A shark spotter is standing at lookout point 25m above the waters edge. He spots a shark in the water at an angle of depression of 50. If the swimmer that is also in the water is sim from the foot of the lookout spot, how far is the shark from the swimmer?
Answers
The shark is 29.78 from the swimmer.
What is angle of depression?Angle of depression is the angle between the line of sight and the vertical or perpendicular to the earth surface.
Analysis:
The height of the lookout, the distance of shark from swimmer and line of sight form a right angle triangle.
So that, tan 50 = distance of shark from swimmer/25
Distance of swimmer = 25 tan 50
Distance of swimmer from shark = 25(1.1910 = 29.78m
In conclusion, the distance of the shark from the swimmer is 29.78m
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The distance of the shark from the swimmer is 21m
TrigonometryFrom the question, we are to determine the distance the shark is from the swimmer
In the diagram,
S is the position of the shark
M is where the shark spotter is standing
and B is the position of the swimmer
The distance between the shark and the swimmer is /BS/
Using SOH CAH TOA
[tex]tan 50^\circ = \frac{25}{/BS/}[/tex]
[tex]1.19175 = \frac{25}{/BS/}[/tex]
∴ [tex]/BS/ = \frac{25}{1.19175}[/tex]
/BS/ = 20.97755
/BS/ ≅ 21 m
Hence, the distance of the shark from the swimmer is 21m.
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Related Questions
PLEASE HELP ASAP
What is an
equation of the line that passes through the points (3,3) and (3, -3)
Answers
Thus, slope is not defined. So there is no equation.
dentify the 17th term in the arithmetic sequence.
a1 = 11, d = −2
PLEASE HELP!!!!! IMA DESPRATE
Answers
The arithmetic sequence has a common difference, and a first term and the 17th term in the arithmetic sequence is -21
How to determine the 17th term?The given parameters are:
First term, a = 11Common difference, d = -2The nth term of an arithmetic progression is:
Tn = a + (n - 1)d
So, we have:
T17 = a + 16d
Substitute the given values
T17 = 11 - 16 * 2
Evaluate
T17 = -21
Hence, the 17th term in the arithmetic sequence is -21
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What is the reference angle for 292°?
O A. 12°
O B. 22°
O C. 68°
O D. 78°
Answers
C. 68°
292° lies on 4th quadrant.
Reference angle:1st quadrant: angle
2nd quadrant: 180° - angle
3rd quadrant: angle - 180°
4th quadrant: 360° - angle
So, reference angle: 360° - 292° = 68°
Please solve with explanation (high points)
Answers
The measure of the length GF is 4.2 units and IH is 2.27 units. Then the measure of angle ∠ACB will be 24.35°.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The triangle ΔABC and triangle ΔGFC are similar triangles. Then we have
GF / BA = CF / BC
GF / 5.62 = 8.88 / 12.42
GF = 4.018
GF ≅ 4.02
The triangle ΔABC and triangle ΔIHC are similar triangles. Then we have
IH / BA = HC / BC
IH / 5.62 = 5.02 / 12.42
IH = 2.271
IH ≅ 2.27
Then the angle ∠ACB will be
∠ACB = tan⁻¹ (5.62 / 12.42)
∠ACB = tan⁻¹ 0.452
∠ACB = 24.35°
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Let A = {1, 2, 3} and R be the following relation on A;
R = {(1, 1), (1, 2), (1, 3), (3, 1), (2, 3)}
Answers
Answer:
The relation is reflexive as
(1,1),(2,2),(3,3)∈R
(2,1)∈R will not imply (1,2)∈R,
hence R is not symmetric
(2,1),(1,3)∈R doesn't imply (2,3)∈R, hence R is not transitive
Step-by-step explanation:
hope this helps if not let me know have a blessed day
What are the x-intercepts of the graph of the given function f(x)=3(x+7)(x-9) show your work
Answers
Answer:
x intercepts = (9,0), (-7,0)
Step-by-step explanation:
First lets expand the factored equation.
f(x) = 3(x + 7) (x - 9)
.... = 3x + 21 (x - 9)
....= 3x^2 - 27x - 21x - 189
....= 3x^2 - 6x - 189
lets make the quation equal to 0 and use the Factorization method to solve for x.
