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).
a. what is the length y
b. find out the area of the shaded part
The value of length y is,
y = 4 cm
And, The area of the shaded part is, 20 cm²
We have to given that;
A figure is shown in image.
Hence, We get;
The value of y is,
y = 4 cm
And, The area of the shaded part is,
⇒ 4 × 5
⇒ 20 cm²
Thus, The value of length y is,
y = 4 cm
And, The area of the shaded part is, 20 cm²
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solve for x line LK is 59; line LM no measurement; line MK no measurement; angle L is 90 degrees and angle K is 58 degrees
The value of x which I suppose is the angle M is calculated to be 32°
Calculation of angles in a triangleIn a right-angled triangle KLM, it is a known fact that the sum of the three angles in any triangle is 180°.
Since angle L is a right angle and has a measure of 90°, we can find angle M by subtracting the sum of angles K and L from 180°.
Thus,
angle M = 180° - angle K - angle L
= 180° - 58° - 90°
= 32°
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A fireworks mortar is launched straight upward from a pool deck platform 6 m off the ground at an initial velocity of 48 m/sec.
The height of the mortar can be modeled by h(t)=-4.9t^2+48t+6, where h(t) is the height in meters and t is the time in seconds after launch. What is the maximum height? Round to the nearest meter.
Check the picture below.
so the maximum height will occur at its vertex y-coordinate.
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-4.9}t^2\stackrel{\stackrel{b}{\downarrow }}{+48}t\stackrel{\stackrel{c}{\downarrow }}{+6} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 48}{2(-4.9)}~~~~ ,~~~~ 6-\cfrac{ (48)^2}{4(-4.9)}\right) \implies \left( - \cfrac{ 48 }{ -9.8 }~~,~~6 - \cfrac{ 2304 }{ -19.6 } \right)[/tex]
[tex]\left( \cfrac{ 48 }{ 9.8 } ~~~~ ,~~~~ 6 +\cfrac{ 2304 }{ 19.6 } \right) ~~ \approx ~~ (4.89~~,~~\text{\LARGE 124})[/tex]
Question 1 (Multiple Choice Worth 6 points)
(02.08 MC)
The table of values forms a quadratic function f(x)
x f(x)
-5-28
-40
-3 20
-2 32
-1 36
0 32
1 20
What is the equation that represents f(x)?
Of(x)=x²-2x+8
Otx) = 4x² + 8x-32
Of(x)=x²+2x-8
Of(x)=-4x2²-8x+32
Answer:
The answer to this question is --> f(x) = -4x^2-8x+32
Hope this helps
help please, math question Calculate the perimeter
The Perimeter of the given figure rectangle will be 60m. The correct option is 1.
Perimeter refers to the total length of the boundary of a two-dimensional shape or object. It is the distance around the edge of a shape. To find the perimeter of a shape, you add up the lengths of all its sides.
The perimeter of a rectangle is given by the formula:
P = 2(l + w)
where P is the perimeter, l is the length, and w is the width.
Using the values you provided, we can substitute them into the formula:
P = 2(18 + 12) = 2(30) = 60 meters
Therefore, the perimeter of the rectangle with a length of 18 meters and a height of 12 meters is 60 meters.
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IXL PLEASE HURRY FAST
The triangles are not similar. Triangle EFG and Triangle QRS are not similar. ΔEFG not ~ ΔQRS
Similar triangles: Determining if the triangles are similarFrom the question, we are to determine if the given triangles are similar
From one of Triangle similarity theorems, AA (or AAA) or Angle-Angle Similarity theorem.
The Angle-Angle similarity theorem states that If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other
In the given diagram,
In triangle EFG
m ∠E = 104°
m ∠F = 45°
m ∠G = 180° - (104° + 45°) = 31°
In triangle QRS
m ∠R = 100°
m ∠Q = 45°
m ∠S = 180° - (100° + 45°) = 35°
Since no two angles of one of the triangles are equal to any two angles of other triangle, the triangles are not similar
Hence,
ΔEFG not ~ ΔQRS
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find the surface area of the pyramid. round to the nearest whole number. a=20 b=20 c=7 d=7
Answer:
569 square units
Step-by-step explanation:
You want the surface area of the 8-sided shape that has a square "base" 7 units on a side, and a "height" of 20 units.
Slant heightThe slant height of each triangular face is the hypotenuse of a right triangle with legs 7/2 units and 20 units. That height is ...
h = √(3.5² +20²) = √412.25 ≈ 20.304 units
Surface areaThe area of one triangular face is ...
A = 1/2bh
A = 1/2(7)(20.304) . . . one face
There area 8 congruent triangular faces, so the total area is ...
