The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary Prove that the height of the tower is 6 m.
Kindly help!
Answers
Answer:
Proof explained below
Step-by-step explanation:
Tan trigonometric ratio
\(\sf \tan(\theta)=\dfrac{O}{A}\)
where:
\(\theta\) is the angleO is the side opposite the angleA is the side adjacent the angleDraw a diagram to help visualize the scenario (see attached).
If the angles are complementary, their sum is 90°.
Therefore, let one of the angles be \(x\) and the other angle be \(90^{\circ}-x\).
Use the tan trig ratio to create two equations with the missing side length.
Right triangle ACD
Given:
\(\theta = x\)O = CD (tower)A = 9 mSubstituting the given values into the tan trig ratio:
\(\implies \tan (x)= \dfrac{\textsf{CD}}{9}\)
Right triangle BCD
Given:
\(\theta = 90^{\circ} - x\)O = CD (tower)A = 4 mSubstituting the given values into the tan trig ratio:
\(\implies \tan (90^{\circ} - x)= \dfrac{\textsf{CD}}{4}\)
\(\textsf{As }\:\tan(90^{\circ} - x)= \cot (x):\)
\(\implies \cot(x)= \dfrac{\textsf{CD}}{4}\)
\(\implies \dfrac{1}{\tan(x)}= \dfrac{\textsf{CD}}{4}\)
\(\implies \tan(x)= \dfrac{4}{\textsf{CD}}\)
Therefore, the two equations are:
\(\textsf{Equation 1}: \quad \tan (x)= \dfrac{\textsf{CD}}{9}\)
\(\textsf{Equation 2}: \quad \tan(x)= \dfrac{4}{\textsf{CD}}\)
Substitute one equation into the other and solve for CD:
\(\implies \sf \dfrac{CD}{9}=\dfrac{4}{CD}\)
\(\implies \sf CD \cdot CD= 4 \cdot 9\)
\(\implies \sf CD^2=36\)
\(\implies \sf CD=\sqrt{36}\)
\(\implies \sf CD= \pm 6\)
As distance cannot be negative, CD = 6 m only, thus proving that the height of the tower is 6 m.
Related Questions
P(2-r)-17=109 what is the answer
Answers
Answer:
126
P = -------------
2 - r
Step-by-step explanation:
Solve for P: P(2-r)-17=109
Combining the constant terms:
P(2 - r) = 126
Dividing both sides by (2 - r) isolates P:
126
P = -------------
2 - r
can you put this into one sentence The Soviet team dominated the second period. The Americans scored twice in the last period. The Americans finally took the lead.
Also put two of these words in it Although or so unless.
40 points
Answers
the americans scored twice in the last period although the soviet team dominated second period, after that the americans finally took the lead
(this is english not math change your question when you have to do this again)
Six Less than four times a number is
-70
Answers
The answer is 286
Step-by-step explanation:
70 x 4 = 280 plus 6 equals 286
You had 150 , but you are spending 2 each day. What algebraic expression models this situation?
Answers
If you had $150, but you are spending $2 each day, then the algebraic expression model of this situation is 150-2x
Given,
The total amount you had = $150
The amount you spend in each day = $2
Consider the number of days = x
Then the algebraic expression for this situation is 150-2x
Hence, If you had $150, but you are spending $2 each day, then the algebraic expression model of this situation is 150-2x
Learn more about algebraic expression here
brainly.com/question/953809
#SPJ4
Determine whether the relation is a function. Then list the domain and range.
{(1, -2), (-1,2), (-2,4), (1,3)}
Answers
The domain of the relation is 1,-1,-2, and 1. The range of the function is -2,2,4, and 3.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and the independent variable.
A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values. The domain of the function is defined as the set of all the possible values of the function.
The domain of the relation is 1,-1,-2, and 1. The range of the function is -2,2,4, and 3.
To know more about functions follow
https://brainly.com/question/2833285
#SPJ1
) a new machine is known to reduce pollutants. however, it is expensive. the epa estimates that one-third of plants has this new machine. what is the probability that fewer than 11% of the plants in the random sample own this machine?
Answers
The probability that fewer than 11% of the plants in the random sample on this machine is 0.0823.
Given:
The likelihood of a plant having a modern machine is 1/3.
To discover:
The likelihood is that less than 11% of the plants in an arbitrary test have an unused machine.
