The solution to a trignometric equation sin²x - 1 = 0 is x = { π/2, 3π/2}
Consider a trignometric equation,
sin²x - 1 = 0
We need to solve this trigonometric equation for all values of angle x such that 0≤ x < 2π
Consider equation,
sin²x - 1 = 0
sin²x = 1
Takin square root,
sin(x) = ±1
when sin(x) = 1, then x = π/2
and when sin(x) = -1 then x = 3π/2
Therefore, required values of angle x = { π/2, 3π/2}
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Given the polynomial 9x2y6 − 25x4y8, rewrite as a product of polynomials.
(9xy3 − 25x2y4)(xy3 + x2y4)
(9xy3 − 25x2y4)(xy3 − x2y4)
(3xy3 − 5x2y4)(3xy3 + 5x2y4)
(3xy3 − 5x2y4)(3xy3 − 5x2y4)
The polynomial can be written as a product of polynomials as (3xy³ - 5x²y⁴)(3xy³ + 5x²y⁴)
option C.
What is the product of the polynomial?To rewrite the polynomial as the product of its form, we will factor the polynomial as shown below;
9x²y⁶ − 25x⁴y⁸ = x²y⁶(9 − 25x²y²)
The function (9 − 25x²y²), can factored using difference of two squares;
(9 − 25x²y²) = 3² − (5xy)²
3² − (5xy)² = (3 - 5xy)(3 + 5xy)
The final equation as the product of its factors is calculated as;
9x²y⁶ − 25x⁴y⁸ = x²y⁶(3 - 5xy)(3 + 5xy)
= (3xy³ - 5x²y⁴)(3xy³ + 5x²y⁴)
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You select a marble without looking and then put it back. If you do this 12 times, what is the best prediction possible for the number of times you will pick an orange marble?
If we assume that the marbles are equally likely to be picked, then the probability of picking an orange marble is 1/3.
The number of times an orange marble is picked in 12 trials follows a binomial distribution with parameters n = 12 and p = 1/3.
The expected value of the number of orange marbles picked is given by:
E(X) = np = 12 * (1/3) = 4
Therefore, the best prediction possible for the number of times an orange marble will be picked is 4.
Answer:
The probability of selecting either a purple or a blue marble for the 6 marbles is 0.3333 or 33.33%
Step-by-step explanation:
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What is the volume of this figure?
Enter your answer in the box.
yd³
The volume of the composite figure is
4095 cubic ydHow to find the volume of the composite figureThe volume is calculated by dividing the figure into simpler shapes. and adding the individual volumes
The simple shapes used here include
trapezoid andrectangleVolume of rectangle = length x width x depth
= 30 * 9 * 7
= 1890 cubic yd
Volume of trapezoid = 1/2 (sum of parallel lines) x height x depth
= 1/2 (30 + 19) x 10 x 9
= 2205 cubic yd
Total volume
= 1890 cubic yd + 2205 cubic yd
= 4095 cubic yd
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Simplify the expression: 8y + 4 - 3y + 12
Find the 15th term of the geometric sequence 9, 18, 36, ...
Answer: 147,456
Step-by-step explanation: 9, 18, 36, 72, 144, 288, 576, 1,152, 2,304, 4,608, 9,216, 18,432, 36,864, 73,728, 147,456
Required information
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Hitzu Company sold a copier (that costs $6,500) for $13,000 cash with a two-year parts warranty to a customer on August 16 of Year 1. Hitzu expects warranty costs to be 4% of dollar sales. It records warranty expense with an adjusting entry on December 31. On January 5 of Year 2, the copier requires on-site repairs that are completed the same day. The repairs cost $121 for materials taken from the parts inventory. These are the only repairs required in Year 2 for this copier.
1. How much warranty expense does the company report for this copier in Year 1?
2. How much is the estimated warranty liability for this copier as of December 31 of Year 1?
3. How much is the estimated warranty liability for this copier as of December 31 of Year 2?
4. Prepare journal entries to record (a) the copier’s sale; (b) the adjustment to recognize the warranty expense on December 31 of Year 1; and (c) the repairs that occur on January 5 of Year 2.
