A surveyor measures the angle of elevation at 20° for a point 5 miles away what is the vertical change in elevation from the point where the surveyor is standing to the point 5 miles away???
help please
Answers
Step-by-step explanation:
there are just some big words trying to confuse you.
it just means that there is a right-angled triangle :
there is the point on the ground, where the surveyor is standing.
then there is the elevated point up there, where the surveyor was measuring the angle to.
and then there is the point on the ground directly under this elevated point. at this point in the ground we have the right angle (90°).
this height of the elevated point above this ground point is what we are looking for, and it is one leg of the right-angled triangle.
the ground distance from the surveyor to the ground point under the elevated point is 5 miles and the second leg.
the direct line of sight from the surveyor to the elevated point is inclined up by 20°, and is the Hypotenuse (baseline opposite of the 90° angle) of the triangle.
remembering that the sum of all angles in a triangle is always 180°, we also know the angle at the elevated point :
180 - 90 - 20 = 70°
now we are using the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
where the sides are always opposite to their associated angles.
so, we have in our triangle
height/sin(20) = 5/sin(70)
height = 5×sin(20)/sin(70) = 1.819851171... miles
so, the elevated point is 1.819851171... miles above the elevation of the surveyor.
Related Questions
Trina is trying to decide which lunch combination to order at a sandwich shop: 4, 5, 6, or
7. Each combination comes with the choice of an apple, an orange, or a pear. How many
possible outcomes are there for a lunch combination and a piece of fruit?
apple
orange
pear
apple
5
orange
pear
apple
orange
pear
apple
orange
pear
Type the answer in the box.
10
Answers
in fgh, m f=60 degrees g= 68 degrees. which side of fgh is the shortest
Answers
Answer:
h=52 and h is the shortest
Step-by-step explanation:
180-f-g=h step 1. -f from 180
180-60=120 step 2. -g from 120
120-68= 52
h=52 degrees
If P Is inversely proportional to the square of q and p is 22 when a is 8 determine p when Q is equal to 4
Answers
The value of p is equal to 76 when q is equal to 4
Given :
If p is inversely proportional to the square of q
when y is inversely proportional to x then [tex]y=\frac{k}{x}[/tex]
given that p is inversely proportional to the square of q. the equation becomes
[tex]p=\frac{k}{q^2}[/tex]
when p is 19 the value of a is 8
Replace the values and find out q
[tex]p=\frac{k}{q^2}[/tex]
[tex]22=\frac{k}{8^2}[/tex]
[tex]22=\frac{k}{64}[/tex]
Multiply both sides by 64
k=1216
Now we find out p when q is 4
Replace k value and q value to find out p
[tex]p=\frac{k}{q^2}[/tex]
[tex]p=\frac{1216}{4^2}[/tex][tex]p=76[/tex]
The value of p is equal to 76 when q is equal to 4
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Answer:
P = 88.
Step-by-step explanation:
P = k/q^2
22 = k/ 8^2
k = 22 * 64 = 1408.
So P = 1408/q^2
When q = 4:
P = 1408/4^2
q = 88
pls help i beg you!
A plumber charges a flat fee of $79 to visit a home and examine a clogged drain. The plumber charges an additional $24 per hour spent fixing the drain. The total cost, C (in dollars), for fixing a drain that takes H hours is given by the following.
c=79+24h
Answer the following questions.
(a)
What is the total cost for fixing a drain that takes 7 hours?
$?
(b)
If the plumber charged a total of $343, how many hours did he spend fixing the drain?
?hours
Answers
Answer:
for "A" the answer is 247$
For "B" the answer 11 hours
Step-by-step explanation:
alia is shopping for school clothes she want to buy 5 T-shirts for 6 each and pair of shoes for 20 she thinks that she will spend about 30 is the answer reasonable
Answers
Answer:
it's not reasonable because the t-shirts alone cost 30 and the shoes cost 20 so it would cost 50 altogether.
if u want u can answer question 14 and 15 but if u don’t just answer 14
Answers
Answer:
For #14, (around) 108 times.
#15 = 53
Step-by-step explanation:
14)
2.69*10^5 = 269000
2.5*10^3 = 2500
269000/2500 = 107.6
Rounding up, we get 108
15)
√(53 - 8)2 + (31 - 3)2
= √(45)2 + (28)2
= √2809
= 53
Hope this helped! I would love a Brainliest if this helped you!
A prism with a length of 4 inches, height of 4 inches, and width of 3 inches. How many more 1 in. cubes does the container need to be completely filled?
