Answers
Ship M travels E 15 km, then N35E 27 km. Its sub travels down 48° 2 km from that location.
Ship F travels S75E 20 km, then N25E 38 km. The treasure is expected to be at this location 2.18° below horizontal from the port.
Find:
1a. The distance from port to Ship M
1b. The distance from port to the sub
1c. The angle below horizontal from the port to the sub
2a. The distance from port to Ship F
2b. The depth to the expected treasure location
2c. The distance from port to the expected treasure location
Solution:
It can be helpful to draw diagrams. See the attached. The diagram for depth is not to scale.
There are several ways this problem can be worked. A calculator that handles vectors (as many graphing calculators do) can make short work of it. Here, we will use the Law of Cosines and the definitions of Tangent and Cosine.
Part 1
1a. We are given sides 15 and 27 of a triangle and the included angle of 125°. Then the distance (m) from the port to the ship is given by the Law of Cosines as
m² = 15² +27² -2·15·27·cos(125°) ≈ 1418.60
m ≈ 37.66
The distance from port to Ship M is 37.66 km.
1b. The distance just calculated is one side of a new triangle with other side 2 km and included angle of 132°. Then the distance from port to sub (s) is given by the Law of Cosines as
s² = 1418.60 +2² -2·37.66·2·cos(132°) ≈ 1523.41
s ≈ 39.03
The distance from port to the sub is 39.03 km.
1c. The Law of Sines can be used to find the angle of depression (α) from the port. That angle is opposite the side of length 2 in the triangle of 1b. The 39.03 km side is opposite the angle of 132°. So, we have the relation
sin(α)/2 = sin(132°)/39.03
α = arcsin(2·sin(132°)/39.03) ≈ 2.18°
The angle below horizontal from the port to the sub is 2.18°.
Part 2
2a. We are given sides 20 and 38 of a triangle and the included angle of 100°. Then the distance (f) from the port to the ship is given by the Law of Cosines as
f² = 20² +38² -2·20·38·cos(100°) ≈ 2107.95
f ≈ 45.91
The distance from port to Ship F is 45.91 km.
2b. The expected treasure location is at a depth that is 2.18° below the horizontal from the port. The tangent ratio for an angle is the ratio of the opposite side (depth) to the adjacent side (distance from F to port), so we have
tan(2.18°) = depth/45.91
depth = 45.91·tan(2.18°) ≈ 1.748
The depth to the expected treasure location is 1.748 km.
2c. The distance from port to the expected treasure location is the hypotenuse of a right triangle. The cosine ratio for an angle is the ratio of the adjacent side to the hypotenuse, so we have
cos(2.18°) = (port to F distance)/(port to treasure distance)
(port to treasure distance) = 45.91 km/cos(2.18°) ≈ 45.95
The distance from the port to the expected treasure is 45.95 km.
Part 3
It seems the Mach 5 Mimi is the ship most likely to have found the treasure. That one seems ripe for attack. Its crew goes to a location that is 2.18° below horizontal. The crew of the FTFF don't have any idea where they are going. (Of course, the pirate ship would have no way of knowing if it is only observing surface behavior.)
Related Questions
You are wearing a pair of cargo pants with six pockets. You've put $10 in one of the pockets, but you cannot remember which one. After checking two pockets without success, what is the probability that the money will be in the next pocket you check? NextReset
Answers
The total number of ways left over is 4 for your next try
The number of pockets that will be successful is 1
Since there are 6 pockets all together. And you checked two of them and neither of them had the $10. so you cannot forget those 2 when figuring this out, and now there are 4 pockets left unchecked
The probability that the money will be in next pocket is 0.25.
We have a pair of cargo pants with six pockets and $10 in one of the pockets.
We have to find out the probability that the money will be in the next pocket you check after checking two pockets without success.
