Hi! I just wanted to double check and make sure that I worked the question correctly
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Statement Problem: A boat on the river is 700ft from the base of a dam. The dam is 2460ft above water level. Given that someone standing on the boat stands 5ft above water level, what is the angle of elevation from the individual standing on the boat to the top of the dam? State your answer in radian rounded to 4 decimal places.
Solution:
We would represent the information in a diagram as;
Applying the trigonometry ratio for tangent, we have;
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]Thus,
[tex]\begin{gathered} \tan \theta=\frac{2460}{700} \\ \theta=\tan ^{-1}(3.5143) \\ \theta=74.1161^o \end{gathered}[/tex]Now, we would convert the angle from degrees to radians. We have;
[tex]\begin{gathered} 74.1161^o\times\frac{\pi}{180}\text{rad} \\ =1.2936rad \end{gathered}[/tex]
Related Questions
suppose that there are two types of tickets: advanced and same day. advance tickets cost $25 and same day tickets are $30.for one performance there were 65 tickets sold in all. and the total amount paid for them was $1800.how many tickect of each were sold
Answers
The number of advance and same day tickets sold are 25 and 35 respectively.
How many tickect of each were sold?let
number of advance tickets sold = xNumber of same day tickets sold = yx + y = 65
25x + 30y = 1800
From (1)
x = 65 - y
Substitute x = 65 - y into (2)
25x + 30y = 1800
25(65 - y) + 30y = 1800
1625 - 25y + 30y = 1800
5y = 1800 - 1625
5y = 175
y = 175/5
y = 35
Substitute y = 35 into (1)
x + y = 65
x + 35 = 65
x = 65 - 35
x = 25
Therefore, Simultaneous equation is used to determine the number of advance and same day tickets sold.
25 advance tickets and 35 same day tickets were sold.
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8 - Arrange from LEAST to GREATEST without the use of a calculator
Answers
Given the numbers:
[tex]3^{\frac{1}{3}},\text{ }4^{\frac{1}{2}},\text{ }\sqrt[3]{9},\text{ 1}^8,\text{ \lparen-}\frac{1}{2})^{-2}[/tex]Let's arrange the numbers from the least to the greatest without the use of a calculator.
Now, let's first simplify each term.
We have:
[tex]\begin{gathered} 3^{\frac{1}{3}}=\sqrt[3]{3} \\ \\ 4^{\frac{1}{2}}=\sqrt{4}=2 \\ \\ \sqrt[3]{9} \\ \\ 1^8=1 \\ \\ -(\frac{1}{2})^{-2}=(-2)^2=4 \end{gathered}[/tex]Therefore, arranging the numbers from the least to the greatest, we have:
[tex]\begin{gathered} 1 \\ \\ \\ 3^{\frac{1}{3}} \\ \\ \\ 4^{\frac{1}{2}} \\ \\ \sqrt[3]{9} \\ \\ \\ (-\frac{1}{2})^{-2} \end{gathered}[/tex]Please help as soon as you can
Answers
The coordinates of the triangle S'T'U' is (2, -1), (5,3), (1, -4) and the triangle S"T"U" is (1,3), (4,5),(0,-2)
Coordinates:
Basically, the pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes is known as coordinates.
Given,
The triangle STU is graphed at S(2,-1) T(5,-3) U(1,4). Triangle STU is reflected over the x-axis to create triangle S'T'U' and then translated by the rule (x,y) ->(x-1,y+2) to create S"T"U".
Here we need to find the coordinates for triangle S'T'U' and S"T"U".
In order to find the correct transformation for this triangle, we have to do the following,
The formula that is used to reflect a coordinate point about the x-axis.
