Jerome and eric start their hike at point a and follow the trail in the counterclockwise direction. they stop at point w to eat lunch. how manu total miles have jerome and erick hicked when they stop for lunch

Answer:

The colony of bats will take 1.612 hours to cover an area of 80,000 square miles.

Step-by-step explanation:

As the colony of bats emerges from a cave and spreads out in a circular pattern, the area covered ([tex]A[/tex]) by the colony, measured in square miles, is represented by the following geometrical formula:

[tex]A = \pi\cdot r^{2}[/tex]

Where:

[tex]r[/tex] - Distance of the bat regarding the cave, measured in miles.

In addition, each bat moves at constant speed and distance is represented by this kinematic formula:

[tex]r = r_{o}+\dot r \cdot \Delta t[/tex]

Where:

[tex]r_{o}[/tex] - Initial distance of the bat regarding the cave, measured in miles.

[tex]\dot r[/tex] - Speed of the bat, measured in miles per hour.

[tex]\Delta t[/tex] - Time, measured in hours.

The distance of the bat regarding the cave is now substituted and time is therefore cleared:

[tex]A = \pi \cdot (r_{o}+\dot r \cdot \Delta t)^{2}[/tex]

[tex]\sqrt{\frac{A}{\pi} }-r_{o} = \dot r \cdot \Delta t[/tex]

[tex]\Delta t = \frac{1}{\dot r} \cdot \left(\sqrt{\frac{A}{\pi} }-r_{o} \right)[/tex]

Given that [tex]\dot r = 99\,\frac{mi}{h}[/tex], [tex]A = 80,000\,mi^{2}[/tex], [tex]\pi = 3.14[/tex] and [tex]r_{o} = 0\,mi[/tex], the time spent by the colony of bats is:

[tex]\Delta t = \left(\frac{1}{99\,\frac{mi}{h} } \right)\cdot \left(\sqrt{\frac{80,000\,mi^{2}}{3.14} }-0\,mi \right)[/tex]

[tex]\Delta t \approx 1.612\,hours[/tex]

The colony of bats will take 1.612 hours to cover an area of 80,000 square miles.

Answer:

B:  1.6 hours

Step-by-step explanation:

Answer:

[tex]\dfrac{A}{x}+\dfrac{B}{x-6}[/tex]

Step-by-step explanation:

Given the function [tex]\dfrac{37}{x(x-6)}[/tex], to write the form of its partial fraction on decomposition, we will separate the two functions separated by an addition sign. The numerator of each function will be constants A and b and the denominator will be the individual factors of each function at the denominator. The partial fraction of the rational function is as shown below.

[tex]= \dfrac{37}{x(x-6)}\\\\= \dfrac{A}{x}+\dfrac{B}{x-6}[/tex]

Since we are not to solve for the constants, hence the partial fraction is [tex]\dfrac{A}{x}+\dfrac{B}{x-6}[/tex]

Answer:

The equations needed to solve this problem are:

y = 12 + 6x

y = 12x

The number of posters completed by each Avenger will be 24.

Step-by-step explanation:

The information provided are:

So, after x day the number of poster completed by Ms. Ironperson will be:

y = 12 + 6x

And after x day the number of poster completed by Mr. Thoro will be:

y = 12x

Thus, the equations needed to solve this problem are:

y = 12 + 6x

y = 12x

Compute the value of x as follows:

12x = 12 + 6x

6x = 12

x = 2

The number of posters completed by each Avenger is:

y = 12x = 12 × 2 = 24

Thus, the number of posters completed by each Avenger will be 24.

Answer: B

Step-by-step explanation:

We can define the North as our positive y-axis, and the East as the positive x-axis.

