When 59,527 is divided by 23, the quotient is 2,588 R ___.Numerical Answers Expected!Answer for Blank 1:

Solve the system: x' = (2 4 -1 6)x

sertanlavr [38]

Answer:

$x=e^{8t}+c$

Step-by-step explanation:

we have given x'=(24-16)x=8x

x' denotes the differenation

$\frac{dx}{dt}=8x$ differentiation is performed with respect to t

by variable separable method we can write

$\frac{dx}{x}=8dt$

on integrating both side

$lnx=8t+c$

$x=e^{8t}+c$ (property of log )

so the solution for x will be $x=e^{8t}+c$

6 0

4 years ago

Please show work on these questions!!!

asambeis [7]

Answer:

- 14π/9; 108°; -√2/2; √2/2

Step-by-step explanation:

To convert from degrees to radians, use the unit multiplier $\frac{\pi }{180}$

In equation form that will look like this:

- 280° × $\frac{\pi }{180}$

Cross canceling out the degrees gives you only radians left, and simplifying the fraction to its simplest form we have $-\frac{14\pi }{9}$

The second question uses the same unit multiplier, but this time the degrees are in the numerator since we want to cancel out the radians. That equation looks like this:

$\frac{3\pi }{5}$ × $\frac{180}{\pi }$

Simplifying all of that and canceling out the radians gives you 108°.

The third one requires the reference angle of $\frac{3\pi }{4}$ .

If you use the same method as above, we find that that angle in degrees is 135°. That angle is in QII and has a reference angle of 45 degrees. The Pythagorean triple for a 45-45-90 is (1, 1, √2). But the first "1" there is negative because x is negative in QII. So the cosine of this angle, side adjacent over hypotenuse, is $-\frac{1}{\sqrt{2} }$

which rationalizes to $-\frac{\sqrt{2} }{2}$

The sin of that angle is the side opposite the reference angle, 1, over the hypotenuse of the square root of 2 is, rationalized, $\frac{\sqrt{2} }{2}$

And you're done!!!

7 0

4 years ago

15c² - 5c. Factorise completely

KATRIN_1 [288]

Looking at the problem, what we must do to complete this question is to completely factor the expression that was provided. The expression that was provided is $15c^2 - 5c$ .

The first step that we must do is to take a look at the expression and see what the two pieces of the expression have in common. We can see that both $15c^2$ and $-5c$ have the number 5 and the variable c associated with them so we can factor out those two.