1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sergeinik [125]
3 years ago
14

The distance between Lincoln, NE, and Boulder, CO, is about 500 miles. The distance between Boulder, CO, and a third city is 200

miles. Assuming the three cities make a triangle on the map, which values represent the possible distance, d, in miles, between Lincoln, NE, and the third city?
Mathematics
2 answers:
GenaCL600 [577]3 years ago
6 0
We know that

The sum of the lengths of any two sides of a triangle is greater than the length of the third side (Triangle Inequality Theorem)

Let 

A------> Lincoln, NE

B------> Boulder, CO

C------> third city


we know that

in the triangle ABC

AB=500 miles

BC=200 miles

AC=x


Applying the Triangle Inequality Theorem

1) 500+200 > x------> 700 > x------> x < 700 miles

2) 200+x > 500----> x > 500-200------> x > 300 miles


the solution for x is 

300 < x < 700

the interval is------> (300,700)

the possible distances, d, in miles, between Lincoln, NE, and the third city, are in the range between 300 and 700 miles
gavmur [86]3 years ago
5 0

Answer:

300 and 700 I just did it I hoped it helped

You might be interested in
Somebody help with both questions
Minchanka [31]
1. X=5
2. I think I’m not sure is - 5.04
8 0
3 years ago
Anybody who knows Pre Calc?? My last offer here<br> Solution PLS!
4vir4ik [10]

Answers:

  • true speed = 26.935546 knots
  • true bearing = 102.265139 degrees

The values are approximate. Round them however you need to.

====================================================

Explanation:

The diagram you have drawn is correct if you're only considering one current. Specifically current #1 which has the bearing of 290 degrees moving at 25 knots.

The red angle is 290 degrees. The remaining portion that is needed to get a full 360 degrees is 360-290 = 70. This adds to the blue portion in quadrant 1, which is 90, and we get 70+90 = 160. So the blue angle is 160 degrees.

The vector for current #1 is <25*cos(160), 25*sin(160)>

This approximates to <-23.4923155, 8.5505036>

All of this is for current #1.

------------

Vector #2 is much more simple in terms that there aren't messy decimal approximations here. The direction is due north, which means that the vector is pointing straight up toward 90 degrees.

We can then say: <12*cos(90), 12*sin(90)> = <12*0, 12*1> = <0, 12>

Vector #2 is <0,12>

When you wrote <12,0>, you were on the right track, but you had the coordinates swapped in the wrong order.

----------

Then we have to account for a wind going 4 knots in the southwest direction. This is at the angle 225 degrees (we rotate 180 degrees plus another 45 to get 225). So,

vector #3 = <4*cos(225), 4*sin(225)> = <-2.8284271, -2.8284271>

This vector's coordinates are approximate

---------

To recap everything so far, vectors 1 through 3 are the following

  • p = <-23.4923155, 8.5505036>
  • q = <0, 12>
  • r = <-2.8284271, -2.8284271>

I'm using variables to represent the vectors at this point, so we can then add them up to get...

s = p+q+r

s = <-23.4923155, 8.5505036> + <0,12> + <-2.8284271, -2.8284271>

s = <-23.4923155+0+(-2.8284271), 8.5505036+0+(-2.8284271)>

s = <-26.3207426, 5.7220765>

Vector s represents the sum of the three vectors p, q, and r. The two currents and the wind ultimately combine together to push the boat in the direction and along the length of vector s.

----------------------

Now that we know the coordinates of vector s, we use them to find the true speed and true bearing of the boat.

speed = sqrt(a^2 + b^2)

speed = sqrt( (-26.3207426)^2 + (5.7220765)^2 )

speed = 26.935546 knots, which is approximate

angle = arctan(b/a)

angle = arctan(5.7220765/(-26.3207426))

angle = -12.265139

Add 360 to this angle to find that we get to the coterminal angle of -12.265139+360 = 347.734861 degrees

This angle is in quadrant 4, which is the southeast quadrant. If we rotate another 360-347.734861 = 12.265139 degrees, going counterclockwise, then we'll face directly east. Then another 90 degree counterclockwise rotation has us face directly north.

In total, the true bearing is approximately 90+12.265139 = 102.265139 degrees

So we'll start aiming north, and then rotate roughly 102.265139 degrees toward the east to get to the true bearing.

4 0
3 years ago
Which are perfect square trinomials? Select two options.
Paul [167]

Answer:

C and D

Step-by-step explanation:

just took the quiz

3 0
3 years ago
Read 2 more answers
A large dump truck will empty its full load of stone onto a small plot of land for storage. The rock forms a cone that is 9 feet
Zanzabum
Volume of a cone = (1/3) * Area of Base * height
144 * 3 / 9 = Area of Base
Area of the Base = 48



6 0
3 years ago
Read 2 more answers
Santosh spent $200, before tax, on a DVD player and DVDs. The player cost $120, new DVDs cost $15 and used DVDs cost $5. Santosh
gizmo_the_mogwai [7]

Answer:

Santosh purchased 4 new and 4 used DVDs.

Step-by-step explanation:

From the information given, as you know that Santosh spent $200 and that the DVD player cost $120, you can say that the new and used DVDs cost $80, which can be expressed as:

15x+5y=80, where:

x refers to the number of new DVDs

y refers to the number of used DVDs

Now, as the statement indicates that Santosh purchased the same number of new and used DVDs, this means that x is equal to y and you can replace y with x and solve for x:

15x+5x=80

20x=80

x=80/20

x=4

According to this, the answer is that Santosh purchased 4 new and 4 used DVDs.

3 0
3 years ago
Other questions:
  • How do I find the domain n range of this graph​
    12·1 answer
  • Which of the following statements are not proportional 4/6=9/12 2/3=12/18 5/4=10/8 7/5=36/25
    15·2 answers
  • What kind of molecule is represented in the diagram?
    12·2 answers
  • The first two steps in determining the solution set of the system of equations,
    11·1 answer
  • Which of the following is the inverse of the function given below?
    5·2 answers
  • The sum of two factors of 48 is nineteen. The larger factor,
    12·1 answer
  • Find the slope of the line passing through the points (3, -2) and (1, -8).
    13·1 answer
  • Help test due tonight ! *no links please *
    9·1 answer
  • You bought a video game for $35. You got it on sale
    5·1 answer
  • Please help I don’t understand
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!