The warranty expense that the company report for this copier in Year 1 is $650.
The estimated warranty liability for this copier as of December 31 of Year 1 is $650
The estimated warranty liability for this copier as of December 31 of Year 2 is $556
How to calculate the valueThe warranty expense that the company report for this copier in Year 1 is:
= 13000 × 5%
= $650.
Also, the estimated warranty liability for this copier as of December 31 of Year 2 is $556
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In a certain board game, a 12-sided number cube showing numbers 1-12 is rolled. In this game, a number cube must be rolled until a number 9 or higher appears.
Is it appropriate to use the geometric distribution to calculate probabilities in this situation?
O Yes, the geometric distribution is appropriate.
O No, since each trial is not independent of the other trials.
O No, because it is not looking for the first occurrence of success.
O No, since a success and failure on each trial cannot be defined.
Answer:
THE ANSWER IS (A)
Step-by-step explanation:
BECAUSE I JUST DID AT
A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at each answer. Let X be the number of questions answered correctly. Find P (4) and P (more than 2)
The probability P (4) and of getting more than 2 questions correct are 0.017 and 0.113 respectively.
The number of ways the student can answer each question is 4 (since there are 4 choices), so the probability of getting any one question correct by guessing is 1/4, and the probability of getting any one question wrong by guessing is 3/4.
We can use the binomial probability formula to find the probability of getting a specific number of questions correct out of the 10:
[tex]P(X = k) = ( ^kC _n) * p^k * (1-p)^(n-k)[/tex]
a) P(4) represents the probability of getting exactly 4 questions correct out of 10.
[tex]P(X = 4) = (^{10}C_4) * (1/4)^4 * (3/4)^{(10-4)} \approx 0.017[/tex]
So the probability of getting exactly 4 questions correct is approximately 0.017.
b) P(more than 2) represents the probability of getting 3, 4, 5, ..., or 10 questions correct out of 10. We can use the complement rule to find this probability:
P(more than 2) = 1 - P(X ≤ 2)
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)\\= (^{10} C_0) * (1/4)^0 * (3/4)^{10}+ (^{10} C_1) * (1/4)^1 * (3/4)^9+ (^{10} C_2) * (1/4)^2 * (3/4)^8\\\approx 0.887[/tex]
So,
P(more than 2) = 1 - P(X ≤ 2) ≈ 1 - 0.887 ≈ 0.113
Therefore, the probability of getting more than 2 questions correct is approximately 0.113.
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Round to the nearest tenth, then find the sum. 35.26 + 8.32 + 6.78 i will give 12 points pleas help me in in a test
Answer:
Step-by-step explanation:
35.26 rounded to 35.3
8.32 rounded to 8.3
6.78 rounded to 6.8
35.3 + 8.3 = 43.6
43.6 + 6.8 = 50.4
The answer is 50.4.
39.26 rounds to 35.3
8.32 rounds to 8.3
6.78 rounds to 6.8
When you add them together, you get 50.4.
the scatter plot shows the relationship between the number of chapters and the total number of pages for several books.Use trend line to predict how many oages there would be in a book with 19 chapters?show work.
A)180pages
B)170pages
C)200 pages
D)190 pages
There are 190 pages would be in a book with 19 chapters.
We have to given that;
The scatter plot shows the relationship between the number of chapters and the total number of pages for several books.
Now, We get;
For 19 chapters at x - axis,
The value of pages at y - axis is, 190
Thus, There are 190 pages would be in a book with 19 chapters.
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Suppose 217 subjects are treated with a drug that is used to treat pain and 53 of them developed nausea. Use a 0.01 significance level to test the claim that more than 20% of users develop nausea.
There is not enough evidence to support the claim that more than 20% of users develop nausea at a 0.01 significance level.
We have,
Based on a sample of 217 subjects, 53 of them developed nausea.
To test this claim, a hypothesis test is conducted using a significance level of 0.01.
