Simplify each only using positive exponents: 2x^-3 • 4x^2 2x^4 • 4x^-3 2x^3y^-3 • 2x
1 answer:
<h2>Answer:</h2>
a. 2x^-3 • 4x^2
To solve this using only positive exponents, follow these steps:
i. Rewrite the expression in a clearer form
2x⁻³ . 4x²
ii. The position of the term with negative exponent is changed from denominator to numerator or numerator to denominator depending on its initial position. If it is at the numerator, it is moved to the denominator. If otherwise it is at the denominator, it is moved to the numerator. When this is done, the negative exponent is changed to positive.
In our case, the first term has a negative exponent and it is at the numerator. We therefore move it to the denominator and change the negative exponent to positive as follows;
iii. We then solve the result as follows;
=
Therefore, 2x⁻³ . 4x² =
b. 2x^4 • 4x^-3
i. Rewrite as follows;
2x⁴ . 4x⁻³
ii. The second term has a negative exponent, therefore swap its position and change the negative exponent to a positive one.
iii. Now solve by cancelling out common terms in the numerator and denominator. So we have;
Therefore, 2x⁴ . 4x⁻³ =
c. 2x^3y^-3 • 2x
i. Rewrite as follows;
2x³y⁻³ . 2x
ii. Change position of terms with negative exponents;
iii. Now solve;
Therefore, 2x³y⁻³ . 2x =
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Cos x = 1 - +
-
+ ...
Step-by-step explanation:
We use Taylor series expansion to answer this question.
We have to find the expansion of cos x at x = 0
f(x) = cos x, f'(x) = -sin x, f''(x) = -cos x, f'''(x) = sin x, f''''(x) = cos x
Now we evaluate them at x = 0.
f(0) = 1, f'(0) = 0, f''(0) = -1, f'''(0) = 0, f''''(0) = 1
Now, by Taylor series expansion we have
f(x) = f(a) + f'(a)(x-a) + +
+
+ ...
Putting a = 0 and all the values from above in the expansion, we get,
Cos x = 1 - +
-
+ ...
Answer:
(A).
Step-by-step explanation:
The equation of any straight line; a linear equation, can be interpreted as , where 'm' is the slope of the line, 'b', is the y-intercept, and the values of 'x' and 'y' are simply coordinates!
Let's find the slope of the straight line, and that can be done in various ways. Since they gave us two points, I would use the following formula to find slope:
Let's assign each coordinate(s) to correspond to the formula (It doesn't matter what order, as long as you follow the rule that you've set up).
So now that know this, we can just plug in the values that we know, which we already know everything.
→ This then gives us;
, which means the slope is -3! Now we have one part of the equation. This means that we can easily eliminate options B and D since they give a slope of positive three, which is false.
Now, let's move onto the y-intercept. How do we solve that? The y-intercept is generally known as a point that crosses the y-axis. This means that the <em>x value</em> is always going to be zero. This means that we know the point on the graph is: . So all we have to do is use that information, and look at the graph! It looks like there is a point that does an x-value of zero.
We can see that the point we are looking at is; , and the y-value is only what we are looking for. So now, we know that several components of the graph. We know so far that the slope is -3 and the line crosses the y-axis at (0,3), now we move on to determine the inequality part of the graph.
There are rules that determine how a graph is shaded—and let's figure that out.
Shading above the line is represented when 'y' is greater than the inequality itself.
Shading below the line is represented when 'y' is less than the inequality.
The shading occurs below the line, right? That means y is less than the inequality, and since the line is solid, the line can also equal the inequality. Now; with all of this to mind, y is less than or equal to -3x +3 is written or known as; , which means the answer is A.
About 115°
Step-by-step explanation:
- By 2 pi r, total circumference is about 942
- Length of an arc = 2 pi r (theta/360)
- We needed to find theta(angle) here
- Easily putting all the values gives us 115°