the bearing of two points x and y from z are 45° and 135° respectively . if |zx|=8cm and |zy|=6cm, find |xy|.
Answers
Answer:
[tex]|{\sf XY}| = 10\; {\rm cm}[/tex].
Step-by-step explanation:
Refer to the diagram attached. The dashed segment attached to [tex]\!{\sf Z}[/tex] points to the north. Rotating this segment clockwise with point [tex]{\sf Z}\!\![/tex] as the fixed center of rotation would eventually align this segment with the one between point [tex]\!\!{\sf Z}[/tex] and point [tex]\!\!{\sf X}[/tex]. The bearing of point [tex]{\sf X}[/tex] from point [tex]{\sf Z}[/tex] is the size of the angle between these two line segments when measured in the clockwise direction.
Subtract the bearing of [tex]{\sf Y}[/tex] from [tex]{\sf Z}[/tex] from the bearing of [tex]{\sf X}[/tex] from [tex]{\sf Z}[/tex] to find the measure of the angle [tex]\angle {\sf YZX}[/tex]:
[tex]\begin{aligned}\angle {\sf YZX} &= 135^{\circ} - 45^{\circ} \\ &= 90^{\circ}\end{aligned}[/tex].
Thus, triangle [tex]\triangle {\sf YZX}[/tex] is a right triangle ([tex]90^{\circ}[/tex]) with segment [tex]{\sf YX}[/tex] as the hypotenuse. It is given that [tex]|{\sf XZ}| = 6\; {\rm cm}[/tex] whereas [tex]|{\sf ZY}| = 6\; {\rm cm}[/tex]. Thus, by Pythagorean's Theorem:
[tex]\begin{aligned}|{\sf ZY}| &= \sqrt{|{\sf ZX}|^{2} + |{\sf ZY}|^{2}} \\ &= \sqrt{(8\; {\rm cm})^{2} + (6\; {\rm cm})^{2}} \\ &= 10\; {\rm cm}\end{aligned}[/tex].
Related Questions
Write the equation of the line in slope-intercept form Slope=5/3 Y-Intercept=4
Answers
Answer:
y=5/3x+4
Step-by-step explanation:
Slope intercept formula: y=mx+b
m=slope
b=Y-Intercept
Answer:
[tex]\sf y=\dfrac{5}{3}x+4[/tex]
Step-by-step explanation:
Given:
[tex]\textsf{slope of $\dfrac{5}{3}$, and a y-intercept of $4$}[/tex]
⇒ Slope-Intercept Form: y = mx + b
where:
m is the slopeb is the y-intercept (when x = 0)Substitute the given values:
[tex]\sf\\ \implies y=mx+b\\\\\implies y=\dfrac{5}{3}x+4[/tex]
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Let (-7, 2) be a point on the terminal side of 0.
Find the exact values of sin0, sec 0, and tan 0.
Answers
By applying the definitions of trigonometric functions, the exact values of the sine, secant and tangent of the point on the terminal side are [tex]\sin \theta = \frac{2}{\sqrt{53}}[/tex], [tex]\sec \theta = -\frac{\sqrt{53}}{7}[/tex] and [tex]\tan \theta = -\frac{2}{7}[/tex].
How to determine the exact values
In this question we need to find the exact values of three trigonometric functions associated with the terminal side of an angle. The following definitions are used:
Sine
[tex]\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}[/tex] (1)
Secant
[tex]\sec \theta = \frac{\sqrt{x^{2}+y^{2}}}{x}[/tex] (2)
Tangent
[tex]\tan \theta = \frac{y}{x}[/tex] (3)
If we know that x = - 7 and y = 2, then the exact values of the three trigonometric functions:
Sine
[tex]\sin \theta = \frac{2}{\sqrt{53}}[/tex]
Secant
[tex]\sec \theta = -\frac{\sqrt{53}}{7}[/tex]
Tangent
[tex]\tan \theta = -\frac{2}{7}[/tex]
By applying the definitions of trigonometric functions, the exact values of the sine, secant and tangent of the point on the terminal side are [tex]\sin \theta = \frac{2}{\sqrt{53}}[/tex], [tex]\sec \theta = -\frac{\sqrt{53}}{7}[/tex] and [tex]\tan \theta = -\frac{2}{7}[/tex].