The null hypothesis, denoted as H0, assumes that the true proportion of users who develop nausea is less than or equal to 20%, while the alternative hypothesis, denoted as Ha, assumes that the true proportion is greater than 20%.
If the test statistic, calculated from the sample data, falls in the rejection region, which is determined based on the significance level and the degrees of freedom, then the null hypothesis is rejected, and it can be concluded that there is sufficient evidence to support the alternative hypothesis.
In this case,
If the test statistic falls in the rejection region, it means that the evidence suggests that more than 20% of users of the pain drug develop nausea, and the claim that less than or equal to 20% of users develop nausea is not supported by the data.
Thus,
There is not enough evidence to support the claim that more than 20% of users develop nausea at a 0.01 significance level.
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Lenny bought a motorcycle. He paid 10.5% in tax. The Tax added $1260 to the price of the motorcycle.
What is the price of the motorcycle not including tax?
The price of the motorcycle not including tax will be $12,000.
Given that:
Lenny bought a motorcycle. He paid 10.5% in tax.
The percentage is given as,
Percentage (P) = [Tax] / Initial value x 100
The price of the motorcycle not including tax is calculated as,
10.5 = (1260 / Initial value) x 100
0.105 = 1260 / Initial value
Initial value = 12,000
The price of the motorcycle is $12,000.
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Larry cut a ribbon into 8 equal pieces. If the ribbon was 26 m long, how many meters long was each piece?
As per the unitary method, each piece is 3.25 meters long by dividing the total length of the ribbon by the number of pieces.
Larry has cut a ribbon into 8 equal pieces. The total length of the ribbon is 26 m. We need to find out the length of each piece of the ribbon.
To do this, we can use the unitary method. We know that the ribbon is divided into 8 equal pieces, so each piece is 1/8th of the total length of the ribbon.
Therefore, we can find the length of each piece by dividing the total length of the ribbon by 8:
Length of each piece = Total length of ribbon / Number of pieces
Length of each piece = 26 m / 8
Length of each piece = 3.25 m
So, each piece of the ribbon is 3.25 meters long.
We used the unitary method by finding the value of one unit (1/8th of the ribbon) and then using it to calculate the value of other units (the length of each piece).
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Find the x intercept of the line 1x -2y =23
Answer: x=23
Step-by-step explanation:
Answer: 23
Step-by-step explanation:
When you have a value on the x-axis, your y=0
plug in y=0 to find your x-intercept
1x-2(0)=23
1x=23
x=23
ANSWER AS SOON AS POSSIBLE MUST ANSWER BEFORE 10:30-35 TO GET BRAINLYS!!!
Answer:
look at the photo
Step-by-step explanation:
The time it takes to preform a task has a continuous uniform distribution between 43 min and 57 min. What is the the probability it takes between 48 and 49.9 min. Round to 4 decimal places. P(48 < X < 49.9) =
The probability of the task taking between 48 and 49.9 minutes is 0.1357 or 13.57% (rounded to four decimal places).
To calculate this probability, we first need to find the total probability of the entire range between 43 and 57 minutes. This can be found by subtracting the lower bound from the upper bound and dividing by the total range:
P(43 < X < 57) = (57 - 43) / (57 - 43) = 1
Since the probability of the entire range is 1, we can find the probability of any sub-interval by dividing the length of the sub-interval by the length of the total range. Therefore, the probability of the task taking between 48 and 49.9 minutes is:
P(48 < X < 49.9) = (49.9 - 48) / (57 - 43) = 1.9 / 14 = 0.1357 or 13.57%
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The profit equation for the sale of pressure cookers for the company Kitchen Masters is PP = −120pp2 + 19,800pp − 727,450. Which of the following is a sale price for the immersion blenders, p, that will allow Kitchen Masters to achieve a profit, P, of $89,300?
Where the above factors are given, a sale price of approximately $84 for the immersion blenders will allow Kitchen Masters to achieve a profit of $89,300.
Why is this so?The profit equation for the sale of pressure cookers for the company Kitchen Masters is:
P = −120p² + 19,800p − 727,450
To find the sale price for the immersion blenders, p, that will allow Kitchen Masters to achieve a profit, P, of $89,300,
Let the profit equation = 89,300.
Now, we solve for p:
89,300 = −120p² + 19,800p − 727,450
Adding 727,450 to both sides:
816,750 = -120p² + 19,800p
Dividing both sides by -120:
-6,805 = p² - 165p
Rearrange the equation to make it Quadratic
p² - 165p + 6,805 = 0
Now we can solve for p using the quadratic formula:
p = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = -165, and c = 6,805.
p = (-(-165) ± √((-165)² - 4(1)(6,805))) / 2(1)
p = (165 ± √((27,225 - 27220)) / 2
p ≈ 83.618 or p ≈ 81.382
Therefore, a sale price of approximately $84 for the immersion blenders will allow Kitchen Masters to achieve a profit of $89,300.
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I am unsure about how to do this problem, pictured below.
Answer:
Step-by-step explanation:
150/2 = 75
500/75 = 6.6666666667 hours
it will take 6.2/3 hours to reach 500 bacteria cells
NOT SURE ABOUT EXPERSION BUT YOU COULD TRY THIS
p = 75t
Given that a culture of bacteria grows at a rate proportional to its size. Where the culture starts with 50 cells, then grows 150 after time, "t" equals 2 hours.
We are asked to:
> (a) Find an expression, P(t), to model the number of cells present after "t" hours.
> (b) Determine the time at which the population is at 500 cells.
For part (a):
Since the culture of bacteria grows at a rate proportional to its size, we can model it as the following differential equation.
[tex]\Rightarrow \frac{dP}{dt}=kP; \ Where \ P =P_0 \ at \ t=0 \ and \ P=3P_0 \ at \ t=2[/tex]
Solve the first-order separable differential equation with the given initial condition.
[tex]\Longrightarrow \frac{dP}{dt}=kP \Longrightarrow \frac{1}{P}dP=kdt \Longrightarrow \int\limits {\frac{1}{P} } \, dP=\int\ {k} \, dt \Longrightarrow ln(P)=kt+c[/tex]
[tex]\Longrightarrow e^{ln(P)}=e^{kt}+e^{c} \Longrightarrow P=ce^{kt}[/tex]
Plug in the initial condition.
[tex]\Longrightarrow P_0=ce^{k(0)} \Longrightarrow P_0=c(1) \Longrightarrow \boxed{c=P_0}[/tex]
[tex]\Longrightarrow P=ce^{kt} \Longrightarrow \boxed{P=P_0e^{kt}}[/tex]
Use the second initial condition to find "k."
[tex]\Longrightarrow 3P_0=P_0e^{k(2)} \Longrightarrow 3=e^{k(2)} \Longrightarrow 3=e^{2k} \Longrightarrow ln(3)=ln(e^{2k})[/tex]
[tex]\Longrightarrow k=\frac{ln(3)}{2} \Longrightarrow \boxed{k \approx 0.5493}[/tex]
Thus, the equation to model the situation is,
[tex]\boxed{\boxed{P(t)=50e^{0.5493t}}} \therefore Sol.[/tex]
For part (b):
[tex]P=10P_0[/tex]
[tex]\Rightarrow 10P_0=P_0e^{0.5493t} \Longrightarrow 10=e^{0.5493t} \Longrightarrow ln(10)=ln(e^{0.5493t})[/tex]
[tex]\Longrightarrow ln(10)=0.5493t \Longrightarrow t=\frac{ln(10)}{0.5493} \Longrightarrow \boxed{t=4.192 \ hrs}[/tex]
Thus, the time it takes the population to reach 500 is approx. 4.192 hours.
a rock is thrown straight up with an initial velocity of 3m/s. The mass of the rock is approximately 0.2kg. Air resistance acts on the rock with a force numerically equal to 0.5v where v is the velocity of the rock. Acceleration due to gravity is 9.8 m/s^2. Set up and solve a differential equation to find the velocity of the rock as a function of time
The velocity of the rock as a function of time is given by:
[tex]v(t) = 3 - 4.9exp(-2t/0.2) m/s[/tex]
where 4.9 is the value of mg in SI units.
