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3 years ago

What are all solutions to the differential equation dy/dx=sec^2*x ?

Mathematics

1 answer:

zysi [14]3 years ago

4 0

Answer:

y=tanx+C

Step-by-step explanation:

$\frac{dy}{dx} = {sec}^{2} \: x \\ \\ dy = {sec}^{2} \: x \: dx \\ integrating \: both \: sides \\ \\ \int \:1\: dy = \int {sec}^{2} \: x \: dx \\ \\ \huge \red{ \boxed{ \therefore \: y = tan \: x + c}} \\$

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(no links or files) Solve this equation using the quadratic formula. This question should be solved both ways. (1) Quadratic For

meriva

Quadratic formula is x = -b+ or- sq rt b^2-4ac / 2a
a=2 b=5 c=-3
-5 +or- sqrt 5^2-4(2)(-3) / 2(2)
-5 +or- sqrt 49/ 4
-5 + 7 /4 = 2/4 = 1/2
-5 - 7 /4 = -12/4 = -3

Factoring a*c is 2*-3 =-6
Factors of -6 that add to 5 are 6 and -1
Split 5x into +6x-1x
2x^2+6x-1x-3 and group
2x(x+3)-1(x+3)
(x+3)(2x-1)=0
x+3=0 gives x=-3
2x-1=0 gives x=1/2

4 0

3 years ago

ASAP PLZZZ The axis of symmetry for the graph of the function f start bracket x end bracket equals one-quarter x square plus b x

Lilit [14]

Answer:

$b=-3$

Step-by-step explanation:

The given function is $f(x)=\frac{1}{4}x^2+bx+10$ .

When we compare to $ax^2+bx+=0$ , we have

$a=\frac{1}{4}$ and c=10

The equation of the axis of symmetry of a vertical parabola is:

$x=-\frac{b}{2a}$

Also from the question the axis of symmetry is x=6

We substitute the values to get:

$6=-\frac{b}{2*\frac{1}{4}}$

$6=-\frac{b}{\frac{1}{2}}$

$b=-\frac{1}{2}*6$

$b=-3$

7 0

3 years ago

Read 2 more answers

What's 1+1? <br><br>Brainliest With The Correct Answer

GrogVix [38]

2 is the answer.........

4 0

3 years ago

Read 2 more answers

Which is better to buy 14 rolls of paper towels for $18

Feliz [49]

In order to find out what deal is better:

We have to find the unit rate for each deal

Total amount of paper towels ÷ The price

So it would be....

18 ÷ 14 = 1.285714
12 ÷ 10 = 1.2

Short Answer:

The better deal is 10 rolls of paper towels for $12.

Long Answer:

I wanted to find out the price per roll of paper towel for each deal so I created a unit rate problem which is the numerator divided by the denominator. From there, I was able to get my answers, compare which one was less than the other, and select the best deal.

Hopefully this helped >-<

3 0

2 years ago

Is an obtuse angle larger then acute ?and why.. plz help

Vinvika [58]

Hey there! How are you doing today?

When we are dealing with angles, it's imperative to know what measurements of angles are labeled.

There are three types of angles:
1.) Acute
2.) Right
3.) Obtuse

Let's define all three of these and then answer our question with the information given.

An acute angle is an angle that measures less than 90 degrees. An example of this is:

Ex1) A triangle has the angle measurements of 90, 45, and x. Solve for x.
Remember that the angles of a triangle must sum up to 180 degrees. To solve for x, we need to combine 90 and 45, then subtract the sum from 180.

90 + 45 = 135
180 - 135 = 45

The missing angle 'x' is 45 degrees, which is an acute angle since it measures less than 90 degrees.

Now let's move on to our second angle, the right angle. This is a pretty basic one and can be discovered without much observation or even work required.
A right angle measures 90 degrees exactly, no more and no less, and generally has a box in a corner of a geometrical figure.

Since we've covered both an acute and right angle, let's discuss what an obtuse angle is. An obtuse angle is an angle that measures more than 90 degrees. You can discover these angles in triangles, octagons, and other geometrical figures.

Now, let's review what we've learned and find our answer.

The question asks if an obtuse angle is larger than an acute angle.
Since we have learned an acute angle measures less than 90 degrees, and an obtuse angle measures more than 90 degrees, we can answer the question with:

An obtuse angle is larger than an acute angle.

I hope this helps, and feel free to comment any questions or concerns about this in the comment box below this answer.
Have a great day, Larissa!

7 0

3 years ago