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2 years ago

What two number being multiplied to get -81

Mathematics

1 answer:

Natalka [10]2 years ago

7 0

The answer would be -9 times -9 to get -81

if I'm mistaken then 9 times 9 would be 81

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Where should the point P be chosen on line segment AB so as to maximize the angle θ? (Assume a = 4 units, b = 5 units, and c = 9

taurus [48]

From the figure, let the distance of point P from point A on line segment AB be x and let the angle opposite side a be M and the angle opposite side c be N.

Using pythagoras theorem,
$\tan M= \frac{a}{b-x} \\ \\ M=\tan^{-1}\left(\frac{a}{b-x}\right)$
and
$\tan N= \frac{c}{x} \\ \\ N=\tan^{-1}\left(\frac{c}{x}\right)$

Angle θ is given by
$\theta=180-M-N \\ \\ =180-\tan^{-1}\left(\frac{a}{b-x}\right)-\tan^{-1}\left(\frac{c}{x}\right)$

Given that a = 4 units, b = 5 units, and c = 9 units, thus
$\theta=180-\tan^{-1}\left(\frac{4}{5-x}\right)-\tan^{-1}\left(\frac{9}{x}\right)$

To maximixe angle θ, the differentiation of <span>θ with respect to x must be equal to zero.
i.e.
$\frac{d\theta}{dx} = -\frac{4}{x^2-10x+41} + \frac{9}{x^2+81} =0 \\ \\ -4(x^2+81)+9(x^2-10x+41)=0 \\ \\ -4x^2-324+9x^2-90x+369=0 \\ \\ 5x^2-90x+45=0 \\ \\ x^2-18x+9=0 \\ \\ x=9\pm6 \sqrt{2}$

Given that x is a point on line segment AB, this means that x is a positive number less than 5.

Thus
$x=9-6 \sqrt{2}=0.5147$

Therefore, The distance from A of point P, so that </span>angle θ is maximum is 0.51 to two decimal places.

6 0

2 years ago

Assume that blood pressure readings are normally distributed with a mean of 123 and a standard deviation of 9.6. If 144 people a

Vanyuwa [196]

Answer:

The probability is 0.9938

Step-by-step explanation:

In this question, we are asked to calculate the probability that the mean blood pressure readings of a group of people is less than a certain reading.

To calculate this, we use the z score.

Mathematically;

z = (mean - value)/(standard deviation/√N)

From the question, we can identify that the mean is 125, the value is 123 , the standard deviation is 9.6 and N ( total population is 144)

Let’s plug these values;

z = (125-123)/(9.6/√144) = 2.5

Now we proceed to calculate the probability with a s score less than 2.5 using statistical tables

P(z<2.5) = 0.9938

8 0

2 years ago

5) Linda picked a basket of apples. She gave half of the apples to a neighbor, then 10 apples to her mother, then half of the re

mihalych1998 [28]

Answer:

is it 8 apples to her mother or 10 since I had this exact problem?

Step-by-step explanation:

3 0

2 years ago

N his road trip, Leon stops to refuel and get some snacks. He has the following purchases:

tresset_1 [31]

Answer:

C. Paid $2.60 too much

Step-by-step explanation:

Gas 12 x 2.89 = 34.68

granola 2 x 1.59 = 3.18 x 1.075 = 3.4185

apple .89 x 1.075 = 0.95675

vitamin water 2 x 1.39 = 2.78 x 1.075 = 2.9885

34.68
3.4185
0.95675
+ 2.9885
---------------------
$42.04

$44.64
- $42.04
---------------------
$2.60

3 0

2 years ago

Tell whether the ordered pair is a solution of the equation<br> y=5x; (15,-3)

n200080 [17]

Answer:

This ordered pair is NOT a solution of the equation.

Step-by-step explanation:

First, it is important to note that ordered pairs consist of (x, y) so in this case

x = 15 and y = -3. And that any variable directly next to a number calls for multiplication. So, plugging in the variables the equation would look like

"-3 = 5 x 15"

To see if 5 x 15 = -3 we will multiply them. 5 x 15 actually equals 75 not -3. So we know this ordered pair is NOT the solution for the problem.

3 0

2 years ago