There is enough evidence to conclude that the new components have reduced the rate of defective chips produced.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that the amount has decreased, that it still is of 12, hence:
[tex]H_0: \mu = 12[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the amount has decreased, that is, it is less than 12, hence:
[tex]H_1: \mu < 12[/tex]
We have a left-tailed test, with a significance level of 0.05, hence the test statistic needed for there to be enough evidence is less than -1.645, which is the critical value.
What is the test statistic?The equation that determines the test statistic is given as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The parameters in this problem are of:
[tex]\overline{x} = 8, \mu = 12, \sigma = 3.3586, n = 12[/tex]
Hence the test statistic is of:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{8 - 12}{\frac{3.3586}{\sqrt{12}}}[/tex]
z = -4.13.
Less than the critical value, hence there is enough evidence that the amount has decreased.
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Does A and B have the same solution
A. 4x + 2 = 6 - x
B. 5x + 2 = 6
Answer:
No, A and B do not have the same solution.
To find the solution to A, we need to isolate the variable x on one side of the equation and solve for its value. We can do this by subtracting x from both sides of the equation and then adding 2 to both sides. This gives us:
4x + 2 - x = 6 - x + 2
3x = 8
x = 8/3
To find the solution to B, we need to isolate the variable x on one side of the equation and solve for its value. We can do this by subtracting 2 from both sides of the equation. This gives us:
5x + 2 - 2 = 6 - 2
5x = 4
x = 4/5
As we can see, the solutions to A and B are different, so A and B do not have the same solution. The solution to A is x = 8/3, and the solution to B is x = 4/5.
Step-by-step explanation:
Explain whether this dilation is an enlargement or a reduction, and how you know. Triangle a b c is enlarged to triangle a prime b prime c prime.
Triangle ABC to triangle A'B'C' is enlarged by the dilation.
What is meant by dilation?Dilation is the process of enlarging a shape, figure, or line. In mathematics, dilation means Reducing the object's size by dilation is a change. The items are enlarged or shrunk through dilation. An image that retains the original shape is created by this alteration. A dilation in mathematics is a function f from a metric space M into itself that fulfills the formula d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real number. A resemblance of the space exists in Euclidean space when a dilation like this occurs.
The query leads us to believe that:
Triangle A'B'C' is created by enlarging triangle ABC.
The diagram also demonstrates that triangle A'B'C"s side lengths are longer than ABC's.
The dilation is hence an augmentation
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Answer:
The dilation is an enlargement because the image, triangle A'B'C', is larger than the pre-image, triangle ABC.
Step-by-step explanation:
edge 2023
agent bourne transferred classified files from the cia mainframe into his flash drive. the drive has 72 megabytes on it before the transfer, and the transfer happened at a constant rate. after 136 seconds there were 1,160 megabytes on the drive. the drive had a maximum capacity of 3,000 megabytes.
Answer: The speed was 4.1 MB/sec.
We first find the amount that was transferred within the first 125 seconds:
549-36.5=512.5
Now we divide this by 125, the number of seconds:
512.5/125 = 4.1
The speed of the transfer is 4.1 megabytes per second.
It took 235 seconds for the drive to be completely filled.
Step-by-step explanation:
m<1 = please help will give brainliest
Answer:
88
Step-by-step explanation:
What function equation is represented by the graph
f(x)=-3z+6.
F(x)=6x-3.
F(x)=6z+2.
F(x)=3x+2
The equation represented by the graph is f(x) = -3x + 6
What is a linear function?
A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. Here,
'm' is the slope of the line
'b' is the y-intercept of the line
'x' is the independent variable
'y' (or f(x)) is the dependent variable.
the straight line cuts the axes at (0,6) and (2,0)
Equation of straight line in slope-intercept form is f(x) = mx + c
when x = 0 f(x) = 6
6 = m(0) + c
c = 6
when x = 2, f(x) = 0
0 = 2m + c
2m = -c, but c = 6
2m= -6
m = -6/2
m = -3
Equation of line becomes f(x) = -3x + 6
In conclusion f(x) = -3x + 6 is the equation that is represented by the graph.
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A recipe calls for 6 ounces of raisins. How many milligrams of raisins is this? (1 ounce = 28.35 grams and 1 gram = 1,000 milligrams)
170.1 milligrams
1,701 milligrams
17,010 milligrams
170,100 milligrams
A recipe calls for 170,100 milligrams of raisins.
What are units ?
Units are the measuring and contrasting devices for many things. When all measurement units are identical, comparisons are simple. Depending on how they are used, several units can be categorized.