Answers
There are 10 number of 1 cubic inches box required to fill the container completely.
What is a cuboid?
It is defined as the six-faced shape, a type of hexahedron in geometry.
It is a three-dimensional shape.
We have:
A prism with a length of 4 inches, height of 4 inches, and width of 3 inches.
The volume of the prism box = 4×4×3 = 48 cubic inches
Here some data are missing.
We are assuming there are 38 1 cubic inches box already in the big box.
So,
= 48 - 38
= 10
Thus, there are 10 number of 1 cubic inches box required to fill the container completely.
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Find the surface area of the space figure represented by the net.
A) 264 in.2
B) 290 in.2
C) 145 in.2
D) 242 in.2
Answers
Answer:
290 in^2.
Step-by-step explanation:
Adding all the areas of rectangles:
= 11*8 + 11*3 + 11*8 + 11*3 + 3*8 + 3*8
= 290 in^2.
Answer:
B) 290 in²
Step-by-step explanation:
Area of a rectangle = length × width
⇒ SA of the net = 2(11 × 8) + 2(11 × 3) + 2(8 ×3)
= 176 + 66 + 48
= 290 in²
Find the area of the regular polygon
Answers
Answer:
a = 337.214 m2
Step-by-step explanation:
hope this helps
graph the following features ( need this fast by the next 2 hours please help !! )
Y-intercept = -3
Slope = 2
Answers
Slope is 2/1 or y/x so (1,2)
See picture, it might help
A simple random sample from an infinite population is a sample selected such that.
Answers
A simple random sample from an infinite population is a sample selected such that each element is selected independently and from the same population.
What is Simple Random Sampling?Simple random sampling is known to be a types of sampling where there are no laws, rules etc., on how to select the samples.
Note that it is seen easiest way of sampling and as such, A simple random sample from an infinite population is a sample selected such that each element is selected independently and from the same population.
See full question below
A simple random sample from an infinite population is a sample selected such that:
a. each element is selected independently and from the same population
b. each element has a 0.5 probability of being selected
c. each element has a probability of at least 0.5 of being selected
d. the probability of being selected changes
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Pls answer this asap
Answers
Answer:
9.5 feet
Step-by-step explanation:
Area of square garden = side length²
⇒ 90 = l²
⇒ l = √90
⇒ l = 3√10
⇒ l = 9.5 feet (nearest tenth)
The length of one side lies between the whole numbers 9 and 10.
Answer:
9 and 10
side length = 9.5 ft (nearest tenth)
Step-by-step explanation:
Area of a square = s² (where s is the side length)
Therefore, if the square garden measures 90 ft², the length of one side will be √90.
To find the two whole numbers that √90 lies between, find the perfect square either side of 90.
Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, ...
Therefore, 90 lies between 81 and 100:
⇒ 81 < 90 < 100
Square root the numbers:
⇒ √81 < √90 < √100
⇒ 9 < √90 < 10
Therefore, the length of one side of Grandma's garden is between 9 and 10.
To estimate √90 to the nearest tenth, find the difference between the three numbers:
[tex]81 \overset{+9}{\longrightarrow} 90 \overset{+10}{\longrightarrow} 100[/tex]
As 90 is almost in the middle of 81 and 100,
⇒ √90 = 9.5 (nearest tenth)
According to the calculator, √90 = 9.486832981... = 9.5 (nearest tenth)
which verifies the estimation.
-3(x + 9) = 15
Enter value for x
Answers
Answer:
x = -14
Step-by-step explanation:
-3(x + 9) = 15Divide each side by -3.
-3(x + 9)/-3 = 15/-3x + 9 = -5Subtract 9 from each side.
x + 9 - 9 = -5 - 9x = -14Answer:
x = -14
Step-by-step explanation:
-3(x + 9) = 15
-3 × x + -3 × 9 = 15-3x + (-27) = 15+27 on both sides-3x = 42[tex] \frac{ - 3x}{ - 3} = \frac{42}{ - 3} [/tex]x = -14Which of the following can be the third side of a triangle whose other two sides measure 8 inches and 10 inches
A) 17inches
B) 18inches
C) 19 inches
D) 20 inches
Answers
Please help with this problem about circles and tangents. solve for X.
Answers
As tangents from a single point to the circle are equal in measure
AC=BCABC is isosceles
<A=60°
We know the radius hits any tangent on right angles
So
<PAC=90°<PAD=90-60=30°Now
cosØ=Base/Hypotenusecos30=6/x√3/2=6/x√3x=12x=12/√3accurate value
x=6.9Answer:
[tex]x=4\sqrt{3}[/tex]
Step-by-step explanation:
If two tangents to a circle meet at one exterior point, the tangent segments are congruent. Therefore, AC = BC
This means that ΔABC is an isosceles triangle and so
∠ABC = ∠BAC = 60°
The tangent of a circle is always perpendicular to the radius.