A = 8(1/2)(7)(20.304) = 8(7)√412.25 ≈ 568.51 ≈ 569
The total surface area is about 569 square units.
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Jennifer has watched 40 minutes of a movie, which is 20% of the movie. What
is the total length in minutes of the movie?But is not 210
Answer: 200
Step-by-step explanation: 20% of 200 is 40
Answer:
200
Step-by-step explanation:
Since 20% of the movie is equal to 40 minutes of the entire movie, simply just keep adding 40 repeatedly until you hit 100%.
40+40+40+40+40=200
^ ^ ^ ^ ^
20+20+20+20+20=100
Which of the following expressions are equivalent to the expression below? 8 x + 32 y 4 ( 4 x + 8 y ) − 2 ( 4 x ) 8 ( x + 4 y ) ( 2 x + 12 y ) + ( 6 x + 18 y )
The expressions that are equivalent to the expression 8x + 32y are:
4(4 x + 8y) − 2(4x)
8(x + 4y)
How to write equivalent expressions?Equivalent expressions are expressions that work the same even though they look different.
If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s).
Let's simply the options to see if they are equivalent to the expression 8x + 32y:
4(4 x + 8y) − 2(4x) = 16x + 32y - 8x
= 8x + 32y
8(x + 4y) = 8x + 32y
(2x + 12y) + (6x + 18y) = 2x + 6x + 12y + 18y
= 8x + 30y
Therefore, only 4(4 x + 8y) − 2(4x) and 8(x + 4y) are equivalent to the expression below.
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Complete Question
Which of the following expressions are equivalent to the expression below?
8x + 32y
4(4 x + 8y) − 2(4x)
8(x + 4y)
(2x + 12y) + (6x + 18y)
What is 0.3 x 0.5? Show me work
Answer: 0.15
I don't really know how to show you work on here but you can think about it like this. if 5 x 3 is 15, and if there is a decimal like 0.3 x 0.5 it would result in the answer getting smaller as you're multiplying decimals if that makes sense... so it would result in the answer being 0.15. Sorry if it wasn't a good explanation.
Please help solve this for me
Answer:
i believe the answer would be option D
Step-by-step explanation:
X + y = 8
If x = -1 what is y?
Answer: 9
Step-by-step explanation:-1 plus 9 equals 8
Answer: y = 9
Step-by-step explanation:
First of all, you right out your equation
x + y = 8
Secondly, you sub in the values you have
-1 + y = 8
Then you can swap your answer and y
-1 + 8 = y
Work out the answer
-1 + 8 = 9
Answer is y = 9
[8 points] Find the y-intercept and graph the equation by
making a table of values with three points,
2) y=-3x+2
SEENE
Answer:
The answer is (0,2) (1,-1) (2,-4)
Step-by-step explanation:
The slope is -3.
Because of this, you go down 3 and to the side 1 (it's also called rise/run).
I REALLY HOPE THIS HELPS!!!!
Need help??? With this question
Answer:
28+36+y=180
64+y=180
y=180-64
y=116°
A restaurant serves a 20 ounce steak. How much does the steak weigh in ponds and ounces?
At age 20, someone sets up an IRA (individual retirement account) with an APR of 5%. At the end of each month he deposits $65 in the account. How much will the IRA contain when
←he
retires at age 65? Compare that amount to the total deposits made over the time period.
After retirement the IRA will contain $ 131,718.42
(Do not round until the final answer. Then round to the nearest cent as needed.)
The total deposits made over the time period is $
(Type a whole number)
CETT
Answer:
total deposits: $35,100
Step-by-step explanation:
You have the value of an annuity earning 5% with payments of $65 a month for 45 years as $131,718.42. You want to know the total value of payments.
Payments12 payments per year of $65 for 45 years will have a total value of ...
12·65·45 = 35100
Total deposits will be $35,100.
This is for math nation unit 1 please help!!
Answer: it’s C, cubic
Step-by-step explanation:
Answer:
[C] Cubic
Step-by-step explanation:
Let find define all the answer choices:
Linear- Straight Line
Quadratic - shape of a U or an upside down U
Cubic - trivalent graphs, are graphs all of whose nodes have degree 3
Exponential- curve that has a horizontal asymptote and it either has an increasing slope or a decreasing
As a result, the graph given is a Cubic graph.
RevyBreeze
The principal P is borrowed at a simple interest rate r for a period of time t. Find the loans future value A or the total amount due at time t
P= 5000
r=4.5%
t = 6 months
The future value or the total amount due at time t for the loan is $5112.50.
