Two towers face each other separated by a distance = 15 m. As seen from the top of the first tower, the angle of depression of the second tower’s base is 60° and that of the top is 30°. What is the height (in meters) of the second tower?
Answers
Answer:
Height of second tower = 17.32m
Step-by-step explanation:
I have attached a diagram depicting the question.
From the diagram, The first tower is depicted by side AEB and the second tower CD.
While d is the distance that separates the two towers and it's given as 15m.
Now, since the angle of depression of the second tower’s base is 60°, then for triangle BAC. Angle C = 60°.
Thus; using trigonometric ratios;
tan 60° = AB/AC.
This gives; AB = d*tan 60°
Similarly, for the triangle BED, BE = d*tan 30°
Since, AE = CD, thus ;
CD = AB − BE
CD = d (tan 60° − tan 30°)
CD = 15(1.7321 − 0.5774)
CD = 15 × 1.1547
CD ≈ 17.32 m.
So, height of second tower = 17.32 m
Related Questions
If f(x)=x^3 and g(x) = 2x+7, what is g(x) when x =2
Answers
Answer:
g(2)=11
Step-by-step explanation:
We want to find g(x), or y, when x is equal to 2. We have the equation:
g(x)=2x+7
We know that x=2, so we can substitute 2 in for x.
g(2)=2(2)+7
Multiply 2 and 2 first
g(2)=4+7
Add 4 and 7
g(2)=11
Answer:
Yes 11 is the right answer
Step-by-step explanation:
Write an equation that best represents the line
Answers
a man owned 75 shares of stock worth $50 each the corporation declared a dividend of 8% payable in stock how many shares did he then own
Answers
Answer:
81 shares
Step-by-step explanation:
Data provided in the question
Number of shares owned = 75 shares of stock
Per share value = $50
Dividend declared = 8%
Based on the above information. the number of shares owned is
[tex]= Number\ of \ shares\ owned \times dividend\ declared\ percentage + Number\ of \ shares\ owned[/tex][tex]= 75\shares \times 8\% + 75\shares[/tex]
= 81 shares
We simply added the number of shares owned and the number of shares owned after considered the dividend declared percentage so that the correct shares owned could arrive
In how many different ways can a person select one book from 3 novels, one book from 5 biographies and one book from 7 self-help books?
a). 15
b). 105
c). 3
d). 22
Answers
Answer:
[tex] Ways = 3*5*7= 105[/tex]
And that's equivalent to:
[tex] Ways= (3C1) (5C1) (7C1) =3*5*7=105[/tex]
Where C represent the term combinatory defined as:
[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]
And then the number of ways to select the three books are 105, and the best option would be:
b). 105
Step-by-step explanation:
For this case we can use the multplication principle of counting or sometimes called the product rule.
We have a total of 3 novels, 5 biographies and 7 self-help books. And we can find the number of ways that a person can select the three books with theis product:
[tex] Ways = 3*5*7= 105[/tex]
And that's equivalent to:
[tex] Ways= (3C1) (5C1) (7C1) =3*5*7=105[/tex]
Where C represent the term combinatory defined as:
[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]
And then the number of ways to select the three books are 105, and the best option would be:
b). 105
We want to see in how many different ways a person can select one book from 3 novels, one book from 5 biographies and one book from 7 self-help books, the correct option is b: 105.
To get the numbe of different ways, the first thing we need to do is find the selections.
Here we have 3 selections:
Novel selection.Biography selectionSelf-help selection.Now we need to find the number of options for each of these selections, and just multiply the numbers of options.
we have:
Novel selection: 3 optionsBiography selection: 5 optionsSelf-help selection: 7 optionsNumber of different ways of selecting = 3*5*7 = 105
So the correct option is b.
If you want to learn more, you can read:
https://brainly.com/question/3349431
What is the volume of the pyramid?
A solid oblique pyramid has an equilateral triangle as a base
with an edge length of 4/3 cm and an area of 12/3 cm.
O 12/3 cm3
16/3 cm
24/3 cm3
32/3 cm3
Answers
Answer:
16/9 cm³Step-by-step explanation:
Volume of a triangular pyramid = 1/3 * Base area * height
Given the Base area = area of the equilateral triangle = 12/3 cm
Height of the pyramid = length of its edge = 4/3 cm
Substituting this values in the formula we have;
V = 1/3 * 12/3 * 4/3
V = 48/27
V = 16/9 cm³
The volume of the given triangular pyramid is; B: 16/3 cm²
What is the Volume of the Pyramid?
Formula for volume of a triangular pyramid is;
V = ¹/₃ * Base area * height
We are given;
Base area = area of the equilateral triangle = 12 cm²
Height of the pyramid = length of its edge = 4/3 cm
Thus;
V = ¹/₃ * 12 * (4/3)
V = 16/3 cm³
Read more about Volume of Pyramid at; https://brainly.com/question/16203922
Which is not an example of a triangular prism?
