Answers
Answer:
18.7 units
Step-by-step explanation:
In this right-angled triangle, you are provided with:
Two angles (i.e. 36° and 90°)
One side (i.e. Line AC, which is 11 units)
Line AB is known as the 'hypotenuse' of the right-angled triangle, which is what needs to be determined.
On the basis of 36° angle:
The side opposite (i.e. Line AC) is known as the 'opposite' or 'perpendicular side'
The side adjacent (i.e. Line BC) is known as the 'adjacent' or 'base'
Trigonometric function:
The trigonometric function, which connects an angle, it's opposite side and the hypotenuse is the 'sine function':
sinФ = [tex]\frac{opposite}{hypotenuse}[/tex]
sin36° = [tex]\frac{11}{x}[/tex]
Cross-multiplication is applied:
x needs to be isolated and made the subject of the equation:
xsin36° = 11
≡ x = [tex]\frac{11}{sin36^{o}}[/tex]
∴ x = 18.7 units (Rounded off to 3 significant figures)
Related Questions
how do you solve trigonometry word problems when you aren't given a drawing/image?
Answers
To do trigonometry, you need to have a clear understanding of triangles and the relationships between their sides and angles. To do trigonometry without images or diagram, let's go straight to the explanation below.
Solving trigonometry without imagesWhen solving trigonometry word problems without a drawing/image, the following steps can be helpful:
Read the problem carefully and identify the known and unknown quantities.Determine which trigonometric function (sine, cosine, or tangent) can be used to solve the problem, based on the information given.Use the definition of the chosen trigonometric function to write an equation relating the known and unknown quantities.Solve the equation for the unknown quantity.Check your answer by verifying if it makes sense in the context of the problem.It is important to note that in order to use trigonometry, you need to have a clear understanding of triangles and the relationships between their sides and angles.
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In 1852, an Indian mathematician, Radhanath Sikdar, used measurements and trigonometry to calculate the height of Peak XV in the Himalayas (later to be named Mount Everest). This required the use of a device that measured angles from the ground to the top of an object. By measuring the angle to the top of Peak XV from two different spots, and knowing the distance between these spots, Sikdar may have come up with a drawing like the following: The angle of elevation to the top of the peak (from point B) was measured to be 32 degrees. From a point 17409.7 feet closer (point A), the angle of elevation was 45 degrees. Find the height Sikdar calculated for Peak XV.
Answers
The height Sikdar calculated for Peak XV is approximately 29105.77 feet.
How to calculate the heightLet's first find the height of point A above the ground. We can use the tangent function:
tan(45) = height of A / d
height of A = d * tan(45)
height of A = 17409.7 * tan(45) = 17409.7 feet
h / (d - 17409.7) = height of A / d
h = (height of A * (d - 17409.7)) / d
h = (17409.7 * (17409.7 / tan(32) - 17409.7)) / (17409.7 / tan(32))
= 29105.77 feet
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suppose a problem is in canonical form and the associated basic feasible solution is degenerate, and x\ is a basic variable with the value zero. the pivot operation is performed with the x\ variable extracted from the basis. describe the new basic feasible solution
Answers
The new basic feasible solution will have x\ as a non-basic variable and a new basic variable with a value not equal to zero.
When a problem is in canonical form and the associated basic feasible solution is degenerate, this means that one of the basic variables has a value of zero. If the pivot operation is then performed with the basic variable with a value of zero extracted from the basis, the new basic feasible solution will have x\ as a non-basic variable and a new basic variable with a value not equal to zero. This is because the pivot operation involves exchanging the extracted basic variable with one of the non-basic variables. Therefore, the new basic feasible solution will not be degenerate, as the new basic variable will have a value not equal to zero.
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Proof Write a two-column or paragraph proof.
GIVEN: CAB is a right angle. AD is an altitude.
PROVE: ABC ~ DAC
Answers
As the acute angles of a right triangle are complementary, the measures of angle C and angle DAC add up to 90 degrees.
what is triangle ?Given that it has three sections and three corners, a triangle qualifies as a polygon. It corresponds to the fundamental geometric shapes. Triangle ABC is the term used to refer to a triangle only with vertices A, B, and C. Once the points are not collinear, a unique plane and triangular in Geometric forms are discovered. Triangles are polygon because they have three parts and three corners. The points where its three sides of the triangle converge are referred to as the triangle's corners. Three pyramid angles are multiplied ta yield 180 °.
given
Provided that segment AD is an altitude, AD in triangle ABC is perpendicular to hypotenuse BC.
