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2 years ago

A boat sails on a bearing of 038°anf then 5km on a bearing of 067°.

Mathematics

1 answer:

I am Lyosha [343]2 years ago

7 0

This question is not complete

Complete Question

A boat sails 4km on a bearing of 038 degree and then 5km on a bearing of 067 degree.(a)how far is the boat from its starting point.(b) calculate the bearing of the boat from its starting point

Answer:

a)8.717km

b) 54.146°

Step-by-step explanation:

(a)how far is the boat from its starting point.

We solve this question using resultant vectors

= (Rcos θ, Rsinθ + Rcos θ, Rsinθ)

Where

Rcos θ = x

Rsinθ = y

= (4cos38,4sin38) + (5cos67,5sin67)

= (3.152, 2.4626) + (1.9536, 4.6025)

= (5.1056, 7.065)

x = 5.1056

y = 7.065

Distance = √x² + y²

= √(5.1056²+ 7.065²)

= √75.98137636

= √8.7167296826

Approximately = 8.717 km

Therefore, the boat is 8.717km its starting point.

(b)calculate the bearing of the boat from its starting point.

The bearing of the boat is calculated using

tan θ = y/x

tan θ = 7.065/5.1056

θ = arc tan (7.065/5.1056)

= 54.145828196°

θ ≈ 54.146°

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Which sequence could be partially defined by the recursive formula f (n + 1) = f(n) + 2.5 for n ≥ 1?

horrorfan [7]

Option C: –10, –7.5, –5, –2.5, … is the sequence that could be partially defined by the recursive formula $f(n+1)=f(n)+2.5$

Explanation:

The given recursive formula is $f(n+1)=f(n)+2.5$ for $n\geq 1$ and $f(1)=-10$

We need to determine the sequence.

The sequence can be determined by substituting n = 1, 2, 3, 4,....

2nd term of the sequence:

Substituting n = 1 in the formula $f(n+1)=f(n)+2.5$ , we get,

$f(1+1)=f(1)+2.5$

Simplifying, we have,

$f(2)=-10+2.5=-7.5$

Thus, the 2nd term of the sequence is -7.5

3rd term of the sequence:

Substituting n = 2 in the formula $f(n+1)=f(n)+2.5$ , we get,

$f(2+1)=f(2)+2.5$

Simplifying, we have,

$f(3)=-7.5+2.5=-5$

Thus, the 3rd term of the sequence is -5

4th term of the sequence:

Substituting n = 3 in the formula $f(n+1)=f(n)+2.5$ , we get,

$f(3+1)=f(3)+2.5$

Simplifying, we have,

$f(4)=-5+2.5=-2.5$

Thus, the 4th term of the sequence is -2.5

Therefore, the sequence is –10, –7.5, –5, –2.5, …

Hence, Option C is the correct answer.

3 0

2 years ago

The weight, y, in pounds, of kittens was tracked for the first 8 weeks after birth where t represents the number of weeks after

marshall27 [118]

Answer:

Step-by-step explanation:

The mentioned relationship for the weight, in pounds, of the kitten with respect to time, in weeks, is

$\hat y =1.7 +1.48t$

Weight of the kitten after 10 weeks

$\hat y =1.7 +1.48\times 10$

$\hat y =16.5$ pounds

This modeled equation is based on the observation of the early age of a kitten where the kitten is in its growth period, but in the early stage the growth rate in the weight of the kitten was the same but the growth of any living beings continues till the adult stage. So, after some time, in real life situation, this weekly change in weight will become zero, So, this model is not suitable to measure the weight of the kitten over the larger time period.

Here, t= 10 weeks is nearby the observed time period, so the linearly modeled equation can be used to predict the weight.

Hence, the weight of the kitten after 10 weeks is 16.5 pounds.

8 0

2 years ago

Matt and Shirley, working together, can rake the yard in 10 hours. Working alone, Shirley takes twice as long as Matt. How long

AysviL [449]

5 hours is the answer

4 0

2 years ago

Find x in the given figure if m∠AOC = 124°.

Nastasia [14]

Answer:

A) 8

Step-by-step explanation:

Add angles AOB and BOC to get angle AOC.

Since we know the value of AOC is 124 and AOB+BOC=AO

Then (8x+25)+(6x-13)=124.

Combine like terms to get 14x+12= 124.

Solve for x by subtracting 12 from 124, then divide the answer by 14.

3 0

2 years ago

Suppose the firm in this example considers a second product that has a unit profit of $5 and requires 2 hours of production time

user100 [1]

The question is incomplete, here is the complete question

Recall the production model from Section 1.3:

Max 10x

s.t. 5x ≤ 40

x ≥ 0

Suppose the firm in this example considers a second product that has a unit profit of $5 and requires 2 hours for each unit produced. Assume total production capacity remains 40 units. Use y as the number of units of product 2 produced. . Show the mathematical model when both products are considered simultaneously.

Answer:

Max Profit: 10x + 5y

5x + 2y ≤ 40

x ≥ 0, y ≥ 0

Explanation:

x= number of units of product 1 produced

y = number of units of product 2 produced

Since the first product, x, has a unit profit of $10 and Max1 is 10x

Second product, y, has a unit profit of $5, Max2 = 5y

The maximum profit when both products are considered simultaneously is 10x + 5y

Max Profit = 10x + 5y

Time required for each unit of x is 5hours

Therefore, time required for x units is 5x hours

Time required for each unit of y is 2hours

Therefore, time required for y units is 2y hours

Time required for the simultaneous production of both products is 5x + 2y

Since production capacity remains 40 units, 5x+2y ≤40

NB: The values of x and y cannot be negative

5 0

1 year ago