The forces acting on the rock are the force due to gravity and the force due to air resistance. The force due to air resistance is given by 0.5v, where v is the velocity of the rock.
The force due to gravity is given by the mass of the rock (0.2 kg) times the acceleration due to gravity [tex](9.8 m/s^2)[/tex]. Using Newton's second law, we can set up the following differential equation:
[tex]m(dv/dt) = -mg - 0.5v[/tex]
where m is the mass of the rock, g is the acceleration due to gravity, and v is the velocity of the rock as a function of time t.
We can simplify this differential equation by dividing both sides by m:
[tex]dv/dt = (-g - 0.5v/m)v[/tex]
This is a separable differential equation, which we can solve using the separation of variables:
[tex](1/(-g - 0.5v/m)) dv = dt[/tex]
Integrating both sides gives:
[tex]-2ln(-g - 0.5v/m) = t + C[/tex]
where C is a constant of integration.
Solving for v gives:
[tex]v(t) = -0.5mg + C'exp(-2t/m)[/tex]
where C' = exp(C).
We can find the value of C' using the initial condition that the initial velocity of the rock is 3 m/s:
[tex]v(0) = -0.5mg + C' = 3[/tex]
[tex]C' = 0.5mg + 3[/tex]
Substituting this into the equation for v(t) gives:
[tex]v(t) = -0.5mg + (0.5mg + 3)exp(-2t/m)[/tex]
Therefore, the velocity of the rock as a function of time is given by:
[tex]v(t) = 3 - 4.9exp(-2t/0.2) m/s[/tex]
where 4.9 is the value of mg in SI units.
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. Amanda lets her new pony exercise by letting the pony run in circles while
attached to a rope, which Amanda holds in the center of the ring. If the part of
the rope between Amanda's hand and the pony is 30 feet long, how far does
the pony run in one circle. Round your answer to the nearest tenth. (Draw a sketch to help.
Answer:
188.5 ft
Step-by-step explanation:
One Circle = perimeter
= 2 nr
= 2 x 3.14 x 30
= 188.5 ft
Which figure has two more faces than a rectangular prism ?
The figure that has two more faces than a rectangular prism is a Square pyramid.
How many faces does it have ?There are precisely six faces that a rectangular prism contains, which consists of a pair of identical rectangles for its top and bottom planes as well as four lateral faces consisting of corresponding right-angled, congruent rectangles. Hence, a solid figure that has two more sides than the aforementioned rectangular prism could only have eight total faces without exception.
An example of such an entity is a square pyramid whose base constitutes of four equal-length sides with four corresponding triangular surfaces converging at one single vertex on the summit's tip. Within this context, it possesses five faces (one square and four isosceles triangles), thus exceeding by two faces compared to the former geometric model.
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What value of x satisfies the equation
(793x)3 = 343q36?
The value of x satisfies the equation is 4
What are index forms?Index forms are described as mathematical forms that are used to represent numbers or values that are too large or small in more convenient ways.
From the information given, we have that;
(7q³ˣ)³ = 343q³⁶
expand the bracket for the values
7³. q⁹ˣ = 343q³⁶
Now find the common exponents, we have;
7³. q⁹ˣ= 7³. q³⁶
Divide the values, we have;
q⁹ˣ = q³⁶
Equate the exponents, we get;
9x = 36
Divide both sides by the coefficient of x, we get
9x/9 = 36/9
Divide the values
x = 4
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What is the area of this polygon?
Answer:
78
Step-by-step explanation:
(5+8)×12/2=78
(5+8)×12/2=78
Please help with my geometry.
What is the area of the segment?
r = 3m
central angle = 98°
(1000 8 13. DIG DEEPER A 4,500-gram bag of soil costs $3, and an 18-kilogram bag of soil costs $10. Which is the less expensive way to buy 18,000 grams of soil? Explain.
It is cheaper to buy 18-kilogram bag of soil. The cost of the 18-kilogram is $10 and the cost of the cost of the other option is $12.