Triangle DAC is a right triangle, as it should be. As the acute angles of a right triangle are complementary, the measures of angle C and angle DAC add up to 90 degrees.
The same holds true for angles C and CBA's measurements.
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At a specific spot along the coast of North Carolina, the continental shelf extends out from the shoreline into the ocean. At that point, the depth of the water is . From there, the ocean floor slopes down to the oceanic crust which begins from the shoreline at a depth of . Find the slope of the ocean floor connecting the edge of the continental shelf and the beginning of the oceanic crust. That section of the ocean floor is called the continental slope.
Answers
The slope of the ocean floor is: slope = (y2 - y1) / x
What is slope?
The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.
The slope of the ocean floor can be found by using the formula for the slope of a line:
slope = (change in y) / (change in x)
where the change in y is the difference in depth between the edge of the continental shelf and the beginning of the oceanic crust, and the change in x is the distance along the ocean floor between these two points.
Let's call the depth of the water at the edge of the continental shelf "y1" and the depth of the water at the beginning of the oceanic crust "y2". Then, the change in y is:
change in y = y2 - y1
Similarly, let's call the distance along the ocean floor between these two points "x". Then, the change in x is:
change in x = x
So, the slope of the ocean floor is:
slope = (y2 - y1) / x
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Sue has a bag of 18 sweets. 5 of the sweets are blue 7 of the sweets are red 6 of the sweets are green Sue takes at random a sweet from the bag. Write down the probability that Sue
(i) takes a red sweet,
(ii) does not take a green sweet,
(ii) takes a yellow sweet
Answers
Answer:
i).7/18
ii).0/18
iii).0/18.
Step-by-step explanation:
Total bag of sweet = 18
Blue sweet = 5
Red sweet = 7
Green sweet = 6
i). Probability that Sue takes a red sweet = 7/18
ii). Does not take a Green sweet = 0/18
iii). takes a yellow sweet = 0/18.
Which three statements about the expression x² + 7x + 6 are true?
Responses
A 2 is the coefficient of one term of the expression.2 is the coefficient of one term of the expression.
B 7 is the coefficient of one term of the expression.7 is the coefficient of one term of the expression.
C x is a variable in the expression.x is a variable in the expression.
D The expression has three terms.The expression has three terms.
E 6 is a factor of the expression.
Answers
The quadratic equation has the following three features:
B. 7 is the coefficient of one term of the expression.
C. x is a variable in the expression.
D. The expression has three terms.
How to analyze quadratic expression
In this question we have the case of a quadratic equation in standard form, whose features must be understood by direct inspection. At first sight we get the following conclusions:
The quadratic equation has three terms.The coefficients of the three terms are 1, 7, 6.The variable of the quadratic equation is x.Lastly, we get the following roots from the quadratic equation:
x² + 7 · x + 6 = 0
(x + 1) · (x + 6) = 0
x = - 1 or x = - 6
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pls help me i dont understand
Answers
Answer:
Let's call the initial fee "x". The equation for the total cost of using a computer for t minutes at the internet cafe can be expressed as:
C = x + 0.60t
Knowing that the total charge to use a computer for 5 minutes would be $6, we can use this information to find the value of x:
C = x + 0.60 * 5
6 = x + 3
x = 6 - 3
x = 3
So, the equation representing the total cost of using a computer for t minutes at the internet cafe is:
C = 3 + 0.60t
Step by step
C = We know the total charge is $6
m = We know the price per minute is .60
t = We know the variable (minutes) is 5
Using slope intercept formula
y = mx + b is our formula
Fill in the known values to find b
$6 = .60(5) + b
b is our unknown, the starting cost or constant, the base charge for using the computer regardless of minutes
$6 = .60(5) + b
Multiply
$6 = 3 + b
Subtract 3 from both sides to solve for b
$6-3 = 3 - 3 + b
Simplify
$3 = b
Now we can write our equation
C = .60t + 3
after a long period of time, you observe the chain and see that it is in state 1. what is the conditional probability that the previous state was state 2?
