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Dvinal [7]
2 years ago
5

A ship at position (1, 0) on a nautical chart (with north in the positive y direction) sights a rock at position (4, 7). What is

the vector joining the ship to the rock?
What angle θ does this vector make with due north? (This is called the bearing of the rock from the ship. Round your answer to two decimal places.)
Mathematics
1 answer:
PilotLPTM [1.2K]2 years ago
3 0

Answer:

  • (3, 7)
  • 23.20°

Step-by-step explanation:

The vector in component form is the difference of the coordinates of its end points:

  rock - ship = (4, 7) - (1, 0) = (3, 7) . . . . vector from ship to rock

__

The angle from North can be found using the tangent relation:

  tan(bearing) = (east distance)/(north distance) = 3/7

  bearing = arctan(3/7) ≈ 23.1986°

The bearing of the rock is 23.20°.

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Answer:

3.88

Step-by-step explanation:

y = 23.28/6 x

y = 3.88 x

so, the constant of proportionality is 3.88

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2 years ago
Which of the following are possible equations of a parabola that has no real solutions and opens downward?
bekas [8.4K]

Answer:

y =  -  {(x - 4)}^{2}  - 2

y =  -  {(x + 4)}^{2}  - 2

Step-by-step explanation:

The vertex form of a parabola is given as

y = a {(x - h)}^{2}  + k

If this parabola opens downward, then a<0.

This means for a function opening downward not to have a solution, the k value must also be negative and taking a square root of a negative number will not give real solution.

From the given options, examples of such functions are:

y =  -  {(x + 4)}^{2}  - 2

and

y =  -  {(x  - 4)}^{2}  - 2

6 0
2 years ago
Read 2 more answers
C=wtc/1000 solve for w
Nutka1998 [239]
For this case we have the following equation:
 C =  \frac{wtc}{1000}
 To clear w, we must follow the following steps:
 1) The value of t multiplied by c pass to divide the other side of the equation:
 \frac{w}{1000} =  \frac{C}{tc}
 2) the value of 1000 is passed to multiply to the other side of the equation:
 w = \frac{1000C}{tc}
 Answer:
 
The cleared equation for w is:
 
w = \frac{1000C}{tc}
3 0
2 years ago
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your friend deposits $9500 in an investment account that earns 2.1% annual interest. what is the balance after 11 years when the
solmaris [256]

Answer:

The answer is "$ 11,961.43"

Step-by-step explanation:

Given values:

P =  $ 9500

r= 2.1 %

time (t)= 11 year

total quarterly year =4

Formula:

A= P (1+\frac{r}{n})^{nt}\\\\

quarterly time = 4 \times 11

                         = 44

A= P (1+\frac{r}{n})^{nt}\\\\

A = 9500 ( 1+ \frac{0.021}{4})^{44}\\\\A = 9500(\frac{4+ 0.021}{4} )^{44} \\\\A = 9500(\frac{4.021}{4} )^{44} \\\\A= 9500 (1.00525)^{44}\\\\A= 9500(1.25909819)\\\\A= 11,961. 43\\

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