After leaving camp for a three-day journey into the frozen tundra, Daniela has just returned to camp. The
three days of her journey can be described by displacement (distance and direction) vectors d , d), and dz.
where each vector indicates Daniela's displacement from the start of her day to the end of her day.
di = 8i +3
d, is not given
az = i +47
(Distances are given in kilometers, km.)
What distance did Daniela travel on day two?
kilometers
(Round your final answer to the nearest tenth.)
In what direction did Daniela travel on day two? Assume 0° is the rightward direction.
(Round your final answer to the nearest degree. Your answer should be between 0 and 360°.)
Answers
Answer:
a) 8.7 km
b) 187.6°
Step-by-step explanation:
Given
Travel vectors (distance)∠(direction) ...
d₁ = 8∠3°d₂ = unknownd₃ = 1∠47°total travel was a round tripFind
(Rounded to the nearest tenth ...)
a) |d₂|
b) ∠d₂
Solution
In order for the sum of the three travel vectors to represent a round trip, their sum must be zero. That is, the value of d₂ must be the opposite of the sum of the other two vectors. A vector calculator can find the desired value easily. Here, we will show the calculation using the law of cosines and the law of sines.
__
a) A diagram can be helpful. Since we want to find the opposite of the sum of the given vectors, we can start by drawing their sum. In our diagram, d₁ is segment AB, and d₃ is segment BC. Their sum is the segment AC.
The internal angle ABC is the supplement of the difference of the angles for d₁ and d₃, so is 180° -(47° -3°) = 136°. Then the law of cosines gives length AC as ...
AC² = AB² +BC² -2AB·BC·cos(B)
AC² = 8² +1² -2·8·1·cos(136°) = 65 -16cos(136°) ≈ 76.5094
AC ≈ √76.5094 ≈ 8.747
The distance traveled on day 2 is about 8.7 km.
__
b) Given the side lengths of a triangle and one angle, the law of sines can be used to find the other angles. Here, it is convenient to find the internal angle at A. The law of sines tells us ...
sin(A)/BC = sin(B)/AC
sin(A) = BC/AC·sin(B)
A = arcsin(BC/AC·sin(B)) = arcsin(1/8.747·sin(136°)) ≈ 4.555°
The direction angle from C to A will be the sum of the 3° direction angle of AB and the internal triangle angle A we just found, added to 180°. That sum is ...
∠CA = 180° +3° +4.6° = 187.6°
∠d₂ = 187.6°
Answer:
Distance traveled 8.6 kilometers on day two
Daniela traveled in a direcrion of 234degrees on day two
Step-by-step explanation:
I had the same exact question and found the answers after having it incorrect
Related Questions
An icicle is in the shape of an inverted cone with a diameter of 9 mm and a height of 27 mm. In cubic millimeters, how much frozen water is in the icicle? Use 3.14 for . Round your answer to the nearest hundredth.
Answers
Answer:
volume ≈ 572.27 mm³
Step-by-step explanation:
The icicle is in the shape of an inverted cone with a diameter of 9 mm and a height of 27 mm. To find how much in cubic millimetres the frozen water is in the icicle can be calculated below.
In other words the question want us to find the volume of the cylinder. The volume of the cone can be represented as follows:
volume of a cylinder = 1/3πr²h
where
r = radius
h = height
diameter = 9 mm
height = 27 mm
r = diameter/2 = 9/2 = 4.5
volume = πr²h
volume = 1/3 × 3.14 × 4.5² × 27
volume = 1/3 × 3.14 × 20.25 × 27
volume = 1/3 × 63.585 × 27
volume = 1716.795/3
volume = 572.265 mm³
volume ≈ 572.27 mm³
Answer:
572.27 mm³
Step-by-step explanation:
Alex puts his spare change in a jar every night. If he has $11.09 at the end of January, $22.27 at the end of February, $44.35 in April, $75.82 in July, $89 in August, and $114.76 at the end of October, perform a linear regression on this data to complete the following items. What does the value of the correlation coefficient tell you about the correlation of the data? Write the equation of the best-fitting line. On average how much money does Alex add to the jar each month? Alex wants to buy a video game console at the end of December for $140. Will he have enough for this purchase. Show equation. THANK YOU!
