Answer:
The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).
Step-by-step explanation:
The final position of the surveyor is represented by the following vectorial sum:
[tex]\vec r = \vec r_{1} + \vec r_{2} + \vec r_{3}[/tex] (1)
And this formula is expanded by definition of vectors in rectangular and polar form:
[tex](x,y) = r_{1}\cdot (\cos \theta_{1}, \sin \theta_{1}) + r_{2}\cdot (\cos \theta_{2}, \sin \theta_{2})[/tex] (1b)
Where:
[tex]x, y[/tex] - Resulting coordinates of the final position of the surveyor with respect to origin, in kilometers.
[tex]r_{1}, r_{2}[/tex] - Length of each vector, in kilometers.
[tex]\theta_{1}, \theta_{2}[/tex] - Bearing of each vector in standard position, in sexagesimal degrees.
If we know that [tex]r_{1} = 42\,km[/tex], [tex]r_{2} = 28\,km[/tex], [tex]\theta_{1} = 32^{\circ}[/tex] and [tex]\theta_{2} = 154^{\circ}[/tex], then the resulting coordinates of the final position of the surveyor is:
[tex](x,y) = (42\,km)\cdot (\cos 32^{\circ}, \sin 32^{\circ}) + (28\,km)\cdot (\cos 154^{\circ}, \sin 154^{\circ})[/tex]
[tex](x,y) = (35.618, 22.257) + (-25.166, 12.274)\,[km][/tex]
[tex](x,y) = (10.452, 34.531)\,[km][/tex]
According to this, the resulting vector is locating in the first quadrant. The bearing of the vector is determined by the following definition:
[tex]\theta = \tan^{-1} \frac{10.452\,km}{34.531\,km}[/tex]
[tex]\theta \approx 16.840^{\circ}[/tex]
And the distance from the camp is calculated by the Pythagorean Theorem:
[tex]r = \sqrt{(10.452\,km)^{2}+(34.531\,km)^{2}}[/tex]
[tex]r = 36.078\,km[/tex]
The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).
(04.02 MC)
4
What is the y-intercept of the line perpendicular to the line y = x + 1 that includes the point (4, 1)?
Answer:
The intercept of the line perpendicular to the line [tex]y = x + 1[/tex] is 5.
Step-by-step explanation:
The line [tex]y = x + 1[/tex] has a slope 1. By Analytic Geometry, the slope of the line perpendicular to the original line is determine by the following formula:
[tex]m_{\perp} = -\frac{1}{m}[/tex] (1)
Where:
[tex]m[/tex] - Slope of the original line.
[tex]m_{\perp}[/tex] - Slope of the line perpendicular to the original line.
If we know that [tex]m = 1[/tex], then the new slope is:
[tex]m_{\perp} = -\frac{1}{1}[/tex]
[tex]m_{\perp} = -1[/tex]
A line is defined by the following expression:
[tex]y = m\cdot x + b[/tex] (2)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]m[/tex] - Slope.
[tex]b[/tex] - Intercept.
If we know that [tex](x,y) = (4,1)[/tex] and [tex]m = -1[/tex], then the intercept of the line perpendicular to the original line:
[tex]b = y - m\cdot x[/tex]
[tex]b = 1+4[/tex]
[tex]b = 5[/tex]
The intercept of the line perpendicular to the line [tex]y = x + 1[/tex] is 5.
i’ll give brainilist . Mrs.Shivers, the 8th grade guidance counselor, solved for the value of x in the triangle below. She said that x=70 based off what Ms.Willis taught her. Which of the following statements best justifies Mrs.Shiver's answer?
Answer:
she is correct
Step-by-step explanation:
because according to the Pythagorean theorem the interior of a triangle has to be 180 degrees total.
and a straight line has an angle of 180
so the inside of the C angle is 50
60+50+70=180
PLs, help me with this geometry question.
Answer:
x = 49
Step-by-step explanation:
The central angle AOB is equal to the measure of the arc that subtends it, so
∠ AOB = 82°
OA = OB ( both radii of the circle ), then Δ AOB is isosceles and the 2 base angles are congruent, then
x = [tex]\frac{180-82}{2}[/tex] = [tex]\frac{98}{2}[/tex] = 49
If x + x = 9, then x =
Answer: x = 4.5
Step-by-step explanation: First, do x + x, since they are like terms. That equals 2x. The equation is now 2x = 9. Divide both sides by 2. x = 4.5.
x + x = 9
2x = 9
÷2 ÷2
---------------------
x = 4.5
x + x = 9
4.5 + 4.5 = 9
Suppose that your statistics professor tells you that the scores on a midterm exam were approximately
normally distributed with a mean of 78 and a standard deviation of 7. The top 15% of all scores have
been designated A’s. Your score is 89. Did you earn an A? Explain.
Answer:
YesStep-by-step explanation:
z-score representing 85% is 1.04 (from table)
Let x be the score representing the lower limit of 85%.
