Two ships set sail in different directions from the same place. Tyler's ship sail 35 miles while Noah's ship sails for 42 miles. At the same time they are 56 miles apart. What was the angle between their paths when they started?
Answers
Answer:
The angle between their paths when they started is 93°.
Step-by-step explanation:
The Law of Cosines
It relates the length of the sides of a triangle with one of its internal angles.
Let a,b, and c be the length of the sides of a given triangle, and x the included angle between sides a and b, then the following relation applies:
[tex]c^2=a^2+b^2-2ab\cos x[/tex]
When the two ships travel in different directions from the same point in the plane, they form an angle we called x in the image below.
Tyler's ship sails a=35 miles and Noah's ship sails for b=42 miles. At some time they are c=56 miles apart.
Since we know the values of all three side lengths, we solve the equation for x:
[tex]\displaystyle \cos x=\frac{a^2+b^2-c^2}{2ab}[/tex]
Substituting values:
[tex]\displaystyle \cos x=\frac{35^2+42^2-56^2}{2(35)(42)}[/tex]
Calculating:
[tex]\displaystyle \cos x=-\frac{147}{2940}=-\frac{1}{20}[/tex]
Computing the inverse cosine:
[tex]x = \arccos(-0.05)[/tex]
[tex]x \approx 93^\circ[/tex]
The angle between their paths when they started is 93°.
Related Questions
1 + 1???????????????????
Answers
Answer:
2
Hopefully that's the answer you wanted XD
Answer:
2
Step-by-step explanation:
Find the solution to the system of the equations shown below: y = -4x + 11
y=1/2x+2
Answers
Hello!
[tex]\large\boxed{x = 2}[/tex]
Set the two equations equal to each other to solve:
y = -4x + 11
y = 1/2x + 2
-4x + 11 = 1/2x + 2
Add 4x to both sides:
-4x + 4x + 11 = 1/2x + 2 **Convert 4x into 8/2x***
11 = 9/2x + 2
Subtract 2 from both sides:
11 - 2 = 9/2x + 2 - 2
9 = 9/2x
Divide both sides by 9/2:
9 * (2/9) = 9/2x * (2/9)
x = 2.
-8 - x = x - 4x
how does x equal to 4 and how do u do this
Answers
Answer:
x=4
Step-by-step explanation:
-x=-3x+8
-x+3x=-3x+8+3x
2x=8
2x/2 = 8/2
x = 4
How are y'all doing today?
Answers
Answer:
goooooooooooooooooood
Step-by-step explanation:and you?
Answer:
Great!
Step-by-step explanation:
But in the future please only post questions, since this is a homework site.
A 10 kg bag of mangoes costs $12.
Find the price per kg of mangoes.
Answers
Answer:
1.2
Step-by-step explanation:
Help ASAP. If this is hard to understand look at the picture I provided. Thanks On which number line do the points represent -52 and +2? (4 points)
R
T
tohoto
HH
-10 8 7 6 5 4 3 2
-1
0 1
2
3
4
5
7
8
9 10
HôtéttH
-1098-7
-3
2
0
1
2
3
4 5 6 7
8 9 10
R
T
Holt
9
8 -7
. 5 4 3
2
.
0
1
2
3
4
5
7
8 9 10
R
T
10 9 8 7 6 5 4 3 2 1
1 2 3 4 5 6 7
8 9 10
Answers
Answer:
The last choice
Step-by-step explanation:
So, - 5 1/2 is negative so it's on the left side of 0. 2 is a positive number so it's on the right side of the 0.
The last choice shows one blue dot on -5 1/2 and the other on 2, so it is correct
Consider the function f(x) = x(x-4.
If the point (2+c,y) is on the graph of f(x), the following point will also be on the graph of f(x):
A) (c-2,y)
B) (2-c,y)
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(2-c,y) is the answer for the problem.
solve this please!!!!!