To find the future value or the total amount due at time t for a loan with a principal P, a simple interest rate r, and a period of time t, we can use the formula for calculating simple interest;
A=P + (P × r × t)
where; A = future value or total amount due at time t
P = principal amount
r = simple interest rate
t = time period (in years)
Given the values; P = $5000
r = 4.5% (or 0.045 as a decimal)
t = 6 months (or 0.5 years)
We can substitute these values into the formula and calculate the future value;
A = 5000 + (5000 × 0.045 × 0.5)
A = 5000 + 112.5
A = $5112.50
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solve each rational equation. list excluded values
x+4/x+5=6/x^2+10+25
at irvs cycle rental shop irv rents all kinds of cycles: unicycles, tandem bikes, regular bikes, and even tricycles for little kids. he parks all the cycles in front of his shop with a helmet for each rider strapped to the cycles. this morning irv counted 57 helmets and 115 wheels parked in front of his store. he knows he had an equal number of unicycles and tandem bikes. he also knows that he has 32 regular bikes. how many unicycles, tandem bikes, and tricycles does irv have
The number of unicycles, tandem bikes, and tricycles that IRVS Cycle Rental has are:
unicycles - 8 tandem bikes - 8 tricycles - 9 How to find the items the shop has ?The relevant equations, ( assuming that unicycles as U, tandem bikes as T, and tricycles as R ) are:
U + T + 32 + R = 57
U + 2T + 2 x 32 + 3R = 115
U = T
Using substitution, we get:
U + 2T + 64 + 3R = 115
U + 2T + 3R = 51
U + 2U + 3R = 51
3U + 3R = 51
Solving gives:
2U + R = 25
U + R = 17
U = 8
Solving for R, we have :
8 + R = 17
R = 17 - 8
R = 9
U and T are the same so T is 8 as well.
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(Time limit) Tell if the graph is a function or not.
Give me the domain and range.
The graph is a function: yes.
The domain of this function is: x ≥ -3.
The range of this function: all real numbers.
What is a range?In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain.
Furthermore, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left-hand side of the graph to the right-hand side.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-3, ∞}, x ≥ -3, or -3 ≤ x ≤ ∞.
Range = {-∞, ∞} or all real numbers.
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For the ordered stem-and-leaf plot given, find:
a. the minimum value
b. the maximum value
c. the number of data with values greater than 25.
d. the number of data with values of at least 40.
e. the percentage of the data with value less than 15.
From a stem-and-leaf plot,
1. The minimum value = 13
2. The maximum value = 62
3. The number of data with values greater than 25 = 16
4. The number of data with values of at least 40 = 4
5. The percentage of the data with value less than 15 = 6.25%
We know that on a stem and leaf plot, the minimum is the first value and the maximum is the last value.
From the stem-and-leaf plot,
a) the minimum value is 13
b) the maximum value is 62
c) the number of data with values greater than 25:
26, 27, 28, 28, 31, 31, 32, 34, 34, 35, 38, 39, 42, 43, 47, 62
So, the number of data with values greater than 25 = 16
d) the number of data with values of at least 40:
42, 43, 47, 62
So, the required number = 4
e) the percentage of the data with value less than 15:
the data with values less than 15 are: 13, 14
So, the number of the data with values less than 15 are: 2
The total number of data values = 32
So, the required percentage would be,
P = (2/32) × 100
P = 6.25%
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HELP ME PLEASE PICTURE INCLUDED
Answer:
0.67 million miles per day
Step-by-step explanation:
You want the average rate of change of the function d(t) = ∛(6t²) on the interval [4, 8], where d is in millions of miles, and t is in days.
Average rate of changeThe average rate of change of the function on the interval [a, b] is given by ...
rate of change = (d(b) -d(a))/(b -a)
As the table in the attachment shows, this is approximately ...
rate of change = (7.268 -4.579)/(8 -4) ≈ 0.67
The average rate of change on the interval 4 ≤ t ≤ 8 is about 0.67 million miles per day.
__
Additional comment
Mercury has an orbit of about 88 days at a distance of roughly 36 million miles from the Sun. Already at that distance, the General Theory of Relativity comes into play, making predictions from Newtonian physics somewhat problematic. It is unlikely this formula has any relation to reality for t much less than 200.
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Solve the trigonometric equation for all values 0 <= x < 2pi
sin^2 x -1 = 0
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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1. Quadrilateral LBMN is the result of a 180 degree rotation of Quadrilateral ABCD around point B, write the corresponding angles and segments in the table below.
In the quadrilateral ABCD and LBNM the corresponding angles and line segments are as follow,
∠A = ∠L, ∠D =∠M , ∠C = ∠N , and
AB = LB , CD = NM , DA = ML.
Quadrilateral ABCD rotates 180 degrees around point B,
New quadrilateral formed named LBMN
The corresponding angle after rotation of 180 degrees around B is equals to,
B remain at same position.