Camping tents
Roofs
a shoebox
a skateboard ramp
Answers
Answer:
a shoe box
Step-by-step explanation:
i'm not 100% sure but isn't a shoe box rectangular?
2/9 - 2/15 as a fraction in lowest terms
Answers
The numerator and the denominator have no common prime factors.
Their prime factorization:
2 is a prime number;
9 = 32;
Convert the angle θ = 3 π 5 θ= 5 3π theta, equals, start fraction, 3, pi, divided by, 5, end fraction radians to degrees.
Answers
Answer: 3pi/5 and 5/3pi?
Step-by-step explanation:
Answer:
Step-by-step explanation:
3pi/5 * 180/pi
3/5 * 180/1
3/1 * 36
3*36
108 degrees
5/3pi * pi/180
5/3 * 1/180
1/3 * 1/36
1/108
Least multiple of 5 and 25
Answers
Answer:
25
Step-by-step explanation:
25 is a multiple of 5, so is the least multiple of both 5 and 25.
Answer:
Hey there!
That would be 25.
Hope this helps :)
Ty’s experimental probability of winning a certain game is 1/3. Jana’s expiremental probability of winning the same game is 3/4. If Ty and Jana each played the game 120 times, how many more games would Jana expect to win over Ty?
Answers
Answer:
Jana is expected to win 40 more games over Ty.
Step-by-step explanation:
If Ty plays the game 120 times, he is expected to win in 1/3 part of 120 games, which is ( 1/3 * 120 =) 40 games.
If Jana plays the game 120 times, she is expected to win in 2/3 part of 120 games, which is ( 2/3 * 120 =) 80 games.
If Jana is expected to win 80 times an Ty is expected to 40 times, then Jana is expected to win ( 80 - 40 =) 40 more games over Ty.
Write the equation in standard form and then find the center (h, k) and
x^2+8x+ y2 + 4y - 5= 0
Answers
Answer:
Center is at (-4, -2) and the radius = 5.
Step-by-step explanation:
Convert to Standard form:
x^2 + 8x + y2 + 4y - 5= 0
Completing the square:
(x + 4)^2 - 16 + (y + 2)^2 - 4 = 5
(x + 4)^2 + (y + 2)^2 = 5 + 16 + 4
(x + 4)^2 + (y + 2)^2 = 25
(x - h)^2 + (y - k)^2 = r^2 Comparing:-
The center is at (-4, -2) and the radius = 5.
200 students, which was 40% of the 7th graders said that the dress code was an important issue at school. How many students are in the 7th grade?
Answers
Answer:
there are 80 students
Step-by-step explanation:
Get 14 points, Plz help me with this question, and give the right answer cause it's important
Answers
Answer:
D
Step-by-step explanation:
A car manufacturer has a failure rate in their oil gasket of 2%. What is the probability that , of 1200 cars built, 50 will develop a failure in the gasket?
Answers
Answer:
4%
Step-by-step explanation:
Please give me Brainly
Noah paid off a loan with a simple interest rate of 9.7% in 4 months. What was the APR?
29.1%
3.23%
2.43
15.5%
9.7%
Answers
Answer:
9.7% for 4 months = 9.7 * 3 = 29.1% for the year.
Step-by-step explanation:
4 number lines. Graph A goes from 95 to 100. An open circle is at 98 and everything to the right is shaded. Graph B goes from negative 74 to negative 69. An open circle is at negative 72 and everything to the right is shaded. Graph C goes from negative 100 to negative 95. An open circle is at negative 98 and everything to the left is shaded. Graph D goes from negative 74 to negative 69. An open circle is at negative 72 and everything to the left is shaded.
Which graph is the solution to the inequality?
y - 13 > -85
13 < -85 + y
y + 13 < -85
Answers
Answer:
B A C
Step-by-step explanation:
It is what it is
Answer:
4 number lines. Graph A goes from 95 to 100. An open circle is at 98 and everything to the right is shaded. Graph B goes from negative 74 to negative 69. An open circle is at negative 72 and everything to the right is shaded. Graph C goes from negative 100 to negative 95. An open circle is at negative 98 and everything to the left is shaded. Graph D goes from negative 74 to negative 69. An open circle is at negative 72 and everything to the left is shaded.