Answers
So if I’m thinking correctly we subtract 180 from 217 which gives us 37. We then add that to 104 and subtract the sum from 180 which gives us b. So,
180-104+37
180-141=39
So b should equal 39 degrees, to check we add all the respective angles up,
104+39+37=180
Please answer!!!!!!!!!!!!!!
Answers
PLEASE HELP
Alex wants to paint one side of his skateboard ramp with glow-in-the-dark paint, but he needs to know how much area he is painting. Calculate the area of the isosceles trapezoid.
140 ft2
160 ft2
180 ft2
200 ft2
Answers
Answer:
D.) 200ft²
Step-by-step explanation:
The formula for the area of a trapezoid:
[tex]A=\frac{1}{2} (b_{1}+b_{2})h[/tex]
where:
[tex]b_{1}[/tex] and [tex]b_{2}[/tex] are the basesh is the heightInsert the given values:
[tex]A=\frac{1}{2}(16+24)*10[/tex]
Simplify the equation using PEMDAS. Simplify parentheses:
[tex]A=\frac{1}{2}*40*10[/tex]
Simplify multiplication:
[tex]A=\frac{1}{2}* 400[/tex]
Simplify multiplication. Use the rule [tex]\frac{a}{b}*c=\frac{ac}{b}[/tex] :
[tex]A=\frac{1*400}{2}\\\\A=\frac{400}{2}[/tex]
Simplify division:
[tex]A=200[/tex]
The area is 200ft²
:Done
Which graph represents the function y = 2 x - 2?
Answers
Answer:
the third one!
Step-by-step explanation:
What is the equation of the line that has a slope of -4 and passes through ( 9, -5)
Answers
Answer:
y = -4x + 31
Step-by-step explanation:
y = mx + b
y = -4x + b
-5 = -4(9) + b
-5 = -36 + b
b = 31
x - y = 11 and 2x + y = 19 by elimination
Answers
Answer:
(14,3)
Step-by-step explanation:
2x + y = 19
x - y = 11
-2(x - y) = -2(11)
-2x + 2y = -22
-2x + 2y = -22 + 2x + y = 19
3y = -3
y = 3
-------------------------------------------------
x - y = 11
x - 3 = 11
x = 11 + 3
x = 14
2.
What is the area of a triangle whose vertices are J(-2,1), K(4,3), and L(-2,-5) ?
(7 points)
a. What is the formula for the area of the triangle?
b.
Find the length of the base. Do not round to a decimal.
C.
Find the length of the height. Do not round to a decimal.
d. Find the area of the triangle.
Answers
Answer:
Area: T = 18
a. The triangle area using Heron's formula: T= sqrt(s(s−a)(s−b)(s−c) )
b. 2[tex]\sqrt{10}[/tex]
c. h = 5.69
d. T = 18
Step-by-step explanation:
a. T= sqrt(s(s−a)(s−b)(s−c) )
T=sqrt( 11.16(11.16−10)(11.16−6)(11.16−6.32) )
T= sqrt(324 )
T =18
b. We compute the base from coordinates using the Pythagorean theorem
c= sqrt( ((−2−4)^2)+ ((1−3) ^2) )
c= sqrt(40) = 2sqrt(10)
c. Calculate the heights of the triangle from its area
Consider this function. f(x)=2x-2 Which graph represents the inverse of function f?
Answers
Answer:
f(x) = x + 2/2 is the inverse
Step-by-step explanation:
Answer:
f(x) = x + 2/2 is the inverse
Step-by-step explanation:
Please answer correctly !!!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!!
Answers
The sum of two complementary angles is 90 degrees.
Angle A + Angle B = 90
Let Angle B = X
5x + 2 + x = 90
Combine like terms:
6x +2 = 90
Subtract 2 from both sides:
6x = 88
Divide both sides by 6:
x = 88/6
x = 14.67
Angle B = 14.67 degrees ( rounded to the nearest hundredth)
Write the slope intercept from of the equation of the line that passed though the given points.
