A helicopter starting on the ground is rising directly
into the air at a rate of 25 ft/sec. You are running on the
ground starting directly under the helicopter at a rate of 10
ft/sec. What is the rate at which the distance between you and the helicopter is changing when the helicopter has risen to a height of 60 ft in the air, assuming that, initially, it was 30 ft above you?
I want to understand how any why this is solved. So images/diagrams, detailed step by step breakdowns solutions are VERY much appreciated. Thanks!
Answers
Answer:
Oook, quick setup: pick a cartesian plane, be [tex](0;y(t))[/tex]the position of the helicopter as time passes, and [tex](x(t);0)[/tex] your position as you start running. In my horrible sketch, the green line is the distance when you start running, the red line is the distance you need, in general what you want is to move one end of the segment up, the other right, and stretch it.
That distance is easily found with the formula for the distance between two points in the plane, or [tex]d=\sqrt{(\Delta x)^2+(\Delta y)^2}= \sqrt{x^2(t)+y^2(t)}[/tex] (playing a bit with the squares). At this point we need to write down expressions for both [tex]x(t), y(t)[/tex] and find at what value of t we need to evaluate our distance.
For the sake of semplicity, let's start measuring times the moment you start running. Since speed is constant, both expressions will be of the form [tex]s=vt+s_0[/tex]
The equation for the runner becomes simply [tex]x(t)=10t[/tex], since you haven't moved until the heli is high enough.
The equation of the helicopter is [tex]y=25t+30[/tex] since the heli is 30ft above ground when you start running.
Finally, we need to know how many seconds have passed when the heli is at 60 ft above ground. that happens when [tex]60=25t+30 \rightarrow t=\frac{30}{25} = 1.20s[/tex]. in this time, you are at [tex]x(1.2)=10(1.2)=12ft[/tex] from the origin.
Plugging it in the distance formula you get: [tex]\sqrt{12^2+60^2}= \sqrt{144+3600}=4\sqrt {234}\approx 61.2ft[/tex]
Related Questions
Ted likes to run long distances. He can run 20 kilometers in 95 minutes. How far will Ted run in 285 minutes? (numeric only) *
Answers
[tex]\boxed{\boxed{\Large \text{Ted will run 60 kilometres in 285 minutes.}}}[/tex]
Step-by-step explanation:Using the distance-time-speed relationship:
[tex]\boxed{\Large \text{speed = $\frac{\rm distance}{\rm time}$}}[/tex]
[tex]\boxed{\Large \text{distance = speed $\times$ time}}[/tex]
[tex]\boxed{\Large \text{time = $\frac{\rm distance}{\rm speed}$}}[/tex]
so if Ted can run 20 kilometres (distance) in 95 minutes (time), then his speed = 20 ÷ 95 = 4/19 km/min.
Using this result, to calculate how far Ted will run in 285 minutes, we can say that distance = 4/19 × 285 = 60 kilometres.
∴ Ted will run 60 kilometres in 285 minutes.
[tex]\hrulefill[/tex]
To learn more about speed:
https://brainly.com/question/31756299
2 years,18 month.express the first quantity as a percentage of the second quantity
Answers
Answer:
2 years= 12 months
12÷18×100= 66.67%( approx)
2) 20cm=200mm
225÷200×100
=112.5%
Step-by-step explanation:
Answer:
2 years= 12 months
12÷18×100= 66.67%( approx)
Step-by-step explanation:
PLEASE HELP WILL MARK BRAINIEST!!!!!!!
Answers
Answer:
Option a is the best method with compass and straight edge.
Step-by-step explanation:
rotate segment AE about point F 144 degrees
Answers
Answer:
DC
Step-by-step explanation:
If we rotate a segment around a point 360 degrees, we have rotated it around to its original point. Similarly, if we rotate it 180 degrees, we have rotated it to the side opposite of where it once was relative to the point.
What we can do is see how much 144 degrees is of 360 and use that to determine how far around we rotate AE around F.
144/360
divide by 12 because that is a common factor of both the numerator and denominator
12 / 30
divide by 2 because that is a common factor
6/15
divide by 3 because that is a common factor
2/5
Therefore, 144/360 = 2/5. This means that we rotate segment AE 2/5 of the way around point F. We have 5 sides in the polygon ABCDE, and each represents 1/5 of the way around. Going counterclockwise, ED represents 1/5, DC represents 2/5, and so on. We are looking for 2/5, so DC is our answer
10x-9y=24
y= x-2
find x and y
Answers
Answer:
x=6,y=4
Step-by-step explanation:
10x-9(x-2)=24
10x-9x+18=24
x=24-18
x=6
sub x
y=6-2
y=4
Answer:
x=6 y=4
Step-by-step explanation:
Substitute x-2 in for y: 10x-9(x-2)=24
Distribute: 10x-9x+18=24
Subtract 10x-9x=1x
Subtract 18 from both sides
x=6
Substitute 6 for x
y=6-2
y=4
x=6 y=4
16,40 and 56 LCM
Solve this problem
Answers
Answer:
LCM = 2^4 x 5^1 x 7^1 = 560
Step-by-step explanation:
I hope this helps you !!Which fractions are equivalent to the fraction below. 20/32
Answers
Answer:
5/8
Step-by-step explanation:
The answer is 5/8 because 4*5 equals 20 and 4*8 equals 32. Therefore, you have to do the same thing you do to the numerator to the denominator. In addition, you I divided 20 by 4 which is 5 and 32 divided by 4 is 8. So, it is 5/8.
Kaitlyn drove 360 miles in 9 hours. If she continues driving at the same speed, how far will she have driven in 11 hours?
Answers
Answer:
440 miles
Step-by-step explanation:
First, you need to calculate the number of miles per hour. To do this, take the total number of miles traveled and divide it by the number of hours it took. 360/9=40. This means Kaitlyn drove at 40 miles per hour. Then, we need to multiply 40 by 11 to figure out the number of miles she drove in 11 hours because her speed stayed the same. 40*11=440. This means Kaitlyn will have driven 440 miles in 11 hours.
Hope this helps! :)
what is the slope of (8,3) (-5,3)
Answers
Answer:
-13x. (I think)
Step-by-step explanation:
someone please help me giving brainlist
Answers
Answer:
A
Step-by-step explanation:
9. Sofija buys a bracelet for $14.50 plus 8% tax.
Momoka buys a necklace for $12 plus 8% tax.
Enter the sum, in dollars, that Sofija and
Momoka paid, including tax.
Answers
Answer:
$12.96
Step-by-step explanation:
Before Tax Price: $12.00
Sale Tax: 8.00% or $0.96
After Tax Price: $12.96
The perimeter of the shape is
feet.
Answers
Answer:
This doens't realy make sense dude
PLEASE HELP WILL MARK BRAINIEST!!!!!
Answers
Answer:
The bisector of a given angle
Step-by-step explanation:
Because, the given picture shows an acute angle and the markings on it are of which you can see when a bisector is being searched for.
A book store is hosting a special night in which familles can enjoy a story and craft time. Tickets to the event must be bought ahead of time and are $1.50 for children and $2.50 for adults. So far, 45 children's tickets have been sold, which is 60% of the total tickets sold. How many tickets have been sold so far? Show or explain how you got your answer.steps please
Answers
Answer:
45
Step-by-step explanation:
just typing this so I'll have 20
Enter the correct answer in the box. Write your answer in the form y = mx + b, using the appropriate inequality symbol in place of the equal sign. HELP MEEE ASAPPPP ILL GIVE BRAINLIEST!!!!!!
Answers
Answer:
y > - x - 4
Step-by-step explanation:
1) Find the equation of the line
2) The equation of the line is y = - x - 4
3) Identify where the graph is shaded
4) It is shaded above and to the right of the line
5) This means that it is more positive/ greater than the unshaded areas
6) Switch the = sign to > to signify the inequality
7) All done!
Step-by-step explanation:
the delimiter line is going through the points (-4, 0) and (0, -4).
the line function
y = mx + b
m is the slope of the line, b is the y-intercept (the y value when x = 0).
the slope is the ratio of "y coordinate change / x coordinate change" when going from one point to another.
so, for the 2 found points :
x changes by +4 (from -4 to 0)
y changes by -4 (from 0 to -4).
the slope m is then
-4/+4 = -1
and the y-intercept is -4 (as explained).
so, the line is
y = -x - 4
and the graphic says that all values greater than our equal to the line values are valid, so
y >= -x - 4
Hello plz help with these two.