Which graph is the solution to the inequality?
y - 13 > -85
✔ B13 < -85 + y
✔ Ay + 13 < -85
✔ CStep-by-step explanation: edgunity!
hope this helps! :)
The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years. He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53. The university's record indicates that the mean SAT score for entering students from previous years is 1,520. He wants to find out if his claim is supported by the evidence at a 5% level of significance. Referring to Scenario 9-9, what is the critical value
Answers
Answer:
Step-by-step explanation:
To test the hypothesis is the mean SAT score is less than 1520 at 5% significance level
The nul hypothesis is
[tex]H_0; \mu \geq 1520[/tex]
The alternative hypothesis is
[tex]H_0 ; \mu\leq 1520[/tex]
The test statistic is
[tex]t=\frac{\bar x- \mu}{(\frac{s}{\sqrt{n} } )}[/tex]
[tex]t= \frac{1501-1520}{(\frac{53}{\sqrt{20} } )} \\\\=-1.603[/tex]
The t - test statistics is -1.603
The t - critical value is,
The small size is small and left tail test.
Look in the column headed [tex]\alpha = 0.05[/tex] and the row headed in the t - distribution table by using degree of freedom is,
d.f = n - 1
= 20 - 1
= 19
The t - critical value is -1.729
The conclusion is that the t value corresponds to sample statistics is not fall in the critical region, so the null hypothesis is not rejected at 5% level of significance.
there is insignificance evidence ti indicate that the mean SAT score is less than 1520. The result is not statistically significant
Answer:
Critical value = -1.729
Step by Step explanation:
Given:
n = 20
X' = 1501
Standard deviation = 53
Mean, u = 1520
Level of significance, a = 0.05
The null and alternative hypotheses:
H0 : u = 1520
H1 : u < 1520
This is a lower tailed test.
Degrees of freedom, df = 20 - 1 = 19
For critical value:
[tex]t critical = - t_a, _d_f [/tex]
From t table df = 19, one tailed
[tex]t critical = -t _0._0_5, _1_9 = -1.729[/tex]
Critical value = -1.729
Decision: Reject null hypothesis H0, if test statistic Z, is less than critical value.
Test statistic Z =
[tex] Z = \frac{X' - u}{\sigma / \sqrt{n}} [/tex]
[tex] Z = \frac{1501 - 1520}{53/ \sqrt{20}}= -1.603[/tex]
Z = -1.603
For p-value:
From excel,
P(t< -1.603) = t.dist( -1.603, 19, 1)
= 0.06269
≈ 0.0627
P value = 0.0627
Since test statistic Z, -1.603, is greater than critical value, -1.729, we fail to reject the null hypothesis H0.
There is not enough statistical evidence to conclude that mean is less than 1520.
Let s be the solid obtained by rotating the region shown in the figure about the y-axis (Assume a = 5 and b = 2)
Sketch a typical approximating shell.
What are its circumference c and height h?
c(x) =
h(x) =
Use shells to find the volume V of S.
V =
Answers
Answer:
see attached for a figurec(x) = 2πxh(x) = 5x(x -2)^2V = 32π/3Step-by-step explanation:
The volume is the summation of the volumes of the shells. The volume of a shell is its circumference ...
c(x) = 2πx
multiplied by its height ...
h(x) = 5x(x -2)^2
and its thickness, dx.
That summation is the integral ...
[tex]\displaystyle V=\int^2_0 {2\pi x(5x)(x-2)^2} \, dx=10\pi\int^2_0 {(x^2-2x)^2} \, dx=10\pi\left(\dfrac{2^5}{5}-\dfrac{4(2^4)}{4}+\dfrac{4(2^3)}{3}\right)\\\\\boxed{V=\dfrac{32\pi}{3}}[/tex]
The circumference of the shell is c(x) = 2πx
The height of the shell is [tex]h(x) = 5x(x-2)^{2}[/tex]
The required volume of the shell is [tex]\frac{32\pi}{3}[/tex].
Given that,
S be the solid obtained by rotating the region,
Where, a = 5 and b =2
We have to determine ,
What are its circumference c and height h.
According to the question,
The volume is the summation of the volumes of the shells. The volume of a shell is its circumference ,c(x) = 2πx
And the height of the shell.
[tex]h(x) = 5x(x-2)^{2}[/tex]
The volume of the shell is given by,[tex]V = \int (circumference) \ )(height )\ . dx\\\\[/tex]
Where dx thickness of the shell.
Substitute the value in the equation,
[tex]v = \int\limits^2_0 {2\pi x .(5x) (x-2)^{2} }\, dx\\\\v = \int\limits^2_0 {10\pi x^{2} (x-2)^{^{2}} \ d x\\\\\\v =10\pi \int\limits^2_0 {x^{2}.(x^2+4-4x)} \, dx \\\\V = 10\pi \int\limits^2_0( {x^{4} + 4x^{2} - 4x^{3}) \, dx[/tex]
[tex]v = 10\pi \ [ \dfrac{x^{5}}{5} + \dfrac{4x^{3}}{3} - x^{4}]^{2}_0\\\\v = 10\pi [ \dfrac{2^{5}}{5} + \dfrac{4.2^{3}}{3} - 2^{4} - \dfrac{0^{5}}{5} -\dfrac{4.0^{3}}{3} + 0^{4}]}\\\\v = 10\pi \ [ \dfrac{32}{5} + \dfrac{32}{3} - 16 -0-0+0]\\\\v = 10\pi [\dfrac{96+160-240}{15}]\\\\v = 10\pi [\dfrac{16}{15}]\\\\v = \dfrac{32\pi }{3}[/tex]
Hence, The required volume of the shell is [tex]\dfrac{32\pi}{3}[/tex].