What is the cheaper way of buying 18,000 grams of soil?Cost of buying 18,000 grams of soil using the 4500 gram bag = (18,000 / 4,500) x $3 = $12
The second step is to convert 18 kilogram to grams.
1 kg = 1000 grams
18 x 1000 = 18,000 grams
18,000 grams cost $10.
Thus, it is cheaper to buy 18-kilogram bag of soil.
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Given g(x)=x²-6x-16, which statement is true?
The zeros are -8 and 2, because the factors of gare (x+8) and (x-2).
The zeros are -8 and -2, because the factors of g are (x + 8) and(x+2).
The zeros are -2 and 8, because the factors of gare (x+2) and (x-
8).
The zeros are 2 and 8, because the factors of gare (x-2) and (x-
8).
Since g(x) = x² - 6x - 16, a statement which is true include the following: C. The zeros are -2 and 8, because the factors of g are (x+2) and (x-
8).
What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Next, we would solve the quadratic function by using the factorization method as follows;
g(x) = x² - 6x - 16
0 = x² - 6x - 16
0 = x² - 8x + 2x - 16
0 = x(x - 8) + 2(x - 8)
(x - 8)(x + 2)
x = 8 or x = -2.
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Given PQ|| BC, what is PB?
9.6 units
10 units
13 units
14 units
Using the triangle proportionality theorem, the length of side PB in the given triangle is 10
Calculating the length of a side of a triangleFrom the question, we are to determine what the length of PB is in the given triangle
From the Triangle Proportionality Theorem which states that "If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally".
Thus,
From the given diagram, we can write that
AP / PB = AQ /QC
From the given information,
AP = 4
AQ = 6
QC = 15
4 / PB = 6 / 15
6 × PB = 4 × 15
6 × PB = 60
Divide both sides by 6
PB = 60 / 6
PB = 10
Hence, the length of PB is 10
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PLEASE HELP FAST I’M HAVING A LITTE TROUBLE PLEASE GIVE THE RIGHT ANSWER
Answer:
C) 1/2 and 8
Step-by-step explanation:
-2x + y = 7 Eq. 1
6x + y = 11 Eq. 2
From Eq. 1:
y = 7 + 2x Eq. 3
From Eq. 2:
y = 11 - 6x Eq. 4
Equalyzing Eq. 3 and Eq. 4:
7 + 2x = 11 - 6x
2x + 6x = 11 - 7
8x = 4
x = 4/8
x = 1/2
From Eq. 3:
y = 7 +2* 1/2
y = 7 + 1
y = 8
Check:
From Eq. 2
6x + y = 11
6*1/2 + 8 = 11
3 + 8 = 11
solve each rational equation. list excluded values
x+4/x+5=6/x^2+10+25
From the top of a 200 meters high building, the angle of depression to the bottom of a second building is 20 degrees. From the same point, the angle of elevation to the top of the second building is 10 degrees. Calculate the height of the second building to the nearest hundred meters.
Let's call the height of the second building "x". We can use trigonometry to solve for x.
First, let's draw a diagram to help visualize the problem:
A B
\ /
\ /
\ / x
\/
C
Where:
A is the top of the 200 meters high building
B is the bottom of the second building
C is the point from which the angles of depression and elevation are measured
x is the height of the second building
From the diagram, we can see that:
angle BCA = 20 degrees (angle of depression)
angle BAC = 10 degrees (angle of elevation)
AB = 200 meters
Using the tangent function, we can write:
tan(20) = x / AB (tangent of angle BCA)
tan(10) = x / (AB + x) (tangent of angle BAC)
We can solve these equations for x:
x = AB * tan(20) (multiply both sides by AB)
x = (AB * tan(10)) / (1 - tan(10)) (multiply both sides by 1 - tan(10), then simplify)
Plugging in the values we know:
x = 200 * tan(20)
x = (200 * tan(10)) / (1 - tan(10))
Using a calculator:
x ≈ 67.35 meters
Therefore, the height of the second building is approximately 67 meters (to the nearest hundred meters).