What is the formula to calculate the probability of an event ?The formula to calculate the probability of an event is -
[tex]P(A) = \frac{Total\;number\;of\;favorable\;outcomes}{Total\;number\;of\;outcomes\;in \;sample\; space} =\frac{n(A)}{n(S)}[/tex]In the question it is given -
Total money = $10
Total no. of pockets = 6 = n(S)
After two unsuccessful check in two pockets, new sample space =
n(S') = n(S) - 2 = 4
Hence, the probability that the money will be in the next pocket you check is -
P(A) = [tex]\frac{1}{4} = 0.25[/tex]
Hence, the probability that the money will be in next pocket will be 0.25.
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Find three consecutive odd integers such that the sum of the smallest and 7 times the largest is 68
Answers
x = smallest
y = middle
z = largest
x + 7z = 68 ← This equation represents the given information
We can assume that "z" is less than 11 because 7*11 = 77, which is greater than 68.
Our possible consecutive odd integers could be:
a) 1, 3, 5
b) 3, 5, 7
c) 5,7, 9
Lets to plug in the "x" and "z" values
a) 1 + 7(5) = 1+ 35 = 36 This is incorrect, because 36 ≠ 68
b) 3 + 7(7) = 3 + 49 = 52 This is incorrect as well, because 52 ≠ 68
That leaves our final choice. Let's check to be certain
c) 5 + 7(9) = 5 + 63 = 68
5, 7, 9 is the 3 consecutive integers such that the sum of the smallest and 7 times the largest is 68.
The three consecutive odd integers such that the sum of the smallest and 7 times the largest is 68 are: Integers 5, 7 and 9.
Let;
x = smallest odd integer(x+2) = middle odd integer(x +4) = largest integerThe question however suggests that;
The sum of the smallest number and 7 times the largest number is 68.
Therefore;
x + 7(x+4) = 688x + 28 = 688x = 40x = 5.In essence,
the smallest number is x = 5.the middle number is x+2 = 7.the largest number is x+4 = 9Read more:
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Jane has $10000 to invest in AAA and AA bonds. The AAA bond yields a 5% and requieres a minimum investment of $1000. The AA bond yields an average of 8% and requires a minimum investment of $2000. Jane requires that at least three times as much money should be invested in the AAA bond as in the AA bond
Answers
$10,000 to invest
AAA bonds - minimum of $1,000 yields 5%
AA bonds - minimum of $2,000 yields 8%
Jane requires that at least three times as much money should be invested in the AAA bond as in the AA bond
Let x represent the investment in AA bond.
x + 3x = 10,000
4x = 10,000
x = 10,000 / 4
x = 2,500
Jane should invest 2,500 to AA bond.
Jane should invest 7,500 to AAA bond. This amount is 3 times the amount invested in AA bond.
2,500 * 8% = 200
2,500 + 200 = 2,700
7,500 * 5% = 375
7,500 + 375 = 7,875
Jane's $10,000 investment will earn $575 interest for a total of $10,575.
Which equation could be the equation of this parabola?
A. y = -2x^2
B. x = -2y^2
C. x = 2y^2
D. y = 2x^2
Answers
Parabolas in the form of [tex]\sf x=y^2[/tex] open to the left or to the right.
Since this parabola opens upward, we know it must be in the form of [tex]\sf y=x^2[/tex]. Also, if the coefficient of 'x' is positive, it opens upward, but if it is negative, it opens downward. This parabola opens upward, so we know that the coefficient of 'x' must be positive. Therefore, our answer must be D, [tex]\sf y=2x^2[/tex]
How would you write the following phrase as a number expression eight more than triple a number
Answers
Shirley is drawing triangles that have the same area. The base of each triangle varies inversely with the height. What are the possible base and height of a second triangle if the first triangle's base is 16 and its height is 6 ?
Answers
base 8, height 12
base 4, height 24
base 2, height 48
base 1, height 96
base 32, height 3
base 48, height 2
base 96, height 1
how to erite a sequence of 1/4 , 1/2,3 write a rule for the sequence 1/4 1/2 3/4
Answers
a1= 1/4
d= 1/4
an= 1/4 + (n-1)(1/2) - First you need to distribute the 1/2 to both the n and -1 to get: an= 1/4 + 1/2n -1/2.
