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
f(x) = (x - 5) (2x - 7) (7x - 3) has zeros at x = -3.5, x = 3/7, and x = 5.
what is the sign of f on the interval 3/7 < x < 5 ?
1. f is always positive on the interval.
2. f is always negative on the interval.
3. f is sometimes positive and sometimes negative on the interval.
Answers
The function f(x) will be sometimes positive and sometimes negative on the interval so option (3) will be correct.
What is a function?
A certain kind of relationship called a function binds inputs to essentially one output.
In other terms, a function is a relationship between variables, and the type of relationship that exists between the variables defines the function, such as y = sinx and y = x +6.
Given function is
f(x) = (x - 5) (2x - 7) (7x - 3)
The term (x - 5) will be negative if x < 5.
The term (2x - 7) will be negative if x<3.5
Let's say if x = 4 then (x - 5) will be negative but (2x - 7) will be positive and hence overall value will be negative.
But if x = 3 then (x - 5) will be negative and (2x - 7) will also be negative and hence overall value will be negative
Hence the function f is sometimes positive and sometimes negative on the interval.
For more about the function
brainly.com/question/23712366
#SPJ5
Answer:
always negative the other guy was wrong because when you wrote 2x - 7 you meant 2x + 7 I know this because it’s on Khan Academy
Step-by-step explanation:
help
1) find the value of x
2)find length of a side of the square
Answers
Answer:
x = 12 , s = 41
Step-by-step explanation:
The sides of a square are equal , so
4x - 7 = 3x + 5 ( subtract 3x from both sides )
x - 7 = 5 ( add 7 to both sides )
x = 12
Then
length of side s is
s = 4x - 7 = 4(12) - 7 = 48 - 7 = 41
Which angles are supplementary to each other?
Angle 4 and Angle 2
Angle 5 and Angle 2
Angle 4 and Angle 3
Angle 2 and Angle 7
Answers
Answer:
The answer is Angle 4 and Angle 3.
Answer:
It's answer is angle 4 and angle 3
Krista invested money in the stock of a foreign company. Lately, the government of the country where the company is based introduced new tax laws and fiscal policies. What type of risk does Krista face as an investor?
Answers
Answer: legislative risk
Step-by-step explanation:
Legislative risk refers to a form of risk whereby there's likelihood of a business making a loss on an investment due to governmental action.
Legislative risk implies an amendment or an abolition of laws which has a direct impact on investments. Regarding the question, the introduction of the new tax laws and fiscal policies is a legislative risk.
Answer:
c
Step-by-step explanation:
Find the domain for the rational function f(x)=x+1/x-2
Answers
Step-by-step explanation:
here's the answer to your question
PLEASE HELP IT IS DUE IN TWO HOURS AND I CANT UNDERSTAND IT PLSSSSSS
Answers
The distance from Tre’s house to Owen’s house is 10 miles.
The distance from Owen’s house to Alejandro’s house is 14 miles.
The distance from Alejandro’s house to the beach is about 10.77 miles.
The total distance of the trip to the beach is about 33.53 miles
Step-by-step explanation:
question 1…. help please
Answers
Answer: The number = 3 /4 or 4 / 3
Concept:
Here, we need to know the idea of a reciprocal.
Reciprocal is also called the multiplicative inverse. It is similar to turning the number upside down which is found by interchanging the numerator and denominator.
Number ⇒ Reciprocal = 1 / Number
Solve:
STEP ONE: Set up the equation
Let x = the number
Let 1 / x = the reciprocal
x + 1 / x = 25 / 12
STEP TWO: Multiply x on both sides
(x + 1 / x) · x = (25 / 12) · x
x² + 1 = 25x / 12
STEP THREE: Multiply 12 on both sides
(x² + 1) × 12 = (25x / 12) × 12
12x² + 12 = 25x
STEP FOUR: Subtract 25x on both sides
12x² + 12 - 25x = 25x - 25x
12x² - 25x + 12 = 0
STEP FIVE: Solve for the quadratic equation
(3x - 4) (4x - 3) = 0 ⇔ (Factorization of the equation)
(x - 4 / 3) (x - 3 / 4) = 0
x = 4 / 3 or x = 3 / 4
Hope this helps!! :)
Please let me know if you have any questions
The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.
Answers
Show that the line 4y = 5x-10 is perpendicular to the line 5y + 4x = 35
Answers
Step-by-step explanation:
concept :concept :When two lines are perpendicular, then the product of their slopes is equivalent to -1.concept :When two lines are perpendicular, then the product of their slopes is equivalent to -1.Equation of line in the form y = mx + c have m as slope of line and c as y-intercept.concept :When two lines are perpendicular, then the product of their slopes is equivalent to -1.Equation of line in the form y = mx + c have m as slope of line and c as y-intercept.Solution:concept :When two lines are perpendicular, then the product of their slopes is equivalent to -1.Equation of line in the form y = mx + c have m as slope of line and c as y-intercept.Solution:Given equations of lines areconcept :When two lines are perpendicular, then the product of their slopes is equivalent to -1.Equation of line in the form y = mx + c have m as slope of line and c as y-intercept.Solution:Given equations of lines are4y = 5x-10concept :When two lines are perpendicular, then the product of their slopes is equivalent to -1.Equation of line in the form y = mx + c have m as slope of line and c as y-intercept.Solution:Given equations of lines are4y = 5x-10or, y = (5/4)x(5/2). .....(1)5y + 4x = 355y + 4x = 35ory = (-4/5)x + 7. ......(2)Let m and n be the slope of equations i and ii, respectively.Let m and n be the slope of equations i and ii, respectively.Here, m = 5/4Let m and n be the slope of equations i and ii, respectively.Here, m = 5/4n= -4/5Let m and n be the slope of equations i and ii, respectively.Here, m = 5/4n= -4/5therefore, mx n = -1Let m and n be the slope of equations i and ii, respectively.Here, m = 5/4n= -4/5therefore, mx n = -1Hence, the lines are perpendicular.Pls help Which of the following exponential equations is equivalent to the logarithmic equation below ? In x = 7
Answers
Answer:
Step-by-step explanation:
Let's write that out completely:
[tex]ln_e(x)=7[/tex] The rule for going from log to exponential is what I call the "circular rule" in my classes and the kids never forget it. Take the base of the log, raise it to the power of the number on the other side of the equals sign, and then circle back to set it equal to the argument.
e is the base. Raise e to the 7th and circle back to set the whole thing equal to x (x is called the argument):
[tex]e^7=x[/tex] choice C.
A square has a perimeter of of 28 m. What is the length of each side
Answers
Answer:
a square has 4 sides therefore the formula for perimeter of a square would be 4a where a is the number of sides. in this case, we want to know the length of each side so we divide total length (28) by number of sides which is 4 and we get 7m
Answer:
the side lengths of a square are equal. Second, know that the sum of all 4 side lengths gives us the perimeter.
What is the initial value of the sequence?
1
2
3
8
Answers
Answer:
2
Step-by-step explanation:
The initial value is the y value of the first term shown ( when x=1)
y = 2 when x=1
The initial value is 2
Answer:
What is the initial value of the sequence?
1 2 <<<CORRECT 3 8
Step-by-step explanation:
Edge 2021
Calculate the mean of the following list of numbers: 10, 12, 7, 9, 9, 11, 15, 9
PLEASE HELP!!!!
9
9.5
10.67
10.25
Answers
82/8=10.25
Find the length of side x in simplest radical form with a rational denominator.
459
4
95
Answer: 2 =
Submit Answer
HELP HELP HELP HELP PLSSSSSSS
Answers
Answer:
x= 2/2
Step-by-step explanation:
What is the nth term for number sequence
2;5;7;12;19
Answers
Answer:
13
Step-by-step explanation:
Have a nice day
Add.
(3x2 – 2x) + (4x-3)
O A. 7x2- 5x
O B. 12x3 - 14x2 + 6x
O C. 3x2 - 6x + 3
O D. 3x2 + 2x-3
Answers
Answer:
O D. 3x2 + 2x-3
Answer:
A.7x2-5x questions 2of 20
find the value of a) 4:12
Answers
Step-by-step explanation:
1:4 bcos u need to divide both sides by 4
HELP!!!!!! so many points for this one!!!!!! x^2+y^2+4x-2y=-1
The equation of a circle in the xy-plane is shown above. What is the radius of the circle
A.2
B.3
C.4
D.9
Answers
Answer:
A. 2Step-by-step explanation:
Given circle:
x² + y² + 4x - 2y = -1Convert the equation into the standard form of (x - k)² + (y - h)² = r²:
x² + 4x + 4 + y² - 2y + 1 = -1 + 4 + 1(x + 2)² + (y - 1)² = 2²As per above:
r = 2Correct choice is A
A.2
Answer:
Solution given:
equation of a circle is:
x²+y²+4x-2y=-1
x²+y²+4x-2y+1=0
Comparing above equation with
ax²+by²+2gx+2fy+c=0
we get
a=1
b=1
g=2
f=-1
c=1
now
radius of a circle (r)=[tex]\sqrt{g²+f²-c}[/tex]
substituting value
r=[tex]\sqrt{2²+(-1)²-1}=2[/tex]
therefore radius of a circle is 2 units
the sum of two numbers is 10, the sum of their squares is 58 determine the two numbers
Answers
Answer:
7 and 3
Step-by-step explanation:
Using the given information, one can form an equation. Let the first number be (x) and the second (y). For two equations based on the given information.
"the sum of two numbers is 10"
x + y = 10
" the sum of their squares is 58 determine"
[tex]x^2+y^2=58[/tex]
Solve for the equation for (x), then substitute the expression for (x) into the second equation. Simplify and solve to find the value of (y), and backsolve for the value of (x).
x + y =10
x = 10 -y
Substitute into the other equation:
[tex]x^2+y^2=58[/tex]
[tex](10-y)^2+y^2=58[/tex]
Simplify, remember the pattern for opening a binomial squared:
[tex](a - b)^2=a^2-2ab+b^2[/tex]
Apply this pattern here to simplify,
[tex](10-y)^2+y^2=58[/tex]
[tex]100-20y+y^2+y^2=58[/tex]
Simplify further,
[tex]100-20y+y^2+y^2=58[/tex]
[tex]2y^2-20y+100=58[/tex]
Inverse operations,
[tex]2y^2-20y+100=58[/tex]
[tex]2y^2-20y+42=0[/tex]
Factor, take out a common factor that all of the terms have. Then rewrite the quadratic trinomial as the product of two linear binomials. Remember the general pattern for factoring, add the inverse of the factors of the constant term to the variable, the sum of these factors must equal the coefficient of the linear term of the quadratic trinomial.
[tex]2y^2-20y+42=0[/tex]
[tex]2(y^2-10y+21)=0[/tex]
[tex]2(y-7)(y-3)=0[/tex]
Now use the zero product property to solve, the zero product property states that any number times zero equals zero.
[tex]2(y-7)(y-3)=0[/tex]
[tex]y = 7, y = 3[/tex]
Since the sum of (7) and (3) is (10), one has found the values of (y), it can be either (7) or (3), it doesn't matter which equals which.
what is the value of x
Answers
Answer: 24(option A) is the answer
exterior angle = 360/n
so, n = 15
then, 360/15 = 24
A right triangle has a 12in base and an 8in height. What is the area of the triangle, in in??
Answers
Answer:
48
Step-by-step explanation:
using the formula 1/2 b*h
8*12=96
96/2=48
Jo bought a used car for $6000 and paid a 15% deposit. How much did he still have to pay?
Answers
Answer:
900 is the correct awnser
Brianna's Bakery offers 3 flavors of bagels. Customers can choose from plain, cinnamon, or blueberry bagels. Yesterday, a customer ordered 144 bagels for a company meeting. The order was for twice as many blueberry bagels as plain bagels and 3 times as many cinnamon bagels as blueberry bagels.
How many cinnamon bagels did the customer order
Answers
Answer:
96 darling
Step-by-step explanation:
youre gonna take all the times this was teice as mich as that
like this:blueberrybagel twice as much 2
than plain bagels 1
cinnamonbags 3 times as much than
blueberry bagels 2×3= 6+
=9
EACH portion contains144:9=16 bagels
blueberry ones16×2=32
plain ones16×1=16
cinnamon ones 3×32=96
First, find the length of each edge of the cube.
Then, find the volume.
Answers
since in a cube length, width and height are equal,
h = 6
w = 6
l = 6
and volume is 6³ = 216cm³
hope it helps :)
10,4,7
The above set 4 numbers have a mean of 8
what could the mystery number
Answers
Answer:
11
Step-by-step explanation:
To calculate the mean you add all the numbers and divide by the number of numbers. There are 4 numbers in this set so we will divide by 4.
Let x be the unknown number,
(10+4+7+x)/4=8(mean)
To solve for x, we first mutliply both sides by 4.
To simplify the left side we can add 10+4+7 and get 21 where now our equation is 21+x=32. Subtract 21 on both sides and you will get 11 which is our answer.
Plug-in 11 and solve for the mean to verify where we do indeed get 8 as the mean.
Someone Help! PLEASE!
Jesse is taking the tests needed to join the math team. His scores were 89, 92, 94. What's the lowest score he can get on the fourth test and still have a 90 average?
Answers
Answer:
The lowest score could be 85
Step-by-step explanation:
Let the lowest score = x
(x + 89 + 92 + 94)/4 = 90 Add the 3 scores you know
(x + 275)/4 = 90 Multiply both sides by 4
(x + 275) = 360 Remove the brackets.
x + 275 = 360 Subtract 275
x = 360 - 275
x = 85
Can someone help pls
Answers
X intercepts (green dots): (-3,0), (-1,0)
Y intercept (black dot): (0,9)
Vertex (red dot): (-2,-3)
Help anyone can help me do the question,I will mark brainlest.
Answers
Answer:
a) 30
b)600pi
Step-by-step explanation:
For the first questions, since the arc is 240°, the area of the sector and circumference will be 240/360 or 2/3 of the total of the circles'. Therefore 125.6 x 3/2 is the circumference, which is 188.4. When we divide this by 6.28, we get 30
Now, since the area is pi r^2 where we know that r=30, we get 900pi as the area of the whole thing, however since the sector is 2/3 of the whole circle, 2/3 x 900pi = 600pi
Verify the identity.
[tex]cot (x-\frac{\pi }{2})=-tan[/tex]
Answers
Answer:
True
Step-by-step explanation:
assuming that you meant to write
cot (x-π//2) = - tan x
the identity is TRUE because,
- you can graph cot (x-π//2) and - tan x, and see that the graphs overlap
OR
-you solve for cot (x-π/2)
useful to know is that :
cot x=1/tan x, tan x = sin x/cos x,
cos(x) =cos(-x), sin(-x) = -sin x,
cos(π/2 -x) =sin x, sin (π/2-x) =cos x
cot (x-π/2) = 1/tan (x-π/2) , yet tangent is sin x/cos x
cot (x-π/2) = cos (x-π/2) /sin (x-π/2) , factor -1
cot (x-π/2) = cos -(π/2-x) /sin -(π/2-x), use facts: cos(x) =cos(-x), sin(-x) = -sin x
cot (x-π/2) = cos (π/2-x) / -sin (π/2-x), use cos(π/2 -x) =sin x, sin (π/2-x) =cos x
cot (x-π/2) = sin x / -cos x , again sin x /cos x = tan x
cot (x-π/2) = -tan x
Express -5/8 as a rational number with -24 as the denominator
Answers
Answer:
Step-by-step explanation:
Hello!
-5/8 = (-5*-3)/ (8*-3) = 15/-24
