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3 years ago

Please I need help with this?

Mathematics

1 answer:

Alik [6]3 years ago

3 0

9514 1404 393

Answer:

(a) positive and increasing

Step-by-step explanation:

Point c is on the x-axis, and point d is above it. The curve between points c and d is positive and increasing.

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In the drawing below, lines a and b are parallel lines cut by the transversal c. Jeremiah wishes to find angles that are congrue

ValentinkaMS [17]

B and D are the answers.

6 0

4 years ago

A central angel in this diagram is

Paha777 [63]

Answer:

it looks like an acute angle

4 0

3 years ago

How do you do this question?

AfilCa [17]

<h3>4 Answers: A, B, C, D</h3>

=======================================================

Explanation:

f(x) is continuous when x >= 1. The only discontinuity for f(x) is when x = 0, but 0 is not part of this interval.

f(x) is positive for any valid x value in the domain since x^6 is always positive. In general, x^n is positive for all x when n is any even number.

f(x) is decreasing. You can see this through a table of values or through a graph. For anything in the form 1/(x^k), it will be a decreasing function because x^k gets larger, so 1/(x^k) gets smaller, when x goes to infinity.

--------------------

The conditions to use the integral test have been met. So we have to see if $\displaystyle \int_1^{\infty}f(x)dx$ converges or not.

Let's integrate and find out

$\displaystyle \int \frac{1}{x^6} dx = \int x^{-6} dx\\\\\\ \displaystyle \int \frac{1}{x^6} dx = \frac{1}{1+(-6)}x^{-6+1}+C\\\\\\ \displaystyle \int \frac{1}{x^6} dx = \frac{1}{-5}x^{-5}+C\\\\\\ \displaystyle \int \frac{1}{x^6} dx = -\frac{1}{5}*\frac{1}{x^5}+C\\\\\\ \displaystyle \int \frac{1}{x^6} dx = -\frac{1}{5x^5}+C\\\\$

So we have

$\displaystyle g(x) = \int f(x) dx\\\\\\\displaystyle g(x) = \int \frac{1}{x^6} dx\\\\\\\displaystyle g(x) = -\frac{1}{5x^5}+C\\\\\\$

Meaning that,

$\displaystyle \int_{a}^{b} f(x) dx = g(b)-g(a)\\\\\\\displaystyle \int_{a}^{b} \frac{1}{x^6} dx = \left(-\frac{1}{5b^5}+C\right)-\left(-\frac{1}{5a^5}+C\right)\\\\\\\displaystyle \int_{a}^{b} \frac{1}{x^6} dx = -\frac{1}{5b^5}+\frac{1}{5a^5}\\\\\\$

If we plug in a = 1 and apply the limit as b approaches positive infinity, then the expression $-\frac{1}{5b^5}+\frac{1}{5a^5}$ will turn into $\frac{1}{5}$

Therefore,

$\displaystyle \int_{1}^{\infty} \frac{1}{x^6} dx = \frac{1}{5}\\\\\\$

Because this integral converges, this means the series $\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^6}$ also converges as well by the integral test.

7 0

3 years ago

A flying cannonball’s height is described by formula y=−16 <img src="https://tex.z-dn.net/?f=%20t%5E%7B2%7D%20" id="TexFormula1"

Morgarella [4.7K]

Y = -t ^ 2 + 300t - 16
We find the first derivative and calculate its roots.
We make the second derivative, and calculate the sign taken in it by the roots of the first derivative, and if:
f '' (a) <0 is a relative maximum
f '' (a)> 0 is a relative minimum

y '= - 2t + 300 = 0
-2t + 300 = 0
t = 300/2 = 150

y'' = - 2
y'' (150) = - 2 (is a relative maximum)

the highest point of the trajectory is reached for t = 150s.
The height for that time is
y = - (150) ^ 2 + 300 (150) - 16 = 67484

answer
67484
t = 150s.

4 0

3 years ago

A linear function contains these points: (0,-1) & (3,8)

Elenna [48]

Answer:

slope: 3

y-intercept: (0, -1)

Find slope:

$\sf slope : \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points$