Answers
the answer is about $22 each month and no he will not have enough
Estimate by rounding each number to the nearest ten thousand and then subtract
Answers
Answer:
50,000
Step-by-step explanation
80,000 - 30,000 = 50,000
2.65 multiply by 100
Answers
Answer:
265
Step-by-step explanation:
Answer:
265
Step-by-step explanation:
gimme brainliest plz
whats the solution to the model below?
X=3
x=1
x=2
x=7
Answers
Answer:
[tex]2x + 4 = 10[/tex]
[tex]2x = 6[/tex]
[tex]x = 3[/tex]
Slope is found by dividing the change in ____ by the change in ____. x; y y; x
Answers
Answer:
Change in Y by the Change in X.
Step-by-step explanation:
Slope can be found by dividing the rise (change in y) by the run (change in x).
[tex]m =\frac{rise}{run} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Answer: y;x
Step-by-step explanation: USATESTPREP
You’re welcome :)
What is the slope of each line? Line A: y = negative 5 x minus 2 Line B: y = 2 x + 3 The slope of line A Equals negative 5. The slope of line B Equals 2. The slope of line A Equals negative 2. The slope of line B Equals 3. The slope of line A Equals 5. The slope of line B Equals negative 2. The slope of line A Equals 3. The slope of line B Equals negative 2.
Answers
Answer:
A. -5, 2
Step-by-step explanation:
I got it right.
The slope of line A equals negative 5 and the slope of line B equals 2. Then the correct option is A.
What is the equation of line?The equation of line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.
The equations of line are given below.
Line A: y = –5x – 2
Then the slope of the line A will be
Slope A = –5
Line B: y = 2x + 3
Then the slope of the line B will be
Slope A = 2
The slope of line A equals negative 5.
The slope of line B equals 2.
Then the correct option is A.
More about the equation of line link is given below.
https://brainly.com/question/21511618
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Point A (-3, 5) is rotated 180º about the origin. What are the coordinates of A' after the rotation?
Answers
A point when rotated 180º about the origin flips the sign of the coordinates. Thus, point A' after rotating point A (-3,5) 180º about the origin would have coordinates (3,-5).
Explanation:A rotation of 180º about the origin essentially changes the signs of the coordinates. If we have Point A as (-3, 5), after a 180° rotation about the origin, you'll get Point A', which will be the opposite of Point A. That means it turns (-3, 5) to (3, -5).
Rotation about the origin flips the point across both axes. This is based on a rule in mathematics: When we rotate a point 180° about the origin, (x, y) becomes (-x, -y).
The coordinates of A' after the 180° rotation are (3, -5).
Learn more about Rotation here:https://brainly.com/question/34828607
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lol2
Where's the Lie?
Here are three statements that Tiana wrote about this
exponential
One of the statements is a lie. Which is it?
A. For very large values of x, the exponential has very large
values of y.
OB. The y-intercept of the exponential is (0,1).
C. The point (-2,4) is on the exponential.
Explain how you know it's a lie.
Answers
Answer:
A.
Step-by-step explanation:
As the x value is increasing the y is decreasing because the graph shows exponential decay.
The graph of a simple exponential function always pass through (0,1)
The statement that is a lie is (a) For very large values of x, the exponential has very large values of y.
From the graph, we have the following highlights
The graph passes through point (0,1); this means that the y-intercept is (0,1).The graph passes through (-2,4)The above highlights mean that options (b) and (c) are true, while option (a) is a lie
Option (a) is a lie because, as the value of x increases, the value of y increases.