The position of the airport is the (0, 0)

Then the position of the first plane is: (200 km north and 50 km east)

(50km, 200km)

The position of the other plane is: (30 km north and 100 km west)

(-100km, 30km)

Now, if we have two points (a, b) and (c, d)

The distance between those points is:

D = √( (a - c)^2 + (b - d)^2)

Then the distance between the planes is:

D = √( (50km - (-100km))^2 + (200km - 30km)^2)

D = √( (150km)^2 + (170km)^2)

D = 226.7km

Then the distance is closest to 200km, the correct option is B.

On a coordinate plane, we have:

The closest distance between the planes is 200km

The positions of the two planes is given as:

[tex]A = (50,200)[/tex] --- 50km east and 200km north

[tex]B = (-100,30)[/tex] --- 100km west and 30km north

The distance between the planes is calculated using the following distance formula:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

So, we have:

[tex]d = \sqrt{(50--100)^2 + (200-30)^2}[/tex]

[tex]d = \sqrt{150^2 + 170^2}[/tex]

[tex]d = \sqrt{51400}[/tex]

[tex]d = 226.72km[/tex]

From the list of given options, 200km is the closest to 226.72km

Hence, the closest distance between the planes is 200km

See attachment for the positions of both planes

Read more about distance at:

https://brainly.com/question/16310813

Answer:

A) No solution

Step-by-step explanation:

The absolute value of a quantity is either zero or positive. It cannot be negative.

For the absolute value of a quantity to be less than or equal to -1, it means the absolute value of the quantity is negative. This cannot be, so there is no solution.

Answer: A) No solution

Answer:

no solutions

Step-by-step explanation:

An absolute value is non negative

The smallest value of an absolute value is 0

0 ≤ -1

This is never true so there is no solution

Answer:

15

*ignore this answers have to be a minimum of 20 characters.

Answer:

15

Step-by-step explanation:

1+2=3

3+3=6

6+4=10

10+5=15.

Answer:

Step-by-step explanation:

Given,

Perpendicular ( P ) = 36

Base ( b ) = 36

Hypotenuse ( h ) = ?

Finding the hypotenuse :

Using the Pythagoras theorem :

[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]

plug the values

⇒[tex] \sf{ {h}^{2} = {36}^{2} + {36}^{2} }[/tex]

Evaluate the power

⇒[tex] \sf{ {h}^{2} = 1296 + 1296}[/tex]

Add the numbers

⇒[tex] \sf{ {h}^{2} = 2592}[/tex]

Squaring on both sides

⇒[tex] \sf{h = 36 \sqrt{2} }[/tex] units

Hope I helped!

Best regards!!

Answer:

20/:&&:/$/686th

Step-by-step explanation:

ggbnk

Answer:

here I think

Step-by-step explanation:

8y + 5 - 10y - 2 = (8y-10y)+(5-2)=-2y+3

Answer:

12i

Step-by-step explanation:

Step 1: Write it out

√-144

Step 2: Factor

√144(√-1)

Step 3: Evaluate

12i

Answer:

The correct option is four.

Step-by-step explanation:

The associative property implies that the values are added however we want, i.e. the numbers can be grouped in any way and the answer would still be the same.

The associative property of addition is:

[tex](a+b)+c=a+(b+c)[/tex]

The expression provided is:

(13 + 15 + 20) + (20 + 47 + 18)

The answer provided by four students are:

Jeremy : (20 + 13 + 15) + (20 + 47 + 18)

Layla : (20 + 47 + 18) + (13 + 15 + 20)

Keith : (13 + 20) + (20 + 47 + 18) + 15

Melinda : (13 + 15 + 20 + 20) + (47 + 18)

So, all the four students correctly applied only the associative property to rewrite the expression.

The correct option is four.

Answer: The answer is A or one lol

Step-by-step explanation:

Answer:

Step-by-step explanation:

The length of one revolution of the sprocket is ...

  C = 2πr = 2π(1.5 in) = 3π in

Then the length of 3250 revolutions is ...

  3250(3π in) = 30,630.53 in

About 30,631 inches of chain travel past the sprocket in one minute.

__

There are 12 inches in a foot, so the number of feet is ...

  30,630.53 in/(12 in/ft) = 2552.54 ft

About 2553 feet of chain travel past in one minute.

Answer:

Mark answer C and D as correct

Step-by-step explanation:

Recall that a bisector cuts the side in two equal segments, then KH has to be half of 136 that is KH = 68

Also KHZ and HLZ are right angle triangles that share the same hypotenuse, so they are congruent triangles, which means that HL must equal KH  and therefore the full side HJ must be 68 times 2 = 136

Answer:

Hey there!

We can write the proportion:

[tex]88/4840 = x/1155[/tex]

101640=4840x

x=21

The car would need 21 gallons of gas to travel 1155 miles.

Let me know if this helps :)

Answer:

21 gallons

Step-by-step explanation:

4,840 miles = 88 gallons

=> 1155 miles = x gallons

=> Cross-multiply

=> 4840 * x = 1155 * 88

=> 4840x = 101640

=> 4840x/4840 = 101640/4840

=> x = 21

The car can travel 1,155 miles using 21 gallons.

Answer:

C. There is a 0.60 probability that it will rain somewhere in the region at some point during the day.

Step-by-step explanation:

The probability that it will rain is given by =p= 60% = 0.6

60​% chance of rain in a certain region means that the probability of rain in the given region is 0.6 at any time of the day in any part of the region.

So Choice C is the best option.

Choice A is wrong because 60% of the region does not mean 60% of the rain.

Choice B is also wrong because 60​% of the day  does not mean 60% of the rain.

The weather report tells about the rain , not the region or part of the day. So choice C is the best option

Answer:

Speed = 5m/s

Total time taken = 6 seconds

Step-by-step explanation:

Shota's initial position = 30 metres below the edge of a volcano

If Shota climbed at a constant rate:

Shota's position after 4.5 seconds = 7.5meters below the edge of the volcano

Shota's climbing speed :

Distance covered / time taken

Distance covered = (30 - 7.5) = 22.5 meters

Hence, speed = (22.5 / 4.5) = 5m/s

Time taken to reach edge of volcano:

Time left to reach edge = (distance left to cover / speed)

Time left to reach edge = (7.5 / 5) = 1.5 seconds

Total time taken: (4.5 + 1.5) = 6 seconds

Answer:

x=25°

Step-by-step explanation:

Sum of angles of a triangle equals 180°

Hi

I guess that the most obvious answer is

x = 1

Answer:

x = 1

Step-by-step explanation:

10/x + 2/x = 12

x(10/x + 2/x) = 12*x

10x/x + 2x/x = 12x

10 + 2 = 12x

12 = 12x

x = 12/12

x = 1

Verify:

10/1 + 2/1 = 12

10 + 2 = 12

Answer:

2 2/3 hours

Step-by-step explanation:

Before it was 5 hours for 1 guitar, or 5 hours/guitar

Now it is 7 guitars in 3 hours or 7/3 hours/guitar

7/3 = 2 1/3

5 hours - 2 1/3 hours = 15/3 hours - 7/3 hours = 8/3 hours = 2 2/3 hours

The reduced the time it takes to build 1 guitar by 2 2/3 hours.

Use the Pythagorean theorem.

Distance = sqrt(16^2 + 5^2)

Distance = sqrt(256 + 25)

Distance = sqrt(281)

Distance = 16.763

Rounded to the nearest tenth = 16.8 miles

Answer:

X = -3

Step-by-step explanation:

x - 5 = 3x + 1

-6 = 2x

x = -3

Hope it helped u if yes mark me BRAINLIEST!

Tysm!

;)

The equation formed by the information, 5 less than a number is equivalent to 1 more than three times the number is x - 5 = 3x + 1. And the number is x = -3.