3x^2 - 6x - 189= 0
3(x^2 - 2x - 63) = 0
3(x - 9) (x + 7) = 0
x - 9 = 9 and x + 7 = -7
x = 9,
x = -7
Check the picture of the necessary information
Answers
in this case if it refers to the data from 2009 it would be 39:61
Help me on this!! Asap!!
Answers
Answer:
D. Fundamental Principle of CountingD. 32B. 12 waysD. 24B. 18Step-by-step explanation:
Q1
The Fundamental Principle of Counting states that we can find the total number of ways that two or more separate tasks can happen by multiplying the number of ways each task can happen separately.Q2
No. of ways = 2⁵ = 32Q3
No. of ways = 4 x 3 = 12 waysQ4
⁴P₃ = 4! / 1! = 4 x 3 x 2 = 24Q5
No. of ways = 2 x 3 x 3 = 18Ms. Wall will roll a dice. What is
the probability that she will roll an even number?
Answers
Answer:
50%
Step-by-step explanation:
half of the numbers on dice are even
Please help and show work if possible thanks
Answers
Step-by-step explanation:
a.
the arc angle AC = 180° (since this is a diameter).
the arc angle BC = 60°.
so,
arc angle AB = arc angle AC - arc angle BC = 120°.
b.
the exterior angle of a circle segment at the circle arc is half of the interior angle at the center of the same segment.
the angle A = arc angle BC / 2 = 30°.
c.
the same principle as in b.
the angle C = arc angle AB /2 = 60°.
d.
the arc angle AD = the angle at AOD (that is how arc angles are defined).
the angle AOD = the angle AOF.
the sum of all angles in a triangle is always 180°.
angle AOD = AOF = 180 - 90 - angle A = 60°.
e.
as explained, this is the same as the arc angle AD and therefore the same as d.
it is 60°.
f.
the arc angle CE = the arc angle AD = 60°.
remember, the angles of intersecting lines are the same (just side mirrored) on both sides of each line.
g.
the arc angle ABE = arc angle AB + arc angle BC +
+ arc angle CE = 120 + 60 + 60 =
= 240°
h.
the angle AOE = the arc angle AE = the remainder of 360 minus the arc angle ABE of g.
so, angle AOE = 360 - 240 = 120°
Find the Product:
0.2 x 0.3
Answers
Answer:
0.06
Step-by-step explanation:
The product of 2 numbers means that we have to multiply them.
So, we do 0.2 x 0.3 = 0.06
To do this, we convert the decimal fractions into whole numbers by multiply both by 10.
ie. 0.2 x 10 = 2
and
0.3 x 10 = 3
Now multiply together
2 x 3 = 6.
However, we have to remember that we multiplied both numbers by 10 (ie. 10 x 10 = 100) so we must remember to divide the answer by 100
...0.06
Hope this helps!
- profparis
Answer:
=0.06
Step-by-step explanation:
0.2
× 0.3
= 0.06
therefore the answer is 0.06
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y < 3x + 2
y > 3x + 2
y < One-thirdx + 2
y > One-thirdx + 2
Answers
The linear inequality is represented by the graph will be, y > 3x + 2. Option B is correct.
What is linear inequality?Linear inequalities involve at least one linear algebraic expression. A polynomial of degree 1 is compared to another algebraic expression of degree less than or equal to 1.
The line is passes through the following points;
(x₁,y₁) to (x₂,y₂)
(-3,-7) to (0,2)
The equation is found as;
[tex]\rm y-y_1 = \frac{y_2-y_1}{x_2-x_1 } (x-x_1)\\\\\ \rm y-(-7) = \frac{(2-(-7))}{(0-(-3))} (x-(-3))\\\\ y+7 =\frac{9}{3} (x+3)\\\\ y+7 = 3x+9 \\\\ y=3x+2[/tex]
The graph because the shading is above the line and does not include the line.
The linear inequality is represented by the graph will be, y > 3x + 2
Hence, option B is correct.
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On the coordinate plane shown below, points H and F have coordinates ( − 2 , − 3 ) and ( − 4 , 2 ) , respectively. Use the distance formula to determine the straight line distance between points H and F . In your final answer, include all of your calculations.