Answers
Problem 1
Answer: Choice D--------------
Explanation:
The vertices are (-12,0) and (12,0). Both of which are on the same horizontal line. Because of this, we have a hyperbola that opens leftward and rightward. Such hyperbolas are of the form
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]
where (h,k) is the center and the a,b terms help set up the asymptotes.
The midpoint of the vertices (-12,0) and (12,0) is the point (0,0). This is the center. So we know that h = 0 and k = 0.
For left/right opening hyperbolas, the asymptotes can be described as the equations:
y = (b/a)x
y = (-b/a)x
Or we can condense them into [tex]y = \pm \frac{b}{a}x[/tex]. Compare this to the given equation [tex]y = \pm\frac{5}{12}x[/tex] to see that b = 5 and a = 12.
Therefore, we get the following:
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1\\\\\frac{(x-0)^2}{12^2}-\frac{(y-0)^2}{5^2}=1\\\\\frac{x^2}{144}-\frac{y^2}{25}=1[/tex]
That points us to choice D.
You chose the correct answer.
=============================================================
Problem 2
Answer: Choice A--------------
Explanation:
Divide both sides by 3600 so we can turn that "3600" into "1". Then our goal is to get that "1" to its own side like so:
[tex]25x^2-144y^2 + 3600 = 0\\\\\frac{25x^2-144y^2 + 3600}{3600} = \frac{0}{3600}\\\\\frac{25x^2}{3600}-\frac{144y^2}{3600} + \frac{3600}{3600} = 0\\\\\frac{x^2}{144}-\frac{y^2}{25} + 1 = 0\\\\\frac{x^2}{144}-\frac{y^2}{25} = -1\\\\-\frac{x^2}{144}+\frac{y^2}{25} = 1\\\\-\frac{x^2}{12^2}+\frac{y^2}{5^2} = 1\\\\[/tex]
We see that a = 12 and b = 5 like earlier, so we end up with the same asymptotes as before. The only difference is that this hyperbola opens upward/downward rather than left/right.
You made the correct choice in picking answer A. Both of your answers are correct. Nice work.
2/7>b+5/7 solve the inequality
Answers
[tex]\dfrac 27 >b +\dfrac 57\\\\\implies 2 > 7b +5~~~;[ \text{Multiplying both sides by 7}]\\\\\implies 2-5>7b\\\\\implies -3>7b\\\\\implies -\dfrac 37 >b\\\\\implies b<-\dfrac 37\\\\\\\text{Interval,}~ \left(-\infty, -\dfrac 37 \right)[/tex]
prove the identity.
(1-sin^2x)tanx=cosxsinx
Note that each Statement must be based on a Rule
Answers
[tex](1-\sin^2 x) \tan x \\\\=\cos^2 x \cdot \dfrac{\sin x}{\cos x}\\\\=\cos x \sin x[/tex]
Help me plzzzzzzz! I need this today!
Answers
Answer:
it looks like y int is about 2550
Step-by-step explanation:
If 3(x - 2) = 6, then x
Answers
Answer:
8
Step-by-step explanation:
3(x - 2) = 6
3x - 6 = 6
x - 6 = 2
x = 8
hope it helps :)
mark brainliest!!
A desk drawer is shaped like a rectangular prism. The height of the drawer is 7 inches. The bottom of the drawer has an area of 210 square inches.
What is the volume of the desk drawer?
Enter your answer in the box.
Answers
Answer:
1470 inches cubed
Step-by-step explanation:
Vol=length × width × height
But ALSO,
length × width = Area,
So we find another Volume equation,
Vol = BaseArea × height
This is the information you are given in the question.
Vol = 210 × 7
Vol = 1470 inches cubed
I'll give brainliest to the right answer!!!
Find three consecutive odd integers such that the difference of twice the second and the first is 11.
Answers
Answer:
7, 9, 11
Step-by-step explanation:
question: Find three consecutive odd integers such that the difference of twice the second and the first is 11.
make the 3 consecutive odd intergers x, y, and z.
numbers are consective (come right after another) AND odd, meaning you would add 2 every time. therefore:
x+2=y
y+2=z
given that: "difference of twice the second and the first is 11."
difference means subtraction
second number is the variable y
first number is the variable x
2y-x=11
----------------
3 equations:
2y-x=11
x+2=y
y+2=z
----------solve by substitution
x+2=y
x =y-2 into 2y-x=11
2y-(y-2)=11
2y-y+2=11
y=9
second number is 9
-----
numbers are 7, 9, 11
Which term has the definition "A relationship in which two variables change at the same rate
Answers
(i believe thats what it is)
rewrite in simplest terms -8(-10u+6u-7)-10u
Answers
Answer:
22u + 56
Step-by-step explanation:
-8(-10u + 6u - 7) - 10u
1.) Combine like terms
-8(-10u + 6u - 7) - 10u
-8(-4u - 7) - 10u
2.) Distribute
-8(-4u - 7) - 10u
-8(-4u) -8(-7) - 10u
32u + 56 - 10u
3.) Combine like terms
32u + 56 - 10u
22u + 56
Therefore, the simplified equation is 22u + 56.
Answer:
22u+56
Step-by-step explanation:
1. simplify each term:
32u+56−10u
2. Subtract 10u from 32u.
22u+56
Hope this helps :)
Getting trained and licensed as a truck driver involves a one-time cost of $450. Gas and insurance end up costing about $2 per mile. For the first delivery, you will get paid $350 plus $6 per mile that you drive. Write 2 equations and solve this system.
Answers
The question is an illustration of a system of linear equations.
The system of linear equations is: [tex]y=450 + 2x[/tex] and [tex]y = 350 + 6x[/tex]The solution to the equation is (25,500)Let the number of miles be x.
Getting trained and licensed
One time cost: $450Gas and Insurance: $2 per mileSo, the equation is:
[tex]y=450 + 2x[/tex]
Delivery
First delivery: $350Rate: $6 per mileSo, the equation is:
[tex]y = 350 + 6x[/tex]
Hence, the system of linear equations is:
[tex]y=450 + 2x[/tex] and [tex]y = 350 + 6x[/tex]
To solve the equation, we equate both, as follows:
[tex]450 + 2x = 350 + 6x[/tex]
Collect like terms
[tex]6x - 2x = 450 - 350[/tex]
[tex]4x = 100[/tex]
Divide both sides by 4
[tex]x = 25[/tex]
Substitute 25 for x in [tex]y=450 + 2x[/tex]
[tex]y = 450 + 2 \times 25[/tex]
[tex]y = 450 + 50[/tex]
[tex]y = 500[/tex]
Hence, the solution to the equation is (25,500)
Read more about linear equations at:
https://brainly.com/question/14323743
Can someone help with this math problem?
Answers
Answer:
Hope it will help you a lot.
A sum of $1290 is to be divided between two people in the ratio of 7 to 8. How much does each person receive?
Answers
we know that $1290 is to be divided on a 7:8 ratio, so we'll start off by dividing 1290 by (7+8) and give each person accordingly
[tex]1290~~ at~~ 7:8\implies 7\cdot \cfrac{1290}{7+8}~~ :~~8\cdot \cfrac{1290}{7+8} \\\\\\ 7\cdot 86~~:~~8\cdot 86\implies 602~~ :~~688[/tex]
Pls answer this question
Yesterday, 5/6 of the 120 students in a contest gave their speeches. How many students gave their speeches.
Answers
Answer:100 Estudiantes dieron su discurso
Step-by-step explanation:
120÷6=20
20x5=100
100 Students
How?
120÷6=20
You can do this,
or you can do
120×1/6=20
_____________________________________________
20×5=100
Therefore,
100 students gave their speeches.
If I have a 93.3 in my class and I took a test, got 75% on it (the test is worth 20 points) what would my grade be? I need help ASAP!!!!
Answers
Answer:
it will be an 91 or 88
Step-by-step explanation:
Josh and Adelina are staff members for a political candidate. They are considering hiring callers who will call voters and ask for donations. (picture below)
a) only adelina's
b) only josh's
c) both statements are correct
d) neither statements are correct
Answers
Answer:
Adelina
Step-by-step explanation: