Answer:
The coefficient of x²
a) 1
b) -4
the coefficient of x² is the number in front of the x²(variable).
Coefficient= Constanta
I hope this helps
if u have question let me know in comments ^_^
Answer:
a) 1.
b) -4.
Step-by-step explanation:
The coefficient is the number multiplying x2. If it is 1 it is usually omitted.
AB = 3.2 cm
BC= 8.4 cm
The area of triangle ABC is 10 cm²
Calculate the perimeter of triangle ABC.
Give your answer correct to three significant figures.
Answer:
Therefore, perimeter of the given triangle is 18.300 cm.
Step-by-step explanation:
Area of the triangle ABC = [tex]\frac{1}{2}(\text{AB})(\text{BC})(\text{SinB})[/tex]
10 = [tex]\frac{1}{2}(3.2)(8.4)(\text{SinB})[/tex]
Sin(B) = [tex]\frac{10}{3.2\times 4.2}[/tex]
B = [tex]\text{Sin}^{-1}(0.74405)[/tex]
B = 48.08°
By applying Cosine rule in the given triangle,
(AC)² = (AB)² + (BC)²-2(AB)(BC)CosB
(AC)² = (3.2)² + (8.4)² - 2(3.2)(8.4)Cos(48.08)°
(AC)² = 10.24 + 70.56 - 35.9166
(AC)² = 44.88
AC = [tex]\sqrt{44.8833}[/tex]
AC = 6.6995 cm
Perimeter of the ΔABC = m(AB) + m(BC) + m(AC)
= 3.200 + 8.400 + 6.6995
= 18.2995
≈ 18.300 cm
Therefore, perimeter of the given triangle is 18.300 cm
The Muller family are on holiday in New Zealand. a. They change some euros (€) and receive $1962 (New Zealand dollars). The exchange rate is €1 = $1.635. Calculate the number of euros they change. [3] b. The family spend 15% of their New Zealand dollars on a tour. Calculate the number of dollars they have left. [4]
Answer:
a. €1200;$1667.70
Step-by-step explanation:
a. Number of euros
[tex]\text{euros} = \$1962 \times \dfrac{\text{1 euro}}{\text{\$1.635}} = \textbf{1200 euros}[/tex]
b. Dollars remaining
Dollars on hand = $1962.00
Less 15 % spent = 0.15 × 1962 = -294.30
Balance remaining = $1667.70
If a person invests $120 at 8% annual interest, find the approximate value of the investment at the end of 5 years. A. $164 B. $180 C. $401 D. $176
Answer:
[tex]\large \boxed{\sf \bf \ \ \ D. \ \$ 176 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
After 5 years, we will get
[tex]120*(1+8\%)*(1+8\%)*(1+8\%)*(1+8\%)*(1+8\%)\\\\=120*(1+8\%)^5\\\\=120\cdot 1.08^5\\\\= 176.3193...[/tex]
Thank you
Jeania's parents have given her a interest-free loan of $100 to buy a new pair of running shoes She has to
pay back the loan with monthly payments of $20 each.
Write a function rule for the balance of the function (p), where p represents the number of
payments Jeania has made.
Answer:
The balance on the loan f(p) = $100 - $20 × p
Step-by-step explanation:
The parameters of the question are;
The loan amount = $100
The amount of monthly payment for the loan = $20
The function rule for the balance of the function f(p) where p is the number of payments is given as follows;
The balance on the loan, f(p) = The loan amount less the total amount paid
The total amount payment Jeania has made = Amount of monthly payment × Number of months paid, p
The total amount payment Jeania has made = $20 × p
∴ The balance on the loan, f(p) = $100 - $20 × p
Which gives;
f(p) = $100 - $20 × p.
* Graph these numbers on a number line.
-5,3, -2,1
-5
-5,3,-2,1 on a number line
<-|----|----|----|----|----|----|----|----|->
-5 -2 0 1 3
Plzz solve this for me... The Question is to simplify this.
Answer:
[tex] \boxed{ \frac{ \sqrt{3} }{2} }[/tex]Step-by-step explanation:
[tex] \frac{2 \sqrt{3} }{3} - \frac{ \sqrt{3} }{6} [/tex]
Expand the fraction to get the Least common denominator
[tex] \mathsf{ = \frac{2 \times 2 \sqrt{3} }{2 \times 3} - \frac{ \sqrt{3} }{6} }[/tex]
Multiply the numbers
[tex] \mathsf{ = \frac{4 \sqrt{3} }{6} - \frac{ \sqrt{3} }{6} }[/tex]
Write all numerators above the common denominator
[tex] \mathsf{ = \frac{4 \sqrt{3} - \sqrt{3} }{6} }[/tex]
Collect like terms
[tex] \mathsf{ = \frac{3 \sqrt{3} }{6} }[/tex]
Reduce the fractions with 3
[tex] \mathsf{ = \frac{ \sqrt{3} }{2} }[/tex]
Hope I helped!
Best regards!
A cook uses fifteen 2litter bottles of cooking oil in a week. If he decides to buy 5 litter tins of cooking oil instead how many tins of cooking oil will he use over a 10 week period if the rate at which he uses it remains unchanged.
Answer:
300 liters
Step-by-step explanation:
If he uses 15, 2 liter bottles in a week,
then 15 * 2 = 30 liters in a week.
If he uses the same rate in 10 weeks then,
10 * 30 = 300 liters
Select the correct answer. This set of ordered pairs defines a function. {(-49,7), (-56,8), (-63,9), (-70,10)} Which table represents the inverse of the function defined by the ordered pairs? A.
In the future, you should post all possible answer choices to have a complete post. However, there's enough information to get the answer.
The original set has points in the form (x,y)
The first point is (x,y) = (-49,7) making x = -49 and y = 7. When we find the inverse, we simply swap the x and y values. The inverse undoes the original function and vice versa. So if (-49, 7) is in the original function, then (7, -49) is in the inverse. The rest of the points follow the same pattern.
We end up with this answer
{ (7, -49), (8, -56), (9, -63), (10, -70) }
Expand ( p + 6 )( p - 3 )
Answer:
[tex]\Large \boxed{p^2 +3p-18}[/tex]
Step-by-step explanation:
[tex]( p + 6 )( p - 3 )[/tex]
Expand brackets.
[tex]p(p-3)+6(p-3)[/tex]
[tex]p^2 -3p+6p-18[/tex]
Combine like terms.
[tex]p^2 +3p-18[/tex]
Answer:
p² + 3p - 18
Step-by-step explanation:
(p + 6) (p-3)
Break it apart to make it easier to see:
p(p-3) = p² - 3p
6(p-3) = 6p - 18
Add both parts together(Combine Like terms):
p² - 3p + 6p - 18 = p² + 3p - 18
can some1 help me out with this problem
Answer:
see explanation
Step-by-step explanation:
Compare the coordinates of corresponding vertices.
C(7, - 2 ) → C'(- 3, 7 )
x- direction 7 → - 3 , that is - 10 of a shift
y- direction - 2 → 7, that is + 9 of a shift
Thus the translation rule is
(x, y ) → (x - 10, y + 9 )
The volume of a sphere whose diameter is 18 centimeters is π cubic centimeters. If its diameter were reduced by half, its volume would be of its original volume.
Answer:
3053.5517 cm^3 ; 1/8
Step-by-step explanation:
Given the following :
Volume (V) of sphere = (4/3)πr^3 where r = radius
Diameter of sphere = 18 ; radius(r) = diameter / 2 = 18/2 = 9cm
V = (4/3) × π × 9^3
V = 1.3333 × π × 729
V = 3053.5517 cm^3
When diameter(d) is reduced to half
d = d/2
Volume (V1) of sphere with diameter 'd' =
V1 = (4/3)π(d/2)^3
Volume (V2) of sphere with diameter 'd' reduced to half, d = d/2, d/2 * 1/2 = d/4
V2 = (4/3)π(d/4)^3
V1 / V2 = [(4/3)π(d/2)^3] / [(4/3)π(d/4)^3]
V1 / V2 = (d/2)^3 / (d/4)^3
V1 / V2 = [d^3 / 2^3] / [d^3 / 4^3]
V1 / V2 = 8 / 64
V1 / V2 = 1 / 8
Answer:
first blank is 972
second blank is 1/8
yup
Step-by-step explanation:
If sine theta equals one over three, what are the values of cos θ and tan θ?
Answer:
cos theta = √8/3
tan theta = √8/8
Step-by-step explanation:
sin theta = 1/3
1² + x² = 3²
x = √8
cos theta = √8/3
tan theta = 1/√8 = √8/8
I REALLY NEED HELLP with these 3 questions PLLZZZZ!!!!
Answer:
Below
Step-by-step explanation:
6)
The sum that we have is 85 +99
We want to express it as the product of a whole number thar is greater than 1 and a sum of two whole numbers.
Notice that: 85 = 84+1
● 85 + 99 = 84 + 1 + 99 = 84 + 100
84 and 100 are even numbers so we can factor using 2.
● 84 + 100 = 2(42 +50)
2 is greater than one and 42+50 is the sum of two whole numbers so all the conditions are satisfied.
■■■■■■■■■■■■■■■■■■■■■■■■■■
7)
Dasha go on business trips every 9 months while Charlie go every 6 months.
They came back at the same time.
So Charlie has to wait 6 months before going and Dasha nine months.
Dasha will be alone home for 3 months so she doesn't need to hire someone.
Here is what happens:
● Both Dasha and Charlie are home.
● After 6 months Charlie go and Dasha is at home
● after 3 months Dasha goes also and Charlie is home
● after 3 months charlie go and Dasha is home
● after 3 months both are home.
● aftet 3 months they both go
So the period is:
● 6+3+3+3+3 = 18
So after 18 months they should hire someone.
The picture below makes the understanding easier. ( x is Charlie and y is Dasha)
■■■■■■■■■■■■■■■■■■■■■■■■■■
8)
Pime factorisation
● 96÷2= 48
● 48÷2= 24
● 24 ÷ 2 = 12
● 12 ÷ 2 = 6
● 6÷2 = 3
● 3÷3 = 1
=> 96 = 2 × 2 ×2×2×2 ×3 =2^5 ×3
● 80÷ 2 = 40
● 40 ÷ 2 = 20
● 20÷2 = 10
● 10÷2 = 5
● 5÷5 = 1
=> 80 = 2×2×2×2×5 = 2^4 × 5
So the GCF is 2^4 wich is 16
He can make 16 party
● 80÷16 = 5
There will be 5 boxes of raisin in each one
● 96÷16 = 6
There will be 6 pencils in each party
Find x
A. 4√6
B. 4√6/3
C. 16√6/3
D. 32√3/3
Answer:
C
Step-by-step explanation:
let hypotenuse of triangle with 60°=y
[tex]\frac{8\sqrt{2}}{y} =sin ~60\\8 \sqrt{2}=y \times \frac{\sqrt{3}}{2} \\y=\frac{16 \sqrt{2}}{\sqrt{3}} =\frac{16 \sqrt{6}}{3}[/tex]
Please answer this question now
Answer:
94 degrees
Step-by-step explanation:
Measure of arc BCD = 53+135 = 188 degrees.
Measure of angle A = 188/2 = 94 degrees
Answer:
50
Step-by-step explanation:
If a person invests $250 at 9% annual interest, find the approximate value of the investment at the end of 15 years
Answer:
The end balance is $910.62 and the total interest $660.62. (That is without tax or inflation rate) I hope this helps.
Step-by-step explanation:
Answer:
without tax: interest total=$660.62
Step-by-step explanation:
I multiplied...
round 12.1975 to the nearest thousandth.
Answer:
12.198
Step-by-step explanation:
the thousandth is the third digit after the decimal point, so you round the next number after it, which is 5. so you round it up, ends with 12.198
We get 12.198 after rounding it to the nearest thousandth.
How to round off decimal places?The rounding off decimal places is similar to the basic round-off. We check the previous number. If it is greater than or equal to 5, we increase the value up to which we are rounding by 1, or else keep it the same when the previous digit is less than 5.
The order of digits for decimal places is opposite to the normal number system.
In the number system we have units place, then tens place, then hundreds place, then thousands place, and like that.
In the decimal number system, we start from the highest and go on decreasing.
The first decimal place is the tenth place.
The second decimal place is the hundredth place.
The third decimal place is the thousandth place.
And so on.
How to solve the question?In the question, we are asked to round 12.1975 to the nearest thousandth.
As discussed above, the nearest thousandth means rounding off up to the third decimal place.
So we round off 12.1975 up to the third decimal place, that is, we round off up to 7.
The next digit is 5, so we increase 7 by 1 to 8.
Thus, we get 12.198 after rounding it to the nearest thousandth.
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Carolyn was training for cross-country season on an indoor track. During her workout, she ran 24 laps around a track that measured 110 meters. What was the total distance Carolyn ran in kilometers?
Answer:
2.64 km
Step-by-step explanation:
24*110=2640 meters
2640/1000=2.64 km
(07.06A) Which scenario best matches the linear relationship expressed in the equation y = 13.50x + 300? Bobby has $300 in the yearbook fund and spends $13.50 on each yearbook. Bobby has $13.50 in the yearbook fund and spends $300 on each yearbook. Bobby has $300 in the yearbook fund and earns $13.50 for each yearbook sold. Bobby has $13.50 in the yearbook fund and earns $300 for each yearbook sold.
Answer:
Bobby has $300 in the yearbook fund and earns $13.50 for each yearbook sold.
Step-by-step explanation:
The value of the expression when x is zero is 300. For each increment of 1 in x, the value of the expression increases by 13.50. This best matches the scenario ...
Bobby has $300 in the yearbook fund and earns $13.50 for each yearbook sold.
An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Hope this can help you.
Answer:
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Step-by-step explanation:
a) Simplify the expression and explain each step. (2 points)
4(3x+2) -2
= ?
Answer:
6 (2 x + 1)
Step-by-step explanation:
Simplify the following:
4 (3 x + 2) - 2
Hint: | Distribute 4 over 3 x + 2.
4 (3 x + 2) = 12 x + 8:
12 x + 8 - 2
Hint: | Group like terms in 8 + 12 x - 2.
Grouping like terms, 8 + 12 x - 2 = 12 x + (8 - 2):
12 x + (8 - 2)
Hint: | Subtract 2 from 8.
8 - 2 = 6:
12 x + 6
Hint: | Factor out the greatest common divisor of the coefficients of 12 x + 6.
Factor 6 out of 12 x + 6:
Answer: 6 (2 x + 1)
SOMEONE HELP PLEASE. Kylie is raising money for a school trip by selling packs of cookies and bags of chips. The price of each pack of cookies is $1 and the price of each bag of chips is $2. Yesterday Kylie made $42 and she sold 3 times as many bags of chips as packs of cookies. Graphically solve a system of equations in order to determine the number of packs of cookies sold, x, and the number of bags of chips sold, y.
Answer:
cookies (x): 6 soldchips (y): 18 soldStep-by-step explanation:
It is convenient to let a graphing calculator draw the graph for you. It can also display the solution: (x, y) = (6, 18).
__
The equations of interest are ...
x + 2y = 42 . . . . . . revenue from sale of x cookies and y chips
y = 3x . . . . . . . . . . 3 times as many chips as cookies
Answer:
\underline{\text{Variable Definitions:}}
Variable Definitions:
x=
x=
\,\,\text{the number of packs of cookies sold}
the number of packs of cookies sold
y=
y=
\,\,\text{the number of bags of chips sold}
the number of bags of chips sold
Each pack of cookies sells for $1, so xx packs of cookies will bring in 1x1x dollars. Each bag of chips sells for $2, so yy bags of chips will bring in 2y2y dollars. Therefore, the total amount 1x+2y1x+2y equals \$42:$42:
1x+2y=42
1x+2y=42
Since Kylie sold 3 times as many bags of chips as packs of cookies, she sold more bags of chips, so if we multiply 3 by the number of packs of cookies sold, we will get the number of bags of chips sold, meaning yy equals 3x.3x.
y=3x
y=3x
\underline{\text{Write System of Equations:}}
Write System of Equations:
1x+2y=
1x+2y=
\,\,42
42
y=
y=
\,\,3x
3x
\underline{\text{Solve for }y\text{ in each equation:}}
Solve for y in each equation:
\begin{aligned}\color{indianred}{1x}+2y = 42\hspace{10px} & \hspace{10px}\color{green}{y}\color{green}{=}\color{green}{3x} \\[10px] 2y = \color{indianred}{-1x}+42\hspace{10px} & \hspace{10px} & \\[10px] \frac{2y}{2} = \frac{-1x+42}{2}\hspace{10px} & \hspace{10px} & \\[10px] \color{blue}{y} \color{blue}{= -\frac{1}{2}x+21}\hspace{10px}\hspace{10px} & \hspace{10px} & \end{aligned}
1x+2y=42
2y=−1x+42
2
2y
=
2
−1x+42
y=−
2
1
x+21
y=3x
Step-by-step explanation:
In politics, marketing, etc. We often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%). In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 32% with a margin of error of 2.2%. Describe the conclusion about p using an absolute value inequality.
Answer: |p-72% |≤ 4%
Step-by-step explanation:
Let p be the population proportion.
The absolute inequality about p using an absolute value inequality.:
[tex]|p-\hat{p}| \leq E[/tex] , where E = margin of error, [tex]\hat{p}[/tex] = sample proportion
Given: A poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% .
|p-72% |≤ 4%
⇒ 72% - 4% ≤ p ≤ 72% +4%
⇒ 68% ≤ p ≤ 76%.
i.e. p is most likely to be between 68% and 76% (.
The conclusion about p using an absolute value inequality is in the range of 29.8% to 34.2%.
What is absolute value inequality?An expression using absolute functions and inequality signs is known as an absolute value inequality.
We know that the absolute value inequality about p using an absolute value inequality is written as,
[tex]|p-\hat p| \leq E[/tex]
where E is the margin of error and [tex]\hat p[/tex] is the sample proportion.
Now, it is given that the poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76%. Therefore, p can be written as,
[tex]|p-0.72|\leq 0.04\\\\(0.72-0.04)\leq p \leq (0.72+0.04)\\\\0.68 \leq p\leq 0.76[/tex]
Thus, the p is most likely to be between the range of 68% to 76%.
Similarly, the proportion of people who like dark chocolate more than milk chocolate was 32% with a margin of error of 2.2%. Therefore, p can be written as,
[tex]|p-\hat p|\leq E\\\\|p-0.32|\leq 0.022\\\\(0.32-0.022)\leq p \leq (0.32+0.022)\\\\0.298\leq p\leq 0.342[/tex]
Thus, the p is most likely to be between the range of 29.8% to 34.2%.
Hence, the conclusion about p using an absolute value inequality is in the range of 29.8% to 34.2%.
Learn more about Absolute Value Inequality:
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a number when divided by 10 leaves the remainder 5. If the same number is doubled, and divided by 10, the new remainder is _____
Answer:
10
Step-by-step explanation
50 divided by 10 is 5 so
50 times 2 which is 100 divided by 10 is 10
Please answer question now
Answer:
MN = 3
Step-by-step explanation:
The following are congruent to each other as each pair are tangents of a circle drawn from the same external point:
PQ = QJ = 1
JK = KL = 4 - 1 = 3
MN = ML
Thus, ML = KM - KL
ML = 6 - 3 = 3
Therefore, MN = ML = 3 (both are tangents drawn from the same external point, M.
A video rental company offers a plan that includes a membership fee of $7 and charges $1 for every DVD borrowed. They also offer a second plan, that costs $29 per month for unlimited DVD rentals. If a customer borrows enough DVDs in a month, the two plans cost the same amount. How many DVDs is that? What is that total cost of either plan? If a customer rents ___ DVDs, each option costs $___.
If a customer rents 22 DVDs, each option costs $29
This only applies to one month.
=================================================
Work Shown:
x = number of DVDs borrowed
y = total cost
Plan A has a cost of x+7 dollars since x represents the cost of renting the x DVDs plus the membership fee of $7. We can say y = x+7.
Plan B has a fixed cost of $29 per month, so y = 29. There is no x here to worry about as the cost is the same no matter how many DVDs you rent.
y = x+7 and y = 29 are dealing with the same y value. We can use substitution to solve for x
----------------
y = 29 ... start with second equation
x+7 = 29 .... replace y with x+7 (valid because y = x+7)
x+7-7 = 29-7 ... subtract 7 from both sides
x = 22
If the customer rents 22 DVDs, then plan A will charge y = x+7 = 22+7 = 29 dollars, which is the same as the flat rate cost plan B charges.
If the customer rents more than 22 DVDs per month, then its smarter to go with plan B (since plan A's cost will be larger). Otherwise, go for plan A.
----------------
In terms of a graph, you can graph both y = x+7 and y = 29 together on the same xy axis. The line y = x+7 goes through (0,7) and (1,8). The line y = 29 goes through (0,29) and (1,29). Both lines intersect at (22,29) to indicate that x = 22 and y = 29 pair up together.
7.45 x 10^3 in standard notation
Answer:
7450
Step-by-step explanation:
Move the decimal to the right 3 times.
The standard notation is 7450
What is standard notation?Standard and scientific notation are the ways to represent numbers mathematically. We write numbers in standard and scientific notations using the rules for respective mathematical concepts. Here, 7.56×1011 7.56 × 10 11 is a scientific notation. 756,000,000,000 756 , 000 , 000 , 000 is standard notation.
Given:
7.45 x 10^3
So, when there is multiplication in decimals then the decimal point would shift to the right side.
Then,
7.45* 1000
=7450
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This is a very hard math question. Whoever answers correctly will get a brainlist too! Find the value of b. Then find the angle measures of the pentagon.
Answer:
Below
Step-by-step explanation:
The sum of the 5 angles is 540°
● b+(b+45)+90+(2b-90)+(3/2)b = 540
3/2 is 1.5
● b+b+45+90+2b-90+1.5b = 540
● 2b +45+2b+1.5b = 540
● 5.5 b +45 = 540
● 5.5b = 495
● b = 495/5.5
● b = 90°
Answer:
b = 90
Step-by-step explanation:
b + (b + 45) + 90 + (2b - 90) + (3/2)b = 540
b + b + 45 + 90 + 2b - 90 + (3/2)b - 90 = 540 - 90
b + b + 45 + 2b - 90 + (3/2)b = 450
2b + 2b + (45 * 2) + (2 *2b) - (90 * 2) + (2 * (3/2)b) = 450 * 2
2b + 2b + 90 + 4b - 180 + 3b = 900
11b - 90 = 900
11b - 90 + 90 = 900 + 90
11b = 990
b = 990 / 11
b = 90
check:
b + (b + 45) + 90 + (2b - 90) + (3/2)b = 540
90 + (90 + 45) + 90 + (2*90 - 90) + (3/2)*90 = 540
90 + 135 + 90 + 90 + 135 = 540
540 = 540 --- OK
pls help. A granola mix sells for $8.99 a pound. Tung wants to buy a bag of granola mix that weighs 7.8 pounds. The bag of granola mix will cost about $16. $17. $63. $72.
Answer:
about 72 dollars
Step-by-step explanation
"about" tells us to round our numbers. Therefore, 7.8 becomes 8. As each pound is $8.99, we multiply the two and get 71.92, which is "about" 72.
Answer:
$72
Step-by-step explanation:
To find the cost, multiply the price per pound by the number of pounds.
8.99(7.8)
= 70.12
This is closest to $72
A power failure on the bridge of a Great Lakes freighter has resulted in the ship's navigator having to do her own calculations. She measures the angle between the ship's course and a lighthouse on shore as 32°. After the ship has travelled 1500 m, she measures the angle to be 72°. Determine if the ship was closer to or farther from the lighthouse at the second sighting, and by what distance. (4 marks)
It is impossible to measure the length of a particular swamp directly. Kendra put a stake in the ground and measured from the stake to opposite ends of the swamp, the results being 410 m and 805 m. She measured the angle between the distances to be 57°. What is the length of the swamp? (4 marks)
Answer:
1) The ship is closer
2) 675.73 m
Step-by-step explanation:
1) The given parameters are;
The initial angle between the ship's course and the lighthouse = 32°
The final angle between the ship's course and the lighthouse = 72°
The distance traveled by the sip between he two positions = 1500 m
Therefore we have a triangle formed between the distance covered by the ship and the two distances of the ship from the lighthouse, a and b
Where;
a = The initial distance fro the lighthouse
b = The final distance fro the lighthouse
The angles of the triangle are
32°, (180 - 72) = 108° and 180 - 32 - 108 = 40°
By sine rule we have;
1500/(sin(40)) = a/(sin(108)) = b/(sin(32)) =
Therefore, a = sin(108°) × 1500/(sin(40°)) = 2219.37 m
b = (sin(32°)) × 1500/(sin(40°)) = 1236.61 m
Therefore, a > b
The initial distance fro the lighthouse > The final distance fro the lighthouse, which shows that the ship is closer
2) By cosine rule we have
a² = b² + c² - 2× b×c×cos(A)
Where the given measurements by Kendra are;
410 m and 805 m with an included (in between) angle of 57°, we have;
Let b = 410 m, c = 805 m, and A = 57°, we have;
a² = 410^2 + 805^2 - 2× 410×805×cos(57 degrees) = 456608.77 m²
a = The length of the stream = 675.73 m.