Therefore, ∠PAC = 90°
With this information, we can calculate ∠PAD:
⇒ ∠PAD + ∠BAC = ∠PAC
⇒ ∠PAD + 60° = 90°
⇒ ∠PAD = 90° - 60°
⇒ ∠PAD = 30°
We now have a side length and an angle of ΔPAD (shown in orange on the attached diagram). So using the cos trig ratio, we can calculate [tex]x[/tex]:
[tex]\sf \cos(\theta)=\dfrac{A}{H}[/tex]
where:
[tex]\theta[/tex] is the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)Given:
[tex]\theta[/tex] = ∠PAD = 30°A = AD = 6H = AP = [tex]x[/tex][tex]\implies \cos(30^{\circ})=\dfrac{6}{x}[/tex]
[tex]\implies x=\dfrac{6}{\cos(30^{\circ})}[/tex]
[tex]\implies x=\dfrac{6}{\frac{\sqrt{3}}{2}}[/tex]
[tex]\implies x=4\sqrt{3}[/tex]
describe full the graph that has the equation x^2 + y^2=9
Answers
Answer:
see explanation
Step-by-step explanation:
the equation of a circle centred at the origin is
x² + y² = r² ( r is the radius )
x² + y² = 9 ← is in this form
with centre (0, 0 ) and r = [tex]\sqrt{9}[/tex] = 3
this then is the equation of a circle whose centre is (0, 0 ) with radius 3
Answer:
Step-by-step explanation:
Discussion
First of all, the graph is of a circle. Anytime you see x^2 + y^2 = r^2, you are dealing with a circleThe center is at 0,0. If it was anything else then x or y or both would be modified. (x+4)^2 + ( y - 3)^2 = 25 does not have it's center at 0,0Third, the radius of the circle is the square root of r^2. In this case, r^2 = 9 so r = sqrt(9) or r = 3Complete the square and graph: 9y²−x − 18y +10=0
Answers
Answer:
See below ~
Step-by-step explanation:
Completing the square :
9y² - x - 18y + 10 = 09y² - 18y + 9 - 9 - x + 10 = 0(3y - 3)² - x + 1 = 0Graph :
Answer:
x = 9(y - 1)² + 1
see attached for graph
Step-by-step explanation:
Completing the squareGiven equation:
9y² - x - 18y + 10 = 0
As there is a y² in the equation, this implies it is a sideways parabola.
To complete the square for a sideways parabola, collect the y variable terms on the left and everything else on the right:
⇒ 9y² - 18y = x - 10
Factor out the leading coefficient from the left side:
⇒ 9(y² - 2y) = x - 10
Take the coefficient of y, half it, then square it: (-2 ÷ 2)² = 1
Add this inside the parentheses, and add the distributed value of this to the right side:
⇒ 9(y² - 2y + 1) = x - 10 + 9
Factor the parentheses and simplify the right side:
⇒ 9(y - 1)² = x - 1
Add 1 to both sides to make x the subject:
⇒ x = 9(y - 1)² + 1
Graphing the parabolaConic form of a sideways parabola with a horizontal axis of symmetry:
x = a(y - k)² + h
(where (h, k) is the vertex and y = k is the axis of symmetry)
If a > 0, the parabola opens to the right, and if a < 0, the parabola opens to the left.
Therefore, for x = 9(y - 1)² + 1
vertex = (1, 1)axis of symmetry: y = 1a > 0 ⇒ the parabola opens to the rightTo find the x-intercept, set y = 0 and solve for x:
⇒ x = 9(0 - 1)² + 1
⇒ x = 9(-1)² + 1
⇒ x = 9(1) + 1
⇒ x = 10
Therefore, the y-intercept is (10, 0)
As the axis of symmetry is y = 1, the other value of y when x = 10 is y = 2
Plot the vertex and points. Add an axis of symmetry to help draw the curve. Draw the parabola opening to the right.
**graph attached**
11 gallons of water are used to completely fill 5 fish tanks. if each tank holds the same amount of water, how many gallons will each tank hold? solve on paper and check your work on zearn. express your answer as a mixed number
Answers
Answer:
[tex]2\frac{1}{5}[/tex]
Step-by-step explanation:
The 11 gals of water are equally split up into 5 tanks, so divide 11 by 5.