Answers
Answer:
[tex]\sf \sqrt{29}[/tex]
Step-by-step explanation:
To find the distance between points H(-2, -3) and F(-4, 2), use the distance formula.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where:\\ \phantom{ww}$\bullet$ $d$ is the distance between two points. \\\phantom{ww}$\bullet$ $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
Substitute the points into the distance formula and solve for d:
[tex]\begin{aligned}d&=\sqrt{(x_F-x_H)^2+(y_F-y_H)^2}\\\\&=\sqrt{(-4-(-2))^2+(2-(-3))^2}\\\\&=\sqrt{(-4+2)^2+(2+3)^2}\\\\&=\sqrt{(-2)^2+(5)^2}\\\\&=\sqrt{4+25}\\\\&=\sqrt{29}\end{aligned}[/tex]
Therefore, the exact distance between points H and F is [tex]\sf \sqrt{29}[/tex].
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PLEASE HELP!!!!!!!!
Note: please add the answer next to the number its from so I can know which question was answered
Answers
2)B
1) K < or equal to -5 so smaller than -5 with closed circle
2)K < or equal to 1 so less than 1 with closed circle
Each has a radius of 5 in and a height of 12 in. How much more water can the cylinder hold than the cone? (Use л=3.14)
Answers
The cylinder holds 3 times more water than the cone
volume of the cylinder is (pi) (r^2) (height), volume of the cone is (1/3)(pi)(r^2)(height)
Cone is 1/3 of cylinder volume so cylinder holds 3 times the amount
Cylinder holds 942 cu units, cone holds 314,
Answer cylinder holds 628 cu units more than cone
cyl= 3.14 x 5^2 x 12=942
Cone= 1/3 x 3.14 x 5^2 x 12 = 314
Each of these labelled bags contains two apples.
One bag contains two green apples, another two red apples and the third one green and one red apple.
All three bags are mislabelled. You may look at only one apple from any one of the bags.
Which bag should you select from to be sure you can determine the content of all three bags?
Answers
Step-by-step explanation:
I just answered this.
the key is that ALL current labels are wrong. not "could be wrong", but "definitely wrong".
you need to pick an apple from the originally "red/green" labeled bag.
since that label is wrong, it must be one of the pure color bags.
so, that bag gets the label for the color that we picked.
now we look at the other 2 bags. they are both wrongly labeled, but there are only 2 options : the second color (which we did not use to label the first bag) and "red/green".
the bag with the color label we just assigned to our first bag must therefore get the second color label (if it were "red/green", it would mean that the third bag was actually correctly labeled, which was not the case), and the bag currently with the second color label is the actual "red/green" bag.
pls answer quickly, thanks !!
Answers
Answer:
14762 ft³
Step-by-step explanation:
Volume of top prism
V = 61 x 8 x (19 - 3)V = 488 x 16V = 7808 ft³Volume of bottom prism
V = 61 x 38 x 3V = 183 x 38V = 6954 ft³Total volume = Volume (top) + Volume (bottom)
7808 + 695414762 ft³If a bag of marbles contains 10 blue and 30 green, what is the complement for the probability of choosing a green marble.
Answers
Answer:3/4
Step-by-step explanation:there are 30+10=40 marble
you choose 30 green. 30/40=3/4
A square is shown below. Which expression can be used to find the area, in square units, of the shaded triangle in the square
Answers
Answer:
1/2 × 6 × 6
Step-by-step explanation:
the triangle takes up half of the square
the area of a square = side length²
side length = 6
so area of square = 6² = 6 × 6
because the triangle takes up half of the square
the area of the shaded triangle would = 1/2 × 6 × 6
Can someone help me with number 2 please?
Answers
Answer:
I notice that the size of the watermelons has grown at a steady positive rate over the seven days.
Find x. (x+10)+(3x-5)+x=180
For a triangle
Answers
Explanation: Remove the parentheses because they’re not important for this particular problem. Then combine all liked terms. Then you should be able to solve it like a normal algebraic problem.
Tell whether the following ratios shows proportion or not. Write
your answer on the space provided before each number.
