A running race follows a triangular course. The first leg of the race is in a straight line, covering 4.4km. Runners turn an angle of 79 deg for the second leg, and then turn again 77 deg to head back to the start line to finish the race. What is the length of the entire race, to the nearest tenth of a kilometer?
Answers
Answer:
The length of the entire race is 9,5km
Step-by-step explanation:
Required
Determine the length of the race.
To aid my explanation, I have added an attachment which shows the triangular course.
From the attachment, we have:
A as the starting point and the following measurement;
[tex]\angle B = 11^{\circ[/tex]
[tex]\angle C = 13^{\circ} + 79^{\circ} = 92^{\circ[/tex]
[tex]\angle A + \angle B + \angle C = 180^{\circ}[/tex]
[tex]\angle A = 180^{\circ} - (\angle B + \angle C )[/tex]
[tex]\angle A = 180^{\circ} - (11^{\circ}+92^{\circ})[/tex]
[tex]\angle A = 77^{\circ}[/tex]
[tex]\angle B = 11^{\circ[/tex]
[tex]\angle C = 92^{\circ[/tex]
[tex]c = 4.4km[/tex]
Apply sine rule
[tex]\frac{a}{sin\ A} = \frac{b}{sin\ B} = \frac{c}{sin\ C}[/tex]
[tex]\frac{a}{sin\ 77^{\circ}} = \frac{b}{sin\ 11^{\circ}} = \frac{4.4}{sin\ 92^{\circ}}[/tex]
[tex]\frac{a}{sin\ 77^{\circ}} = \frac{b}{sin\ 11^{\circ}} = \frac{4.4}{0.9994}[/tex]
[tex]\frac{a}{sin\ 77^{\circ}} = \frac{b}{sin\ 11^{\circ}} = 4.403[/tex]
Split to solve for a and b
[tex]\frac{a}{sin\ 77^{\circ}} =4.403[/tex]
[tex]\frac{b}{sin\ 11^{\circ}} = 4.403[/tex]
Make a the subject
[tex]\frac{a}{sin\ 77^{\circ}} =4.403[/tex]
[tex]a = 4.403 * sin(77^{\circ})[/tex]
[tex]a = 4.403 * 0.9744[/tex]
[tex]a = 4.3km[/tex]
Make b the subject
[tex]\frac{b}{sin\ 11^{\circ}} = 4.403[/tex]
[tex]b = 4.403 * sin(11^{\circ})[/tex]
[tex]b = 4.403 * 0.1908[/tex]
[tex]b = 0.8km[/tex]
The length of the race is:
[tex]Length = a + b + c[/tex]
[tex]Length = 4.3km + 0.8km + 4.4km[/tex]
[tex]Length = 9.5km[/tex]
Related Questions
What is the area of a square with side lengths of 3/5 units? Please explain how you know.
Answers
When trying to an area of a square, you multiply one side by another side to get the answer (length x width).
3/5 x 3/5 = 9/25
Numerator x numerator.
Denominator x denominator.
The airplane travels 1,650 miles in 3 hours. What is
the unit rate?
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Answer:
550 miles per hour
Step-by-step explanation:
Eight less than 7 times a number is -29.
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Answer:
7x-8=-20
Step-by-step explanation:
Jimmy invests $2500 in an account with a 5% interest rate, making no other deposits or withdrawals. What will Jimmy’s account balance be after 8 years if the interest is compounded 6 times each year?
URGENT PLEASE
Answers
Answer:
We conclude that the total amount accrued, principal plus interest, from compound interest on an original principal of $2500 at a rate of 5% per year compounded 6 times per year over 8 years is $3723.38.
Step-by-step explanation:
Given
Principle P = $2500
Interest rate r = 5% = 0.05
Time period t = 8 years
To determine
Accrue Amount A = ?
Using the compound interest equation
[tex]A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}[/tex]
where:
A represents the Accrue Amount
P represents the Principal Amount
r represents the interest rate
t represents the time period in years
n represents the number of compounding periods per unit t
Important tip:
Given that the interest is compounded 6 times each year, therefore, the value of n = 6.now substituting P = 2500, r = 0.05, t = 8 and n = 6 in the equation
[tex]A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}[/tex]
[tex]A=2500\left(1+\frac{0.05}{6}\right)^{\left(6\right)\left(8\right)}[/tex]
[tex]\:A=2500\left(1+\frac{0.05}{6}\right)^{48}[/tex]
[tex]A=2500\times 1.48935[/tex] ∵ [tex]\left(1+\frac{0.05}{6}\right)^{48\:\:}=1.48935[/tex]
[tex]A=\:3723.38[/tex] $
Therefore, we conclude that the total amount accrued, principal plus interest, from compound interest on an original principal of $2500 at a rate of 5% per year compounded 6 times per year over 8 years is $3723.38.
Evaluate the following algebraic expression, if (x = 5, y = 3)
x² +9y - 5
Answers
Answer: 47
Step-by-step explanation:
simply substitute the constants with 5 and 3.
(5)^2 + 9(3) - 5 = 47
5 squared+9(3)-5. 5 squared is 25. 9(3) is 27. 25+27-3 equals 49
Due in 10 minutes please help !! ASAP Erin buys 2 packs of potatoes costing £2 each, 3 packs of carrots for £3 per pack, and 3 turnips costing 90p each.
If she pays with a £20 note, how much change would she get in pounds, £?
Answers
2(2) + 3(3) =
4 + 9 = 13
I don't know what 90p means but basically, u have to multiply that by 3 and add it to our current total which is 13.
Then, u substract the total cost from the 20 and you should get the change.
What is the prime factorization of 91?
Answers
Answer:
The factors of 91 by prime factorization are 1, 7, 13 and 91. Here, 7, and 13 are the prime factors of 91.
Step-by-step explanation:
Pls HAAAAAAAALLLLPPPPP plez
I give brainliest to whoever answers correctly w/ an explanation first
answer the question below
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Answers
If a submarine descends to the ocean floor which is 2,100 feet below sea level in 3 hours, what is the rate of descent?
Answers
Answer:
700 feet per hour is the rate of descent
Step-by-step explanation:
3 hours is 2100 so 2100/3 is 700 which is per hour
The number of branches of an oak tree and a birch tree since 1950 are represented by the following tables:
Determine whether the data described in the tables is best modeled by a linear function or an exponential function
Answers
Answer:
oak tree is a linear function and birch tree is exponential
Step-by-step explanation:
cuz i just did it
The oak tree have a liner function and the birch tree have exponential function .
What is linear function?Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
What is exponential function?An exponential function is a mathematical function of the following form:
f ( x ) = [tex]a^{x}[/tex]. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828.
According to the question
The number of branches of an oak tree and a birch tree since 1950 are represented by the following tables:
Number of Oak trees (x) Number of branches f(x)
0 34
3 46
6 59
9 70
12 82
So in this table we can see that there is increment in number of branches but in a pattern approx.
i.e
f(x) = 34 + 4(x)
where x will be Number of Oak trees
therefore it is a Linear function
Number of Birch trees (x) Number of branches f(x)
0 8
10 33
20 128
30 512
40 2049
So , in this table is increasing in a very fast pace but in a pattern approx.
i.e
f(x) = [tex]8*4^{\frac{x}{10} }[/tex]
Therefore it is an exponential function
Hence, The oak tree have a liner function and the birch tree have exponential function .
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Answers
Answer:
1080
Step-by-step explanation:
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Answers
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Step-by-step explanation:
Monday = m
Tuesday = m + 15
Wednesday = m + 15 + 30 = m + 45
Thursday = 2 × m = 2m
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Step-by-step explanation:
Answer: (-7,3)
Step-by-step explanation:
A
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Answers
Answer:
D. m≥12
Step-by-step explanation:
You first need to transfer the -6 over to the 18. The negative turns into a positive, therefore you add. 18+6 is 24. You now have 2m≤24. Bring the 2 over. You are dividing. 24/2 is 12.
Answer:
The answer is D.
Step-by-step explanation:
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Answers
Answer:
24
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
44 - (5 x 4) = 44 - 20
= 24
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A. 11%
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D. 98%
Answers
Answer:
90%
Step-by-step explanation:
18/20 × 100 = 90%
I hope this helps!
Answer:
Sean answered 90% of the questions in the quiz correctly
oh whoopsie somebody answered already but oh well- 乁[ᓀ˵▾˵ᓂ]ㄏ
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9514 1404 393
Answer:
terms: 2
degree: 1
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The expression has two terms, separated by a minus sign.
The degree of the expression is the exponent of the only variable, 1. (Typically, a coefficient of 1 and/or an exponent of 1 are not shown.)
terms: 2; degree: 1
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Step-by-step explanation:
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Answer:
angles
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Step-by-step explanation:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Answers
Answer:
175 = 7·5·5
Step-by-step explanation:
A student asked to write a prime factorization of 175. He wrote 7·25
The prime factorization of 175 will be given by :
[tex]175=7\times 5\times 5[/tex]
It means, he has written it wrong as 7·25. It should be 7·5·5.
Hence, this is the required solution.
Answer:
175 = 7·5·5
Step-by-step explanation:
A student asked to write a prime factorization of 175. He wrote 7·25
The prime factorization of 175 will be given by :
It means, he has written it wrong as 7·25. It should be 7·5·5.
Hence, this is the required solution.
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Answers
The composite score range for the ACT is D) 1 to 36.
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Answers
Answer:
-1/2
Step-by-step explanation:
first point is 1,-4
second point is 5,-6
Slope is y2-y1/x2-x1
-6 - -4 / 5 - 1
-2/ 4
-1/2
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Answers
Answer:
x=9
Step-by-step explanation:
Step-by-step explanation:
133=7+14x
133-7=14x
14x=133-4
14x=129
14x=129
14 14
x=129
14
Graphf (x) = 3x + 4 and a h(x) = -f(x).
Answers
Answer:
I think the answer is 56 .
Explain why the net shown here cannot be the net of a cube
Answers
Answer:
there is an extra square missing
Step-by-step explanation:
John makes 2 cookies a day. Write an equation that shows the relationship between the days and number of cookes John
makes. Write an equation
Answers
Answer:
2x
x = each day
Step-by-step explanation:
Answer:
y= 2(x)
Step-by-step explanation:
The Y is the cookies. X is the days. Every day that John bakes, he makes 2 cookies. So you multiply the days by 2 to find the number of cookies he bakes.