Answers
The conditional probability that the previous state was state 2 given that the chain is currently in state 1 is equal to the probability of transitioning from state 2 to state 1.
The conditional probability of transitioning from one state to another in a Markov Chain is dependent on the transition probabilities between the states. In this case, the conditional probability of transitioning from state 2 to state 1 is equal to the probability of transitioning from state 2 to state 1. This probability can be determined by looking at the transition matrix of the Markov Chain. The transition matrix specifies the probability of transitioning from one state to another. Therefore, the conditional probability of transitioning from state 2 to state 1 given that the chain is currently in state 1, is equal to the probability of transitioning from state 2 to state 1 as specified in the transition matrix.
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In the figure alongside, ZABC = ZACP. Prove that AABC-AAPC and find the lengths of AB and PB.
Answers
From the given triangle, the lengths of AB and PB becomes: 9 cm and 4 cm respectively.
What is a triangle?Tri-, which means "three," and angulus, which means "angle or corner," are the origins of the Latin word triangulus, which means "three-cornered" or "having three angles." A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. 180 degrees is the summation of the triangle's three angles.
In ΔAPC and ΔABC
∠ABC = ∠ACP and ∠BAC = ∠CAP
∴ ΔABC ≅ ΔACP
Because ∠ABC = ∠ACP, thus ∠A = ∠A, so, ∠ABC = ∠ACP
As, ΔABC ≅ ΔACP
∴ AB = BC = AC = CP (the corresponding sides of a similar triangle are proportional)
∵ BC = 12, AC = 6, CP = 8
∴ AB = (6/8) × 12
or, AB = 9 cm
as, ΔABC ≅ ΔACP
∴ AP : AC = AC : AB
or, AP = (6/9) × 6
or, AP = 4 cm
next, PB = AB - AP
PB = 9 - 4 cm
PB = 5 cm
Thus, the lengths of AB and PB becomes: 9 cm and 4 cm respectively.
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The complete question is as follows:
Find the absolute value.
[0.73]
Answers
Answer: 0.73
Step-by-step explanation: Because finding the absolute value only means finding how far away a number is from 0 on a number line, the answer is 0.73.
a flag pole that is 15 feet tall casts a shadow that is 21.1 feet long. at the same time of day, the shadow of a nearby tree is 12.7 feet long. how tall is the tree?
Answers
In linear equation, 24.9 tall is the tree .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
We can set up a proportion comparing the height of each object to the length of the shadow.
h/15 = 21.1/12.7
h = 1.66 * 15
h = 24.9
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we are interested in the choices of majors of this year's entering freshmen at our university. we randomly survey 10% of them. (a) what is the population? (b) what is the sample? (c) what is the parameter? (d) what is the statistic?
Answers
According to the random survey, the majors chosen by the freshmen of our university were:
(a) The population is the entering freshmen at the university. (b) The sample is the 10% of the entering freshmen who are randomly surveyed. (c) The parameter is the proportion of entering freshmen who choose a major. (d) The statistic is the proportion of surveyed freshmen who choose a major.To get a better understanding of the proportions of students choosing certain majors, universities can survey a sample of their entering freshmen. This survey should be representative of the population, so it should be conducted using a randomized sampling technique.
The survey should ask questions about the major the student is planning on pursuing and other relevant information, such as the student's interests and motivations.
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3a + 6b - 8a +9b
Please show your work
Answers
Answer & Step-by-step explanation:
To simplify the expression 3a + 6b - 8a + 9b, we can combine the like terms (terms with the same variable).
First, we can combine the 3a and -8a terms since they have the same variable 'a'. When we subtract 8a from 3a, we get -5a.
Then, we can combine the 6b and 9b terms since they have the same variable 'b'. When we add 6b and 9b, we get 15b.
Putting it all together, we get:
3a + 6b - 8a + 9b = -5a + 15b
Therefore, the simplified expression is -5a + 15b.
3a+6b-8a+9b
9b+6b-8a+3a
15b-5a
5(3b-a)
Hector is at school, 7200 feet from home. He leaves school and rides his bike home at a rate of 12 feet per second.
Answers
Answer: 6 minutes or 600 seconds. Thats how long it takes for him to ride his bike home
Step-by-step explanation: 7200 divided by 12 is 600
What is the value of the reciprocal of 0.8 ?
Answers
Answer:
⁵/₄ or 1.25
Step-by-step explanation:
Firstly, represent the number as a fraction:
0.8 = ⁸/₁₀ = ⁴/₅
Then, simply flip the top and bottom:
The reciprocal of ⁴/₅ is ⁵/₄
⁵/₄ = 1.25
What is the gradient and y intercept
Answers
Answer:
Step-by-step explanation:How do you find the gradient and y-intercept?The equation y = mx + c is the general equation of any straight line where m is the
Simplify—-
B.) 5/34 + 3/64 + 5/8
Answers
Answer:
29.13
Step-by-step explanation:
5÷34+3÷64+5÷5
= 6.8+ 21.33+ 1
=29.13
Answer:
the person above me is right just did the math for u
Step-by-step explanation:
yea cuz we smart :))
If 6 times the 6th term of an A.P., is equal to 9 times the 9th term, find its 15th term
Answers
As per arithmetic progression the value of 15th term is 0.
An arithmetic progression, or A.P., is a sequence of numbers in which the difference between consecutive terms is constant.
To start, let's call the common difference "d" and the first term "a". We can use the formula for the nth term of an A.P., which is Tn = a + (n-1)d, where Tn is the nth term and n is the position of the term in the A.P.
Using this formula, we can find the 6th term and 9th term. For the 6th term, T6 = a + (6-1)d = a + 5d. For the 9th term, T9 = a + (9-1)d = a + 8d.
Now, using the information given, we can create an equation: 6(a + 5d) = 9(a + 8d). Expanding both sides and simplifying, we get:
6a + 30d = 9a + 72d
Subtracting 9a from both sides, we get:
-3a + 30d = 72d
Subtracting 30d from both sides, we get:
-3a = 42d
Dividing both sides by -3, we get:
a = -14d
Now that we have found the value of "a", we can use the formula for the nth term again to find the 15th term. T15 = a + (15-1)d = -14d + 14d = 0.
So, the 15th term of the A.P. is 0.
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The water level in a tank measures 15 inches and is decreasing 0. 5 inches every minute. How many minutes, x, will it take for the water level to measure 9 inches deep?
Answers
The water level in the tank will take x = 30 minutes to decrease from 15 inches to 9 inches deep. It will take 6 minutes for the water level to decrease by 0.5 inches.
The water level in the tank is currently 15 inches deep and is decreasing by 0.5 inches every minute. In order to determine how many minutes, x, it will take for the water level to measure 9 inches deep, we will need to calculate the difference between the current water level and the desired water level. To do this, we need to subtract 9 inches from 15 inches, and this will give us a difference of 6 inches. Now, since the water level is decreasing by 0.5 inches per minute, we need to divide 6 inches by 0.5 inches, which will give us 12 minutes. Since 12 minutes is equal to 2 intervals of 6 minutes, the water level will take x = 30 minutes to decrease from 15 inches to 9 inches deep.
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como se realiza una encuesta en estadistica
Answers
The steps to conduct a statistical survey are given below.
What is statistical survey?A statistical survey is any structured inquiry designed to obtain aggregated data, which may be qualitative or quantitative where the individual or corporate identities of the respondents are in themselves of little significance.
Given is to conduct a statistical survey.
The steps to conduct a statistical survey are given below -
Step 1: Write your hypotheses and plan your research designStep 2: Collect data from a sampleStep 3: Summarize your data with descriptive statisticsStep 4: Test hypotheses or make estimates with inferential statisticsStep 5: Interpret your resultsTherefore, the steps to conduct a statistical survey are given above.
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{Question in english -
How to conduct a statistical survey}
Please help!!! Can’t figure out the answer.
Answers
The value of the given expression is 1440
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
(x²yz^4)/z
Substitute the values for x,y and z
((-6)²*5*2^4)/2
= (36*5*16)/2
use 16/2 = 8
= 36*5*8
= 1440
The value of the given expression is 1440
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An integer is 3 less than 5 times another. if the product of the two integers is 36 what are the integers?
Answers
Answer:
123Step-by-step explanation:
You want two integers with a product of 36 such that one is 3 less than 5 times the other.