Then you need to add like terms (1/4-1/2) to get an=1/2n-1/4. Hope this helps!
The sequence 1/4, 1/2, 3/4 increases by 1/4 for each subsequent term, defining it as an arithmetic sequence with a common difference of 1/4.
To find a rule for the sequence 1/4, 1/2, 3/4, we can examine the pattern and observe that the sequence consists of fractions that increase by 1/4 each step. Starting with 1/4, when we add 1/4, we get 1/2, and adding another 1/4 to 1/2 gives us 3/4. So the rule of the sequence can be written as 'start at 1/4 and add 1/4 each step'. This pattern is an arithmetic sequence with a common difference of 1/4.
The glass container is filled to a height of 2.25 inches. What percent of the container is filled with sand?
Answers
Part A) How much sand is currently in the container?
[sand currently in the container]=(5)*(4 1/2)*(2.25)-----> (5)*(4.5)*(2.25)
[sand currently in the container]=50.625 in³
the answer Part a) is 50.625 in³
Part B) How much more sand could the container hold before?
[sand could the container hold before]=[5*4.5*3]-[50.625]
[sand could the container hold before]=[67.5]-[50.625]------> 16.875 in³
the answer Part B) is 16.875 in³
Part C) What percent of the container is filled with sand?
the volume of container is [5*4.5*3]=67.5 in³
the volume filled with sand=50.625 in³
therefore
if 100%----------------> 67.5 in³
X---------------------> 50.625 in³
X=(50.625*100)/67.5=75 %
the answer Part C) is 75%
miss Roberts simplified this ratio 2:6 explain how you know she is incorrect can you tell where she might have made a mistake
Answers
Do you go to k12 btw ?
y - 5 = 0.5x2 + 6x - 3 How many x-intercepts does the graph of this quadratic have?
Answers
Y - 5 = 0.5x2 + 6x - 3--------------- > y=0.5x2 + 6x -3+5=0.5x2 + 6x+2
y=0.5x2 + 6x +2
using a graphic tool
see the attached figure
the graph have two x-intercepts----------> (-11.657,0) and (0.343,0)
Answer:
its (A)
Step-by-step explanation:
Please help me with question 5
Answers
By similar triangles ACD is similar to BCD
on the left AD/CD is one ratio
On the right CD/DB is the other. These two ratios are equal because they are corresponding parts.
AD / CD = CD / DB
AD = 3
DB = 12
CD = ??
Substitute.
3/CD = CD/12 Cross multiply
36 = CD^2
sqrt(36) = sqrt(CD^2)
CD = 6 <<<<==== Answer.
A <<<<====Answer.
two angles are supplementary. One angle measures at 75° more than twice the measure if the other. What are the measurements of the two angles?
Answers
a + b = 180 (because supplementary angles means their sum is 180)
a = b + 75
substitute the value of a (b+75) into the first equation to get:
b + 75 + b = 180
simplify to get:
b = 52.5
use this value to substitute into any of the 2 equations to get the value of a:
52.5 + 75 = a
a = 127.5
So, the measurements of the two angles are 52.5° and 127.5°
say they are x and y
x+y=180
and one meauses 75 more than twice the other
x=75+2y
solve
subsitute 75+2y for x in other equation
75+2y+y=180
75+3y=180
minus 75 from both sides
3y=105
divide both sides by 3
y=35
sub back
x=75+2y
x=75+2(35)
x=75+70
x=145
the angles are 145° and 35°
An equipment rental company charges a flat rate of $25, plus $13 per day for insurance. Kyle has $121. Write an inequality to represent the number of days, d, for which he can rent equipment
Answers
Final answer:
The inequality to represent the number of days, d, Kyle can rent equipment with $121 is 25 + 13d ≤ 121. After solving, the result is d ≤ 7, meaning Kyle can rent the equipment for at most 7 days.