(X2,Y2) = (X1,Y1) * (1,-1)
So, based on this rule, the coordinates of S'T'U' is,
S(2,-1) => S'((2 x 1), (-1 x -1)) = > S'(2,-1)
T(5,-3) => T'((5 x 1), (-3 x -1)) => T'(5, 3)
U(1,4) => U'((1 x 1), (4 x -1)) => U'(1, -4)
Now we have to apply the next rule,
=> (x, y) -> (x-1, y+2)
S'(2,1) => S'((2 - 1), (1 + 2)) = > S'(1, 3)
T'(5,3) => T'((5 - 1), (3 + 2)) => T'(4, 5)
U'(1,-4) => U'((1 - 1), (-4 + 2)) => U'(0, -2)
Therefore, the coordinates of S'T'U' is (2, -1), (5,3), (1, -4) and the coordinates of S"T"U" is (1,3), (4,5),(0,-2)
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help meeeeeeeeee pleasee
Answers
Answer: 2.5, 5.3
Step-by-step explanation:
[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3[/tex]
Given 3 and one-tenth times negative 6 times seven-twelfths, determine the product.
eighteen and one sixtieth
negative eighteen and 7 over 120
ten and 17 over 20
negative 10 and 17 over 20
Answers
The given statement expression is equivalent to -2 [tex]\frac{1}{10}[/tex].
What is a expression? What is a mathematical equation? What is Equation Modelling? What are complex numbers?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted [i], called the imaginary unit and satisfying the equation -
[tex]{\displaystyle i^{2}=-1}[/tex]
Every complex number can be expressed in the form a + bi, where [a] and [b] are real numbers
We have the following statement -
3 and one-tenth times negative 6 times seven-twelfths
We can write -
3 (1/10 x - 6) × 7/12
- 3 [tex]\frac{3}{5}[/tex] × 7/12
-18/5 × 7/12
-3/5 x 7/2
- 21/10
- 2 [tex]\frac{1}{10}[/tex]
Therefore, the given statement expression is equivalent to -2 [tex]\frac{1}{10}[/tex].
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fluorescent powder comes in 20 G vials with 12 vials in a set, each vilal a different color. so if I order 3 sets I will have 3 viles of each colorI have 496 cups of paint to fillratio of powder to paint is one part powder to five part paint I know that 3 vials of powder which is 60g= 0.2536 cups. & .2536 cups ×5 parts paint= 1.268 cups of mixture. I got this from theBecks on hereknowing this how many sets of powder do I need to buy in order to us all my paint?
Answers
First you need to know how many cups of powder you are going to need for the 496 cups of paint you already have
[tex]\begin{gathered} 1\text{ CUP POWDER}\Rightarrow5\text{ CUP PAINT} \\ x\text{ CUP POWDER}\Rightarrow496\text{ CUP PAINT} \end{gathered}[/tex]We write this as a ratio
[tex]\begin{gathered} \frac{x}{496}=\frac{1}{5} \\ x=\frac{496}{5} \\ x=99.2 \end{gathered}[/tex]for the 496 cups of paint you will need 99.2 cups of powder.
Continue by seeing how may grams there are in 99.2 cups
[tex]\begin{gathered} 60g\Rightarrow0.2536\text{ CUPS POWDER} \\ x\Rightarrow99.2\text{ CUPS POWDER} \end{gathered}[/tex]write it as a ratio and solve for x again.
[tex]\begin{gathered} \frac{x}{99.2}=\frac{60}{0.2536} \\ x=23470.03155 \end{gathered}[/tex]now find how many vials you will need
[tex]\begin{gathered} 1\text{vial}\Rightarrow20g \\ x\Rightarrow23470.03155g \end{gathered}[/tex]write the ratio and solve
[tex]\begin{gathered} \frac{x}{23470.03155}=\frac{1}{20} \\ x=\frac{23470.03155}{20} \\ x=1173.5\approx1174 \end{gathered}[/tex]If each sets comes with 12 sets, write the ratio and find the number of sets you will need
[tex]\begin{gathered} 1\text{set}\Rightarrow12vials \\ \text{xsets}\Rightarrow1174vials \end{gathered}[/tex][tex]\begin{gathered} \frac{x}{1174}=\frac{1}{12} \\ x=\frac{1174}{12} \\ x=97.83\approx98 \end{gathered}[/tex]you will need 98 sets for this amount of paint.
write the new coordinates after a glide reflection described by. (x,y) (x, y-2) reflection in x=0.
