1. A grand tour of four cities begins at city A and makes successive stops at cities B, C,
and D before returning to city A. If the cities are located as shown in the
accompanying figure, find the total distance covered on the tour. The units are in
miles.
0-900,800)
400,300)
D1-800,0)
ALOO
Using distance between two points, it is found that the total distance covered on the tour is of 3400 miles.
Given two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], their distance is given by:
[tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
In this problem, the formula is used to find the distance covered on each tour, hence:
[tex]d_{AB} = \sqrt{(400 - 0)^2 + (300 - 0)^2} = 500[/tex]
[tex]d_{BC} = \sqrt{(-800 - 400)^2 + (800 - 300)^2} = 1300[/tex]
[tex]d_{CD} = \sqrt{(-800 - (-800))^2 + (0 - 800)^2} = 800[/tex]
[tex]d_{DA} = \sqrt{(0 - (-800))^2 + (0 - 0)^2} = 800[/tex]
Then, the total distance is given by the sum of each separate distance, hence:
[tex]d = d_{AB} + d_{BC} + d_{CD} + d_{DA} = 500 + 1300 + 800 + 800 = 3400[/tex]
The total distance covered on the tour is of 3400 miles.
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Please help me! I’m failing!!!
a. If G(t) = a (1 + r)ᵗ, then G(0) = a corresponds to the starting area of the glacier, which is given to be 142 acres. So a = 142.
The area of the glacier shrinks by 4.4% each year. This means that after 1 year, the area is reduced to
142 - (4.4% of 142) = 142 (1 - 0.044) ≈ 135.75 acres
After another year,
135.75 - (4.4% of 135.75) = 135.75 (1 - 0.044) ≈ 129.78 acres
or equivalently, 142 (1 - 0.044)² acres.
And so on. After t years, the glacier would have an area of
G(t) = 142 (1 - 0.044)ᵗ ⇒ G(t) = 142 × 0.956ᵗ
b. If the year 2007 corresponds to t = 0, then 2012 refers to t = 5. Then the area of the glacier is
G(5) = 142 × 0.956⁵ ⇒ G(5) ≈ 113.39 acres
c. Simply take the difference between G(5) and G(0) :
G(5) - G(0) ≈ 142 - 113.39 ≈ 28.61 acres
d. The average rate of change of G(t) from 2007 to 2012 is given by the difference quotient of G(t) over the interval 0 ≤ t ≤ 5 :
[tex]ARC_{[2007,2012]} = \dfrac{G(5) - G(0)}{5 - 0} \approx \dfrac{113.39 - 142}5[/tex]
so that ARC ≈ -5.72 acres/year. This rate tells us that a little less than 6 acres of glacial ice is lost each year, based on the reduction over the first 5 years.
e. The year 2017 refers to t = 10, so now we compute
[tex]ARC_{[2012,2017]} = \dfrac{G(10) - G(5)}{10 - 5} \approx \dfrac{90.55-113.39}5[/tex]
which comes out to about ARC ≈ -4.57 acres/year. Since this rate is smaller than the ARC between 2007 and 2012, this means that the glacial ice is disappearing at a slower rate in later years.
What is the probability of rolling an even number on a number cube and flipping a tails on a coin?
Answer:
25% or 1 in 4 chance.
Step-by-step explanation:
The chances for rolling an even number are 3/6, because there are 6 numbers total, and 3 are even.
3/6 can be re-written as 1/2.
The chances of landing tails are also 1/2, because there are 2 sides and tails is one of them.
So then, multiply 1/2 by 1/2 to get 1/4.
You are buying candles for an outdoor event. The candles you want come in boxes of 10, and you have enough money to purchase 20 boxes. How many candles can you buy?
Answer:
200 candles
Step-by-step explanation:
20*10 = 200
Another one for you guys
Answer:
50 miles
Step-by-step explanation:
when you match 5 on the side for practice on the x axis, it matches to 50 miles on the y axis
if cassey adds the following two equations, what multiple of the first equation will the sum represent?
x+y=5
2x+2y=10
A:2 B:3 C:4 D:5
Answer: 5
Step-by-step explanation:
If I swim 575 yards for three days how many yards I swim
Step-by-step explanation:
If you swim 575 yards in 3 days, you swim 575 yards.
If you swim 575 yards per day for 3 days, then you swim 3 × 575 yd = 1725 yd
what two integers are between the cube root of 12
Answer: 2 and 3
Step-by-step explanation:
The cube root of 12 is 2.28942848511, so it is between the integers 2 and 3.
AGHHHHHH I REALLY NEED HELP!!!!!!!!!!!! (pls actually answer it though!)
tysm if u answer it:)
Answer:
23/99 or 0.22222222222222.
Step-by-step explanation:
Answer:
23/99
Step-by-step explanation:
Using the image below which could be the first step in order to draw a arc for the construction
Answer:
With its point on A, open the compass on point E
Metallic blocks x,y, and z were placed in the graduates a, b, c. The initial volume of liquid in the equal sized graduates was 40 ml. Which block was placed in which graduate.
Answer:
hope it helps B-Y, C-Z, A-X
What is 0.8782894737 nearest TENTH of a percent?
Answer: 0.9
Step-by-step explanation:
Mark me branliest please
Choose the best response to the question below:
Answer:
d
Step-by-step explanation:
the answer is d because 2×3 equal 6
[tex]\\ \sf\Rrightarrow a*b=ab^2[/tex]
a=2b=3[tex]\\ \sf\Rrightarrow 2*3[/tex]
[tex]\\ \sf\Rrightarrow 2(3)^2[/tex]
[tex]\\ \sf\Rrightarrow 2(9)[/tex]
[tex]\\ \sf\Rrightarrow 18[/tex]
Find the equation of this line.