Explanation:
To represent the number of days, d, that Kyle can rent equipment given he has $121, we set up an inequality taking into account the flat rate and the daily insurance cost. The equipment rental company charges a flat rate of $25 plus $13 per day for insurance. Therefore, the cost for d days would be $25 + $13d. Since Kyle has $121, we can write the inequality as:
25 + 13d ≤ 121.
This inequality shows that the total cost of renting the equipment for d days, which includes the flat rate and the per-day insurance cost, must be less than or equal to the amount Kyle has.
To solve for d, subtract 25 from both sides:
13d ≤ 121 - 25
13d ≤ 96
Now, divide both sides by 13 to find the maximum number of days Kyle can rent the equipment:
d ≤ 96 / 13
d ≤ 7
Thus, Kyle can rent the equipment for at most 7 days.
Kyle can rent equipment for at most 7 days with $121, considering a flat rate of $25 and a $13 per day insurance charge, as represented by the inequality 25 + 13d ≤ 121.
Explanation:To find the inequality that represents the number of days, d, for which Kyle can rent equipment given that he has $121, we need to consider both the flat rate and the per day insurance charge.
The flat rate for renting equipment is $25, and the daily insurance charge is $13 per day. So, the cost for d days would be the flat rate plus the daily charge times the number of days, which can be represented by the following equation:
Cost = Flat rate + (Insurance charge per day × Number of days)
Cost = 25 + 13d
Since Kyle only has $121, he can spend up to that amount. Therefore, the inequality would be:
25 + 13d ≤ 121
To solve for d:
13d ≤ 121 - 25
13d ≤ 96
d ≤ 96/13
≤ 7.38
Since Kyle can't rent equipment for a fraction of a day, we take the whole number part of the division result. This means that Kyle can rent the equipment for at most 7 days.
Which trinomial is the product of the expression below ? (2R-3) (R+12)
Answers
2R^2 + 21R - 36
Explanation:
To answer this question, we will follow these steps:
1- expand the brackets
2- gather like terms
Steps are as follows:
(2R-3)(R+12) = 2R(R) + 2R(12) - 3(R) - 3(12)
= 2R^2 + 24R - 3R - 36
= 2R^2 + 21R - 36
Hope this helps :)
(2R-3) (R+12)---------- > 2R*R+12*2R-3*R-3*12---------- > 2R²+24R-3R-36
2R²+24R-3R-36---------------> 2R²+21R-36
the answer is 2R²+21R-36
Help!
Could it be...??
a. /_ A
b. /_ BCA
c. /_ b
d. /_ CBA
Answers
Given the lengths of two sides of a triangle, find the range for the length of the third side (between what two numbers should the length of the third side be). Write the inequalities for each case. 8 and 13
Answers
5 < third side < 21
Final answer:
The length of the third side of a triangle with side lengths of 8 and 13 must be greater than 5 units and less than 21 units according to the triangle inequality theorem.
Explanation:
To find the range for the length of the third side of a triangle given two sides with lengths of 8 and 13, we can use the triangle inequality theorem.
This theorem states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides and greater than the absolute value of their difference.
The inequalities for the third side, let's call it c, are:
c < 8 + 13c > |13 - 8|Therefore, we can say:
c < 21c > 5So the length of the third side must be greater than 5 units and less than 21 units.
HELP MEEE!!! PLEASE!!!
Answers
Can anyone help me on this question?:) tysm ily
Answers
V=25*40*40+25*35*40=40*1875=75000 cm³
answer: 75000 cm³.
Given ΔJKL : ΔXYZ, find the scale factor.
6 8
---- ----
9 x
Answers
Multiply means and extremes
6x = 72
x = 12
6/9 = 8/12
The scale factor is 4/3 or 1 and 1/3
Hope this helps =)
Answer:
it is 16
Step-by-step explanation:
The pyramid shown has a square base that is 1212 centimeters on each side. The slant height is 1818 centimeters. What is the surface area of the pyramid?