Use the formula to find z-scores:
z = (x - μ)/σWe have:
z = 1.04, μ = 78, σ = 7Substitute the values and solve for x:
1.04 = (x - 78)/7x - 78 = 7.28x = 85.28The lower limit of the top 15% is 85.28.
Since your score is greater than 85.28 you earned an A
what numbers multiplied by itself equals 118?
[tex]\longrightarrow{\green{10.863}}[/tex] ✅
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]10.863 \times 10.863 = 118 \\ \\⇝118.004 = 118 \\ \\ ⇝118 = 118[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
Answer:
±sqrt(118) or approximately ±10.86278
Step-by-step explanation:
What number times itself is 118
We are looking for the sqrt(118) or- sqrt(118)
This is approximately ±10.86278
Write in slope-intercept form an equation of the line that passes through the points (-3, 2) and (1, -10).
A hotel room is originally priced at $159.00 per night during the week (Monday-Thursday). On weekends (Friday - Sunday), the price increases by 12%. What is the price of a hotel room on a Saturday night?
16.
Which of the following are the coordinates of the vertex of y= 3x2 + 3?
A. (3, 0)
B. (0, 3)
C. (–3, –3)
D. (3, 3)
Answer:
D
Step-by-step explanation:
is the correct answer i believe.
Answer:
B. 0,3
Step-by-step explanation:
I took the test and checked the answer, 0,3 is correct.
In 20 words or fewer, can 8 • 7 • 6 be written as 8! . . . and why or why not?
Answer:
No, because factorials are product of all positive integers less than or equal to a given positive integer.
What is the domain of the relation
graphed below?
Answer:
Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
Step-by-step explanation:
wala muna akung ma explantion hahah sore
Recently, the value of a house increased by 20.5%.
What is the current value of the house if its original value
was $550,000?
can someone help with part A please??
Answer:
Step-by-step explanation:
4 days 9 hours 40 minutes
Twenty-five sixth-grade students were asked to estimate how many hours a week they spend talking on the phone. This dot plot represents their reported number of hours of phone usage per week.
Answer:
where is the dot plot??
Step-by-step explanation:
Please help I’ll give brainliest
Answer:
13%
Step-by-step explanation:
Interest Amt = Principal x Interest Rate x Time (in years)
780 = 4000·r·1.5
780 = 6000r
780/6000 = r
r = .13 which is 13%
Easy
1/6 x 1/2x 1/3
help me (￣▽￣)╭
======================================================
Explanation:
The numbers up top are 1,1,1. They multiply to 1*1*1 = 1. So that means 1 is the numerator of the answer.
The numbers down below are 6,2,3. They multiply to 6*2*3 = 36. This is in the denominator for the answer.
That means (1/6)*(1/2)*(1/3) = 1/36
The rule I used is (a/b)*(c/d) = (a*c)/(b*d)
Answer:
1/36
Step-by-step explanation:
Step 1:
1/6 · 1/2 · 1/3 Equation
Step 2:
1/6 · 1/6 Multiply
Answer:
1/36
Hope This Helps :)
Sebastian bought x gallons of gas at a price of $2.91 per gallon at his local gas station. When he paid for the gas, Sebastian also paid $11.40 for granola
bars and a box of tissues.
If Sebastian filled 10 gallons of gas, how much did he spend in all at the gas station?
Answer:
Sebastian spent $40.40 at the gas station.
Step-by-step explanation:
First let's find how much the gas cost.
So it's $2.91 a gallon, and Sebastian fills 10 gallons of gas, so we multiply.
10 * 2.91 = $29.10
Then we add on the $11.40 from the granola bars and the box of tissues.
$29.10 + $11.40 = $40.50
So the final price should be $40.40. Sebastian spent $40.40 at the gas station.
The sum of a number is
4 less then 2 times a
number is 35 what is the number?
21.5
Step-by-step explanation:35 divided by 2 = 17.517.5 + 4 = 21.5Just do the inversePLEASE HELP!!
A wooden block in the shape of a rectangular pyramid is shown below:
A shaded right rectangular pyramid is shown.
If a cross section of the block is cut in a plane parallel to the base of the pyramid, which of the following shapes describes the cross section? (5 points)
a
Triangle
b
Rectangle
c
Trapezoid
d
Hexagon
Step-by-step explanation:
A shaded right rectangular pyramid is shown. where is the shade rectangular pyramid....how do I know the answer when you did post the full
question
Which expression is equivalent to ((4^(5/4)x4^(1/4))/4^1/2)^1/2
?
^16sqrt4^5
Sqrt2^5
2
4
Answer:
2
Step-by-step explanation:
add 5/4 and 1/4 to get 6/4 or 3/2
(4^3/2 ÷ 4^1/2)^1/2 = 4^3/4 ÷ 4^1/4
4^3/4 ÷ 4^1/4 = 4^2/4 or 4^1/2
4^1/2 is the square root of 4, which is 2
Answer:
2
Step-by-step explanation:
In first step use the product rule of exponents .
so exponents going to add up.