[tex]\frac{11}{5}[/tex] then simplifies into [tex]2\frac{1}{5}[/tex]
A card is drawn from a standard deck of 52 playing cards. What is the probability of drawing a club or a red king?
Answers
Answer:
1/2
Step-by-step explanation:
number of required outcome ÷number of possible outcomes
1/2
The height of an equilateral triangle is the square root of 12. Find the perimeter of the triangle.
Answers
the arrows mean "the previous line leads to this line"
the 3 dots means "therefore’
writing fractions with common denominators to add or subtract(Aleks)
Answers
Answer:
3/5+1/3= 9/15+5/15= 14/15
Step-by-step explanation:
Hi there!
To make fractions have a common denominator, multiply both the numerator and the denominator by a number. In this case, 3/5= 9/15, because both the numerator and denominator are multiplied by 3. 1/3= 5/15, using the same rule. 9/15+5/15=14/15
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I HAVE A CYLINDER AND cone WITH THE
Same Dimensions (RADIUS AND HEIGHT OF
BOTH ARE THE SAme). The volume OF THE
cone is 33 CUBIC INCHES. WHAT IS THE
Volume OF THE CYLINDER IN CUBIC
inches?
125 Sunny
Answers
Answer:
99 in³
Step-by-step explanation:
Let the radius and height of each be r and h in. respectively.
Write an equation for the volume of cone.
Volume of cone= ⅓πr²h
⅓πr²h= 33
Multiply both sides by 3:
πr²h= 99
Volume of cylinder= πr²h
We have found the value of πr²h previously, which is 99.
Thus, the volume of the cylinder is 99 in³.
How to work out the mode
Answers
Answer:
mode
is the most common frequent value
the most frequent one is your mode
Q5. the population of an island has decreased by 40% over 50 years.
the population in 2018 was 360
what was the population in 1968?
Answers
Answer:
The population was 600 in 1968
Step-by-step explanation:
The population of an island decreased by 40% over 50 years, so the population in 1968 will be equal to 600.
What is the Percentage?The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.
As per the data provided by the question,
The current population in 2018 = is 360
which is 40% less than the population in 1968.
So, 60% of the total population will be equal to 360.
Let the total population is x.
60% × x = 360
x = (360 × 100)/60
x = 600
Therefore, the population at that time was 600.
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How many layers of 1 inch cubes fill the carton
Answers
Answer:
3
Step-by-step explanation:
4 layers 15 cubes
the total amount of cubes =5*3*4
3
————
i need help!!
math geniuses pls help me!
—-
—————
Answers
Answer:
the answer is A. sorry for dirty handwriting
Two quantities are proportional if their ___ are equal.
A) numerator
B) denominators
C) cross products
Answers
Answer:
C) cross products
Step-by-step explanation:
Let's say you were solving [tex]\frac{1}{2}=\frac{x}{4}[/tex] for example. You would need to use cross products to simplify the problem. Here, the left side would be 1*4, and the right side would be 2*x, giving you [tex]4=2x[/tex], thus, leading to the solution [tex]x=2[/tex]. We can see clearly that the cross products would thus need to be equal to each other.
in a group of 70 people, 37 like tea, 52 like milk and each people likes at least one of the two drinks.
1)how many people like both tea and milk ?
2) how many people like tea only ?
3)how many people like milk only ?
4)show the above information in a Venn diagram.
Answers
Step-by-step explanation:
got the answer see in the image :)
80 volunteers take a meningitis test to help doctors see how accurate this test is at identifying whether someone has meningitis or not. a positive result means the test has identified you as having meningitis. of the volunteers, only 17 people have meningitis. the results show 5 people who have meningitis gets a negative result and 7 people who don't have meningitis get a positive result. what was the accuracy of the test?
Answers
Using it's formula, it is found that the accuracy of the test was of 0.85 = 85%.
What is the accuracy of a test?The accuracy of a test is given by the number of correct results divided by the number of results.
In this problem, there are 80 tests, and of those, 5 + 7 = 12 had incorrect results, hence 68 had correct results.
Hence the accuracy of the test is given by:
a = 68/80 = 0.85 = 85%.
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Can you use Third Angles Theorem to prove that two
are congruent? Explain your reasoning.
triangles
Answers
Answer:
The Third Angle theorem is not enough to prove that two triangles are congruent.
Step-by-step explanation:
It establishes that if two angles of one triangle are congruent with two angles of another triangle, then the third angles are also congruent. This indicates that the two triangles are similar but not identical.