A straight river flows east at a speed of 11 mi/h. A boater starts at the south shore of the river and wants to arrive at a point on the north shore of the river directly opposite the starting point. The motorboat has a speed of 22 mi/h relative to the water. In what direction should the boat be headed?

Answers

Answer 1

Answer:

The direction should the boat be headed is 60 degrees north 30 degrees west and this can be determined by using the trigonometric functions.

Given :

A straight river flows east at a speed of 11 mi/h.
A boater starts at the south shore of the river and wants to arrive at a point on the north shore of the river directly opposite the starting point.
The motorboat has a speed of 22 mi/h relative to the water.

The following steps can be used in order to determine the direction should the boat be headed:

Step 1 - The trigonometric function can be used in order to determine the direction should the boat be headed.

Step 2 - The mathematicalexpression of the cosine function is given by:

$\rm cos\theta=(base)/(hypotenuse)$

where $\theta$ is the direction should the boat be headed.

Step 3 - Now, substitute the known values in the above formula.

$\rm cos\theta=(11)/(22)$

Step 4 - Simplify the above expression.

$\rm cos\theta=(1)/(2)$

$\theta = 60^\circ$

Step 5 - So, the angle from the west axis is given by:

$90-60=30^\circ$

The direction should the boat be headed is 60 degrees north 30 degrees west.

For more information, refer to the link given below:

brainly.com/question/11709244

Answer 2

Answer:

Answer:

N 30 degree W

Step-by-step explanation:

We are given that

Speed of river flows=11 mi/h(East)

Speed of motorboat relative to water=22mi/h

We have to find the direction in which the boat should be headed.

Let direction of the boat = $\theta$

We know that

$Cos\theta=(Base)/(hypotenuse)$

Using the formula

$Cos\theta=(11)/(22)=(1)/(2)$

$Cos\theta=Cos60^(\circ)$

Because $Cos60^(\circ)=(1)/(2)$

$\theta=60^(\circ)$

Angle from the west axis= $90-60=30^(\circ)$ W

Hence, the direction of boat should be headed in N 30 degree W

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Which number is farthest from 1 in the number line?A √1.2

B √1.3

C √1.4

D √1.5

Answers

The answer is D due to it

Simplify: -m(7m + 3) – 4m2
A. 12m+4
B. -11m2-3m
C. -11m2+6m
D.5 m + 4

Answers

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$- m(7m + 3) - 4 {m}^(2) \n - 7m^(2) - 3m - 4 {m}^(2) \n - 11 {m}^(2) - 3m$

Kristen opened a savings account and deposited $800.00. The account earns 7% interest, compounded annually. If she wants to use the money to buy a new bicycle in 3 years, how much will she be able to spend on the bike?

Answers

Answer: she will be able to spend $980 on the bike.

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1 + r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = $800

r = 7% = 7/100 = 0.07

n = 1 because it was compounded once in a year.

t = 3 years

Therefore,.

A = 800(1 + 0.07/1)^1 × 3

A = 800(1 + 0.07)^3

A = 800(1.07)^3

A = $980

Ann Nguyen would like an installment loan for 5,000. Her bank will loan her the money at 12% for 18 months. Her insurance company will loan her the money at 12% for 24 months. Which loan would cost her less?