Can i please have help with this question brainliest for corecct answer
answer is D
graduent should be m¹×m²=-1
and should be the inverse of the other
Find the slope of the graphed line.
ASAP
y = mx+b
y = 1/3x+4
Sincerely,
William
someone answer this asap pls lots of points
Answer:
0.34
Step-by-step explanation:
64^1/2=34
10^-2=0.01
34*0.01=0.34
4d-6=-14+5d
NEED HELP ASAP
Answer:
Hewo There!!!
____________________
Isolate the variable by dividing each side by factors that don't contain the variable.
d = 8
____________________
“Darkness cannot drive out darkness: only light can do that. Hate cannot drive out hate: only love can do that.”
― Martin Luther King Jr., A Testament of Hope: The Essential Writings and Speeches
_______________________
Think of life as a mytery because well it sort of is! You don't know what may happen may be good or bad but be a little curious and get ready for whatever comes your way!! ~Ashlynn
Solve using elimination 5x+7y=9
2x-3y=-37
Answer:
x = -8
y = 7
Step-by-step explanation:
5x + 7y = 9
2x - 3y = -37
1.) First, multiply each side to match either y-values or x-values. (In this example, we'll use match x-values)
10x + 14y = 18 (multiplied by 2)
10x - 15y = -185 (multiplied by 5)
2.) Then, subtract the entirety of one equation to isolate the y-value.
10x + 14y = 18
-10x + 15y = 185
3.) Add and subtract values and divide to find y.
29y = 203
y = 7
4.) Plug-in y to solve for x into one equation, or repeat steps 1-3.
15x + 21y = 27
14x - 21y = -259
29x = -232
x = -8
Which expression is equivalent to 9 x 9 x 9 + 12 x 12 x 12?
Answer:
i think probably 2457 is answer
Which polynomial is prime? x4 3x2 â€"" x2 â€"" 3 x4 â€"" 3x2 â€"" x2 3 3x2 x â€"" 6x â€"" 2 3x2 x â€"" 6x 3.
The polynomial [tex]3x^2+x-6x+3[/tex] is a prime because it is not factorized further and this can be determined by using the factorization method.
Check all the options in order to determine the given polynomial is prime or not.
A) [tex]x^4+3x^2-x^2-3[/tex]
Now, try to factorize the above polynomial.
[tex]x^4+3x^2-x^2-3=(x+1)(x-1)(x^2+3)[/tex]
The given polynomial is factorized further therefore, this polynomial is not a prime.
B) [tex]x^4-3x^2-x^2+3[/tex]
Now, try to factorize the above polynomial.
[tex]x^4-3x^2-x^2+3=(x+1)(x-1)(x^2-3)[/tex]
The given polynomial is factorized further therefore, this polynomial is not a prime.
C) [tex]3x^2+x-6x-2[/tex]
Now, try to factorize the above polynomial.
[tex]3x^2+x-6x-2=(3x+1)(x-2)[/tex]
The given polynomial is factorized further therefore, this polynomial is not a prime.
D) [tex]3x^2+x-6x+3[/tex]
The given polynomial is not factorized further therefore, this polynomial is is a prime.
For more information, refer to the link given below:
https://brainly.com/question/17822016
Which exponential expression represents the numerical expression 9.9.9? O 39 99 0 9x3 O 3x9 1 2 2 3
9³
Step-by-step explanation:
nine to the third power or 9-cubed is the answer b/c multiply the number "9" by itself, three times.
Therefore, 9*9*9" is equal to: 9³
Maurice spent $12.00 of the $25.00 on a gift card. Which decimal represents the fraction the $25.00 Maurice spent?
Answer:
0.60
Step-by-step explanation:
25/2 = 12.5 wich means that it can't be 0.50 or lower so it has to be 0.60
Please answer hurrryy
Answer:
the answer is 270714.285714 or just 270714.2 careful \
Step-by-step explanation:
Find the area of trapezium where area=5cm base=6cm height=8cm
Answer:
44cm2
Step-by-step explanation:
[8×(5+6)]/2
=(8×11)/2
=88/2
=44cm2
Last season, your
favorite basketball
team won 20 games. This
season, your favorite
basketball team won 31
games. What is the
percent change in the
number of games that
your favorite team won
from last season to this
season?
Answer:
55%
Step-by-step explanation:
The percent change formula is written like this:
[tex]|\frac{change - original }{original}|[/tex]. In this scenario, the "change" or new value is 31, because it is this season, and the original is last season. Now, 31-20 = 11, and 11/20 = 55%.
Coby designs a rectangular vegetable garden. What will be the length of the full-size
vegetable garden?
Answer:
168. would be the length
Simplify this expression
[tex]\frac{(a^8a^6)}{a^2} ^\frac{1}{7}[/tex]
Answer:
Step-by-step explanation: The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form.
Tina rolls a dice what is the probability that she rolls a 1 b3 c4 d 3 or 4
Using the probability concept, it is found that there is a [tex]\mathbf{\frac{1}{6}}[/tex] probability that she rolls a 1.
A probability is the number of desired outcomes divided by the number of total outcomes.In a dice, there are 6 sides, one of which is a roll is 1, then:
[tex]p = \frac{1}{6}[/tex]
There is a [tex]\mathbf{\frac{1}{6}}[/tex] probability that she rolls a 1.
For more on probabilities, you can check https://brainly.com/question/24437717
Rania receives $40 for her birthday. Then he spends $15 at the movies.
Answer:
$40-$15= $25 Rania has $25 dollars left
Step-by-step explanation:
Since Rania earned $40 for her birthday and then she spent $15 dollars at the movies, that means that 40-15=25 so she has 25 dollars left.