Measurement is the process of comparing an unknown quantity to an already known quantity. A numerical value with specific units is the measurement's output. Any given object can have its length, mass, capacity (volume), and temperature measured.
1 ounce = 28.35 grams
6 ounces = 6*28.35 grams = 170.1 grams
1 gram = 1,000 milligrams
170.1 grams = 170.1 * 1,000 milligrams = 170,100 milligrams
So, a recipe calls for 170,100 milligrams of raisins.
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Answer:
A recipe calls for 170,100 milligrams of raisins.
Step-by-step explanation:
I took the exam and got it right
Janet, an antique dealer, purchaed a claic toy car a an
invetment. She wrote the equation y = 40x 100 to repreent
the value y in dollar of her invetment x year after he bought it. What are the initial value and rate of change! Explain
Using the provided equation and derivative for the rate, The initial value is 100 and the rate is 40.
What do you mean by equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
What do you mean by derivative?in mathematics, the rate of change of a function with respect to a variable. Derivatives are fundamental to the solution of problems in calculus and differential equations.
y= 40x + 100
x=0 for initial value, We get y=100.
apply derivative on y with respect to x , We get
[tex]\frac {dy}{dx} =40[/tex]
rate =40
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There are 7 songs on each CD. If
you have 60 CD's, how many total
songs will you have?
Answer:
420
Step-by-step explanation:
60 x 7 = 420
Answer: 420
Step-by-step explanation:
If you have 7 songs on each CD then you have 60 CD'S just take 7 and times it by 60.
Factor out the Greatest Common Factor (GCF): 64d5- 32d²
helpppppppppppppppppp
If 12 subtracted from the product of a number n
and 4, the result is -8. Find the value of n.
Answer: -4
Step-by-step explanation:
Select all of the algebraic expressions that could represent the phrase below.
"nine more than the product of 5 times the number of tires t"
9 + 5t
5 ▪ t + 9
(9 + 5)t
(5 × t) + 9
5 + 9t
Answer:
A ; B ; D
Step-by-step explanation:
5t + 9
for commutative property
9 + 5t
5t = 5 x t
5 · t + 9
(5 x t) + 9
at noon, ship a is 8 miles west of ship b. ship a is sailing north at 10mph and ship b is sailing south at 7mph. how fast is the distance between the ships changing at 3:00pm?
The distance between the ships changing at 3.00 p.m is 12.2 mile/mph.
What do you mean by differentiation?
A derivative of a function with respect to an independent variable is what is referred to as differentiation. Calculus's concept of differentiation can be used to calculate the function per unit change in the independent variable.
A function of x would be y = f(x). Next, the formula for the rate of change of "y" per unit change in "x" is as follows:
dy / dx
It is given that ship A is 8 miles west of ship B and ship a is sailing north at 10mph and ship b is sailing south at 7mph
Let x and y be the initial position of the ships A and B
Let x be the distance between A and x
y as the distance between B and x
z as the distance between A and B
Using pythagoras theorem,
[tex]z^{2} =x^{2} +y^{2}[/tex]
Differentiating both sides wrt t,
2z dz/dt = 2x dx/dt + 2y dy/dt
Divide the equation by 2
z dz/dt = dx/dt + dy/dt --- (1)
dx/dt = 10 mile/mph
dy/dt = 7 mile/mph
When t = 3 hours,
x = 30, y = 21 and
z = [tex]\sqrt{x^{2} +y^{2} }[/tex]
Substituting the values
z = √([tex]30^{2} +21^{2}[/tex])
z = √(900 + 441)
z = √1341 = 36.6
Substituting it in equation (1)
36.6 dz/dt =30×10+ 21×7
dz/dt = 447/36.6
dz/dt = 12.2 mile/mph
Therefore, the distance between the ships changing at 3.00 p.m is 12.2 mile/mph.
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How do you read Square-1?
A Rubik's Cube puzzle variation is called Square-1. You must be familiar with the fundamental notation used to denote the puzzle's various moves and positions in order to read the puzzle.
The face serves as the fundamental unit of notation in Square-1. A Square-1 puzzle has four faces, and each face is identified by a letter: U denotes the top face, D the bottom face, F the front face, and B the back face.
You must specify the face you are turning and the direction you are turning it in order to signify a move. For instance, a move like "U" turns the top face in a clockwise direction, whereas "U'" turns it in a counterclockwise direction.
You can adjust the puzzle with a few more complex moves in addition to the fundamental ones. For instance, the move "r" denotes moving the right face in a clockwise direction, while "r'" denotes turning it in a counterclockwise direction.