Then in the second step simplified exponents.
After that Its division rule of exponents. and according to division to the exponents get subtracted.
In the end he would be left with four to the power half. which means square root of 4. which is 2.
What is g(x)?
Please help!
Answer:
A
Step-by-step explanation:
It's just a normal quadratic graph but flipped meaning its just negative x squared
What is the probability of an event that is certain?
Answer:
Nvm my answer is wrong
An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of zero. If there is a chance that an event will happen, then its probability is between zero and 1.
Anthony bought a new rectangular table for his living room the length of the table is 4 feet and the perimeter of the table is 14 feet what is the width of the table ?
A. 4 feet
B.5 feet
C. 2 feet
D.3 feet
Answer:
Option d
Step-by-step explanation:
Length = 4 ftPerimeter = 14 ftWidth = ?→ Perimeter of rectangle = 2(l + w)
→ 14 = 2(4 + w)
→ 14 ÷ 2 = 4 + w
→ 7 = 4 + w
→ 7 - 4 = w
→ 3 ft = w
Therefore, width is 3 ft. (Option D)
cotA + tanA= secAcosecA
Step-by-step explanation:
cotA + tanA
= cosA / sinA+ sinA/ cosA
= cos2A + sin2A / sinA* cosA
= 1 / sinA* cosA
=1/ sinA * 1/ cosA
= cosecA *secA
=secAcosecA
[tex]\frac{cos^2A + sin^2A}{sinAcosA}[/tex]Answer:
Step-by-step explanation:
cotA + tanA = secAcosecA
LHS=cotA + tanA
=[tex]\frac{cosA}{sinA}[/tex] + [tex]\frac{sinA}{cosA}[/tex]
take lcm of the denominator
=[tex]\frac{cosA*cosA + sinA*sinA}{sinAcosA}[/tex](COS^2A + sin^2A =1)
=[tex]\frac{1}{sinAcosA}[/tex]
=1/sinA * 1/cosA
=cosecA*secA
=secAcosecA
therefore LHS=RHS
hence proved.
Please help me with this
Answer:
Step-by-step explanation:
Gabriela has solved incorrectly. 5 should distributed to 9x & (-8) and 4 should be distributed between x & 2
5(9x - 8) = 4*(x + 2)
5*9x - 5*8 = 4*x + 4*2
45x - 40 = 4x + 8
Subtract 4x from both sides
45x - 4x - 40 = 8
41x - 40 = 8
Add 40 to both sides
41x = 8 + 40
41x = 48
x = 48/41
What is the answer for this question?
Answer:
a/e
~~~~~~~~~~
[tex]\frac{(18) ab (20)cd}{ (15) bc (24) de}[/tex]
[tex]\frac{(3) ab (4)cd}{ (3) bc (4) de}\\[/tex]
[tex]\frac{ ab cd}{ bc de}\\[/tex]
[tex]\frac{ a }{ e}\\[/tex]
Step-by-step explanation:
1. Find the value of x and round to the nearest tenth
2. Find the value of y and round to the nearest tenth.
Measure of x :
[tex]\longrightarrow4 \sqrt{5} \: \: units[/tex]
Measure of y :
[tex]\longrightarrow8 \sqrt{5} \: \: units[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{hope \: \: it \: \: helps }}{\orange{....}}}}}[/tex]
An aquarium holds 11.81 cubic feet of water, and is 2.8 feet long and 1.7 feet wide. What is its depth? Round your answer to the nearest whole number.
Answer:
2ft
Step-by-step explanation:
Depth = volume / ( length x width)
11.81 / (2.8 x 1.7)
11.81 / 4.76
depth = 2.48
2 ft (to the nearest whole number)
There are 1,099 souvenir paperweights that need to be packed in boxes. Each box will hold 11 paperweights. How many boxes will be needed?
Answer:
1099/11=99.9
since you can't have 99 boxes, you round to 100 boxes.
you will need 100 boxes.
What are the zeros and x-intercepts of this quadratic function?
y
Select two answers: one for the zeros and one for the x-intercepts.
A. x-Intercepts: (-3,0) and (2.0)
B. X-Intercepts: (0, -3) and (0,2)
C. Zeros: -3 and 2
The answer is ⇒C. Zeros: -3 and 2
A. x-intercepts: (-3,0) and (2,0).
What are zeros & x-intercepts of quadratic function?The zero of the function is where the y-value is zero.
The x-intercept is where the graph crosses the x-axis.
Here, in graph we have,
at (-3,0) and ( 2,0) the quadratic crosses the x-axis.
And, at -3 & 2 the value of y is zero.
Hence, the answer is ⇒C. Zeros: -3 and 2
A. x-intercepts: (-3,0) and (2,0).
To learn more on zeros & x-intercepts of quadratic function click:
https://brainly.com/question/28822774
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