A woman entering an outside glass elevator on the ground floor of a hotel glances up to the top of the building across the street and notices that the angle of elevation is 51°. she rides the elevator up three floors (60 feet) and finds that the angle of elevation to the top of the building across the street is 34°. how tall is the building across the street? (round to the nearest foot.)
Using trigonometric functions, specifically the tangent function, we create two equations corresponding to two right triangles formed by the lines of sight from the ground floor and from 60 feet high in the elevator. Solving those equations simultaneously, we can calculate that the height of the building across the street is approximately 149 feet.
Explanation:This is a trigonometry problem where we're going to establish two right triangles with the elevator as one side, the building across the street as another (the one we're trying to find), and the line of sight as the hypotenuse. From the ground, we form a triangle with the angle of elevation of 51 degrees. Then from 60 feet above the ground, we form another triangle with an angle of elevation of 34 degrees.
Here, we apply tangent of an angle which equals the opposite over adjacent sides in a right triangle. So, we get tan(51) = h/x and tan(34) = (h-60)/x. We have two unknowns here: 'h' which is the height of the building and 'x' the distance from the elevator to the building. Solving these equations simultaneously, we can find 'h'.
If we solve these equations, we'll get 'h' equals approximately 149 feet (rounding to the nearest foot). So, the building across the street is around 149 feet tall.
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if the trapezoid below is reflected across the x axis what are the coordinates of B
If the coordinate B is reflected over x-axis, the resulting coordinate will be (5, -9)
Reflection of imageIf an image is reflected over the x-axis, the resulting coordinate will be (x, -y). The reflections shows the mirror image of a figure.
Given the coordinate B before reflection as (5, 9)> If the coordinate is reflected over x-axis, the resulting coordinate will be (5, -9)
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Betty has 10 more dimes than quarters. If she has $3.45, how many coins does she have?
d = dimes
q = quarters
d=10+q
0.25q +0.10d = 3.45
0.25q + 0.10(10+q) = 3.45
0.25q + 1 +0.10q =3.45
0.35q=2.45
q = 2.45/0.35 = 7
d = 10+7 =17
0.25*7=1.75, 17*0.10 = 1.70, 1.75+1.70 = 3.45
she has 7 quarters and 17 dimes for a total of 24 coins
If BC = 5 and CD = 26, find AC.
Answer:
[tex]AC=\sqrt{130}[/tex]
Step-by-step explanation:
AC is the geometric mean. Solve it using this proportion:
[tex]\frac{BC}{AC}=\frac{AC}{CD}[/tex]
Now fill in the values we know:
[tex]\frac{5}{AC}=\frac{AC}{26}[/tex]
Cross multiply to get
[tex](AC)^2=130[/tex]
That means that
AC = [tex]\sqrt{130}[/tex], which, in decimal form is
AC = 11.40175425
In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = -x2 -6. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).
Select the assumption necessary to start an indirect proof of the statement. If 3a+7 < 28, then a<7.
Are the lines parallel, perpendicular, or neither?
5x + 2y = 10
15x + 4y = -4
Peter bought an antique piece of furniture in 2000 for $10,000. Experts estimate that its value will increase by 12.12% each year. Identify the function that represents its value. Does the function represent growth or decay?
A) V(t) = 10000(1.1212)t; growth
B) V(t) = 10000(0.8788)t; decay
C) V(t) = 10000(1.1212)t; decay
D) V(t) = 10000(0.8788)t; growth
what is larger 0.0013 or 0.02
Write log(x^2-9)-log(x+3) as a single logarithm.
Answer:
b edge
Step-by-step explanation:
PLEASE HELP!! IMAGE ATTACHED find the measure of angle 2
the figure is an equilateral triangle, which all angles are 60 degrees
angle 3 divides a 60 degree angle in half so angle 3 = 30 degrees
the base is a right triangle which is 90 degrees
90+30 = 120
180-120 = 60
Angle 2 is 60 degrees
Given a soda can with a volume of 21 and a diameter of 6, what is the volume of a cone that fits perfectly inside the soda can? (Hint: only enter numerals in the answer blank).
Answer:
Volume of the cone = 7 unit³
Step-by-step explanation:
Soda can has the shape of a cylinder.
Volume of soda can = πr²h
where r = [tex]\frac{6}{2}=3[/tex] units
and volume = 21 unit³
We put the values in the formula to get the value of h.
21 = πr²h
[tex]h=\frac{21}{\pi r^{2} }[/tex]
Now If we fit a cone inside the can, radius of the cone will be equal to the radius of the cylinder and height of the cylinder will be equal to the height of the cone fit inside.
By the formula of volume of cone
Volume = [tex]\frac{1}{3}\pi r^{2}h[/tex]
= [tex]\frac{1}{3}\pi r^{2}( \frac{21}{\pi r^{2} })[/tex]
= [tex]\frac{21}{3}=7[/tex] units³
Volume of the cone is 7 unit³
The vertical ______ of the function secant are determined by the points that are not in the domain.
Which translation will change figure ABCD to figure A'B'C'D'?
A. 7 units left and 6 units up
B. 6 units left and 7 units up
C. 7 units left and 5 units up
D. 5 units left and 7 units up
A carnival ride is in the shape of a wheel with a radius of 20 feet. The wheel has 16 cars attached to the center of the wheel. What is the central angle, arc length, and area of a sector between any two cars? Round answers to the nearest hundredth if applicable. You must show all work and calculations to receive credit.
Refer to the diagram shown below, which shows two of 16 equally-spaced cars attached to the center of the wheel.
The total central angle around the wheel is 2π.
Therefore the central angle between two cars is
(2π)/16 = π/8 = 0.39 radians (nearest hundredth)
The arc length between two cars is
s = (20 ft)*(π/8 radians) = 2.5π = 7.85 ft (nearest hundredth)
The area of a sector formed by two cars is
(1/16)*(π*20²) = 78.54 ft² (nearest hundredth)
Answers: (to the nearest hundredth)
Between two cars,
Central angle = 0.39 radians (or 71.4°)
Arc length = 7.85 ft
Area of a sector = 78.54 ft²
a number diminished by 2 is 6
Which of the following relations represent a function? {(1,-3),(-2,0),(1,4)} {(-2,0),(3,0),(-2,1)} {(3,-8),(-2,0),(4,1)} {(4,12),(4,13),(-4,14)}
To determine if a relation is a function, check for repeated x-values. The relations that represent a function are {(1,-3),(-2,0),(1,4)} and {(3,-8),(-2,0),(4,1)}.
Explanation:In order for a relation to represent a function, each input (x-value) must correspond to exactly one output (y-value). We can determine if a relation is a function by checking for any repeated x-values. If there are no repeated x-values, then the relation is a function. Let's apply this to the given relations:
The relation {(1,-3),(-2,0),(1,4)} represents a function because each x-value is unique.
The relation {(-2,0),(3,0),(-2,1)} does not represent a function because there is a repeated x-value (-2).
The relation {(3,-8),(-2,0),(4,1)} represents a function because each x-value is unique.
The relation {(4,12),(4,13),(-4,14)} does not represent a function because there is a repeated x-value (4).
So, the relations that represent a function are {(1,-3),(-2,0),(1,4)} and {(3,-8),(-2,0),(4,1)}.
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7+2[3(x+1) -2 (3x-1)]
A particular metal alloy a has 20% iron and another alloy b contains 60% iron. how many kilograms of each alloy should be combined to create 80 kg of a 52% iron alloy?
The area of the rectangular playground enclosure at Happy Times Nursery School is 600 meters. The length of the playground is 25 meters longer than the width. Find the dimensions of the playground. Use an algebraic solution.
The solution would be like this for this specific problem:
Area = L * W = 600
Length = W + 25
Substitute and solve for "W":
(W + 25)W = 600
w^2 + 25w - 500 = 0
(w - 15) (w + 40) = 0
Positive solution:
Width = 15 meters
Length = 15 + 25 = 40 meters
So, the dimensions of the playground using an algebraic solution is 15 meters by 40 meters.
To add, the minimum number of coordinates needed to specify any point within it is the informal definition of the dimension of a mathematical space.
At a particular music store, CDs are on sale at $13.00 for the first one purchased and $10.00 for each additional disc purchased. Maria spends $83.00 on CDs. How many CDs has Maria purchased
Answer:
Maria purchased total 8 CDs.
Step-by-step explanation:
At a particular music store, CDs are on sale at $13.00 for the first one purchased and $10.00 for each additional disc purchased.
Maria spends = $83.00
She purchased her first CD for = $13.00
Now balance of her charge = 83.00 - 13.00 = $70.00
other CDs are purchased for $10.00
Therefore, 70.00 ÷ 10.00 = 7 CDs
Total CDs = 7 + 1 = 8 CDs
Maria purchased total 8 CDs.
Write a possible function rule for the following sequence.
11, 15, 19, 23, 27, ...
a(n)=?
if you subtract 23.47 km from 560.589 km, how many significant digits would your answer have?
Three consecutive integers have a sum of 234. What are the three integers?
There are 6 performers who will present their comedy acts this weekend at a comedy club. one of the performers insists on being the last? stand-up comic of the evening. if this? performer's request is? granted, how many different ways are there to schedule the? appearances
since the 6th comic will be last you need to know how many different ways to schedule 5 comics
5x4x3x2 = 120
there are 120 different ways.
How do I set up this equation and solve ?
angles in a triangle need to equal 180 degrees
so x = 180 - 47 - 58
x = 180-105
x= 75 degrees
In a zoo, there are 3 male penguins for every 4 female penguins. What is the ratio of females to the total number of penguins at the zoo? 4 to 7 3 to 7 4 to 3 4 to 1
Final answer:
The correct answer is a ratio of 4 to 7, representing the ratio of female penguins to the total number of penguins in the zoo.
Explanation:
We're given that there are 3 male penguins for every 4 female penguins in a zoo.
To find the ratio of females to the total number of penguins, we first have to add up the total number of penguins, which is 3 males + 4 females = 7 penguins in total.
Now, we can express the ratio of females to the total number of penguins. There are 4 females out of 7 total penguins, so the ratio is 4 females to 7 penguins in total.
Therefore, the correct answer to the student's question is 4 to 7.
I NEED THIS ANSWER
Which linear inequality is represented by the graph?
y > 2x + 3
y < 2x + 3
y > −2x + 3
y < −2x + 3
3!3! = 362,880 81 36
The cosine of the angle is 4/5
The cotangent of the angle is [tex]\(\frac{4}{3}\).[/tex]
In triangle ABC, where angle ABC is a right angle (90 degrees) and sides AB, BC, and AC are given as 6, 8, and 10 units respectively, we can use the cosine and cotangent functions to find the cotangent of angle ABC.
The cosine of an angle in a right-angled triangle is defined as the ratio of the adjacent side to the hypotenuse.
In this case,[tex]\(\cos(\angle ABC) = \frac{BC}{AC} = \frac{8}{10} = \frac{4}{5}\).[/tex]
The cotangent [tex](\(\cot\))[/tex] of an angle is the reciprocal of the tangent (tan).
The tangent is the ratio of the opposite side to the adjacent side.
Therefore,[tex]\(\cot(\angle ABC) = \frac{1}{\tan(\angle ABC)}\).[/tex]
Since [tex]\(\tan(\angle ABC) = \frac{AB}{BC} = \frac{6}{8} = \frac{3}{4}\)[/tex], we can find the cotangent:
[tex]\[ \cot(\angle ABC) = \frac{1}{\tan(\angle ABC)} = \frac{1}{\frac{3}{4}} = \frac{4}{3} \][/tex]
Therefore, the cotangent of the angle is [tex]\(\frac{4}{3}\).[/tex]
The probable question may be:
The cosine of a certain angle is 4/5. What is the cotangent of the angle?
In triangle ABC , Angle ABC=90 degree, AB=6, BC=8 AC=10
Final answer:
The cosine of an angle being 4/5 means that the ratio of the adjacent side to the hypotenuse in a right triangle is 4/5.
Explanation:
The given question states that the cosine of an angle is 4/5. In trigonometry, the cosine function is defined as the ratio of the adjacent side to the hypotenuse in a right triangle. So, if we have a right triangle with an angle A, and the cosine of A is 4/5, it means that the ratio of the length of the adjacent side to the hypotenuse is 4/5.
Thus, we can say that if the length of the adjacent side is 4 units, then the length of the hypotenuse would be 5 units, assuming the units are consistent. This relationship holds true for any right triangle with an angle whose cosine is 4/5.
For example, if we have a right triangle with an adjacent side of 8 units, then the hypotenuse would be 10 units.