Remark
The statement reports typing errors, correct form is shown below:
Let (x, y) = (- 7, 2) be a point on the terminal side of θ. Find the exact value of sin θ, sec θ and tan θ.
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please hurry its due in 5 mins
Answers
Answer:
Divide the shape in two pieces:
A rectangle and a triangle
Find area of rectangle:
A=length*width=5*4=20m^2
Find area of triangle:
base of triangle=5-2=3m
height of triangle=8-4=4m
Area=(1/2)*base*height
=(1/2)(4)(3)=6m^2
Total area=6+20=26m^2
Hope it helps!
How many cubes are needed to build this figure?
4
6
5
3
Answers
Answer:
3
Step-by-step explanation:
because I sense three and You need
can someone please help me with this problem?
Answers
A road is 450 metres long . It takes a woman 5 minutes to walk along the road . Work out the average speed of the woman . Give your answer in metres per second .
Answers
Which graph shows the solution to the system of linear inequalities?
x – 4y < 4
y < x + 1
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything above of the line is shaded. The second solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second solid line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
Answers
Answer:
From the graph in the attachment, it is clear that Option A is correct.
Step-by-step explanation:
The given inequalities are x - 4y ≤ 4 and y < x + 1.
Let us take the first line x - 4y ≤ 4 and remove the inequality and add equality, x - 4y = 4.
Now, we will find the intercept points. Putting y = 0 we will get x = 4 and putting x = 0 we will get y = -1. So, the points are (4,0) and (0,-1).
When we will solve the inequality, we find that portion above the graph satisfies this inequality.
Let us take the second line y < x + 1 and remove the inequality and add equality, y = x + 1.
Now, we will find the intercept points. Putting y = 0 we will get x = -1 and putting x = 0 we will get y = 1. So, the points are (-1,0) and (0,1).
When we will solve the inequality, we find that portion below the graph satisfies this inequality.
All these conditions satisfy the Option A.
The diagram is in the attachment.
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Which of the following could be the equation of the function below?
y = -3 sin (2 (x + pi)) + 2
y = -3 sine (x + pi) + 2
y = 3 sin (4 (x - pi)) + 4
y = 3 sin (2 (x + pi)) + 2
Answers
The equation of the sine function will be y = -3 sin [2(x + π)] + 2. Then the correct option is A.
What is a sinusoidal Function?It is a function that repeats itself in a particular time interval.
The equation is given as
y = A sin (ωx + Ф) + C
Where A is the amplitude, ω is the frequency, Ф is the phase difference, and C is the constant.
From the graph, we have
A = -3
ω = 2
Ф = 2π
C = 2
Then we have the equation will be
y = -3 sin [2(x + π)] + 2
Then the correct option is A.
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A local candy shop sells boxes of chocolate for $3.45 each. If a customer purchases five or more boxes, the cost is only $3 per box, plus the customer has an additional $1 fee per order. If C(x) represents the total cost and x represents the number of boxes, which of the following functions best models this scenario?
C of x equals 3.45 times x if x is less than 5 and 3.00x plus 1 if x is greater than or equal to 5.
C of x equals 3.45 times x if x is less than 5 and 3.00 plus x if x is greater than 5.
C of x equals 3.45 times x if x is less than or equal to 4 and 3.00x minus 1 if x is greater than 5.
C of x equals 3.45 times x if x is less than 4 and 3.00x minus 1 if x is greater than or equal to 5
Answers
The function that best models the scenario is as follows;
x < 5 : C(x) = 3.45x + 1
x ≥ 5 : C(x) = 3x + 1
How to find an equation?A local candy shop sells boxes of chocolate for $3.45 each.
This is when the consumer purchase less than 5 boxes of chocolates.