You can manipulate the problem to find the solution by combining these movements and employing them in various combinations. Reading and utilizing the notation for Square-1 requires effort, but with persistence and time, you may learn to solve the puzzle fast and effectively.
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box 1 contains 3 red and 8 yellow balls, whereas box 2 contains 2 red and 1 yellow balls. a ball is drawn from a randomly selected box. let be the event that the ball is red, and the event that the ball came from box 2. are they independent?
The given events A and B are not independent events.
What is probability?
A probability is a numerical representation of the likelihood or chance that a specific event will take place.Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.As there is no information given on the probability if selecting Box 1 and Box 2, thus we assume the event of selecting any of the boxes as equi-probable
P(A) = 1/2 * 3/11 + 1/2 * 2/3 = 31/66
P(B) = 1/2
P(A|B) = 2/3
Thus, we can see that P(A|B) is not equal to P(A)
So, the events A and B are not independent events.
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ASAPPPPP 45 POINTS HELP HELP DUE IN 2 AND A HALF HOURS
1. During week 0, calculate how many more ants there are in ant colony A than in ant colony B
2. Use the equation to identify the growth rate of ant colony A
3. Find the growth rate of ant colony B
4. Use 1-2 complete sentences to compare the growth rats of ant colony A with ant colony B.
Function: a(x)=210(1.12)^x
Day 0 1 2 3 4 5 6 7
# of ants 210, 235, 263, 295, 330, 370, 415, 464
1) 20 more ants there are in ant colony A than in ant colony B
2) The growth rate of ant colony A is 12%
3) The growth rate of ant colony B is 15%
4) The growth rate of ant colony A is 3% less than that of ant colony B.
What is exponential growth function ?
A process called exponential growth sees a rise in quantity over time. When a quantity's derivative, or instantaneous rate of change with respect to time, is proportionate to the quantity itself, this phenomenon takes place.
1) colony A :
Number of ants = 210
colony B:
Number of ants = 190 ( from the graph )
Find the difference: 210 - 190 = 20 ants
So, 20 more ants there are in ant colony A than in ant colony B
2 ) Exponential growth function: y= a(b)^x
b= 1+ r , r is the growth rate as decimal
We have a(x)=210(1.12)^x
b= 1.12 = 1+0.12
So, r= 0.12 = 12%
3 ) (x,y) = (1,220)
y= a(b)^x
=> 220 = 190(b)^1
=> b= 220/190 = 1.15
b= 1+r
r= b - 1 = 1.15 - 1 = 0.15 = 15%
The growth rate of ant colony B is 15%
4) The growth rate of ant colony A is 3% less than that of ant colony B.
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1) 20 more ants there are in ant colony A than in ant colony B
2) The growth rate of ant colony A is 12%
3) The growth rate of ant colony B is 15%
4) The growth rate of ant colony A is 3% less than that of ant colony B.
What is exponential growth function ?
A process called exponential growth sees a rise in quantity over time. When a quantity's derivative, or instantaneous rate of change with respect to time, is proportionate to the quantity itself, this phenomenon takes place.
1) colony A :
Number of ants = 210
colony B:
Number of ants = 190 ( from the graph )
Find the difference: 210 - 190 = 20 ants
So, 20 more ants there are in ant colony A than in ant colony B
2) Exponential growth function: y= a(b)^x
b= 1+ r , r is the growth rate as decimal
We have a(x)=210(1.12)^x
b= 1.12 = 1+0.12
So, r= 0.12 = 12%
3) (x,y) = (1,220)
y= a(b)^x
=> 220 = 190(b)^1
=> b= 220/190 = 1.15
b= 1+r
r= b - 1 = 1.15 - 1 = 0.15 = 15%
The growth rate of ant colony B is 15%
4) The growth rate of ant colony A is 3% less than that of ant colony B.
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A certain fossil of a beetle contains 15% as much carbon as a living beetle. The age of the fossil can be found using carbon dating.
Calculate the age of this fossil given that the half life of carbon-14 is 5715 years.
Answer:
Fossil
are impressions of plants or animals embedded in rock and preserved. They may be in the form of a body or trace.
The age of the fossils is determined by the Radioactive carbon dating technique in which the half-life of carbon and found radioactive elements is determined to calculate the age of a fossil
Amir Najjar did reearch on the Internet to find the dealer' cot of a new car he wanted to purchae. He found that the dealer' cot of the bae price wa $15,455. 40 and cot of the option wa$585. 0. The dealer will pa the $675 detination charge on to the conumer. If the dealer' cot i 85% of the bae and 82% of the option, what i the car' ticker price?
By using percentage, it can be calculated that-
Sticker price of the car = $14291.75
What is percentage?
Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage
For example 11% means [tex]\frac{11}{100}[/tex] . Here 11 is expressed as a fraction of 100
This is a word problem on percentage
Base price of the car = $15455.40
Cost of option = $585
Destination charge = $675
The dealer's cost is 85% of the base and 82% of the options
Sticker price of the car = [tex]\frac{85}{100}\times 15455 + \frac{82}{100} \times 585 + 675[/tex]
= 13137.09 + 479.7 + 675
= $14291.75
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How is muscular strength commonly measured ?
Muscular strength can be measured based on the amount of weight lifted.
Muscular strength can be measured based on the amount of weight lifted. The upper-body and lower-body strength are measured separately. Muscular strength is typically measured which is known as a One Rep Max (1RM).
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if the coupons are different, how many ways are there to distribute the coupons so that at least one woman receives a coupon?
There are "P(20, 10) - P(15, 10)" options (ways) to distribute the coupons so that at least one woman receives a coupon.
What do you mean by permutation?
A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."
There are P(20, 10) ways to distribute the coupons if they are different, with the only restriction being that no more than one coupon can be given to a shopper. To ensure that all of the coupons go to the guys, there are P(15, 10) ways to distribute them. In order to ensure that at least one coupon is given to a woman, there are P(20, 10) - P(15, 10) options to distribute the coupons.
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Complete Question
10 coupons are given to 20 shoppers in a store. Each shopper can receive at most one coupon. 5 of the shoppers are women and 15 of the shoppers are men.
If the coupons are different, how many ways are there to distribute the coupons so that at least one woman receives a coupon?
radon-222 has a half-life of 3.8 days. an air sample from a basement in colorado was analyzed 5.0 days after it was collected and found to have a radon activity level of 0.17 bq/l. what was the original activity of this sample?
The original activity of the sample can be calculated using the equation A=A0e^(-kt), where A0 is the initial activity, k is the decay constant, and t is the elapsed time.
1. Identify the given values: Half-life (t1/2) = 3.8 days, Activity level (A) = 0.17 bq/L, and Elapsed time (t) = 5.0 days.
2. Calculate the decay constant (k) using the equation k = ln(2)/t1/2.
k = ln(2)/3.8 days
k = 0.1815
3. Calculate the original activity (A0) using the equation A0 = A/e^(-kt).
A0 = 0.17 bq/L/e^(-0.1815)
A0 = 0.21 bq/L
Therefore, the original activity of the sample was 0.21 bq/L.
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If k3 – 9 = 12, what is the value of k?
Answer:
k=7
Step-by-step explanation:
k*3-9=12
3k-9=12
3k=12+9
3k=21
k=[tex]\frac{21}{3}[/tex] cross out 21 and 3
k=7
(a) given any set of seven integers, must there be at least two that have the same remainder when divided by 6? to answer this question, let a be the set of 7 distinct integers and let b be the set of all possible remainders that can be obtained when an integer is divided by 6, which means that b has
Given any set of seven integers there are no two numbers that have same remainder when divided by 6.
The remainder is the value left after the dividion. If a number is not completely divisible by another number then we are left with a value once the division is done. This value is called the Remainder.
Given any set of seven integers, there must be at least two numbers that have same remainder when divided by 6.
So there can be six remainders when divided by 6 i.e. 0,1,2,3,4 and 5.
According to the Piegeonhole principle,
in any set of seven integers two must have the same remainder when divided by seven.
Consider the set of integers 0,1,2,3,4,5 and 66. All of these have different remainders upon division by 8.
Hence there need not be two numbers such that they have same remainders when divided by 6.
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Need help, it’s a word form answer
Answer: Yes, he is correct
Step-by-step explanation:
[tex]\frac{1}{3}*\frac{2}{2}=\frac{2}{6} +\frac{1}{6}=\frac{3}{6}[/tex] The (*) means x or multiply
What is the slope of the line that passes through the points (-8, 2) and (-11, 3)
The slope (m) of the line that passes through the points (-8, 2) and (-11, 3) is -1/3.
What is the slop of the line?
A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
We have,
The line that passes through the points (-8, 2) and (-11, 3),
Slop (m) = ?
The slope formula is:
m = (y₂-y₁) ÷ (x₂-x₁)
so here,
m = (3 - 2) ÷ (-11 - (-8))
m = 1 ÷ (-3)
m = -1/3
Hence, the slope (m) of the line that passes through the points (-8, 2) and (-11, 3) is -1/3.