Let X be the number of plants
out of n plants within the test that has the modern machine.
Since each plant features a likelihood of 1/3 of having the machine, X follows binomial dissemination with parameters n and p=1/3.
We have to discover
P(X < 0.11n).
Utilizing the coherence adjustment, we have:
P(X < 0.11n) = P(X <= 0.10n)
= P(Z <= (0.10n - np)/√(np(1-p))),
where Z may be a standard typical arbitrary variable
Since n isn't given, able to accept a large sufficient test measure such that the binomial dispersion can be approximated by a normal distribution.
A commonly utilized run show of thumb is that this estimation is sensible in case both np and n(1-p) are at the slightest 10.
Since n isn't given, we cannot affirm whether this condition is met or not, but we are going to accept it for the reason of the arrangement.
Utilizing np= n/3 and (1-p)n= (2/3)n, we have:
P(Z <= (0.10n - n/3)/√(n/3 * (2/3)n))
= P(Z <= (0.10 - 1/3)/√(2/9 * n))
= P(Z <= -1.39/√(n))
Employing a standard normal table or calculator, we will discover that P(Z <= -1.39) = 0.0823.
In this manner,
P(X < 0.11n) = P(Z <= -1.39/√(n)) = 0.0823.
To know more about probability refer to this :
https://brainly.com/question/24756209
#SPJ4
The volume of this cone is 36π cubic units.
What is the volume of a cylinder that has the same base area and the same height(in pi)? Need ASAP, due soon
Answers
Answer:
108pi
Step-by-step explanation:
We do not need to know the height and radius, as the formula for the volume of a cone is just a third of the volume of a cylinder. So we have 36pi * 3 or 108pi.
RiDDLe oF tHE DaY: In the beginning of the school semester at Wilson Middle there was a murder. There were four suspects, The principal, Gardener, The counselor and the math teacher. The principal said he was in his office. The counselor said she was at the front office with school staff. The gardener said she was trimming bush leaves. The math teacher said he was giving out the end of semester school test. Who is the murder?
Answers
Answer:
the gardener
Step-by-step explanation:
it always is lol
Answer:
Math teacher
Step-by-step explanation:
It says he was giving the end of semester school test, and its the beginning of the school semester at Wilson Middle.
write the equation of the line graphed below.
i’ll be giving out brainliest, thanks!
Answers
y=mx+b
B= y-intercept, 2
M= slope, -1/4
Negative graph
Non-proportional
20 POINTS ILL MARK U BRAINLIEST PLS
Answers
Answer:
13 + \(\sqrt{89}\)
or
22.43398... (depends on how you round it)
Step-by-step explanation:
1. The question stated that the radius of the circle O is 5, so the length of AO and CO is 5.
2. Since line AB and line CB are both tangent to the circle, they have the same length. CB is 8, so AB will also be 8.
--> Both triangle AOB and COB share one side, and the other side (radius) has the same length, so the third side must be the same length
3. Tangent means having a 90-degree angle with the radius. We know that the triangle AOB is a right triangle since the angle OAB is 90 degrees.
We can use the Pythagorean theorem to find side OB. OB^2 = AO^2 + AB^2.
--> OB^2 = 25 + 64
--> OB^2 = 89
--> OB = \(\sqrt{89}\)
Now that we know the lengths of all three sides, we can add them up.
--> 5 + 8 + \(\sqrt{89}\)
--> 13 + \(\sqrt{89}\)
or
--> 22.43398113....
Consider the following generic C comparison function and its assembly language representation C code: byte compbyte a,byte b)/a in rdi,b in rsi Assembly code cmpb %rsi,%rdi set_inst %a1 ret Your jobs(fill-in blank):now sh given values of a and b g SET instruction and the A.5 points set CI SF OF %al setg 47 23 B.5 points set h SF OF %a setl 23 47 C.5 points ZA SF OF %al set sete 23 23 D.5 points CF ZF SF OF 00%1 set b setne 23 47
Answers
The correct answer is D. setne 23 47. Based on the provided information, I understand that you have a comparison function in C code and its corresponding assembly code. You are asked to fill in the blanks by selecting the appropriate instructions based on the given values of a and b and the status flags SF, OF, ZF, and CF. Let's go through the options:
A. setg 47 23: This option is incorrect because setg is used to set a byte to 1 if the Greater flag (ZF=0 and SF=OF) is set, but the given values of a and b are 47 and 23, respectively, so it does not satisfy the condition for setg to be set.
B. setl 23 47: This option is incorrect because setl is used to set a byte to 1 if the Less flag (SF≠OF) is set, but the given values of a and b are 23 and 47, respectively, so it does not satisfy the condition for setl to be set.
C. sete 23 23: This option is incorrect because sete is used to set a byte to 1 if the Zero flag (ZF=1) is set, but the given values of a and b are 23 and 23, respectively, so it does not satisfy the condition for sete to be set.
D. setne 23 47: This option is correct. setne is used to set a byte to 1 if the Zero flag (ZF=0) is not set, which means the values of a and b are not equal. In this case, the given values of a and b are 23 and 47, respectively, so they are not equal, and setne should be used.
Therefore, the correct answer is D. setne 23 47
To know more about byte visit-
brainly.com/question/32309440
#SPJ11
Find the perimeter of a rectangular garden that has a width of 4x−6 and a length of 2x+4.
im i n t e a r s pLEASE
Answers
Answer:
Perimeter: 2(2x - 7) + 2(3*2 + 4x)
Step-by-step explanation:
Area: (2x - 7) * (3*2 + 4x)
(2x - 7) * (6 + 4x)
8x-42
Perimeter: 2(2x - 7) + 2(3*2 + 4x)
The Perimeter: of the rectangular garden that has a width of 4x−6 and a length of 2x+4 is 2(2x - 7) + 2(3*2 + 4x).
What is perimeter?Perimeter is the sum of length of the sides used to made the given figure.
The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
WE need to find the perimeter of a rectangular garden that has a width of 4x−6 and a length of 2x+4.
Area = (2x - 7) * (3*2 + 4x)
Area = (2x - 7) * (6 + 4x)
Area = 8x - 42
The Perimeter: of the rectangular garden that has a width of 4x−6 and a length of 2x+4 is 2(2x - 7) + 2(3*2 + 4x).
Learn more about perimeter here:
https://brainly.com/question/10466285
#SPJ2
find the volume of and round all answers to the nearest hundredth.
Answers
Answer:
The answer would be : 7,500 <-- (rounded)
Step-by-step explanation: How i got this answer is, i just multiplied all of the sides together since thats what you do with area's. ( 21 x 21 x 17= 7,497)
Now, the last step is to just round the number off. As we see, the "497" is much more closer to the number "500". So we can just simply round "497" to "500". So your final number for the area would be (7,500) ft.
~hope this helped you out in any way, have a gr8 day/night my friend!~
I need this solved as c.l.t
6=n-2n
Answers
Answer:
n= -6
Step-by-step explanation:
I’LL BRAINLIEST YOU IF YOJ GET IT RIGHT
PLEASE HELP ME FIND X!
Answers
Answer:
\(\boxed {\boxed {\sf x=42}}\)
Step-by-step explanation:
The 2 triangles have 2 pairs of congruent angles, so they are similar by the angle-angle postulate. Therefore, their sides are proportional.
The bases, x and 30 are proportional.
The sides are proportional. Make sure to add 25 and 10 to find the side length of the larger triangle. So, the proportional sides are 35 and 25.
Now, set up a proportion. Make sure to keep the sides of the same triangle together horizontally across.
\(\frac {base_1}{base_2}= \frac{side_1}{side_2}\)
\(\frac {x}{30}=\frac {35}{25}\)
Since we are solving for x, we must isolate the variable. It is being divided by 30 and the inverse of division is multiplication. Multiply both sides by 30.
\(30*\frac {x}{30}=\frac {35}{25}*30\)
\(x=30*1.4\\x=42\)
The side x is equal to 42.
Q5... Lids has obtained 23.75% of the
cap market in Ontario. If Lids sold 2600 caps last month, how many
caps were sold in Ontario in total last month? Round up the final
answer. (1 mark)
Answers
The total number of caps sold in Ontario last month is approximately 10948 caps (rounded up).
Given that Lids has obtained 23.75% of the cap market in Ontario and it sold 2600 caps last month. Let us calculate the total caps sold in Ontario last month as follows:
Let the total caps sold in Ontario be x capsLids has obtained 23.75% of the cap market in Ontario which means the percentage of the market Lids has not covered is (100 - 23.75)% = 76.25%.