To know more about Integration click the link given below.
https://brainly.com/question/16649904
Please help me ASAP !!!! Will give brainliest!!!!!!
Please Answer the image below.
Answers
Answer:
I think it’s the first and fourth
Step-by-step explanation:
Hope this helps!!!!
The sum of four consecutive integers is -10. What are the integer
Answers
Answer:
see below
Step-by-step explanation:
Let x be the first integer
x+1 is the next integer
x+2 = next integer
x+3 = last integer
The sum of the 4 integers is -10
x+ x+1 + x+2 + x+3 = -10
Combine like terms
4x+6 = -10
Subtract 6 from each side
4x+6-6 = -10-6
4x = -16
Divide each side by 4
4x/4 = -16/4
x = -4
x+1 = -3
x+2 = -2
x+1 =-1
The integers are -4, -3, -2 ,-1
The angle \theta_1θ 1 theta, start subscript, 1, end subscript is located in Quadrant \text{I}Istart text, I, end text, and \cos(\theta_1)=\dfrac{3}{8}cos(θ 1 )= 8 3 cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, start fraction, 3, divided by, 8, end fraction . What is the value of \sin(\theta_1)sin(θ 1 )sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis?
Answers
Answer:
(√55)/8
Step-by-step explanation:
The sine and cosine are related by ...
sin² +cos² = 1
Then the sine of the angle is ...
sin(θ₁) = √(1 -cos(θ₁)²)
sin(θ₁) = √(1 - (3/8)²) = √(55/64)
sin(θ₁) = (√55)/8
Question 2(Multiple Choice Worth 5 points)
(03.09 LC)
What is the default view in a Word document?
O Copy View
O Editing View
O Paste View
O Reading View
Answers
Answer:
EDITING VIEW
Step-by-step explanation:
Please help me!!!!!
Answers
Answer: is answer b
Step-by-step explanation:
Answer: The answer is B
Step-by-step explanation:I did the quiz
Use the drop-down menus to answer the questions.
What is the probability that a randomly chosen tenth-grader is male?
Answers
Answer:
Step-by-step explanation:
The information given is not enough to determine the probability.
Given the number of male tenth-grader, and the number of all tenth-grader, the probability will then be: (number of male tentg-grader) divided by (the total number of students).
Answer:
What is the probability that a randomly chosen tenth-grader is male?
✔ 80/154
What is the probability that a randomly chosen tenth-grader is male given that the tenth-grader prefers geometry?
✔ 47/87
Are the events “male” and “geometry” independent?
✔ no, P(male) does not equal P(male | geometry)
Step-by-step explanation: These are the answers for edge 2020
This test is gonna be the end of me lol
Answers
Answer:
WC
Step-by-step explanation:
What is the volume of a box with length
1 m, width 8 m, and depth 6 m?
Answers
Answer:
Here is the answer mate. Hope it helps. Please rate my answer and mark as brainlist if you find it helpful.
Answer:
[tex] = 48 {m}^{3} [/tex]
Step-by-step explanation:
[tex]volume = l \times w \times b \\ = 1 \times 8 \times 6 \\ = 48 {m}^{3} [/tex]
which list orders the anglesof trangle abc smallest to largest...ab=130 and ac=120 and bc=180
Answers
Answer:
I think goes 130 and then 180 then 120 it's need to be to have an angle i think.
Step-by-step explanation:
Because it's a-c so abc is 120
a-b is 130 and b-c it's gona be 180
I might be wrong but i have 2 answer 120 130 180 or
130 180 120.
What’s the correct answer for this?
Answers
Answer:
2 is the answer according to me
What is the answer to 4 times 1/2
Answers
Answer: your answer is 2
Step-by-step explanation:
Use the graph to estimate the solution of the system.
x + 2y = 5,
-x + 3y = 6
Which integers is the x-value between?
What is the x-value to the nearest tenth?
Which integers is the y-value between?
What is the y-value to the nearest tenth?
Answers
Answer:
x is between 0 and 1
x is almost 0.5
y is between 2 and 3
y is almost 0.2
Answer:
1st answer: 0 and 1
2nd answer: about 0.6
3rd answer: 2 and 3
4th answer: about 2.2
Step-by-step explanation:
I got it correct! Edge 2021:)