_________ 1. 2:10 = 1:5
_________ 2. 3:6 = 6:3
_________ 3. 5:15 = 1:3
_________ 4. 12:4 = 6:2
_________ 5. 5:15 = 1:3
Answers
Answer:
1. Proportion
2. Not Proportion
3. Proportion
4. Proportion
5. Proportion
Step-by-step explanation:
Hope it helps you :))))))
Have a good day
Christine's parents gave her $70 to spend at the Topsfield Fair. She spent $10 on flowers and needs to buy vases. Each antique flower vase at the fair costs $3. Which represents the number of antique flower vases Christine can buy?
Answers
Answer:
a ≤ 20
Step-by-step explanation:
a = number of lower vases, in $
3a = cost of a flower vases, in $
10 + 3a = = cost of $10 worth of flowers plus a vases
10 + 3a ≤ 70 says that the cost of Christine's flowers and vases purchase
must be less than, or at most equal to $70.
Subtracting 10 rom both sides of the inequalour
gives us an equivalent inequality
3a ≤ 70 - 10 <---> 3a ≤ 60
Multiplying (or dividing) both sides by a positive number
gives us an equivalent inequality, so
a ≤ 60/3 <---> a ≤ 20
What kind of reasoning is used here? If a = b and c = d, then a − c = b − d
Answers
The reasoning used here is coding and decoding.
What are coding and decoding?Coding is a portion of the logical reasoning element that is used to encrypt words, numbers, or codes utilizing specified rules and regulations. The process of decoding patterns into their original forms from supplied forms is known as decoding.
We have an expression:-
a = b and c = d, then a − c = b − d
Therefore the reasoning used here is coding and decoding.
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Find (a) PQ to the nearest tenth and (b) the coordinates of the midpoint of PQ. P(1,4), Q(3,-2)
Answers
Answer:
a) 6.3; b) (2;1).
Step-by-step explanation:
[tex]a) \ |PQ|=\sqrt{(X_P-X_Q)^2+(Y_P-Y_Q)^2}=\sqrt{4+36}=\sqrt{40} =6.3;[/tex]
[tex]b) \ (\frac{X_P+X_Q}{2};\frac{Y_P+Y_Q}{2}); \ = > \ (2;1).[/tex]
Which term best describes the shape of this distribution?
normal
skewed left
skewed right
uniform
Answers
The shape of the distribution described the Left skewed.
What is left- skewed histogram?A left skewed histogram is a histogram that attains a peak (which is the mode) towards the right side of the graph and has a “tail” towards the left side.
A histogram in which most of the data falls to the left of the graph's peak is known as a left-skewed histogram.
A left-skewed histogram is a type of histogram that is not symmetrical and in which the peak of the graph lies to the right of the middle value or the median.
Hence, considering the above definition the given histogram data falls on right side.
So, it is left skewed graph.
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What is
24
1,000
as a decimal?
Answers
When the temperature in London is 5 degrees celsius, the temperature in New York is - 7 degrees C. If the temperature in London falls by 6 degrees, what is the new lower temperature.
Answers
Answer:
the temperature in London would be -1 degrees as 5-6=-1
A committee must be formed with 2 teachers and 4 students. If there are 9 teachers
to choose from, and 9 students, how many different ways could the committee be
made?
Answers
The total number of different committees that can be made is:
C = 4,536
In how many different ways could the committee be made?If we have a set of N elements, the total number of different subsets of K elements that can be made out of these N is:
[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]
So, the 2 teachers (out of 9) can be selected in:
[tex]C(9, 2) = \frac{9!}{7!*2!} = \frac{9*8}{2} = 36[/tex]
36 different ways.
The 4 students (out of 9) can be selected in:
[tex]C(9, 4) = \frac{9!}{5!*4!} = \frac{9*8*7*6}{4*3*2} = 126[/tex]
126 different ways.
The committee is formed by these two groups, so the total number of different committees that can be made is:
C = 36*126 = 4,536
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Find the solution for x2+4x-9=c+1
Answers
Answer: c= [tex]x^{2}[/tex] +4x-10
Step-by-step explanation:
Step 1: Flip the equation.
C+1= [tex]x^{2}[/tex]+4x-9
Step 2: Add -1 to both sides.
c+1+-1=[tex]x^{2}[/tex]+4x-9+-1
c=[tex]x^{2}[/tex]+4x-10