Answers
Answer : Surface area of pyramid = 4406832 square cm.
Explanation :
Since we have given that
Side of square base = 1212 cm
Slant height of pyramid = 1818 cm
As we know that ,
[tex]\text{Surface area of pyramid }=\frac{1}{2}\times perimeter\times \text{ slant height}[/tex]
[tex]\text{ Since, perimeter of square }=4\times side\\=4\times 1212\\=4848 cm[/tex]
Now,
[tex]\text{ Surface area of pyramid }= \frac{1}{2}\times 4848\times 1818\\\\\text{ Surface area of pyramid }=4406832\text{ square cm}[/tex]
Hence, surface area of pyramid = 4406832 square cm.
Which of these is equivalent to 92 + 42? (9 + 4)2 (9 × 4)2 (9 × 9) + (4 × 4) (9 + 9) + (4 + 4)
Answers
9 ^ 2 + 4 ^ 2.
We have then that the equivalent expression for this case is:
(9 × 9) + (4 × 4)
Both expressions give the same result 97
Answer:
(9 × 9) + (4 × 4)
Simplify this equation.
(equation and choices in image)
Answers
b.)x³-7x²+3x+36
(x-4)(x²-3x-9)
Distribute x and -4 to x²-3x-9
=x²(x)-3x(x)-9(x)+x²(-4)-3x(-4)-9(-4)
=x³-3x²-9x-4x²+12x+36
Combine all liked terms
=x³-7x²+3x+36
Which describes the difference between the graph of f(x) = 3x2 + 2 and g(x) = 9x2?
B) The graph of f(x) is obtained by shifting g(x) up 2 units and compressing vertically by a factor of 3.
C) The graph of g(x) is obtained by shifting f(x) right 2 units and stretching vertically by a factor of 3.
D) The graph of f(x) is obtained by shifting g(x) right 2 units and stretching vertically by a factor of 3.
Answers
The solution is, the graph of f(x) is vertically stretched by a factor of 3 and shifted 7 units down, as f(x) = x changes to h(x) = 3x² - 7.
What is transformation of graph?Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.
here, we have,
Given that,
here is a graph of f(x) = x which is transformed into h(x) = 3x² - 7.
The graph of a the equation -
f(x) = x
is a straight line.
now, we get, When it is squared and multiplied by 3, we get -
h(x) = 3x²
which is a parabola stretched by a factor of 3 in vertical direction along
+ y axis.
When 7 is subtracted, it will shift the graph down by 7 units.
h(x) = 3x² - 7
Therefore, the graph of f(x) is vertically stretched by a factor of 3 and shifted 7 units down, as f(x) = x changes to h(x) = 3x² - 7.
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Complete question:
What is the effect on the graph of f(x) = x when it is transformed to
h(x) = 3x2 - 7?
A. The graph of f(x) is vertically stretched by a factor of 3 and shifted
7 units down.
B. The graph of f(x) is horizontally compressed by a factor of 3 and
shifted 7 units to the right.
C. The graph of f(x) is horizontally stretched by a factor of 3 and
shifted 7 units down.
D. The graph of f(x) is vertically stretched by a factor of 3 and shifted
7 units to the right
The heights in centimeters of 5 students are: 165, 175, 176, 159, 172 find the sample median, sample mean and sample variance.
Answers
The mean is: 169.4 cm
The sample variance steps to solve are:
"Work out the Mean (the simple average of the numbers)Then for each number: subtract the Mean and square the result (the squared difference).Then work out the average of those squared differences."
The value of the sample median is 172.
The value of the sample mean is 169.4.
The value of the sample variance is 52.3
What is a median?It is the middle value of the given set of numbers after arranging the given set of numbers in order.
We have,
The heights in centimeters of 5 students are: 165, 175, 176, 159, 172
Now,
Arrange the heights in order.
159, 165, 172, 175, 176
Median = 172
Mean = (159 + 165 + 172 + 175 + 176) / 5 = 847 / 5 = 169.4
Sample variance.
= ∑ (x - Mean)² / (n - 1)
= 209.2 / 4
= 52.3
∑ (x - Mean)²
= (159 - 169.4)² + (165 - 169.4)² + (172 - 169.4)² + (175 - 169.4)² + (176 - 169.4)²
= 108.16 + 19.36 + 6.76 + 31.36 + 43.56
= 209.2
Thus,
The sample mean = 169.4
The sample median = 172
The sample variance = 52.3
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which of the following values of x makes the rational expression below equal to zero? 2x+16/x+5
a. 5
b. -5
c. 8
d. -8
Answers
For this case what you should know is that an indefinite expression are those in which mathematically no numerical value can be obtained.
We have then that a division between zero causes an expression to be undefined.
For x = -5 we have:
(2 (-5) +16) / ((- 5) +5)
(-10 + 16) / (- 5 + 5) = 6/0 (undefined)
Answer:
x = -5
b. -5
Answer:
d. -8
Step-by-step explanation:
Remember that you cannot possibly divide anything by 0, so if the denominator gives as a result 0, you are dealing with an impossibility, in order for a franction to give as a result 0, the numerator has to be 0, so we just need to equalize the numerator to 0 and solve for x to know how can we make the rational expression 0:
2x+16=0
2x=-16
x=-16/2
x=-8
So in order to make the expression equal to 0 x needs to be equal to -8,
find the sum and express it in simplest form.
[tex](b - 3x) + ( - 5b + 6x - 5)[/tex]
Answers
= b - 3x - 5b + 6x - 5
= b - 5b - 3x + 6x - 5
= -4b + 3x - 5
Question 7 plz help me saner this question
Answers
[tex] \frac{8}{4000} * 100 [/tex]
1/5 %
= 0.2%
I hope this helps!
In 2015, the price of a business math text rose to $150. This is 8% more than the 2014 price. What was the old selling price?
Answers
150=1.08x
x=$138.88
Answer: old selling priceof businesss math text rose = $138.89
Explanation:
In year 2015, Price of business math text rose = $150
Suppose privious price (year 2014)= x dollars
Previous price is 8% less than the price in 2015 because given that $150 is 8% more than previous year price.
Now write the linear equation for the given information:
x + 8% of x = 150
Solve for x
x + [tex] \frac{8}{100} [/tex]x = 150
x + 0.08x = 150
1.08x = 150
divide 1.08 both the side
x = [tex] \frac{150}{1.08} [/tex]
x = $138.89
Old selling price = $138.89
How do you turn 43% into a fraction
Answers
To write a percent as a fraction in lowest terms, first remember that a percent is a ratio that compares a number to 100. 43% can be written as the ratio 43 to 100 or 43/100.
Therefore, 43% can be written as the fraction 43/100.
1. Solve w=x+y/z for y.
2. Solve the equation above for z.
Answers
Answer:
y = z(w -x)z = y/(w -x)Step-by-step explanation:
As in any "solve for ..." problem, you reverse (undo) the operations done to the variable of interest. Generally, you do that in reverse order.
1. y is divided by z then the quotient added to x. To solve for y, we subtract x, then multiply by z.
... w - x = y/z . . . . . . . subtract x from the given equation
... z(w -x) = y . . . . . . . multiply by z
___
2. To solve for z, it is more convenient to start with the equation for y that is the result of the first question. We divide that by the coefficient of z.
... z = y/(w -x)
From w=x+y/z, the value of y = z(w - x)
w=x+y/z
This is changing the subject formula. The first thing to do is to subtract x from both sides. This will be:
w - x = x + y/z - x
w - x = y/z
Then, we cross multiply
z(w - x) = y
Therefore, y = z(w - x)
Since y = z(w - x)
Then, to get the value of z goes thus:
z = y/(w - x)
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