The 76.25% of the cap market is represented as 76.25/100, hence, the caps sold in the market not covered by Lids is:
76.25/100 × x = 0.7625 x
The total number of caps sold in Ontario is equal to the sum of the number of caps sold by Lids and the number of caps sold in the market not covered by Lids, that is:
x = 2600 + 0.7625 x
Simplifying the equation by subtracting 0.7625x from both sides, we get;0.2375x = 2600
Dividing both sides by 0.2375, we obtain:
x = 2600 / 0.2375x
= 10947.37 ≈ 10948
Therefore, the total number of caps sold in Ontario last month is approximately 10948 caps (rounded up).Answer: 10948
To know more about percentage visit:
https://brainly.com/question/32197511
#SPJ11
Solve the following equation:9-6x=3
Answers
We are given that,
9 - 6x = 3
In this equation, we have to find the value of 'x'. '
It can be calculated by separating the values of x at one side and constants at the other side.
Therefore, we can re-write this equation as:
9 - 6x = 3
or
- 6x = 3 - 9
-6x = -12
Multiplying both sides by (-1), we get
-1 * (-6x) = -1 * -12
6x = 12
x = 12/6
or
x = 2
Hence, the value of x would be 2.
Help me please. If you help me you will get 100 point on my next question
Answers
Hope I helped :)
If S is a non-empty subset of R^n such that any linear combination of vectors in S is again a vector in S, then S is a subspace of R^n
Answers
Any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.
Given that S is a non-empty subset of Rⁿ such that any linear combination of vectors in S is again a vector in S. Therefore, to prove that S is a subspace of Rⁿ, we have to show that S satisfies three conditions. These conditions are as follows;
The condition for being a subspace of Rⁿ
Firstly, a subspace must be closed under addition. In other words, if x and y are any two vectors in S, then their sum x + y must be in S.
Secondly, a subspace must be closed under scalar multiplication. In other words, if x is any vector in S and c is any scalar, then cx must be in S.
Finally, a subspace must contain the zero vector, denoted by 0.S is a subspace of Rⁿ
From the conditions mentioned above, we can show that S is indeed a subspace of Rⁿ, since S satisfies all the required conditions.
Therefore, we can say that any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.
To know more about subset, click here
https://brainly.com/question/31739353
#SPJ11
Your team scores 10 points in the first game, 3 points in the second game, 2 points in the third game, 5 points in the fourth game, and 0 points in the fifth game. What was the mean number of points your team scored for all 5 games?
Answers
The mean number of points for all 5 games is 4 points.
What is arithmetic mean?The arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean.
The formula for the mean of a given set of data is as follows:
Mean = Sum of Observations/Total number of observations
As per the question,
Here, n = 5
⇒ ∑x = Sum of Observations
⇒ ∑x = 10 + 3 + 2 + 5 + 0 = 20
Mean = ∑x/n
Mean = 20/5
Mean = 4
Hence, the mean of the given data is 4.
Learn more about Arithmetic means here:
brainly.com/question/13000783
#SPJ1
A jeweler is making 15 identical gold necklaces from 30 ounces of a gold alloy that costs $275 per ounce. What is the cost of the gold alloy in each necklace?
Answers
Answer: $550/necklace
Step-by-step explanation:
2 oz per necklace
2 x 275 =550
PLEASE PLEASE PLEASE HELP! I'M SO CONFUSED
which of the equations has no solution?