Read more about exponential functions at:
https://brainly.com/question/11487261
I really need help on this sooo yeah
Answers
Answer:
XVW
Or
WVX
Step-by-step explanation:
Since it's an isosceles triangle, it can either be:
XVW
Or
WVX
NEED HELP ASAP
which set of numbers could represent the lengths of the sides of right triangle
A. 7,9,11
B. 12,18,22
C. 10,15,20
D. 8,15,17
Answers
We have to use Pythagorean Theorem to solve this. We square the two smallest sides, then add. If the sum is the square of the largest side, then it's our answer.
A. 7, 9, 11
49 + 81 = 130 ≠ 121
B. 12, 18, 22
144 + 324 = 468 ≠ 484
C. 10, 15, 20
100 + 225 = 325 ≠ 400
D. 8, 15, 17
64 + 225 = 289 = 289
So, our answer is D
How would you dilate the point (-3,2) by a scale factor of 1/2
Answers
you would multiply each value by the scale factor
22. There are 31 girls and
25 boys in the marching band. When
the band marches, they are in 7 rows.
How many people are in each row?
Answers
Answer:
8
Step-by-step explanation:
To solve this problem, you need to divide the total number of people the by the amount of rows you have to see how many people can fit in each row.
With 31 girls and 25 boys, you have a total of 56 people. Divide 56 by 7 to get 8.
You will have 8 people in each row.
Answer:
8 people.
Step-by-step explanation:
31 + 5 = 36. 36 + 20 = 56.
56 divided by the number of rows which is 7 in this case = 8.
There will be 8 people per row. Consisting of males and females.
P.S
Have an Amazing Day, I Hope this Helps and Good Luck!!
-Faker/Tosrel
Complete the point-slope equation of the line through (-1,6) and (1,5).
Use exact numbers.
Y= 6
Answers
Answer:
Y-6=-1/2(x-(-1) )
Step-by-step explanation:
The Equation for the point-slope of the line is y - 6 = -1/2(x + 1).
What is the slope of a line?A line's slope is defined as the ratio of the change in y coordinates to the change in x coordinates.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
Given coordinates (-1,6) and (1,5).
the slope of line is given by,
m = (y₂- y₁)/(x₂ - x₁)
y₂- y₁ = 5 - 6 = -1
x₂ - x₁ = 1 - (-1) = 2
m = -1/2
to find the equation at y = 6
when y = 6, x = -1
the equation is given by
y - y₁ = m(x - x₁)
y - 6 = -1/2(x -(-1))
y - 6 = -1/2(x + 1)
Hence equation of a line is y - 6 = -1/2(x + 1).
Learn more about the slope of a line;
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Lucia has $600 in her checking account. She wants to spend part of this money on a computer. She wants to have exactly $250 left in her checking account after buying the computer. The equation shown can be used to find t, the amount of money in dollars that Lucia can spend on the computer: t + 250 = 600 Which solution represents the correct answer? *
Answers
Answer:
t = 350
Step-by-step explanation:
subtract 250 from each side, and then you'll have t = 350
Answer:
350
Step-by-step explanation:
600 minus 250 =350
350 plus 250 =600
I basically did the inverse operation to solve this equation
PLZZ HELPPP!!! Each edge of a wooden cube is 6 centimeters long. The cube has a density of 0.71 g/cm3
.
What is the mass of the wooden cube?
Enter your answer in the box.
g
Answers
Answer:
153.36g
Step-by-step explanation:
Density is defined as the ratio of mass per unit volume of a material.
Density = Mass/Volume
Given the edge of a cube which is equivalent to its length L to be 6cm.
Density of the cube = 0.71g/cm³
Volume of the cube = L³
Volume = 6³
Volume of the cube = 216cm³
Mass = Density × Volume
Mass of the cube = 0.71×216
Mass of the cube = 153.36grams
Answer:
153.36 grams
Step-by-step explanation:
Density is mass divided by volume: d = m/v.
Here, we already know that d = 0.71 g/cm³.
We can find the volume of hte cube. The volume of a cube is denoted by:
V = s³, where s is the side length
The cube's length is 6, so plug this in:
V = s³
V = 6³ = 216 cm³
Plug these values in:
d = m/v
0.71 g/cm³ = m / 216 cm³
m = 0.71 * 216 = 153.36 grams
The answer is 153.36 grams.
Martina is currently 12 years older than her cousin Joey. In 4 years she will be 3 times as old
as Joey. Use this information to answer the following questions.
Answers
[tex]\Huge{\underline{\underline{\sf{\red{AnSwEr:}}}}}[/tex]
[tex]\boxed{\sf{Martina's \: Present \: age = 14 \: years}}[/tex]
[tex]\boxed{\sf{Her \: cousin's \: Present \: age = 2\: years}}[/tex]
[tex]\Huge{\underline{\underline{\sf{\green{ExpLaNaTion:}}}}}[/tex]
= Let Martina's cousin's age be = n
= Let her age be = n+12
After four years,
Cousin's age = n+4
Her age = n+12+4=n+16
But according to the question her age = 3(n+4) = 3n+12
Thus,
3n+12=n+16
3n-n=16-12
2n=4
n=4/2
[tex] \boxed{ \sf {n = 2}}[/tex]
Thus ,
Her cousin's present age = n = 2
Her cousin's present age = n = 2Her present age = n+12 = 2+12=14
PLZ HELP!!!!!
3x/2 − 5/12
= 1/4
Answers
Answer:
x=4/9
Step-by-step explanation:
you have to multiply both sides by 12 to get 18x-5=3 then add 5 to both sides which would get you 18x=8, then divide both sides by 18 and you will get 4/9.
Kayla randomly surveyed the eight-grade classes at her school and found that 12 out of 50 own a pet. Based on these data, how many of the 150 eight-grade students in kayla’s school would be expected to own a pet?
Answers
Answer: The answer should be 36
Answer:
36 students
Step-by-step explanation:
Set up a proportion
12/50=x/150
Cross multiply
50x=1800
Divide by 50 on both sides
x=36
So 36 out of 150 8th grades students would be expected to own a pet
Hope this helps! :)
A sphere is cut into 8 congruent pieces. The radius of the sphere is 8 centimeters. One piece is shown in the diagram. What is the surface area of one piece of the sphere, as shown in the diagram? Express the answer in terms of π. 64π cm2 80π cm2 256π cm2 384π cm2
Answers
Answer:
B. 80pi cm^2
Step-by-step explanation:
Answer:
Option number 2
Step-by-step explanation:
Suppose you only look at the height of the bars on the graph. Which conclusion would you MOST LIKELY reach?
A) Twice as many Democrats as Republicans agreed with the court.
B) Twice as many Republicans as Independents agreed with the court.
C) Three times as many Democrats as Republicans agreed with the court.
D) The total number of Republicans and Independents agreeing with the court is half the number of the Democrats that agreed.
Answers
Answer:c
Step-by-step explanation:
15 Points! Can someone help me with this?
Answers
Given:
Spinning top is in the shape of a square pyramid.
Side length of the base = 32 mm
Height of the pyramid = 32 mm
To find:
Volume of the spinning top
Solution:
Volume of the square pyramid:
[tex]$V=\frac{1}{3} b^{2} h[/tex]
[tex]$V=\frac{1}{3} \times (32)^{2} \times 32[/tex]
[tex]$V=1024 \times 32[/tex]
[tex]V=10922.66[/tex] cubic millimeter
The volume of the spinning top is 10922.66 cubic millimeter.
Select the correct answer. If the graph of function g is 6 units below the graph of function f, which could be function g? f(x) = -2x + 7
A. g(x) = -2x − 6
B. g(x) = -2x + 20
C. g(x) = -6x + 7
D. g(x) = -2x + 1
Answers
this is because if you wanted the function to be six below, the slope would not change but the y-intercept would go down 6
Answer:
D
Step-by-step explanation:
d equals 0.5+ 5T do you equals distance in miles and T equals time what are the independent and dependent variables
Answers
Answer:
Jillian walked 0.5 miles before she started jogging at an average pace of 5 miles per hour. The equation d = 0.5 + 5t can be used to relate the total distance, ...
