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3 years ago

Need help please and thank you

Mathematics

1 answer:

viktelen [127]3 years ago

4 0

The answer is B) -x^2-3
This is because you have an exponential graph that is flipped, hence the negative sign, and down 3.

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Which transformation of Figure A results in Figure A' ?

MariettaO [177]

Option B: a counterclockwise rotation of 90° about the origin

Explanation:

From the graph, we can see the coordinates of the figure A are (0,2), (-1,6) and (-4,4)

The coordinates of the figure A' are (-2,0), (-6,-1) and (-4,-4)

<u>Option B: a counterclockwise rotation of 90° about the origin </u>

The transformation rule for a coordinate to reflect a counterclockwise rotation of 90° about the origin is given by

$(x,y)\implies (-y,x)$

Let us substitute the coordinates of the figure A

Thus, we have,

$(0,2)\implies(-2,0)$

$(-1,6)\implies (-6,-1)$

$(-4,4)\implies(-4,-4)$

Thus, the resulting coordinates are equivalent to the coordinates of the figure A'.

Therefore, the figure is a counterclockwise rotation of 90° about the origin .

Hence, Option B is the correct answer.

3 0

3 years ago

Read 2 more answers

The angles of elevation of a balloon from two points A and C on level ground are 24.5 and 41.3, respectively . Points A and C ar

lesya [120]

Answer:

height of the balloon = 1.0494 miles

Step-by-step explanation:

I drew a triangle and labeled angles A, B and C and sides a, b and c.

a = (c · sin A) / sin C = (3.5 · sin 24.5°) / sin 114.2° = 1.4514 / 0.9121 = 1.59 miles

now we have a 90° triangle

h = (a · sin B) / sin 90° = (1.59 · sin 41.3°) / sin 90° = 1.0494 / 1 = 1.0494 miles

5 0

3 years ago

What the square root 11?

Mumz [18]

I hope this helps you

5 0

3 years ago

The weights of Twinkies are Normally distributed with a mean of 1.5 ounces and a standard deviation of 0.1 ounces. a) The middle

tensa zangetsu [6.8K]

Answer:

The middle 99.7% of Twinkies weigh between approximately 1.2 and 1.8 ounces.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 1.5

Standard deviation = 0.1

middle 99.7%

Within 3 standard deviations of the mean, so

1.5 - 3*0.1 = 1.2

1.5 + 3*0.1 = 1.8

So the answer is:

The middle 99.7% of Twinkies weigh between approximately 1.2 and 1.8 ounces.

8 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