a) 3x + 1 = 5
b)2 x = 2
c)x + 5 = x + 3
d) x = 0
Answers
Answer:
C))x + 5 = x + 3
Step-by-step explanation:
here its given that x + 5 = x + 3
so x - x = 5 -3
0 = 2
that doesn't make a sense . so this equation doesn't exist
a)3x + 1 = 5
3x = 4
x = 4/3
b)2 x = 2
x = 1
d) x = 0
Given: tangent
If m 1 = 30° and m = 20°, then m =
10
40
80
Answers
Answer:
80
Step-by-step explanation:
took the test
hello brainly team
I need help
Answers
Ratio remains same
\(\\ \sf\Rrightarrow \dfrac{x}{16}=\dfrac{9}{12}\)
\(\\ \sf\Rrightarrow \dfrac{x}{16}=\dfrac{3}{4}\)
\(\\ \sf\Rrightarrow 4x=48\)
\(\\ \sf\Rrightarrow x=12\)
#2
\(\\ \sf\Rrightarrow \dfrac{4}{10}=\dfrac{6}{x}\)
\(\\ \sf\Rrightarrow \dfrac{2}{5}=\dfrac{6}{x}\)
\(\\ \sf\Rrightarrow 2x=30\)
\(\\ \sf\Rrightarrow x=15\)
x=12
Explanation:\(\frac{x}{16}=\frac{9}{12}\)
\(x=12\)
Question #2 Answer:See the parsing
Explanation:\((x+6)^2={10}^2+x^2\)
\(x^2+12x+36=100+\lambda^2\)
\(12x=64\)
\(x=\frac{16}{3}\)
{\(theorem\)
I hope this helps you
:)
Deone's length was 19.5 inches at birth. Assuming his development proceeds normally, his length should be about ______ inches by his first birthday.
Answers
Deone's length was 19.5 inches at birth. Assuming his development proceeds normally, his length should be about 29.5 inches by his first birthday.
We know that According to the Centers for Disease Control and Prevention (CDC), the average length for a boy at birth is around 20 inches, and the average length for a boy at one year of age is around 30 inches.
To estimate Deone's length at one year of age, we use the average growth rate between birth and one year, which is approximately 10 inches.
So , we add 10 inches to Deone's length at birth of 19.5 inches to estimate his length at one year of age:
⇒ Estimated length at 1 year = 19.5 inches + 10 inches = 29.5 inches
Therefore, Deone's length should be about 29.5 inches by his first birthday, assuming that his development proceeds normally.
Learn more about Normal Growth here
https://brainly.com/question/14455772
#SPJ4
Help please I will give you the brainliest
Answers
Answer:
Step-by-step explanation:
The answer is 570 because if you multiply 38 times 15 = 570 so it is 570. Thank you for answering to hope this helps you if you need more help contact me!
Answer:
$5.70
Step-by-step explanation:
Since it is 15% to make it a decimal you would move the decimal 2 places to the left to make it 0.15 and then multiply like this 38(.15) which is 5.7. So, shipping and handling is $5.70.
A landscaper is designing a display of flowers for an area in a public park. The flower seeds will be planted at points that lie on a circle that has a diameter of 8 feet. the point where any seed is planted must be 2 feet away from the seeds on either side of it. what is the maximum number of flower seeds that can be planted using the design?
after planting the flower seeds the landscaper has 20 seeds left over. the landscaper wants to plant all of the remaining seeds in another circle so that the seeds are 2 feet apart. what is the diameter of the smallest circle that the landscaper can use to plant all of the remaining seeds?
Answers
The z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.
The z-score for P(z ≥ ?) = 0.30 is approximately -0.52.
How to find the Z score
P(Z ≤ z) = 0.60
We can use a standard normal distribution table or a calculator to find that the z-score corresponding to a cumulative probability of 0.60 is approximately 0.25.
Therefore, the z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.
For the second question:
We want to find the z-score such that the area under the standard normal distribution curve to the right of z is 0.30. In other words:
P(Z ≥ z) = 0.30
Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative probability of 0.30 is approximately -0.52 (since we want the area to the right of z, we take the negative of the z-score).
Therefore, the z-score for P(z ≥ ?) = 0.30 is approximately -0.52.
Read more on Z score here: brainly.com/question/25638875
#SPJ1
please help! is this correct?
Answers
Answer:
yes it is.
Step-by-step explanation:
Answer:
A)113cm^2
Step-by-step explanation:
Are my answers correct?
Answers
Answer:
Yes they are both correct.
Step-by-step explanation:
yes they are both correct.
jaun painted 4 portraits in 20 minutes. at that rate how many would he paint in 3 hours
Answers
Answer:
36 portraits
Step-by-step explanation:
4 portraits per 20 minutes. 20 minutes x 9= 3 hours. 9x4 portraits=36 portraits.
Answer:
48 portraits
Step-by-step explanation:
He can do 4 in 20 minutes. So, first figure out how many he can do in an hour. That's another 40 minutes. 40 minutes he does 8 portraits. So, 8 portraits plus 4 portraits is 16. That's one hour of painting. 16 portraits times 3 is 48, which is the amount he would paint in three hours.