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3 years ago

2x-3y=-24x+y=24What is the first steps to solve the system?

Mathematics

1 answer:

olganol [36]3 years ago

7 0

Is this simultaneous equations?
if yes then the first step is
make one of the unknown as the subject

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How many inch are in a mile

makvit [3.9K]

63,360 inches are in a mile...hope this helps!

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3 years ago

Evaluate the integral following

alina1380 [7]

Answer:

$\displaystyle{4\tan x + \sin 2x - 6x + C}$

Step-by-step explanation:

We are given the integral of:

$\displaystyle{\int 4(\sec x - \cos x)^2 \, dx}$

First, we can use a property to separate a constant out of integrand:

$\displaystyle{4 \int (\sec x - \cos x)^2 \, dx}$

Next, expand the expression (integrand):

$\displaystyle{4 \int \sec^2 x - 2\sec x \cos x + \cos^2 x \, dx}$

Since $\displaystyle{\sec x = \dfrac{1}{\cos x}}$ then it can be simplified to:

$\displaystyle{4 \int \dfrac{1}{\cos^2 x} - 2\dfrac{1}{\cos x} \cos x + \cos^2 x \, dx}\\\\\displaystyle{4 \int \dfrac{1}{\cos^2 x} - 2 + \cos^2 x \, dx}$

Recall the formula:

$\displaystyle{\int \dfrac{1}{\cos ^2 x} \, dx = \int \sec ^2 x \, dx = \tan x + C}\\\\\displaystyle{\int A \, dx = Ax + C \ \ \tt{(A \ and \ C \ are \ constant.)}$

For $\displaystyle{\cos ^2 x}$ , we need to convert to another identity since the integrand does not have a default or specific integration formula. We know that:

$\displaystyle{2\cos^2 x -1 = \cos2x}$

We can solve for $\displaystyle{\cos ^2x}$ which is:

$\displaystyle{2\cos^2 x = \cos2x+1}\\\\\displaystyle{\cos^2x = \dfrac{\cos 2x +1}{2}}$

Therefore, we can write new integral as:

$\displaystyle{4 \int \dfrac{1}{\cos^2 x} - 2 + \dfrac{\cos2x +1}{2} \, dx}$

Evaluate each integral, applying the integration formula:

$\displaystyle{\int \dfrac{1}{\cos^2x} \, dx = \boxed{\tan x + C}}\\\\\displaystyle{\int -2 \, dx = \boxed{-2x + C}}\\\\\displaystyle{\int \dfrac{\cos 2x +1}{2} \, dx = \dfrac{1}{2}\int \cos 2x +1 \, dx}\\\\\displaystyle{= \dfrac{1}{2}\left(\dfrac{1}{2}\sin 2x + x\right) + C}\\\\\displaystyle{= \boxed{\dfrac{1}{4}\sin 2x + \dfrac{1}{2}x + C}}$

Then add all these boxed integrated together then we'll get:

$\displaystyle{4\left(\tan x - 2x + \dfrac{1}{4}\sin 2x + \dfrac{1}{2} x\right) + C}$

Expand 4 in the expression:

$\displaystyle{4\tan x - 8x +\sin 2x + 2 x + C}\\\\\displaystyle{4\tan x + \sin 2x - 6x + C}$

Therefore, the answer is:

$\displaystyle{4\tan x + \sin 2x - 6x + C}$

4 0

1 year ago

ABCDE is aregular pentangon<br> X=?

Viefleur [7K]

Answer:

x = 5.2

Step-by-step explanation:

Measure of interior angle of a regular polygon = $\frac{(n-2)\times180}{n}$

Here n = number of sides of the polygon

Interior angle of a regular pentagon = $\frac{(5-2)\times180}{5}$

= 108°

By applying cosine rule in ΔABK,

(BK)² = (AK)² + (AB)² - 2(AK)(AB)cos(108)°

(x + 3)² = 4² + 6² - 2(4)(6)cos(108)°

x² + 6x + 9 = 16 + 36 - (-14.83)

x² + 6x = 57.83

x² + 6x - 57.83 = 0

x = $\frac{-6\pm \sqrt{6^2-4(1)(-57.83)}}{2(1)}$

x = $\frac{-6\pm16.35}{2}$

x ≈ -11.2, 5.2

Since, x can't be negative,

x = 5.2 will be the answer.

6 0

3 years ago

Find the point on the unit circle that corresponds to 5pi/6

natulia [17]

That is (-√3/2, 1/2)

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4 years ago

How does understanding the history of credit make you think

d1i1m1o1n [39]

Knowing the history of credit cards makes you understand why credit cards were created and the reason they were necessary for human societies.

<h3>What is the focus of history?</h3>

History teaches you about the origin of specific elements, in this case, credit cards, and their evolution over time.

<h3>Why is history important?</h3>

History is about both origin and evolution; due to this:

History explains why credit cards emerged and the reason they were necessary.
History shows you the way credit cards have changed or stayed the same due to different causes.

Learn more about history in: brainly.com/question/3583505

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3 years ago