(−1,−2)(1,−4)
Answers
I couldnt find the awnser for this question anywhere
Answers
Marking brainles!!!!
Answers
Answer:
C. 4 ft x 6 ft
Step-by-step explanation:
May I have brainliest please? :)
If 0.5cm = 6 inches you can just double the number you have then multiply that by 6
4cm = 48cm which is 1.5748 feet
6cm =
Answer:
D
Step-by-step explanation:
0.5cm - 6ft
1cm=12ft
2cm= 24
3cm= 36
4cm = 48
5cm= 60
6cm = 72
48 divided by 6 is 8
72 divided by 6 is 12
Solve 2x - 3 = 1 *
**giving BRANIEST to FIRST to answer with CORRECT answer **
Answers
Answer:
2
Step-by-step explanation:
+3 to both sides then
/2 from both sides
How do I fill out this form please help!
Answers
Answer:
what form?
Step-by-step explanation:
Answer:
Thats a good question
Step-by-step explanation:
lol.
For which inequality is x = 5 a solution
Answers
Answer:
x <18
Step-by-step explanation:
The open side of the < always faces the bigger number.
Find the slope given for (-2,-5) and (3,-2)
Answers
Answer:
The slope is 3/5
Answer:
3/5
Step-by-step explanation:
The slope is given by
m = ( y2-y1)/(x2-x1)
= ( -2 - -5) / ( 3 - -2)
= ( -2+5)/( 3 +2)
= 3/5
Narrowing (see also stenosis) artery I77.1. Identify the meaning of the cross reference term indicated in the statement above.
A) The coder is instructed to go to the term stenosis to find a correct code. Mandatory instruction.
B) The coder is instructed to see also stenosis to look for more information if a specific code or subterm cannot be found under the main term Narrowing.
C) Not a mandatory instruction.
D) The coder is instructed to use the I77.1 code if a specific subterm under the main term Narrowing cannot be found.
E) The coder is instructed to use the code I77.1 and then look for an additional code under the term stenosis.
Answers
Answer:
C Not a mandatory instruction
Step-by-step explanation:
CAN SOMEONE HELP ME WITH THIS
Answers
Answer:
The vertices of a triangle 1/4 the size of the shown triangle would be: (1,1), (2,3), (0,3)
Step-by-step explanation:
The swimming team has 84 members. The number of boys on the team is six more than twice the number of girls. How many boys and girls are on the team?
Answers
Answer:
the number of boys and girls on a team is 58 and 26 respectively
Step-by-step explanation:
Given that
Total members in swimming team is 84
Let us assume the number of girls be x
so, the number of boys would be
y = 2x + 6
Now the equation is
x + y = 84
x + 2x + 6 = 84
3x = 78
x = 26
And, y = 2 × 26 + 6
= 52 + 6
= 58
Hence, the number of boys and girls on a team is 58 and 26 respectively
Help!!! i need to get an A!!!
Answers
Answer:
Step-by-step explanation:
What is the answer to 4^8/4^3 in 4^n form
Answers
Answer:
4^5
Step-by-step explanation:
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[tex] \frac{ {4}^{8} }{ {4}^{3} } = {4}^{8} \div {4}^{3} = {4}^{8} \times {4}^{ - 3} = \\ [/tex]
[tex] {4}^{8 - 3} = {4}^{5} [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
PLEASE HELP ASAP I WILL BRAINLIEST
Answers
Answer:
32 minutes and 30 seconds.
Step-by-step explanation:
3 hours = 180 minutes, plus 15 added = 195 so 195 ÷ 6 = 32.5 or 32 mins and 30 seconds
Answer:
32.5 minutes
Step-by-step explanation
60x4-45/6
Find the height of the object next to the triangle using the similarity of the triangle.
Answers
Answer: If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.
Step-by-step explanation: