A pole 11 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Rashaad measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.
Answers
The given question is on trigonometry which requires the application of required function so as to determine the value known. So that the length of the guy wire is 67.0 feet.
Trigonometry is an aspect of mathematics that requires the application of some functions to determine the value of an unknown quantity.
Let the length of the guy wire be represented by l, and the angle that the guy wire makes with the stake be θ. So that applying the appropriate trigonometric function to determine the value of θ, we have:
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
= [tex]\frac{11}{4}[/tex]
Tan θ = 2.75
θ = [tex]Tan^{-1}[/tex] 2.75
= 70.0169
θ = [tex]70^{o}[/tex]
Considering triangle formed by the tower and the stake to determine the value of l, we have;
Cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]
Cos [tex]70^{o}[/tex] = [tex]\frac{23}{l}[/tex]
l = [tex]\frac{23}{Cos 70^{o} }[/tex]
= [tex]\frac{23}{0.3420}[/tex]
l = 67.2515
l = 67 feet
The length of the guy wire is 67 feet.
For more on trigonometric, check: https://brainly.com/question/6459892
Related Questions
Multiply.
[−8⋅4/11]⋅[(−0.1)⋅22]
Answers
Answer:
6.4
Step-by-step explanation:
Hope this helps :D
7th grade math help...
Answers
Answer:
a= 11/30
Step-by-step explanation:
Divide the 5 1/2 miles by the 15 minutes
5.5/15= .36
.36 = 11/30
find the value of x and y
Answers
Answer:
x = 60
y = 30
Step-by-step explanation:
We know that all triangles' interior angles combined must have a sum of 180.
Since the triangle on the left is a equilateral triangle, we know that each angle is equal to 60.
Since we already know that the sum of the two angles in the top right is 90 (shown by the right angle symbol) and we know that the angle that isn't y is equal to 60, we must do the following step:
90 - 60 = y
90 - 60 = 30
y = 30
Now that we know the value of y, it's time to find the value of x.
We know that y = 30 and that the angle in the bottom right is equal to 90 (shown by right angle symbol).
Since all triangles' interior angles combined must have a sum of 180 and we already know that one angle is equal to 30 and the other is equal to 90, we must do the following:
180 - (90 + y) = x
180 - (90 + 30) = x
180 - 120 = x
180 - 120 = 60
x = 60
This gives us the answers y = 30 and x = 60
Find the perimeter. Simplify your answer.
Answers
Answer:
Perimeter = 24p + 17
Step-by-step explanation:
Perimeter = the sum of the sides of the figure.
Perimeter = (7p + 9) + (10p - 1) + (7p + 9)
Perimeter = (7p + 10p + 7p) + (9 - 1 + 9)
Perimeter = 24p + 17
Answer:
24p+17
Step-by-step explanation:
Perimeter of triangle = 2(7p+9)+(10p-1)
= 14p+18+10p-1
= 24p+17
What is the surface area of the cylinder with height 7 cm and radius 5 cm? Round
your answer to the nearest thousandth.
Answers
Answer:
376.991 cm²
Step-by-step explanation:
[tex]SA_{cylinder} = 2\pi r^{2} + 2\pi rh[/tex]
Surface Area = 2π(5²) + 2π(5)(7)
= 50π + 70π
= 120π
= 376.9911184... ≈ 376.991
Derive Surface Area of A CylinderIf you take a look at a net of a cylinder, you can see it is composed of two circles(bases) and a rectangular strip with the length of the diameter of the circle
The formula for the area of a circle = πr², and since there are 2, it is 2πr²
The formula for circumference of a circle = 2πr, and since we are multiplying that by the height by the height of the cylinder, it is 2πrh
∴ 2πr² + 2πrh
if i make 6000 dollars per 5.6 hours how much will I make in total in 24 hours
Answers
Answer:
About $25,714.29
Step-by-step explanation:
Divide 6000 by 5.6 to get dollar per hour rate:
6000/5.6 = 1071.43 dollars per hour
Multiply by 24:
1071.42857 * 24 = 25714.29 dollars
About $25,714.29
Nadia is a stockbroker. She earns 11% commission each week. Last week, she sold $5300 worth of stocks. How much did she make last week in commission? If averages that same amount each week, how much did she make in commission in 2011?
pls answer fast, 25 points to earn
Answers
Answer:
a. $ 583
b. $ 30,316
Step-by-step explanation:
a). 0.11 * 5,300= $ 583 per week( commission )
b). In 2011, 52 weeks.
52* 583 =$ 30,316
A bakery can make 4 cheesecakes for every 5 blocks of cream cheese. Which table represents the relationship between the number of cheesecakes the bakery makes and the number of blocks of cream cheese the bakery uses?