SetupLet x be "the other" integer. Then one is (5x-3), and the product is ...
x(5x -3) = 36
Solution5x² -3x = 36 . . . . . . eliminate parentheses
x² -0.6x = 7.2 . . . . . . . divide by 5
x -0.6x +0.09 = 7.29 . . . . . add (0.6/2)² to complete the square
(x -0.3)² = 7.29
x = 0.3 +√7.29 = 0.3 +2.7 = 3
5x -3 = 5·3 -3 = 12
The two integers are 12 and 3.
2. You are floating in inner tube on Lake Michigan, 260 feet away from the iconic Little Sable Point lighthouse. You remember reading in the brochure that the lighthouse is 107 feet tall. At what angle do you have to look up to see the tip of the lighthouse?
Answers
Answer:
To calculate the angle, you would need to use the tangent of an angle formula: tan(θ) = 107/260. Solving for θ yields an angle of 29.4 degrees. You would have to look up at an angle of 29.4 degrees to see the tip of the lighthouse.
PLEASE MMAYBE EASY QvQ
Answers
Answer:
D. [tex]56.25 mm^{2}[/tex]
Step-by-step explanation:
A = [tex]\frac{A + 2}{2}[/tex]h =
[tex]\frac{16 + 9}{2}[/tex]x4.5
Thus,
=56.25
Option D.
how long would it take to travel 100 km at a speed of 50 km/h
Answers
Step-by-step explanation:
Assuming it is a constant speed of 50km/h
So you travel 50km in one hour
So if you want to go 100km traveling at the constant speed of 50km it will take two hours as you are going 50km for one hour it will take two hours to go 100km.
Is this right please help now ASAPppp
Answers
Answer: Pretty much correct except one thing is wrong.
Step-by-step explanation:
In place of CB you should write AB because the sides doesn't match when you flip the triangle CED.
Hope it helps!
Explanation
We see one angle has two sides 21 and 27
One triangle has two sides 14 and 18
We see vertical angles connect the two, those angles are congruent
Ratio of sides 21:27 = 7:9
Ratio of sides 14:18 = 7:9
So we know
14/21 = 18/27
Or
CE/CB = DC/AC
From this we see the 2nd triangle is a double reflection
It helps me to see congruent sides and the vertices by drawing congruencies on the triangles as I attached
Susan will take out 7500 to buy a used car. the simple interest rate is 5% for 5 years. How much money will she pay the bank back
Answers
Answer: To calculate the amount of simple interest, we use the formula: I = P * r * t, where P is the principal amount (7500), r is the annual interest rate (5%) and t is the time in years (5).
So, the simple interest is: I = 7500 * 5 * 0.05 = 187.5
The total amount Susan will have to pay back to the bank is the principal amount plus the interest:
7500 + 187.5 = $76 87.5
Therefore, Susan will pay the bank back $76 87.5 after 5 years.
Step-by-step explanation:
Use the tax table below to calculate the tax of a head-of-household taxpayer with a taxable income of $27,811.
Answers
The amount of tax owed by a head-of-household taxpayer with a taxable income of $27,811 is given as follows:
$3,062.
How to obtain the amount of tax?The amount of tax is obtained identifying the correct position in the table in this problem.
The person in this problem is the head of the household, meaning that we should observe the last column of the table.
As income of $27,811 is between $27,800 and $27,850, hence, looking at the fourth-to-last row, the amount of tax owed by a head-of-household taxpayer with a taxable income of $27,811 is given as follows:
$3,062.
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A circle has a radius of 4 centimeters. Find the area of the sector of the circle formed by an angle of 55°. If necessary, round the answer to two decimal places.
Select one:
Answers
Answer:
2.44π cm²
or
7.68 cm²
Since the choices are not shown, I do not know whether the choices are in terms of π or totally numeric Choose one of the two above. They are both the same value
Step-by-step explanation:
Area of a circle of radius r is A = πr²
An entire circle encompasses 360°
If a sector of the circle has an angle of Фat the center, the area of the sector is Ф/360 x πr²
Given r = 4 and Ф = 55°
Area of this sector = 55/360 x π (4)² = 55/360 x 16 x π = 2.44π
2.44π = 7.68 cm²