A rotates and point L take the position of A.
D rotates and point M take the position of D.
C rotates and point N take the position of C.
Corresponding angle to A is angle L.
Corresponding angle to D is angle M.
Corresponding angle to C is angle N.
Similarly corresponding segments are of ABCD and LBNM are
Line segment AB corresponds to line segment LB.
Line segment CD corresponds to line segment NM
Line segment DA corresponds to line segment ML.
Therefore, in the quadrilateral the corresponding angles and line segments are ∠A = ∠L, ∠D =∠M , ∠C = ∠N , AB = LB , CD = NM , and DA = ML.
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Select the correct answer.
What is the simplest form of this expression?
(2x-3)(3x²+2x-1)
O A 6x³-5x²²-8x+3
OB. 6x³-5x² - 6x + 2
OC. 6x³-9x² - 4x +3
OD. 6x³-2²-8x+3
The simplest form of the expression (2x-3)(3x²+2x-1) is 6x³ - 5x² - 8x + 3.
What is the simplest form of this expression?Given the expression in the question:
( 2x - 3 )( 3x² + 2x - 1 )
To simplify the expression (2x-3)(3x²+2x-1), we need to use the distributive property of multiplication,
which states that: a(b+c) = ab + ac
Using this property, we can expand the expression as follows:
(2x-3)(3x²+2x-1)
2x(3x²+2x-1) - 3(3x²+2x-1)
6x³ + 4x² - 2x - 9x² - 6x + 3
Add like terms
= 6x³ - 5x² - 8x + 3
Therefore, the simplest form is 6x³ - 5x² - 8x + 3.
Option A) 6x³ - 5x² - 8x + 3 is the correct answer.
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Michel-Eugène Chevreul found that the greatest intensity came from placing ________colors next to each other.
tertirary
analogous
complementary
arbitrary
Answer:
C. complementary
Michel-Eugène Chevreul discovered that placing complementary colors next to each other can create the greatest contrast and vibrancy in color perception. This is because complementary colors are located opposite each other on the color wheel and, when placed side by side, they enhance each other and create a strong visual impact. For example, placing yellow next to violet or blue next to orange can create a dynamic and eye-catching effect. In contrast, placing tertiary colors (colors made by mixing primary and secondary colors) or arbitrary colors next to each other may not create as much contrast or visual interest. Overall, understanding color theory and the relationships between different colors can be helpful for creating visually appealing designs, artworks, or other color-based projects.
rancher wants to enclose a rectangular plot of land, but have a divider in the middle. There is 240 feet of fencing available. What dimension will produce the largest area the rancher can make? What is the max area? Dimensions: __________________ Area:___________ --------------------------------------------------------------------------------------------------------- 2. (10 points) From a thin square piece of cardboard 20 in. per side, square corners (x) are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Dimensions: __________________ Volume:___________ ----------------------------------------------------------------------------------------------------------- 3. (10 points) During a recent oil spill in the gulf, the radius of the spill was increasing at a rate of 10 feet per second. How fast is the circular area of the spill increasing at the moment that the radius is 80 feet? dA = dt __________
The solution is the two dimensions will be 2121.32 by 1414.2.
Here, we have,
let X and Y be the two dimensions.
Area will be X times Y.
XY = 3000000
Y = 3000000 / X
Perimeter = 2x + 3y
substituting the values:
Perimeter = 2x + 3*3000000 / x
= 2x + 9000000 / x
so, we get,
2 = 9000000 / x^2
x^2 = 9000000 / 2 = 4500000
x = sqrt(4,500,000)
= 2121.32
= 1000 sqrt (4.5)
y = 3000000 / 2121.32
= 1414.2
= 1000 sqrt(2)
so the dimensions will be 2121.32 by 1414.2 .
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complete question:
A rancher wants to fence in an area of 3000000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?
Find the remainder when f(x) is divided by x-k, ( SYNTHETIC DIVISION)
[tex]f(x)=2x^3 +5x^2 -12x ; k=-1[/tex]
Explain well, please.
Answer:
15
Step-by-step explanation:
You want the remainder from division of f(x) = 2x³ +5x² -12x by x -(-1).
Synthetic divisionThe table used for synthetic division is built by listing the zero of the divisor at upper left, and the coefficients of the polynomial across the top to the right of that. They are listed in order of decreasing degree, with any necessary zero coefficients put in the appropriate place(s).
The attachment shows the table and the instructions for filling it out. The value at the bottom in the rightmost column is the remainder from the division.
The remainder theorem tells you that is also the value of the function for x = k.
The remainder from f(x) ÷ (x +1) is 15.
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