Answers
Answer:
where is the picture of the tables?
Step-by-step explanation:
(c) Ada is x years old and Bill is y years old.
Last
year,
Bill was 6 times as old as Ada.
(1) Form an equation in x and y and show that it simplifies to y = 6x - 5.
Answers
Using a system of equations, it is found that the simplified equation is y = 6x - 5.
Ada is x years old.Bill is y years old.Last year, Ada was x - 1 years old and Bill was y - 1 years old.
Bill was 6 times as old as Ada, hence:
[tex]y - 1 = 6(x - 1)[/tex]
[tex]y - 1 = 6x - 6[/tex]
[tex]y = 6x - 6 + 1[/tex]
[tex]y = 6x - 5[/tex]
The simplified equation is y = 6x - 5.
For a similar problem, also involving a system of equations, you can check https://brainly.com/question/13773803
Please help me, If you do not know do not answer
Answers
Answers:
FunctionFunctionNot a functionNot a function=================================================
Explanation:
Relation 1 is a function because any input item in the domain leads to exactly one and only one output item in the range. If we had say 2 arrows coming from "chair", and pointing to two different outputs, then we wouldn't have a function. It's perfectly possible to use words in place of numbers when talking about functions. All that matters is that we have one input map to exactly one output. Relation 2 is a function for similar reasoning as relation 1. It's possible to have an output repeated and still have a function. Relation 3 is not a function. Why not? Because of the points (j,v) and (j,t). The input j leads to more than output (v and t at the same time). A similar issue happens with the input 's' also.Relation 4 is also not a function. The repeated input this time is -5 which maps to the outputs z and 'a' at the same time.3 and 4 are not.
Each different x can only have 1 y value.
To form a hyperbola what is the relationship between the base of the cone and the angle of the plane that intersects the cone
A. The plane is a parallel to the base of the cone
B. The plane may be perpendicular to the base of the cone
C. the plane must be at a 45 degree angle to the base of the cone
D. The plane is at an angle that is neither parallel nor perpendicular to the base of the cone
Answers
In the diagram below segment AC is congruent to segment CE and segment BC is congruent to segment DC.
Why is triangle BCA congruent to triangle DCE?
See picture for full problem. Please and thank you!
Answers
Step-by-step explanation:
By reflection
HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE
What is the midpoint of KL?
Answers
Answer:
Find the midpoint between the two points.
(4,4),(-1,2)
Enter the number in scientific notation. 86,792 =
Answers
Answer:
8.6792 × 10 4 (I don't know how to make the four smaller but its 10 to the power of 4).
Step-by-step explanation:
8.6792 × 10 4. is the scientific notation
The quotient of a number, divided by 3, equals-8
Answers
Answer:
x / 3 = -8
Step-by-step explanation:
How many factors of 2 are there in 2³? answers> 1 2 3 5
Answers
Answer:
2
Step-by-step explanation:
2^3= 2*2*2
factors of 8= 1,2,4,8
factors of 2= 1,2
The angles in a triangle are
such that one angle is twice the
smallest angle, while the third
angle is three times as large as the
smallest angle. Find the measures
of all three angles.
Answers
Answer:
30, 60, and 90
Step-by-step explanation:
Let x be the Angle 1
2x is Angle 2
3x is Angle 3
x + 2x + 3x = 180
6x = 180
x = 30 degrees
2x = 60 degrees
3x = 90 degrees
Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day. A sample of 69 stocks traded on the NYSE that day showed that 31 went up. You are conducting a study to see if the proportion of stocks that went up is significantly more than 0.3. You use a significance level of α = 0.05 α = 0.05 . What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) α α greater than α α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is more than 0.3. There is not sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is more than 0.3. The sample data support the claim that the proportion of stocks that went up is more than 0.3. There is not sufficient sample evidence to support the claim that the proportion of stocks that went up is more than 0.3.
Answers
Testing the hypothesis, it is found that:
The test statistic is 2.71.The p-value is 0.0034.The p-value is less than [tex]\alpha[/tex]The test statistic leads to a decision to reject the null hypothesis.The sample data support the claim that the proportion of stocks that went up is more than 0.3.At the null hypothesis, we test if the proportion of stocks that went up is of 0.3, that is:
[tex]H_0: p = 0.3[/tex]
At the alternative hypothesis, we test if the proportion is significantly more than 0.3, that is:
[tex]H_1: p > 0.3[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.For this problem, the parameters are:
[tex]p = 0.3, n = 69, \overline{p} = \frac{31}{69} = 0.4493[/tex]
The value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.4493 - 0.3}{\sqrt{\frac{0.3(0.7)}{69}}}[/tex]
[tex]z = 2.71[/tex]
The test statistic is 2.71.
