MATHEMATICS HIGH SCHOOL

A balloon lifts off the ground and reaches a height of 200m. The total mass of the balloon is 1000 kg. What is the GPE of the balloon?

Answers

Answer 1

Answer:

Answer:

1,960,000Joules

Step-by-step explanation:

Gravitational Potential Energy is expressed as;

GPE = mgh

m is the mass

g is the acceleration due to gravity

h is the height

Given

m = 1000kg

h = 200m

g = 9.8m/s

Substitute;

GPE = 1000 * 9.8 * 200

GPE = 9800 * 200

GPE = 1,960,000Joules

Hence the GPE of the balloon is 1,960,000Joules

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Evaluate 15 − 4 + (7 − 5)2 = __________.

Answers

26? right? cause 15 - 4 is 11, 7 - 5 is 2, 11 + 2 is 13, and 13 x 2 is 26

15-4=11 plus
(7-5)= 2
if is times 2 is 32
if is plus 2 is 15
if is minus 2 is 11
and if is divided by 2 is 6.5
(I'm saying all that because you didn't put any symbol beside the number 2)

Caleb's mother said they will drive 1 /4 hour to get there, and they will drive another 1 /4 hour back. Once they arrive, Caleb's brother will be playing in 3 soccer games. Each soccer game takes 3 4 hour, and there is no break in between games. Calculate how long will they be away from home.

Answers

Answer: They are away for $2(3)/(4)\ hours$ from home.

Step-by-step explanation:

Since we have given that

Time to get there = $(1)/(4)$

Time to get back = $(1)/(4)$

Number of soccer games = 3

Time for each soccer games = $(3)/(4)$

So, total time for 3 games would be

$3* (3)/(4)=(9)/(4)$

So, the time for which they will be away from home is given by

$(1)/(4)+(9)/(4)+\frac{1}4}=(1+9+1)/(4)=(11)/(4)=2(3)/(4)\ hours$

Hence, they are away for $2(3)/(4)\ hours$ from home.

Two towns are 1,100 miles apart. A group of hikers Starts from each town and walks down the trail toward each other. They meet after a total hiking time of 240 hours. If one group travels 2 1/2 mile per hour slower than the other group, find the rate of each group.

Answers

Answer:

3.54 and 1.04

Step-by-step explanation:

Given:

Two towns are 1,100 miles apart.

A group of hikers Starts from each town and walks down the trail toward each other..

They meet after a total hiking time of 240 hours.

If one group travels 2 1/2 mile per hour slower than the other group.

Question asked:

Find the rate of each group.

Solution:

Let speed of faster hiker = $x\ mph$

Speed of slower hiker = $x-(5)/(2)\ mph$

As we know:

$Distance=speed* time$

Total distance between two town = Total combined speed of both hikers $*$ Total combined time taken

$1100=(x+x-(5)/(2) )*240\n \n Dividing\ both\ sides\ by\ 240\n \n 4.58=(x+x-(5)/(2) )\n \n 4.58=2x-(5)/(2) \n \nAdding\ both\ sides\ by\ (5)/(2) \n \n 4.58+ (5)/(2)=2x- (5)/(2)+ (5)/(2)\n \n (2*4.58+5)/(2) =2x\n \n (14.16)/(2) =2x\n \n By \ cross\ multiplication\n \n 2*2x=14.16\n \n 4x=14.16$

$By\ dividing\ both\ sides\ by \ 4\n \n x=3.54\ miles\ per\ hour$

Speed of faster hiker = $x\ mph$ = 3.54 miles per hour.

Speed of slower hiker = $x-(5)/(2)\ mph$ =

$3.54-(5)/(2) =3.54-2.5=1.04\ miles\ per\ hour$

Therefore, speed of faster hiker is 3.54 miles per hour and speed of slower hiker is 1.04 miles per hour.

if you are asked to solve a system of equations in which there is no linear equation to start with, you can sometimes begin by isolating and substituting a variable that is squared in both equations.