Step-by-step explanation:
What is the upper quartile in the box plot? A box-and-whisker plot. The number line goes from 100 to 125. The whiskers range from 104 to 125, and the box ranges from 107 to 122. A line divides the box at 119.
Answers
Answer: cncnnc
Step-by-step explanation:
true false no my
Answer:
Ya'll the answer is 122
Step-by-step explanation:
I checked in with the AI helper and he would always help me, also I got the answer from the AI.
:) hope this helps
and if your ever stuck on a question,
Ginny the AI will come to help u Byeeeee :D
For a class project, a teacher cuts out 15 congruent circles from a single sheet of paper that measures 6 inches by 10 inches. How much paper is wasted?
Answers
Answer:
60 – 15π square inches
Step-by-step explanation:
Assuming a diameter of 2 inches for each circle, then because the height of the sheet is 6 inches and the length is 10 inches, 5 columns of 3 circles each, are formed (see picture attached).
The area of each circle is: (π*D^2)/4 = (π*2^2)/4 = π square inches
The area of the 15 circles is: 15π square inches
The area of the sheet is = 6*10 = 60 square inches
The wasted paper is equal to the difference between the area of the sheet and the area of all circles, that is, 60 – 15π square inches
Answer:
60 – 15π square inches
Step-by-step explanation:
Graph the line x = -3
Answers
Answer:
Draw a vertical line passing through (-3,0)
A square in a rectangle have the same perimeter. The length of a side of the square is 4x-1. The length of the rectangle is 2x+2 and the width is 2x
Answers
The value x is 1, if the perimeter of square and rectangle are same. The perimeter of square and rectangle is 12 units.
Step-by-step explanation:
The given is,
A square in a rectangle have the same perimeter
The length of a side of the square is 4x-1
The length of the rectangle is 2x+2 and width is 2x
Step:1
Let, a - Side of square
l - Length of the rectangle
w - Width of the rectangle
Step:2
Formula for perimeter of square is,
[tex]p=4a[/tex].............................(1)
Formula for perimeter of rectangle is,
[tex]p=2(l+w)[/tex]....................(2)
Step:3
From given,
Equation (1) = Equation (2)
[tex]4a = 2 (l+w)[/tex]
where,
a = 4x-1
l = 2x+2
w = 2x
Substitute the values,
4 ( 4x-1 ) = 2 ( 2x+2+2x )
16x - 4 = 2 (4x + 2)
16x - 4 = 8x + 4
16x - 8x = 8
8x = 8
x = 1
Step:4
Substitute the values of x,
a = 4(1)-1 = 3
l = 2(1)+2) = 4
w = 2(1) = 2
Perimeter of square and rectangle is 12 units
Result:
The value x is 1, if the perimeter of square and rectangle are same. The perimeter of square and rectangle is 12 units.
What is the volume (in cubic feet) of the composite shape rounded to the nearest whole number.
https://lh4.googleusercontent.com/vUIfZHaKxbdifO93idzlasRKfEgvrv14A-EqM3jgStNqNpMzpBqIf2mI5R_S4juEGlQnyVlZfDxjJFMkbmYu5Gt7LyBl241M1XtOtKLHXRidvyOygtO4tvdkcTuU=w147
Answers
Answer:
109.956
Step-by-step explanation:
Formula for Volume of Cylinder: V = (pi)r^2H
84.823 + 25.133 = 109.956 (in cubic feet)
Eric is reading a book that has 144 pages. He reads 8 pages a day. How many days will it take Eric to finish reading the book?
Answers
Answer:
It will take him 18 days to finish the book.
Step-by-step explanation:
[tex]144/8=18[/tex]
Answer:
18
Step-by-step explanation:
You divide 144 by 8 and get the answer.