textrm{ d}x + \int\textrm{d}x =\\\\= -9\dfrac{x^3}{3} + x + K = -3x^3 + x + K.$