The simplest equation used to express and solve for an unknown quantity is a linear equation in one variable. It's simple to depict graphically since it's always a straight line. A linear equation is a simple technique to convey a mathematical proposition. Unknown quantities can be represented by any variable or symbol, however, in most cases, the unknown quantity in a linear equation in one variable is represented by the variable 'x'.  A collection of basic strategies are used to solve a linear equation. To determine the final value of the unknown quantity, the variables are isolated on one side of the equation and the constants are isolated on the other side of the equation.

We are given that 5 less than a number is equivalent to 1 more than three times the number. We are asked to determine the number.

To determine the number, we will let the unknown number be x.

We will now try to make the two equal expressions, equate them to get a linear equation in one variable, and then solve the equation to find x.

First expression: 5 less than the number, that is, x - 5

Second expression: 1 more than three times the number, that is, 3x + 1.

Both the expressions are equal, so we equate them to get our equation:

x - 5 = 3x + 1

To solve for x, we do the following steps.

1. Subtract 3x from both sides of the equation:

x - 5 - 3x = 3x + 1 - 3x

or, -2x -5 = 1 (Simplifying)

2. Add 5 to both sides of the equation:

-2x - 5 + 5 = 1 + 5

or, -2x = 6 (Simplifying)

3. Divide both sides of the equation by (-2):

-2x/(-2) = 6/(-2)

or, x = -3 (Simplifying).

∴ The equation formed by the information, 5 less than a number is equivalent to 1 more than three times the number is x - 5 = 3x + 1. And the number is x = -3.

Learn more about linear equations in one variable at

https://brainly.com/question/24145091

#SPJ2

Answer:

170

Step-by-step explanation:

17 dogs per 30 students or 17/30

Same ratio for 300 students:

So 170 students have a dog

Hi there! Hopefully this helps!

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[tex]\sqrt[]{2}[/tex] × [tex]\frac{8\sqrt{2} }{3}[/tex] ÷ 3 - 1

First, we express [tex]\sqrt{2}[/tex] × [tex](\frac{8\sqrt{2}}{3})[/tex] ≈ 5.333333333 as a single fraction.

[tex]\frac{\sqrt{2 \times 8\sqrt{2} } }{\frac{3}{3} } - 1[/tex]  ≈ 0.777777778

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now we express [tex]\frac{\sqrt{2 \times 8\sqrt{2} } }{\frac{3}{3} }[/tex] ≈ 1.777777778 as a single fraction.

[tex]\frac{\sqrt{2 \times 8\sqrt{2} } }{3 \times 3} - 1[/tex]  ≈ 0.777777778

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Multiply [tex]\sqrt{2}[/tex] ≈ 1.414213562 and [tex]\sqrt{2}[/tex] ≈ 1.414213562 to get 2.

[tex]\frac{2 \times 8}{3 \times 3} - 1[/tex] ≈ 0.777777778

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Multiply 2 and 8 to get 16.

[tex]\frac{16}{3 \times 3} - 1[/tex] ≈ 0.777777778

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Multiply 3 and 3 to get 9.

[tex]\frac{16}{9} - 1[/tex] ≈ 0.777777778

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Convert 1 to fraction [tex]\frac{9}{9} = 1.[/tex]

[tex]\frac{16}{9} - \frac{9}{9}[/tex] ≈ 0.777777778

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Since [tex]\frac{16}{9}[/tex] ≈ 1.777777778 and [tex]\frac{9}{9} = 1[/tex] have the same denominator, subtract them by subtracting their numerators.

[tex]\frac{16 - 9}{9}[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Then you get................

[tex]\frac{7}{9}[/tex]

The relation {(3, 4), (-3, 8), (6, 8)}, is a function, because

all the x–coordinates are different.

It's important to understand that even though two of the y-coordinates

are the same, this relation is still a function.

The y-coordinates do not have any affect

on whether the relation is a function.

Answer:

The  equation is  [tex]x^2 + y^2 +z^2 + 14 x + 3y \ + 14z + 86.25=0[/tex]

Step-by-step explanation:

From the question we are told that  

    The  diameter endpoints is   (-8, -3, -10) and (-6, 1, -4)

Generally the equation of a sphere with center coordinates (a, b , c ) and  radius  r   is mathematically represented as

           [tex](x - a )^2 + (y -b )^2 + (z -c)^2 = r^2[/tex]

Now since we are given the endpoints of the diameter then we can obtain the center coordinates as follows

         [tex](a, b , c) = [ \frac{ -8 +(-6)}{2} , \frac{-3 + (1)}{ 2} , \frac{ -10 + (-4)}{2} ][/tex]

         [tex](a, b , c) = [ -7 , -1.5 , -7 ][/tex]

Now the length of the diameter is evaluated as

    [tex]|d| = \sqrt{ (-8 - (-6 ))^2 + ( -3 - (1) )^2 + ( -10 - (-4))^2 }[/tex]

   [tex]|d| = \sqrt{56 }[/tex]

   [tex]|d| = \sqrt{4 * 14 }[/tex]

   [tex]|d| = 2 \sqrt{ 14 }[/tex]

Now the radius is mathematically represented as

    [tex]r = \frac{|d|}{2}[/tex]

    [tex]r = \frac{ 2 \sqrt{14} }{2}[/tex]

    [tex]r = \sqrt{14}[/tex]

So

   [tex](x - -7 )^2 + (y --1.5 )^2 + (z --7)^2 = ( \sqrt{14} )^2[/tex]

   [tex](x +7 )^2 + (y +1.5 )^2 + (z +7)^2 = 14[/tex]

    [tex]x^2 + 14 x + 49 + y^2 + 3y + 2.25 +z^2 14z + 49 = 14[/tex]

    [tex]x^2 + y^2 +z^2 + 14 x + 3y \ + 14z + 86.25=0[/tex]

Answer:

r(t) and s(t) are parallel.

Step-by-step explanation:

Given that :

the  lines represented by the vector equations are:

r(t)=⟨1−t,3+2t,−3t⟩

s(t)=⟨2t,−3−4t,3+6t⟩

The objective is to determine if the following lines represented by the vector equations below intersect, are parallel, are skew, or are identical.

NOTE:

Two lines will be parallel if [tex]\dfrac{x_1}{x_2}= \dfrac{y_1}{y_2}= \dfrac{z_1}{z_2}[/tex]

here;

[tex]d_1 = (-1, \ 2, \ -3)[/tex]

Thus;

[tex]r(t) = \dfrac{x-1}{-1} = \dfrac{y-3}{2}=\dfrac{z-0}{-3} = t[/tex]

[tex]d_2 =(2, \ -4, \ +6)[/tex]

[tex]s(t) = \dfrac{x-0}{2} = \dfrac{y+5}{-4}=\dfrac{z-3}{6} = t[/tex]

∴

[tex]\dfrac{d_1}{d_2}= \dfrac{-1}{2} = \dfrac{2}{-4}= \dfrac{-3}{-6}[/tex]

Hence, we can conclude that r(t) and s(t) are parallel.

Answer: 352 tickets

Step-by-step explanation:

because multiplying $20 floor tickets by 324 (how many were sold) gives you 6480

subtract from 10000

gives you 3520 (amount made from balcony)

divide by $10

Step-by-step explanation:

Let No. of balcony ticket sold be x

Rate of floor ticket = $20

Rate of balcony ticket = $10

Total Box Office collection :

324 * 20 + 10 * x = $ 10,000

X = 352 tickets

Answer:

Step-by-step explanation:

2(x-3) = 5

Distribute.

2x - 6 = 5

Eliminate the 6.

2x = 11

Divide by 2.

x = 11/2

Answer:

[tex]\frac{11}{2}[/tex]

Step-by-step explanation:

We can use distributive property to simplify the equation, [tex]2x-6=5[/tex]. Now, we can move -6 to the right hand side. [tex]2x=11[/tex]. Finally, we can divide 2, [tex]x=\frac{11}{2}[/tex] or [tex]x = 5\frac{1}{2}[/tex]