Therefore,
x = number of boxes
when x < 5
C(x) = 3.45x + 1
If a customer purchases five or more boxes, the cost is only $3 per box. Therefore,
when x ≥ 5
C(x) = 3x + 1
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What interval includes all possible values of x, where –3(6 – 2x) ≥ 4x + 12
Answers
Answer:
x≥20
Step-by-step explanation:
-3(6-2x)≥4x+12
or, -18+6x≥4x+12
or, -18-12≥4x-6x
or, -40≥-2x
or, -40/2≥-x
or, -20≥-x
or, 20≥x
= x≥20
Please helpppppppppppppp
Answers
Answer:
Inequality would be the answer
need help on this ASAP! please
Answers
Step-by-step explanation:
x=66°
180-118=62°
180-52+62=66°
hope this helps
Explanation: angles on a line add up to 180, so if part of it is 118 you do 180-118 which is 62. So 62 is the angle on the right, then add the left and right angle which is 52 plus 62 which is 114.
And we know a triangle adds up to 180. So 180 take away 114 equals 66
Hope this helps and hope you can understand it
Which shows all the exact solutions of 2sec^2 (x)-tan^4 (x)=-1? Give your answer in radians.
a) pi/3 + kpi and 2pi/3 + kpi
b) pi/3 +2kpi and 5pi/3 +2kpi
c) pi/4 +2kpi, 3pi/4 + 2kpi, 5pi/4 +2kpi, and 7pi/4 +2kpi
d) pi/3 + kpi, 2pi/3 +kpi, 4pi/3 +kpi, and 5pi/3 +kpi
Answers
Answer:
a. 1/3pi+kpi and 2/3pi+kpi
Step-by-step explanation:
2Sec²x
=2+2tan²x-(tan²x)²=-1
Let tan²x=u
-u²+2u+2=-1
-u²+2u+3=0
u²-2u-3=0
(u+1)(u-3)=0
u=-1,u=3
(tan x)²=-1(No solution)
(tan x)²=3
>>tan x=±sqrt(3)
I) tan x=sqrt(3)
>>tan(pi/3)=sqrt 3
Tan(pi+A) =tanA
Tan(pi+pi/3)=tan(pi/3)
>>tan(4/3pi)=sqrt(3)
>>x=4/3pi and 1/3pi
General solution: 1/3pi+kpi
ii) tan x=-sqrt(3)
x=2/3pi(At 2nd quadrant)
x=5/3pi(at 4th quadrant)
General solution: 2/3pi+kpi
7. Miguel draws a square on a coordinate plane. One vertex is located at (5, 4). The
length of each side is 3 units. Circle the letter by all the ordered pairs that could be
another vertex.
A. (5, 1)
B. (5, 7)
C. (7, 8)
D. (2, 6)
E. (2, 1)
Answers
Answer:
A, B and E
Step-by-step explanation:
Answer: A,B and E i did the test
Step-by-step explanation:
q(t)= Q_0 e^-kt where Q represents the quantity remaining after t years and k is the decay constant 0.00043. How long will it take for 500g of radium to decay to 5g?
Answers
It takes 16,064 years for the 500g of radium to decay to 5g.
How long will it take for 500g of radium to decay to 5g?
Here we have the decay equation:
[tex]Q(t) = Q_0*e^{-k*t}[/tex]
Where Q₀ is the initial amount, and k is the decay constant.
We know that:
Q₀ = 500g
k = 0.00043
And we want to find the value of t such that Q(t) = 5g, so we need to solve:
[tex]5 = 500*e^{-0.00043*t}\\\\5/500 = e^{-0.00043*t}\\\\0.001 = e^{-0.00043*t}[/tex]
Now we can apply the natural logarithm in both sides:
[tex]ln(0.001) = ln(e^{-0.00043*t})\\\\ln(0.001) = -0.00043*t\\\\\frac{ln(0.001)}{-0.00043} = t = 16,064.5[/tex]
So it takes 16,064 years for the 500g of radium to decay to 5g.
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solve log7(x+9)-log7(10)
Answers
[tex]\log_7(x+9)-\log_710=\log_77\qquad(x > -9)\\\log_7\dfrac{x+9}{10}=1\\\dfrac{x+9}{10}=7\\x+9=70\\x=61[/tex]
Jamie is walking her neighbors’ dog while they are away. She is keeping track of the total number of blocks she walks over time.
A 2-column table with 3 rows. Column 1 is labeled Minutes with entries 6, 14, 20. Column 2 is labeled Blocks with entries 3, 7, 10.
Does the table represent a proportional relationship?
Yes, because both columns are written in ascending order.
Yes, because the values in the second column are less than the values in the first column.
Yes, because the ratios are equivalent between each pair of values.
No, because the values in the table do not increase by the same amount in each row.
Answers
Answer:
Yes, the relation is proportional because the ratios are equivalent between each pair of values
Step-by-step explanation:
Proportional relationships are relationships with equal ratios.
Entries in the respective columns are:
column 1 (Minutes) column 2 (Blocks) Ratios
6 3 1/2
14 7 1/2
20 10 1/2
As the ratio of Blocks and Minutes is same for every row,
the given table represent a proportional relationship.
hence, option c is correct.
Yes, because the ratios are equivalent between each pair of values.
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Answer: Yes, the relation is proportional because the ratios are equivalent between each pair of values :)
evaluate 2x^2-1 when x=3
Answers
[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's evaluate ~
[tex]\qquad \sf \dashrightarrow \: 2 {x}^{2} - 1[/tex]
plug in the value of x :
[tex]\qquad \sf \dashrightarrow \: 2(3) {}^{2} - 1[/tex]
[tex]\qquad \sf \dashrightarrow \: 2(9) - 1[/tex]
[tex]\qquad \sf \dashrightarrow \: 18 - 1[/tex]
[tex]\qquad \sf \dashrightarrow \: 17[/tex]
The required value is 17
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{Option B, 17}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{2x}^2\textsf{ - 1}[/tex]
Find: [tex]\textsf{When x = 3}[/tex]
Solution: In order to find the value when x is equal to 3 we just need to equate any x to the value of 3 and simplify.
Plug in the values
[tex]\textsf{2x}^2\textsf{ - 1}[/tex][tex]\textsf{2(3)}^2\textsf{ - 1}[/tex]Simplify the expression
[tex]\textsf{2(3 * 3) - 1}[/tex][tex]\textsf{2(9) - 1}[/tex][tex]\textsf{18 - 1}[/tex][tex]\textsf{17}[/tex]Therefore, the answer that would make most sense would be option B, 17.
HELP !!!
A taxi driver uses this formula to work out the price of a journey, in pounds. price of journey = 3 + 2 x distance in miles. Leah has £5, the journey to her home is 2.5 miles. She asks the taxi driver to take her as near to home as possible. How far will she need to walk to arrive home?
Answers
The distance Leah would have to walk home is 1.5 miles
Calculating distanceFrom the question, we are to determine the distance Leah will have to walk home
From the given information,
Price of journey in pounds = 3 + 2 × distance in miles
Let the distance be d
Then,
Price of journey in pounds = 3 + 2d
Since Leah has £5, we can write that
5 = 3 + 2d
5 - 3 = 2d
2 = 2d
∴ d = 2/2
d = 1 mile
This means her money can only cover 1 mile
But the journey to her home is 2.5 miles
Therefore, she will have to walk
2.5 mile - 1 mile = 1.5 miles
Hence, the distance Leah would have to walk home is 1.5 miles
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PLEASE HELP PLEASEEEE!! 100 PTS!
Answers
Answer:
R
H
S
= cos
2
x
Step-by-step explanation:
Hope this helped!
Which expression is equivalent to √48x5, if x>0?
OA. 12x³√3x
OB. 4x³√3
OC. 4x²√3x
D. 12x²√x
Answers
Answer: C
Step-by-step explanation:
[tex]\sqrt{48x^{5}}=\sqrt{16x^{4}}\sqrt{3x}=\boxed{4x^{2}\sqrt{3x}}[/tex]
The volume of a cylinder is 8177 cm³. If the radius is 3 cm, what is the height
of the cylinder?
OA. 9 cm
OB. 18 cm
O C. 12 cm
O D .6cm
Answers
Answer:
None of the options are correct
О E. 289.2 cm
Step-by-step explanation:
Volume of a cylinder = v = л r² h
л = 3.1416 (aprox)
r = radius
h = height
8177 = 3.1416 * 3² * h
8177 = 3.1416 * 9 * h
8177 = 28.2744 * h
8177/282744 = h
h = 289.2 cm
A river flows at 2m/s. Juan’s boat can travel twice as fast down the river as it can go up the river. How fast can the boat go in still water?
Answers
Answer: 2m/s
Step-by-step explanation:
The boat goes twice as fast down the river, which means it goes twice as slow up the river.
Because the river flows at 2m/s, I think the answer is 2m/s
If f(x) = 2x² + 3x and g(x) = x - 2, what is (f+ g)(2) ?
Answers
[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=2x^2+3x\\g(x)=x-2\\\\(f+g)(2)=2\cdot2^2+3\cdot2+2-2=8+6=14[/tex]
Match the function with the graph.
a. y = |x+ 5|
b. y= |x-5| + 2
c. y= |x-5|
d. y=|x| -5
i did a and it was wrong. i don’t understand lol please help
Answers
C. y= |x-5|
you have the right idea, it's being shifted horizontally so the shift would be shown inside of the brackets. However, it would be |x-5| not |x+5| because the graph is shifting to the right.
What are the domain and range of the function represented by the set of
ordered pairs?
{(-7, 1), (-3, 2), (0, -2), (5,5)}
Answers
Answer:
see explanation
Step-by-step explanation:
the domain is the set of x- coordinates from the ordered pairs , that is
domain : { - 7, - 3, 0, 5 }
the range is the set of y- coordinates from the ordered pairs, that is
range : { - 2, 1, 2, 5 }
Select the correct answer. The function g(x) = x2 is transformed to obtain function h: h(x) = g(x) − 5. Which statement describes how the graph of h is different from the graph of g? A. The graph of h is the graph of g vertically shifted up 5 units. B. The graph of h is the graph of g horizontally shifted left 5 units. C. The graph of h is the graph of g vertically shifted down 5 units. D. The graph of h is the graph of g horizontally shifted right 5 units.
Answers
The graph of h(x) is the graph of g vertically shifted down 5 units. Then the correct option is C.
What is a function?Functions are found all across mathematics and are required for the creation of complex relationships.
The function g(x) = x² is transformed to obtain function h:
h(x) = g(x) − 5
h(x) = x² − 5
The graph h(x) get shifted downward by 5 units.
Then the correct option is C.
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What are the domain and range of an exponential parent function?
Help please
Answers
The domain and the range of an exponential parent function, that is, y = eˣ are equal to all real numbers and non-negative numbers, respectively. (Correct choice: C)
How to determine the domain and range of an exponential function
In this problem we should determine what an exponential parent function is. The most common exponential functions have the following form:
[tex]y = A\cdot e^{B\cdot x} + C[/tex] (1)
(1) is an exponential parent function for A = 1, B = 1 and C = 0.
All functions are relations with a domain and range, the domain is an input set related to the range, that is, an output set. In the case of an exponential parent function, the domain and the range of the expression are [tex]\mathbb{R}[/tex] and y ≥ 0, respectively. (Correct choice: C)
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A point P is 45km from Q in a bearing of 75⁰ how far is P north of Q
Answers
Answer:
11.65
Step-by-step explanation:
45 cos 75 (in degrees not radians) =
11.6468570296
jiskha
raka
Round the number to the nearest ten-thousands:
388,725
a. 400,000
b.390,000
c. 388,800
d. 389,000
Answers
Answer:
B is the correct answer
Step-by-Step:
