A boat leaves the marina and sails 13 miles northeast, then 12 miles east. In what direction must the boat sail to head directly back to the marina?

a. 66.55° W of S
b. 23.45° W of S
c. 45.00° E of N
d. 66.55° E of N

Answers

Answer 1

Answer: c

Step-by-step explanation: this answer is Unknown  

Answer 2

The direction of the boat sail to head directly back to the marina which leaves the marina and sails 13 miles northeast, then 12 miles east is 23.45° W of S.

What is the law of cosine?

When the three sides of a triangle is known, then to find any angle, the law of cosine is used.

It can be given as,

[tex]c^2=a^2+b^2-2ab\cos C\\a^2=c^2+b^2-2ab\cos A\\b^2=a^2+c^2-2ab\cos B[/tex]

Here, a,b and c are the sides of the triangle and A,B and C are the angles of the triangle.

A boat leaves the marina and sails 13 miles northeast, then 12 miles east. The image of the problem is attached below.

Thus, the value of the third side is,

[tex]c=\sqrt{12^2+13^2-(2\times12\times13\times \cos 135)}\\c=23.01[/tex]

The measure of the angle x is,

[tex]\angle x=\cos^{-1}\dfrac{23.1^2+13^2-12^2}{2\times23.1\times13}\\\angle x=23^o26'57"\\\angle x=23.449^o[/tex]

Thus, the direction of the boat sail to head directly back to the marina which leaves the marina and sails 13 miles northeast, then 12 miles east is 23.45° W of S.

Learn more about the law of cosine here;

https://brainly.com/question/4372174

A Boat Leaves The Marina And Sails 13 Miles Northeast, Then 12 Miles East. In What Direction Must The

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The value of y varies directly with x. When y = 5.5, x = ¼ . What is the value of y when x is 3? *

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Answer:

The answer is 66

Step-by-step explanation

Answer:

66

Step-by-step explanation:

5.5 in fraction form is 11/2

Divide 11/4 and 1/4

This will get you 22

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Abcd is a cyclic quadrilateral. o is the center of the circle ∠bad = 40°,then angle BCD=?,m(arc BCD) =?,m( arc BAD)=?

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Answer:

m∠BCD = 140°

m(arc BCD) = 80°

m(arc BAD) = 280°

Step-by-step explanation:

In the cyclic quadrilateral, every two opposite angles are supplementary.The measure of the subtended arc to an inscribed angle equals twice the measure of this angle

Let us use these facts to solve the question

∵ ABCD is a cyclic quadrilateral in circle O

∵ ∠BAD and ∠BCD are opposite angles

→ By using the 1st fact above

∴ m∠BAD + m∠BCD = 180°

∵ m∠BAD = 40°

∴ 40° + m∠BCD = 180°

→ Subtract 40° from both sides

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m∠BCD = 140°

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→ By using the 2nd fact above

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→ By using the 2nd fact above

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One of the two points Seamus used to determine the slope of his trendline was (0.00286,4.27). If the slope of his trendline is 8,749 K, what is the y-intercept of his trendline

Answers

Answer:

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Step-by-step explanation:

The slope of his trendline is 8,749 K

The two points that are used to find the slope of his trendline was (0.00286,4.27).

We need to find the y-intercept of his trendline. Slope of equation is given by :

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Step-by-step explanation:

Given f(x,y) = 4x²-9xy+6y³, we are to find the derivative of the function with respect to x keeping y as constant.

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Given:
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Answers

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Answers

Answer:

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Step-by-step explanation:

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Answer:

X=32 and Y=51

Step-by-step explanation:

first to find the answer, we must establish that the sum of 3 angles in any triangle will equal 180 degrees, and both triangles are congruent then we can start making equations. Triangle STU has 2 numbers and one equation on it, the equation for the length of NP will give us y, but first we must get X from the equation for angle TUS which is congruent to angle MNP, so first we must add angle M and angle P together to find angle N, 142+24=166, 180-166=14, so angle N and angle U are both equal to 14 degrees, so, 2x-50=14 first add 50 to both sides then divide by 2 giving us 32=X. Now that we have x, we can find y, 2x32-y=13, we can determine m is equal to 13 m because segment SU is congruent to segment NP, SU is 13 meters, thus NP is 13 meters long as well. first multiply 32 and 2 giving 64, then subtract 64 from both sides, giving you -y=-51, but we don't stop here because y itself can't be negative as that's not what's being asked for, so divide both sides by negative 1 giving you Y=51

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Answer:

Step-by-step explanation:

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Step-by-step explanation:

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Answer:

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Answers

Answer:

Yes the die is fair as the calculated z= -0.224  is less than the Z∝= 1.96

Step-by-step explanation:

x`- u / s/√n< Z∝

x`- 60 /√50/√360 < 1.96

From the above we find that u = 60  and the sample size n= 360 S= √ 50

Z∝= 1.96

Here p = 1/6 ( the probability of getting a 1 out of 6)

q= 5/6

Since it is normal Standard deviation = √npq = √360 * 1/6*5/6= √50

If x`= 30

then

30 - 60  /√50/√360 < 1.96

-30/7.07*18.973  < 1.96

- 0.224 < 1.96

Yes the die is fair as the calculated z= -0.224  is less than the Z∝= 1.96  the null hypothesis that  die rolled is fair is accepted.

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