Which expression is equivalent to the expression shown? (5^4)2

David and Lacey are 2000 feet apart on a coastline. They each look at the same boat in the water. The angle between the coastlin

Ulleksa [173]

By using the given distances and directions, we have;

Part A: 1083.5 feet

Part B: 1921.37 feet

Part C: 58.05°

<h3>How can the distances and directions be calculated?</h3>

The distance between David and Lacey = 2000 feet

David's angle to the boat = 70°

Lacey's angle to the boat = 32°

Part A

The distance of the boat from David is found as follows;

Imaginary lines drawn from the boat to David and then to Lacey form a triangle.

In the triangle, let A = 70°

B = 32°

Therefore by the sum of angles in a triangle, we have;

C = 180° - (70° + 32°) = 78°

By using sine rule we have;

$\frac{a}{sin(A)} = \frac{b}{sin( B )} = \frac{c}{sin(C)}$

David's distance from the boat, b, is therefore;

$\frac{b}{sin( 32 )} = \frac{2000}{sin(78)}$

The angle subtended by the coastline, C, is therefore;

$b = \frac{2000}{sin(78)} \times sin( 32 ) = 1083.5$

David's distance from the boat is 1083.5 feet

Part B

The distance between the boat and Lacey is found as follows;

$\mathbf{ \frac{a}{sin( 70)} }= \frac{2000}{sin(78)}$

$a = \frac{2000}{sin(78)} \times sin( 70 ) = 1921.37$

Lacey's distance from the boat is 1921.37 feet

Part C

When b = 1200 feet, we have;

Finding the vertical distance of the boat from the coastline, we have;

1083.5 × sin(70) = 1018.17

We have;

$\frac{1200}{sin(90)} = \frac{1018.17}{sin( B' )}$

${sin( B' )} = \frac{sin(90)}{1200} \times 1018.17$

The angle between the coastline and his view to the boat, B', is therefore;

B' = arcsine (1018.17÷1200) = 58.05°

Learn more about sine rule here:

brainly.com/question/4372174

#SPJ1

4 0

2 years ago

Write the number in the form a+bi square root of -64+2?

Igoryamba

Answer:

$\sqrt{-64}+2=2+8i$

Step-by-step explanation:

$i=\sqrt{-1}\\\\\sqrt{-64}=\sqrt{(64)(-1)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\ for\ a\geq0\ and\ b\geq0\\\\=\sqrt{64}\cdot\sqrt{-1}=8\cdot i=8i\\\\\text{Therefore:}\\\\\sqrt{-64}+2=8i+2=2+8i$

5 0

3 years ago

A carpenter is refinishing two cupboards. She must add the areas of the cupboards to determine the amount of plywood she needs.

Vesna [10]

You are given the area of both cupboards.

The total area would be found by adding the two areas together:

3a^2 − 5y + 15 + 4a^2 + 5y + 5

Combine like terms:

3a^2 + 4a^2 = 7a^2

-5y + 5y = 0y

15 +5 = 20

The area of both cupboards would be 7a^2+20

5 0

4 years ago

Is 31.669 an integer?

Nataly_w [17]

Answer:

No

Step-by-step explanation:

Integers are whole numbers 1, 2, 3, 4, so on and so on

5 0

3 years ago

Read 2 more answers

Miguel will rent a car for the weekend he can choose one or two plans the first one has no initial favorite cost $.70 per mile d

Radda [10]

Answer:

Step-by-step explanation:

The first plan has no initial fee. If the unknown is the number of miles driven, then the equation for the first plan is

C(x) = .7x

The second plan has a fee plus mileage, so with the unknown again being the number of miles driven, then the equation for the second plan is

C(x) = .6x + 75

If we are looking to solve for the number of miles when the cost is the same, we set the cost functions equal to each other and solve for x:

.7x = .6x + 75 and

.1x = 75 so

x = 750

This is really a very helpful thing to be able to figure out, because if you use the first plan and want to drive MORE than the 750 miles, you will be paying more than if you want to drive more than the 750 miles and choose the second plan. For miles less than 750 plan one is cheaper, for miles greater than 750 plan two is cheaper.

See, there really IS a reason for all this algebra!!

4 0

3 years ago