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3 years ago

What is the unit rate of 9/2

Mathematics

1 answer:

Anuta_ua [19.1K]3 years ago

3 0

Hey there!

To find unit rate, we must get the fraction with a denominator of 1, so we divide this fraction by 2:

$\frac{4.5}{1}$

Hope it helps and have a great day!

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A mine worker is in a tunnel 25 feet below the ground. He descends another 13 feet. What is his final position? i already know t

Marina86 [1]

Answer: -25 - 13

This simplifies to -38

So the worker's final position is 38 feet below the ground.

A diagram is shown below.

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Explanation:

Draw a vertical number line. Plot 0 on it to indicate the ground level, or surface level. Then plot -25 on it, which is below 0. This is 25 feet below the ground.

To move 13 further feet downward, we will subtract 13 from -25. Subtracting a positive means we move downward.

For example, start at the 30th of a building. This is marked as +30 or just 30 on the vertical number line. Subtract off 13 to go down 13 floors and we have 30-13 = 17. So after going down 13 floors, we're at the 17th floor now.

Going back to the problem at hand, we start at -25 and subtract off 13 to get the final answer -25 - 13

The answer is not -25 - -13 and it is not -25 - (-13). This is because the two negatives cancel to be a positive. So -25 - (-13) becomes -25+13. Here we're starting at -25 but then going up 13 feet. Instead we want to go down 13 feet.

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

After we determine the expression is -25 - 13 we will effectively add the positive versions of those numbers like so

25+13 = 38

But the final answer is negative because we're starting underground and moving further underground.

We can write it like this

-25 - 13 = -(25+13) = -(38) = -38

Therefore, if the worker starts off 25 feet underground, and moves 13 feet downward, then the worker ends up 38 feet underground. Again, use the vertical number line to help see this.

Check out the diagram below.

7 0

3 years ago

Each pair of figures is similar find the missing side I need this fast please

garri49 [273]

The answer is 0.2 hope it helps

8 0

3 years ago

Read 2 more answers

Use the the triangle.

KATRIN_1 [288]

For a 45 45 90 triangle if the legs are x length then the hyptonuse is x√2

a.
7=x
so hyptonuse=7√2 in

b.
sin(45°)=(√2)/2

c.
not sure what you need SAS for
but, area=1/2 times base times height
base=height=7
area=1/2 times 7 times 7=24.5 square inches

d. not sure, same as above?

7 0

3 years ago

5) mZ1 = mZx = 122 1 1 Hint: Must find angle 1 first.

gulaghasi [49]

Angle 1 is 3x4 but u have to multiply the c before the z

4 0

3 years ago

Given that sec (x) = 2 and cosec (x) is negative,

weeeeeb [17]

Answer:

i) sin(2x) = $-\frac{\sqrt{3}}{2}$

ii) cot(x+360) = $-\frac{\sqrt{3}}{3}$

iii) sin(x-180) = $\frac{\sqrt{3}}{2}$

Step-by-step explanation:

sec(x) = 2

Since cos(x) is reciprocal of sec(x), this means:

cos(x) = $\frac{1}{2}$

cosec(x) is negative , this means sin(x) is also negative. The only quadrant where cos(x), sec(x) are positive and sin(x), cosec(x) are negative is the 4th quadrant. Hence the terminal arm of the angle x is in 4th quadrant.

Part i)

sin(2x) can be simplified as:

sin(2x) = 2 sin(x) cos(x)

First we need to find the value of sin(x). According to Pythagorean identity:

$sin^{2}(x)=1-cos^{2}(x)\\\\ sin(x)=\pm \sqrt{1-cos^{2}(x)}$

Since, angle is in 4th quadrant, sin(x) will be negative. So considering the negative value of sin(x) and substituting the value of cos(x), we get:

$sin(x)=- \sqrt{1-cos^{2}(x)}\\\\ sin(x)=-\sqrt{1-(\frac{1}{2})^{2}}\\\\ sin(x)=-\frac{\sqrt{3}}{2}$

So,

$sin(2x)=2 \times -\frac{\sqrt{3} }{2} \times \frac{1}{2}\\\\ sin(2x)=-\frac{\sqrt{3}}{2}$

Part ii)

We have to find cot(x + 360)

An addition of 360 degrees to the angle brings it back to the same terminal point. So the trigonometric ratios of the original angle and new angle after adding 360 or any multiple of 360 stay the same. i.e.

cot(x + 360) = cot(x)

$cot(x) = \frac{cos(x)}{sin(x)}\\$

Using the values, we get:

$cot(x)=\frac{\frac{1}{2}}{-\frac{\sqrt{3}}{2} }\\\\ cot(x)=-\frac{\sqrt{3}}{3}$

Part iii)

We need to find the value of sin(x - 180)

sin(x - 180) = - sin(x)

Addition or subtraction of 180 degrees changes the angle by 2 quadrants. The sign of sin(x) becomes opposite if the angle jumps by 2 quadrants. For example, sin(x) is positive in 1st quadrant and negative in 3rd quadrant.

So,

sin(x - 180) = $-(-\frac{\sqrt{3}}{2}) = \frac{\sqrt{3}}{2}$

6 0

3 years ago