Answers
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.
Related Questions
What is another way to write the calculation add 16 and 25, and then multiply by 47?
Answers
Answer:
(16+25)×47
Step-by-step explanation:
..........
(16+25)x47 , theree you go
What factoring pattern can you use to solve x^2+14x+49=0
A (ax+√c)^2=0
B (√a*x+√c)^2=0
C (√a*x+c)(√a*x-c)=0
D (ax+√c)(ax-√c)=c
Answers
Answer:
B (√a*x+√c)^2=0
Step-by-step explanation:
It can be helpful to look a the expanded form of each of these factoring patterns.
A (ax+√c)^2=0 ⇒ a^2x^2 +2a√c*x +c = 0
B (√a*x+√c)^2=0 ⇒ ax^2 +2√(ac)*x +c = 0
C (√a*x+c)(√a*x-c)=0 ⇒ ax^2 -c^2 = 0
D (ax+√c)(ax-√c)=c ⇒ a^2x^2 -c = c
If 'a' and 'c' represent the coefficients in the given equation, then choices A, C, and D can be eliminated. The expanded forms of those end up with a^2 and/or c^2 as coefficients, not 'a' and 'c'.
Choice B is the only sensible one, and fits the given equation.
a = 1, c = 49 ⇒ √a = 1, √c = 7
x^2 +14x +49 = (x +7)^2 = 0 . . . . . factored using Pattern B
10 + (-3 3/8)
Please explain of how i can do this
Answers
Answer:
53/8 or 6.625
Step-by-step explanation:
10 + (-3 3/8)
Convert everything to a fraction having the same denominator.
-3 3/8
-24/3 - 3/8
-27/8
10
80/8
Combine: (80/8 - 27/8) = 53/8 or 6.625
A number written in expanded form is 700,000 + 5,000 + 200 + 80 + 7. What is this number written in word form?
1 seven hundred five thousand, two hundred eighty-seven
2 seventy-five thousand, two hundred eighty-seven
3 seven hundred eighty-two thousand, five hundred seventy
4 seven hundred eighty-two thousand, five hundred seven
Answers
Write from least to greatest
Answers
Answer:
-9.5, -9, -8.5, -4, -2.5, 0, 7.7, 8
Step-by-step explanation:
hopes this helps <3
) It took 2 pumps 6 hours to pump the water out of a pond. How long would it take if 3 pumps
were used?
Answers
Answer:
it would take 2 hours with 3 pumps
Step-by-step explanation:
hope this helps! :D
Solve the system of linear equations by substitution: (SHOW UR WORK)
y=5x-6
y=4x-2
Answers
Answer:
x = 4
y = 2
Step-by-step explanation:
1) y = 5x - 6
2) y = 4x - 2
sub 1 into 2
5x - 6 = 4x - 2
5x - 4x = 6 - 2
x = 4 ---> (3)
sub 3 into 2
y = (4 * 1) - 2
y = 4 - 2
y = 2
Answer:
4
Step-by-step explanation:
Since they both equal y, they are both equivinlent
[tex]5x-6=4x-2[/tex]
[tex]5x=4x+4[/tex]
[tex]x=4[/tex]
CHECK
[tex]20-6=16-2[/tex]
[tex]14=14[/tex]
What is the measure of <1?
What is the measure of <2?
Answers
Answer:
1) 98°
2) 65°
Step-by-step explanation:
Sum of the angles in any triangle = 180°
in first triangle the third inner angle = 180 - (18 + 80) = 82 then measure of (1) = 180 - 82 = 98°
The missing interior angle of the second triangle = 180 - 124 = 56° then measure of (2) = 180 - (59+56) = 65°
Colton and Gage were building a castle together. Colton was 5 times as fast at building the castle than Gage. If it takes 120 blocks to build the castle, how many blocks did Colton build on the castle?
A. 144 blocks
B. 100 blocks
C. 24 blocks
D. 20 blocks
Answers
Answer:
100 blocks.
Step-by-step explanation:
Let x represent number of blocks built by Gage.
We have been given that Colton was 5 times as fast at building the castle than Gage, so number of blocks built by Colton would be .
We are also told that it takes 120 blocks to build the castle. Since Colton and Gage were building a castle together, so number of blocks built by both will be equal to 120.
Hope it helped!
I need help. What is the slope?
Answers
Ok done. Thank to me :>
What’s the difference between an event and in event handler
Answers
Answer:
There’s a subtle, but important difference between these 2 methods of handling events. If you’ll use the first method, event handlers, the difference is that if you add two event handlers for the same button click, the second event handler will overwrite the first and only that event will trigger
Step-by-step explanation:
i hope this answer your questions
evaluate 2x+y for x=1/3 and y=2/3
a.1/3
b.2/3
c.4/3
d.5/3
Answers
Answer:
C. 4/3
Step-by-step explanation:
2 × ⅓ + ⅔
⅔ + ⅔ = 4/3
Use X as ⅓, and use Y as ⅔.
someone please help me! the question is 18.