Answers
To find the new coordinates, we just have to use the given rule
[tex](x,y)\rightarrow(x,y-2)[/tex]Let's apply it to each vertex
[tex]\begin{gathered} A(2,10)\rightarrow A^{\prime}(2,10-2)\rightarrow A^{\prime}(2,8) \\ B(3,-4)\rightarrow B^{\prime}(3,-4-2)\rightarrow B^{\prime}(3,-6) \\ C(-3,1)\rightarrow C^{\prime}(-3,1-2)\rightarrow C^{\prime}(-3,-1) \end{gathered}[/tex]Therefore, the new coordinates are A'(2,8), B'(3,-6), and C'(-3,-1).Tim measured a house and made a scale drawing. In real life, the hall closet is 6 feet long. It is 10 inches long in the drawing. What is the scale of the drawing?
Answers
Answer:
60
Step-by-step explanation:
Four times a number is less than 56. Find the largest integer that satisfies the inequality
Answers
13.
13x4 is 52 which is the largest integer that's less than 56.
14 x 4 is 56 which is equal or less than.
a board of directors consists of ten men and five women. a four-member search committee is randomly chosen to recommend a new company president. what is the probability that all four members of the search committee will be women?
Answers
The probability of all four women being on the search committee as members in it is 1/273.
We have 15 people in total out of which there are 10 men and 5 women. We need four people on the committee out of these 15.
The probability of that happening can be calculated using the formula -
= Probability of all four women getting selected/Probability of all getting selected
= (5!/4!.1!) / (15!/4!11!)
= (5!/4!1!) * (4!11!/15!)
= (5*4*3*2*1) / (15*14*13*12)
= 1/273
From this, we know that if we need to have all four women as members of the search committee, the probability of that happening is 1/273.
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BRAINLIST PLEASE HELP!
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(a) Angle B = Angle C = 65 degree.
(b) Angle x and Angle y is 70 degree .
Given,
In the question:
9. Write a sequence of rigid motion to take figure ABC to figure DEF.
Now According to the question:
Take a figure ABC to figure DEF
So, CB = FE
BA = ED
Angle B = Angle E
10.(a) To find the unknown measure:
In triangle ABC
Angle A = 90 degree
To find the Angle B and C
Let the angle B and C be x
We know that :
Sum of angle triangle is 180 degree
50 + x + x = 180
50 + 2x = 180
2x = 180 - 50
2x = 130
x = 65°
Hence, Angle B = Angle C = 65 degree.
10. (b) Given,
Angle ABC = Angle BAC
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Substitute Angle ABC = y and Angle BAC = x into Angle ABC = Angle BAC .
Angle (ABC + ACB + BAC) = 180 degree (Angle sum theorem)
=> y + 40 + x = 180
=> x + 40 + x = 180
=> 2x = 180 - 40
=> 2x = 140
x = 70°
Hence, Angle x and Angle y is 70 degree .
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Can please help me here
Answers
Answer:B your correct
Step-by-step explanation:the x axis is the domain so if the point is directly on the y axis the x whould be zero so the answer is -1.5
A store that sells cell phones has cell-phone covers in a variety of 6 colors and 6 designs. An employee will randomly choose a cell-phone cover to give to each customer who purchases a new cell
phone. Which simulation best models the outcomes of the possible cell-phone covers?
rolling two number cubes at the same time and recording the results
flipping a coin twice and recording the results
rolling a number cube and recording the results
rolling a number cube, flipping a coin, and recording the results
Answers
Answer: I am pretty sure that the answer is flipping a coin twice and recording the result
Step-by-step explanation: my reasoning is you can compare the results unlike the rest
Hi this is the question that I have. I don’t know if the one that I have chose is right or not. Please help me
Answers
To answer this question we must carefully understand the scope of the numbers of the table.
* It represents the number of adults that listen to audiobooks or not. But not all adults, just the surveyed adults.
* Nothing is said about books, only about audiobooks.
Some of the choices are tricky. For example, second and fourth choices talk about books, so they must be discarded.
The third choice refers to all adults, but the table refers only to the 640 adults that were asked.
The first choice is the best question that can be answered using the table.
help meeeeeeeeeeeeeee pleaseeeeeee
Answers
Answer: 2.5, 5.4
Step-by-step explanation:
[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]
In a video game, Shar has to build a pen shaped like a right triangle for her animals. If she needs 6 feet of fence for the shortest side and 10 feet of fence for the longest side, how many feet of fencing is needed for the entire animal pen?
Answers
If in a video game, Shar has to build a pen shaped like a right triangle for her animals. The feet of fencing that is needed for the entire animal pen is : 24 feet.
How to find the feet of fencing needed?First step is to make use of Pythagorean theorem formula to find the other side of the triangle
c= √a²+b²
Where:
a=Side of right triangle
b=Side of right triangle
c=hypotenuse
= √(10² - 6²)
=√(100 - 36)
= √62
= 8 feet
Now let find the perimeter of the triangle
Perimeter of the triangle = 6 feet + 8 feet + 10 feet
Perimeter of the triangle = 24 feet
Therefore the feet needed is 24 feet.
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Answer:24 feet
Step-by-step explanation:i took a test
(It would be great if there were an explanation, I'm struggling to understand how this works.) Triangle FGH has vertices F(−4, 0), G(0, 4), and H(4, 0). A dilation, centered at the origin, is applied to this triangle. The image has vertices F′(−12, 0), G′(0, 12), and H′(12, 0).
What is the scale factor of this dilation?
Enter your answer in the box.
Nevermind, solved. The answer is 3 because if you multiply each of the original points by 3 you get the new points. Since I already put this question up, you can answer just for points.
Answers
A scale factor is defined as the ratio between the scale of a given original object and a new object.
The scale factor of this dilation is 3.
What is a scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object.
We have,
Triangle FGH has vertices:
F = (−4, 0)
G = (0, 4)
H = (4, 0).
The image of the triangle has vertices:
F′ = (−12, 0)
G′ = (0, 12)
H′ = (12, 0)
We see that,
Multiplying 3 on all the vertices of
F = (−4, 0)
G = (0, 4)
H = (4, 0)
we get,
F′ = (−12, 0)
G′ = (0, 12)
H′ = (12, 0)
This means,
A dilation with a scale factor of 3 is applied to the triangle.
Thus,
The scale factor of this dilation is 3.
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Gabrielle is 15 years older than Milkhail. The sum of there ages is 95 what is Milhails age
Answers
The age of Milkhail is 40 years .
In the question ,
it is given that
the the sum of ages of Gabrielle and Milkhail is = 95
let the age of Milkhail be "m" .
given that Gabrielle is 15 years older than Milkhail
So, the age of Gabrielle is = m + 15
the equation representing the sum of ages is given by
total age = age of Milkhail + age of Gabrielle
95 = m + m + 15
adding the like terms ,
we get
95 = 2m + 15
subtracting 15 from both the sides
2m = 95 - 15
2m = 80
dividing both sides by 2
m = 80/2
m = 40
Therefore , the age of Milkhail is 40 years .
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Jennifer's family is going to see the Atlanta Symphony Orchestra. Tickets cost $79 each, and there is a $14.95 convenience fee for each ticket. If Jennifer's mom buys tickets for 6 people, how much money does she spend in all?
Answers
Answer:
563.7
Step-by-step explanation:
add 79 + 14.95 and multiply that by 6
A stationary store sells large and small packages of greeting cards. Each large package contains h greeting cards. Each small package contains kgreeting cards, which is 4 less than the larger package. Express h in termsof k. *
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In this case the answer is very simple. .
Step 01:
Data
large package = h cards
small package = k cards
Step 02:
large package - 4 = small package
h - 4 = k
h = k + 4
The answer is:
h = k + 4
help meeeeeeeeeeeeeee pleaseeeeeee
Answers
Answer: Width = 4.7 meters, Length = 6.7 meters
Step-by-step explanation:
Let the width be w. Then, the length is w+2.
[tex]w(w+2)=32\\\\w^2 +2w=32\\\\w^2 +2w-32=0\\ \\ w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7\\\\\implies w+2 \approx 6.7[/tex]
Which equation represents a proportional relationship?
OA. y = 4x
OB. y=3x2
OC. y = 5x+2
OD. y = 7
Answers
A is the equation representing proportional relationship .
What is proportional relationship ?Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.
CalculationIf the y intercept is anything but 0, then the linear function is not proportional. So C is not proportional (2 is the y intercept)
B is a quadratic and it will not give proportional results. y/x is not a constant.
D has no x value and is not going to give a proportional result. y/x is undefined.
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Solve for u.
-2|3u| +5 > -5
Answers
The value of u is -5/3 < u < 5/3
We need to calculate the value of u
-2|3u| +5 > -5
-2(3u) + 5 > -5
-6u + 5 > -5
-6u > -10
6u < 10
3u < 5
u < 5/3
-2(-3u) + 5 > -5
6u + 5 > -5
6u > -10
3u > -5
u > -5/3
Therefore, the value of u is -5/3 < u < 5/3
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prime or composite
number 1
67
Answers
67 is a prime number and 1 is neither prime nor composite number.
What is prime number and composite number?
A prime number is a number which has exactly two factors i.e. '1' and the number itself. A composite number has more than two factors, which means apart from getting divided by 1 and the number itself, it can also be divided by at least one positive integer.
The given two numbers are 1 and 67.
Since, the prime numbers from 1 to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
67 has exactly two factors i.e. 1 and the number 67 itself.
Therefore, 67 is a prime number.
Due to the fact that it only has one factor, 1, number is not a prime.
Hence, 67 is a prime number and 1 is neither prime number nor composite number.
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Which of the following are equivalent to the function y = 3cOS X + 2? Check all that apply. A. y = 3cos(-x) + 2 B. y = -3cOS X-2 C. y = 3sin(x + 1) +2 + D. y = 3sin(x-7)+2
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We need to plot the graphs of these functions on the same axis:
[tex]\begin{gathered} \text{From the graph, we s}e\text{ the function} \\ y\text{ = 3cosx + 2 has the same grap as } \\ y\text{ = 3sin(x + }\frac{\pi}{2})\text{ + 2} \\ \\ \text{Please note from angles in trigonometry:} \\ \sin \text{ (90 + }\theta)\text{ = cos }\theta \\ \cos x\text{ = sin (90 + x)} \end{gathered}[/tex]Hence, the correct option
[tex]y\text{ = 3sin(x + }\frac{\pi}{2})\text{ + 2 (option }C)[/tex]I need help with this problem. please if you can?
Answers
Answer:
1. Sometimes True.
2. Sometimes True.
3. Always True.
Explanation:
Given the statements;
1.
A percent of a number is smaller than the original number.
Sometimes True.
When the percentage is less than 100% it will be less than the number which makes the statement true, while when the percentage is greater than or equal 100% then the number will be greater than or equal to the original number which makes the statement false.
2.
It saves you more money to have a coupon for an amount of money off instead of a percent off.
Sometimes True.
It depends on the amount of money off and the percent off. Either of them could save more money.
3.
An improper fraction written as a percent will be greater than 100%.
Always True.
when an improper fraction is written as a percentage it will always be greater than 100%
true or false? The sun of an even whole number and an odd whole number is always odd.
Answers
Answer:
the sum of an even whole number and odd whole number is always odd ,
True
help me solve this
-7+3=?
Answers
-4Answer:
Step-by-step explanation:
Answer:
-7 + 3 = -4
Step-by-step explanation:
May I have Brainliest please? I am so close to getting my next ranking! I just need 2 more for it! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
PAINTINGS Julio is selling paintings that he made. He sells each painting for $25, and he spent $200 on supplies to make the paintings. The function m=25p−200 represents the profit m that Julio earns after selling p paintings. Find the zero of the function. Describe what this value means in the context of the situation.
Answers
The zero of the function m = 25p - 200 is, p = 8 represents her break even.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, He sells each painting for $25, and he spent $200 on supplies to make the paintings.
The function m = 25p - 200 represents the profit m that Julio earns after selling p paintings.
The zeroes of the function is when she break even,
At p = 8 means after selling 8 paintings she will have break even as,
m = 25(8) - 200.
m = 200 - 200.
m = 0.
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Describe how a drywaller might use a formula to estimate the
number of sheets of drywall needed for a room.
Answers
Answer:
Square footage
Step-by-step explanation: