Add as decimal 1.75+1.13

if you know that 7 x 8=56, how can you use the commutative property of multiplication to find the product of 8 x 7 ?

Fofino [41]

Its the same thing because your just switching the order which doesn't matter when your adding or multiplying

5 0

3 years ago

A ship leaves port at 10 miles per hour, with a heading of N 35° W. There is a warning buoy located 5 miles directly north of th

Leno4ka [110]

The value of the angle subtended by the distance of the buoy from the

port is given by sine and cosine rule.

The bearing of the buoy from the is approximately 307.35°

Reasons:

Location from which the ship sails = Port

The speed of the ship = 10 mph

Direction of the ship = N35°W

Location of the warning buoy = 5 miles north of the port

Required: The bearing of the warning buoy from the ship after 7.5 hours.

Solution:

The distance travelled by the ship = 7.5 hours × 10 mph = 75 miles

By cosine rule, we have;

a² = b² + c² - 2·b·c·cos(A)

Where;

a = The distance between the ship and the buoy

b = The distance between the ship and the port = 75 miles

c = The distance between the buoy and the port = 5 miles

Angle ∠A = The angle between the ship and the buoy = The bearing of the ship = 35°

Which gives;

a = √(75² + 5² - 2 × 75 × 5 × cos(35°))

By sine rule, we have;

$\displaystyle \frac{a}{sin(A)} = \mathbf{ \frac{b}{sin(B)}}$

Therefore;

$\displaystyle sin(B)= \frac{b \cdot sin(A)}{a}$

Which gives;

$\displaystyle sin(B) = \mathbf{\frac{75 \cdot sin(35^{\circ})}{\sqrt{75^2 + 5^2 - 2 \times 75\times5\times cos(35^{\circ}) } }}$

$\displaystyle B = arcsin\left( \frac{75 \cdot sin(35^{\circ})}{\sqrt{75^2 + 5^2 - 2 \times 75\times5\times cos(35^{\circ}) } }\right) \approx 37.32^{\circ}$

Similarly, we can get;

$\displaystyle B = arcsin\left( \frac{75 \cdot sin(35^{\circ})}{\sqrt{75^2 + 5^2 - 2 \times 75\times5\times cos(35^{\circ}) } }\right) \approx \mathbf{ 142.68^{\circ}}$

The angle subtended by the distance of the buoy from the port, C is therefore;

C ≈ 180° - 142.68° - 35° ≈ 2.32°

By alternate interior angles, we have;

The bearing of the warning buoy as seen from the ship is therefore;

Bearing of buoy ≈ 270° + 35° + 2.32° ≈ 307.35°

Learn more about bearing in mathematics here:

brainly.com/question/23427938

5 0

2 years ago

Find the vertex, focus, directrix, and focal width of the parabola. negative 1 divided by 40 x squared equals y

Galina-37 [17]

Answer:

2, 8, 90, 160

that is the focal, vertex l, direction

5 0

3 years ago

Logs are stacked in a pile. The top row has 15 logs and the bottom row has 24 logs. How many logs are there in the stack?

ziro4ka [17]

There are two ways you can do this. You can use the longer way:
15+16+17+18+19+20+21+22+23+24 = 195 (starting from the top row, which has 15 logs, up until the bottom row, which has 24 logs, on condition that each second row has one log more than the previous one)

You can also use the formula (where n is the number of rows)
x= (n(first term+last term))/2
x= (10(15+24))/2
x= (10*39)/2
x=390/2
x=195

Either way, there are 195 logs in the stack.

8 0

2 years ago

Read 2 more answers

Find the slop of the line that passes each pair of points. (3,5) and (-3,-5)

melamori03 [73]

Answer:

postitive 2 so (0,2)

Step-by-step explanation:

if you were to graph this the slope would be in my case 2/2 so you would go down 2 and over to the left or right 2 dependin gon negitaves.

5 0

3 years ago