The p-value is the probability of finding a sample proportion of 0.4493 or above, hence, it is 1 subtracted by the p-value of z = 2.71.
Looking at the z-table, z = 2.71 has a p-value of 0.9966.
1 - 0.9966 = 0.0034
The p-value is 0.0034.
Which is less than [tex]\alpha[/tex], and then the test statistic leads to a decision to reject the null hypothesis, and thus:
The sample data support the claim that the proportion of stocks that went up is more than 0.3.
A similar problem is given at https://brainly.com/question/25413788
Find the value of Y - triangle measurments
PLEASE HELP! I WILL GIVE BRAINLIEST!
Answers
Answer:
y=8
Step-by-step explanation:
6y=8y-16
-2y=-16
y-8
congurnet side have congruen angles
[tex]\\ \sf\longmapsto <N=<P[/tex]
[tex]\\ \sf\longmapsto 6y=8y-16[/tex]
[tex]\\ \sf\longmapsto 8y-6y=16[/tex]
[tex]\\ \sf\longmapsto 2y=16[/tex]
[tex]\\ \sf\longmapsto y=8[/tex]
Which expression is an equivalent expression for 2(6y – 4)?
A. 8x – 2
B. 12y – 8
C. 8y
D. 12y + 4
Answers
Answer:
B. 12y-8
Step-by-step explanation:
by multiplying the 2 through the equation
Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why triangle JKL triangle QRS?
Check all that apply.
A. LA
B. LL
C. SAS
D. HL
E SSS
F HA
Answers
Answer:SAS, HL, LL, SSS
Step-by-step explanation:
just did it
The second term of an arithmetic sequence is –5, and the third term is –20. What is the first term?
Answers
Answer:
a₁ = 10
Step-by-step explanation:
The common difference d is calculated as
d = a₃ - a₂ = - 20 - (- 5) = - 20 + 5 = - 15
Then
a₂ - a₁ = d , that is
- 5 - a₁ = - 15 ( add 5 to both sides )
- a₁ = - 10 ( multiply both sides by - 1 )
a₁ = 10
What are Multiple Representations
Answers
Answer:
Thus multiple representations are ways to symbolize, to describe and to refer to the same mathematical entity
Answer:
Thus multiple representations are ways to symbolize, to describe and to refer to the same mathematical entity. They are used to understand, to develop, and to communicate different mathematical features of the same object or operation, as well as connections between different properties.
cahahahahhddbsbshshsjs 98 +_=366
Answers
Answer:
268
Step-by-step explanation:
366 minus 98= 268
CAN I GET BRAINLIEST
You get the final amount given minus that by the first number given you will get the answer for this case it would be.
366-98 that would be 268
A function is described by the equation
f(x) = 3x – 4. If f(x) = 26, what is the
value of x?
Answers
can someone help me on this and tell me how you did it you will get 30 points
Answers
[tex] \frac{2}{3} \div 3 \frac{1}{3} \\ \frac{2}{3} \times \frac{3}{10} \\ = \frac{2}{10} = \frac{1}{5} [/tex]
- BRAINLIEST answerer
Which expression is equivalent to 7/8
A: 5/8 + 2/8 + 1/8
B: 3/8 + 3/8 + 1/8 +1/8
C: 4/8 + 2/8 + 1/8
D: 4/8 + 2/8 + 2/8
Answers
C:4/8+2/8+1/8
brainlist me please
Will mark brainliest
Answers
Answer:
27
Step-by-step explanation:
5p + 3 = 15 Write a situation that this equation could help you solve and explain how each part of the equation relates to the situation you create.
Answers
Expressions can be represented as equations, and vice versa.
A possible situation is as follows:
John is 15 years old, and his age is 3 more than 5 times his brother's age
The equation is given as:
[tex]\mathbf{5p + 3 = 15}[/tex]
This means that:
15 represents John's ageP represents his brother's age5 and 3 are the constants that relate their agesRead more about word equations at:
https://brainly.com/question/20518082
The equation 5p + 3 = 15 can be used to find Mgbafor's age when Okeke's age is five times Mgbafor's age and in three years time, Okeke will be 15 years old.
The equation 5p + 3 = 15 is a linear equation. The equation must represent a variable which when multiplied by 5 and 3 is added yields 15.
Lets assume that Okeke's age is five times Mgbafor's age In three years time, Okeke will be 15 years old. If i am asked to find Mgbafor's age, the equation to use is 5p + 3 = 15, where p = Mgbafor's age.
Learn more: https://brainly.com/question/11897796
How to find derivative of a curved graph.