Answers
A doughnut company finds that its sales are
boosted by advertising according to the
600d
relationship S(d) = where S and d
10+ 0
represent sales and advertising, respectively,
in thousands of dollars. Calculate another
expression for S(d) by performing the
division shown.
Answers
Answer:
Hey will you marry me? serious question
Graph: y = 3 * x + 5
Answers
Answer:
2
Step-by-step explanation:
take the 3 put on the side
solve question 5 all steps
Answers
Answer:
Answer in the pic with steps
Hope it helps
The difference between three times a number and seven is twenty. What is the number?
20
7
13
3
O9
O 27
Answers
Answer:
the number is 9
Step-by-step explanation:
hope this helps
Each car on a commuter train can seat 114 passengers. If the train has 7 cars how many passengers can it seat??
Help me!!!
Answers
Hope it helps*-*
Which point is located in Quadrant III ?
(−1/2, 1/4)
(1/2, −1/4)
(−1/2, −1/4)
I will give you brainliest if you are right
Answers
Answer:
here you go :)
Quadrant lll is always both negative so the answer is (-1/2, -1/4)
Step-by-step explanation:
Find the slope of the line that passes through (-2, -44) and (-1, -70).
Answers
Let m = slope of the line.
m = delta y/delta x
m = (-70 -(-44)/(-1 -(-2)
m = (-70 + 44)/(-1 + 2)
m = -26/1
m = -26
Understand?
Use the distributive property to remove the parentheses.
-9(-6u+v-5)
I need help- I’ll get brainly list
Answers
Answer:
54u - 9v + 45
Step-by-step explanation:
distributive property
Will give brainliest!
Answers
Answer:
- 1/4
Step-by-step explanation:
Where you see X, substitute with 1/3
Solve the power/exponent first:
6(1/3) = 2
That is ; - 4(1/4)^2
Solve the parenthesis:
(1/4)^2 = 1/16
-4(1/16)
= - 1/4
what is the answer to (x-2)^5 ?
Answers
Answer:
x² - 4x + 4
Step-by-step explanation:
(x -2)(x - 2)
x² - 2x - 2x + 4 Expand using FOIL.
x² - 4x + 4 Simplify.
Write the standard form of a polynomial functions whose zeros/roots are
4-3i, 4+3i
and has a lead coefficient of 1
Answers
Answer:
In other words, x = r x = r is a root or zero of a polynomial if it is a solution to the equation P (x) =0 P ( x) = 0.
Step-by-step explanation:
Write an equation for the nth term of the arithmetic sequence. Then find 230 -
-9, -6, -3,0, ...
=
a30
Helpquick
Answers
Answer:
hope it helps you ✨✨✨✨✨✨
You move left 2 units and down 1 unit. You end at (-5, -5.) Where did yo start
Answers
Answer:
(-3, -4)
Step-by-step explanation:
(-5, -5)
2 units right
(-3, -5)
1 unit up
(-3, -4)
just go backwards
Answer:
(-3, -4)
Step-by-step explanation:
The x value in (-5, -5) is -5 and y is -5. To find the original position you reverse the translations done to get to the current position. So you add 2 (because you move 2 units right to reverse) to the x value which gives us -3 and add 1 to the y value (because to reverse we move 1 unit up) which gives us the original y value of -4.
what is the total number of edges on a rectangular prism
Answers
Answer:
12 edges
Step-by-step explanation:
A rectangular prism has 6 faces, 8 vertices (or corners) and 12 edges.
Answer:
12
Step-by-step explanation:
Is this relation a function? Justify your answer.
11
10
.
9
8
7
6
5
.
- NAU
4
3
2
1 2 3 4 5 6 7 8 9 10 11
O A. Yes, because every x-value corresponds with a single y-value.
O B. Yes, because the number of x-values is the same as the number of
y-values.
O C. Yes, because every x- and y-value is positive.
D. No, because two points with the same y-value have different x-
values.
st
Answers
The reason why the given graph relation is considered to be a function is because;
A. Yes, because every x-value corresponds with a single y-value.
From the given graph, we see the (x, y) coordinates as;
(5, 4)
(7, 2)
(6, 9)
(3, 10)
Now, we see that none of the x-values are the same and likewise none of the y-values are the same.
This means that each of the x-values have a unique y-value.
Thus, it can be said to be a function
Read more about properties of functions at;https://brainly.com/question/18427017
What -3/4 equals 2/3
Answers
Answer:
17/12= 1 5/12
Step-by-step explanation:
make the denominator the same as 12
_______ -9/12 =8/12
so add 8+9 to get 17.then keep the denominator as 12. last simpfie it to 1 5/12
Multiply and combine like terms to determine the product of these polynomials:
(2x + 3)(5x − 6)
Answers
Answer:
10x^2+3x-18
Step-by-step explanation:
