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2 years ago

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The submarine is traveling at a depth of 152 feet below sea level. The submarine was given instructions to rise 63 feet and then

drop 84 feet. Write an expression that describes this situation

1 answer:

laiz [17]2 years ago

4 0

The expression should be -152+63-84

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The polar coordinates of a point are 3π 4 and 7.00 m. What are its Cartesian coordinates (in m)? (x, y) = 6.06,−3.5 m

Keith_Richards [23]

Answer:

a) $\left(x,y\right)=\left(4.95,-4.95\right)$

b) $r\angle\theta = 7\angle0.5236\,\text{radians}$

Step-by-step explanation:

Polar coordinates are represented as: $r\angle\theta$ , where 'r' is the length (or magnitude) of the line, and ' $\theta$ ' is the angle measured from the positive x-axis.

in our case:

$7\angle\dfrac{3\pi}{4}$

to covert the polar to cartesian:

$x = r\cos{\theta}$

$y = r\sin{\theta}$

we can plug in our values:

$x = 7\cos{\dfrac{3\pi}{4}} = -7\dfrac{\sqrt{2}}{2}$

$y = 7\sin{\dfrac{3\pi}{4}} = 7\dfrac{\sqrt{2}}{2}$

the Cartesian coordinates are:

$\left(x,y\right)=\left(-7\dfrac{\sqrt{2}}{2},7\dfrac{\sqrt{2}}{2}\right)$

$\left(x,y\right)=\left(4.95,-4.95\right)$

(b) to convert (x,y) = (6.06,-3.5)

we'll use the pythagoras theorem to find 'r'

$r^2 = x^2+y^2$

$r^2 = (6.06)^2+(-3.5)^2$

$r = \sqrt{48.97} \approx 7$

the angle can be found by:

$\tan{\theta} = \dfrac{y}{x}$

$\tan{\theta} = \dfrac{3.5}{6.06}$

$\theta = \arctan{left(\dfrac{3.5}{6.06}\right)}$

$\theta = 0.5236 \text{radians}$

to convert radians to degrees:

$\theta = 0.5236 \times \dfrac{180}{\pi} \approx 30^\circ$

writing in polar coordinates:

$r\angle\theta = 7\angle30^\circ\,\,\text{OR}\,\,7\angle0.5236\,\text{radians}$

5 0

3 years ago

A rectangle has a length of 6.5m and a width of 7.3m what is the area and the perimeter

Bad White [126]

Step-by-step explanation:

<h3><em><u>Given</u></em><em><u>:</u></em></h3>

Length of the rectangle = 6.5 m

Width of the rectangule = 7.3 m

<h3><em><u>Then</u></em><em><u>:</u></em></h3>

<u>First</u><u> </u><u>case</u><u>,</u>

Area of the rectangle

= length × width

= 6.5 m × 7.3 m

= <em><u>47.45</u></em><em><u> </u></em><em><u>s</u></em><em><u>q</u></em><em><u>.</u></em><em><u>m</u></em><em><u> </u></em><em><u>(</u></em><em><u>Ans</u></em><em><u>)</u></em><em><u>(</u></em><em><u>i</u></em><em><u>)</u></em>

<u>Second</u><u> </u><u>case</u><u>,</u>

Perimeter of the rectangle

= 2(length + width)

= 2(6.5 + 7.3)m

= 2 × 13.8 m

= <em><u>27</u></em><em><u>.</u></em><em><u>6</u></em><em><u> </u></em><em><u>m</u></em><em><u> </u></em><em><u>(</u></em><em><u>Ans</u></em><em><u>)</u></em><em><u>(</u></em><em><u>ii</u></em><em><u>)</u></em>

5 0

2 years ago

Read 2 more answers

Solve the given inequality and graph the solution on a number line.

raketka [301]

Answer:

sorry agnor me

Step-by-step explanation:

plz egnore my ideodik nis

4 0

3 years ago

Read 2 more answers

What is 9/10 divided by 3/4?

goldenfox [79]

Answer:

6/5

Step-by-step explanation:

hi! when dividing fractions, we use the KCF rule, which stands for keep,change,flip. we keep the first fraction the same, change the division symbol to multiplication, and flip the second fraction to its reciprocal. therefore, we now have:

9/10 * 4/3

now, we can multiply the numerators and denominators.

36/30

we can simplify this.

6/5

7 0

3 years ago

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10) A wheelchair ramp is getting built at the entrance of a building. The ramp will be 25 feet long from front

mezya [45]

Answer:

The angle complies with the state regulations.

Step-by-step explanation:

The angle of elevation is the angle $\theta$ in the figure, and from trigonometry we find that

$sin(\theta) = \dfrac{1.5ft}{25ft}$

taking the inverse sine of both sides we get

$\theta = sin^{-1}(\dfrac{1.5ft}{25ft})$

which gives

$\theta = 3.44^o$

which is less than 5°, and therefore is well within the state regulations.

3 0

3 years ago