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igor_vitrenko [27]
3 years ago
15

The velocity of the current in a river is C = 0.6i + 0.8j km/hr. A boat moves relative to the water with velocity v=7i km/hr. a.

What is the speed of the boat relative to the riverbed? b. What angle does the velocity of the boat relative to the riverbed make with the vector v? c. What does the angle from part b tell us in practical terms?
Mathematics
1 answer:
AnnyKZ [126]3 years ago
5 0

Answer:

  a. 7.64 km/h

  b. 6.0°

  c. see below

Step-by-step explanation:

a) The total velocity of the boat is ...

  7i +(0.6i +0.8j) = 7.6i +0.8j

The magnitude of this velocity is the speed of the boat, relative to land. That is given by the Pythagorean theorem.

  |7.6i +0.8j| = √(7.6² +0.8²) = √58.4 ≈ 7.642 . . . . km/h

__

b) The angle of the total velocity with respect to the "i" direction (the direction of vector v) is ...

  α = arctan(0.8/7.6) ≈ 6.009°

__

c) The boat is headed in a direction 6° different from its velocity relative to the water. That may need to be accounted for if the boat is traveling any significant distance.

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BRAINLIEST!!!
Sonbull [250]

Answer:

\sqrt{37}

Step-by-step explanation:

The distance d between a point (m , n ) and a line in the form

Ax + By + C = 0 , is calculated as

d = \frac{|Am+Bn+C|}{\sqrt{A^2+B^2} }

Here (m, n ) = (6, 2 ) and

6x - y = - 3 ( add 3 to both sides )

6x - y + 3 = 0 → A = 6, B = - 1, C = 3

d = \frac{|6(6)+-1(2)+3|}{\sqrt{6^2+(-1)^2} }

   = \frac{|36-2+3|}{\sqrt{36+1} }

   = \frac{|37|}{\sqrt{37} }

   = \frac{37}{\sqrt{37} } × \frac{\sqrt{37} }{\sqrt{37} }

   = \frac{37\sqrt{37} }{37} ← cancel 37 on numerator/ denominator

   = \sqrt{37}

7 0
2 years ago
Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(4, 0), Q(0, −4), and R(−8, −4). Triangle P'Q'R' has
Whitepunk [10]

Answer:

Please find attached the required plot accomplished with an online tool

Part A:

1/4

Part B:

P''(-1, 0),  Q''(0, -1), and R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent

Step-by-step explanation:

Part A:

Triangle ΔPQR has vertices P(4, 0), Q(0, -4), R(-8, -4)

Triangle ΔP'Q'R' has vertices P'(1, 0), Q'(0, -1), R'(-2, -1)

The dimensions of the sides of the triangle are given by the relation;

l = \sqrt{\left (y_{2}-y_{1}  \right )^{2}+\left (x_{2}-x_{1}  \right )^{2}}

Where;

(x₁, y₁) and (x₂, y₂) are the coordinates on the ends of the segment

For segment PQ, we place (x₁, y₁) = (4, 0) and (x₂, y₂) = (0, -4);

By substitution into the length equation, we get;

The length of segment PQ = 4·√2

The length of segment PR = 4·√10

The length of segment RQ = 8  

The length of segment P'Q' = √2

The length of segment P'R' = √10

The length of segment R'Q' = 2

Therefore, the scale factor of the dilation of ΔPQR to ΔP'Q'R' is 1/4

Part B:

Reflection of (x, y) across the y-axis gives;

(x, y) image after reflection across the y-axis = (-x, y)

The coordinates after reflection of P'(1, 0), Q'(0, -1), R'(-2, -1) across the y-axis is given as follows;

P'(1, 0) image after reflection across the y-axis = P''(-1, 0)

Q'(0, -1) image after reflection across the y-axis = Q''(0, -1)

R'(-2, -1) image after reflection across the y-axis = R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent as the dimensions of the sides of triangle PQR and P''Q''R'' are not the same.

6 0
3 years ago
What describes this angle? Because I don’t know what the hell it means.
maw [93]

Answer:

Less than a right angle.

Step-by-step explanation:

If you really think about it, a right angle is 90 degrees, and from the looks of it, that angle shown is an acute angle. Acute angles are always smaller than a right angle, so your answer is less than a right angle. :)

5 0
3 years ago
If 14 g of a radioactive substance are present initially and 3 yr later only 7 g​ remain, how much of the substance will be pres
marishachu [46]
It would be 48 bc if you add it all up and subtract it and add again and multiply and divide and multiply within a and the substance of present after 6 yr you will see that i have wasted your time and that is not the answer
5 0
2 years ago
X-4/x-3 is less than 2x-1/2
kifflom [539]

Answer:

yes

Step-by-step explanation:

yes

5 0
2 years ago
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