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a²bc²-5 I need the answer pleaeeeeeees
Answer:
Without knowing the values of the variables in the given expression, it is impossible to determine the value of the expression. In general, the expression is a combination of a number (A), two variables (b and c), and an exponent (2). The value of the expression will depend on the values of these variables and the operations that are performed on them. For example, if A=3, b=2, and c=4, then the value of the expression would be:
(3^2 * 2 * 4^2) - 5
Which is equal to 29. However, if the values of the variables were different, then the value of the expression would also be different. Therefore, it is impossible to determine the value of the expression without knowing the values of the variables.
Step-by-step explanation:
Answer:
(3^2 * 2 * 4^2) - 5, hope it helps.
simplify the expression -4/7i
Answer:
4i/7
Step-by-step explanation:
how many 7-letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contain exactly one a and exactly two bs?
There are 34836480 number of 7-letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contain exactly one a and exactly two bs.
What is permutation?
A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."
In order to fix 7 − letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contains exactly one a and exactly two b, we know that For a sequence having n letters, it is called n letter sequence. Such sequences exist with 26^n cases with repetition of letters are allowed.
So, the number of desired cases are,
= [tex]\frac{7_P_3(24)^4}{2} = 34836480[/tex]
Hence, there are 34836480 number of 7-letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contain exactly one a and exactly two bs.
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Write the inequality that would graph the following:
The inequality to graphed.
y < (-1/2)x + 4
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
The equation of the line from the graph.
y = mx + c
Two coordinates from the graph:
(8, 0) and (0, 4)
m = 4/-8
m = -1/2
Now,
(8, 0) = (x, y)
0 = (-1/2)8 + c
c = 4
Now,
y = (-1/2)x + 4
Thus,
y < (-1/2)x + 4 is the inequality that will graph the given graph.
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An airplane travels at a bearing of 100° (clockwise from North) at 180 km/hr. A wind redirects the plane, blowing at 30 km/hr at a bearing of 42°. Find the true speed of the plane and its new direction by modeling the speeds and directions as vectors.
The first step is converting both the velocity and the wind in vector form, as follows:
Velocity: [tex]\vec{v_1} = 180 \text{ km/hr} \angle 100^\circ[/tex]Wind: [tex]\vec{v_2} = 30 \text{ km/hr} \angle 42^\circ[/tex]Then the true speed of the plane is given by the addition of these two vectors, as follows:
[tex]\vec{v_1} + \vec{v_2} = \sqrt{|v_1|^2 + |v_2|^2 + 2 \cdot |v_1| \cdot |v_2| \cdot \cos(\theta)}[/tex]
The magnitudes of each vector are given as follows:
[tex]|v_1| = 180[/tex].[tex]|v_2| = 30[/tex].The angle between these two vectors is given as follows:
[tex]\theta = 100^\circ - 42^\circ = 58^\circ[/tex]
Thus the resulting speed is obtained as follows:
[tex]\vec{v_1} + \vec{v_2} = \sqrt{180^2 + 30^2 + 2 \cdot 180 \cdot 30 \cdot \cos(58^\circ)} = 197.54[/tex]
The resulting angle of the plane is then obtained as follows:
[tex]\angle = \arctan\left(\frac{|v_1| \cdot \sin(\theta) + |v_2| \cdot \sin(\theta_2)}{|v_1| \cdot \cos(\theta) + |v_2| \cdot \cos(\theta_2)}\right)[/tex]
Hence:
[tex]\angle = \arctan\left(\frac{180 \cdot \sin(58^\circ) + 30 \cdot \sin(42^\circ)}{180 \cdot \cos(58^\circ) + 30 \cdot \cos(42^\circ)}\right)[/tex]
[tex]\angle = 59.87^\circ[/tex]
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Answer:
197.5 km/h
Step-by-step explanation:
You want the resultant speed with an airplane at a speed of 180 km/h at 100° is acted upon by a wind at a speed of 30 km/h at 42°. Angles are bearings CW from north.
SolutionA vector calculator makes short work of this. The resultant speed is ...
197.5 km/h at 92.6°
Law of cosines
The law of cosines can be used to find the side opposite the known angle in the triangle with sides 30 km/h and 180 km/h. The known angle is ...
180° -(100° -42°) = 122°
So, the resultant speed is ...
c = √(a²+b²-2ab·cos(C))
= √(30² +180² -2(30)(180)·cos(122°)) ≈ √39023.13
c ≈ 197.543
The true speed of the plane is about 197.5 km/h.
__
Additional comment
You will notice that we used bearing angles directly in the calculator computation. As long as angles are consistently measured, it doesn't matter how they're measured.
When plotting the vectors on the Cartesian plane, we need to subtract the bearing angles from 90° to make them correspond to the vectors plotted on a map with north at the top.