Fill in the blanks to solve the Pollution Problem.
• What do you want to know?
When the pollution level in the lake will reach 50 tons
• What do you know?
The exponential growth function that models the
problem is P(t) = 3 • e^0.0866t, where P(t) = the number
of tons of ________ in the lake t ________ after 1970.
Answers
If the "Pollution problem" has to do with tons of pollution and the way that amount increases over the years, then the descriptive words might be
.. (pollution, years)
_____
If you actually want to know when the pollution level will be 50 tons, this can be solved a couple of ways.
1) graph the function
.. f(x) = 3*e^(0.0866x) -50
and find the value of x that makes f(x) = 0.
That value is x = 32.487, so the pollution level will reach 50 tons in 2002.
2) Find t that satisfies P(t) = 50.
.. 50 = 3*e^(0.0866t)
.. 50/3 = e^(0.0866t) . . . . .divide by 3 to isolate the exponential term
.. ln(50/3) = 0.0866t . . . . . take the natural log
.. ln(50/3)/0.0866 = t ≈ 32.487
Write the answer in terms of a year number.
.. The pollution level will reach 50 tons in 1970+32 years, 2002.
Related Questions
What is the square of 2/3 I really need help I’m so confused
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A scale on a hiking map shows that 1.5 inches =4 miles. What number of actual miles are represented by 6 inches on the map?
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15 POINT QUESTION! Multiply and simplify. (4x−2)(3x^2−2x+1)
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Then simplify them by adding or subtracting the same objects (same exponents and same variables). If they don't have the same objects, just let them be.
The final answer will be: -12x^3-14x^2+8x-2
Explanation:
We use the distributive property:
4x*3x² - 4x*2x + 4x*1 - 2*3x² - 2*(-2x) - 2*1 = 12x² - 8x² + 4x - 6x² + 4x - 2.
Combining like terms, we have 12x³-14x²+8x-2.
What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 5.5? A rectangle is shown. The length of the rectangle is labeled as 8 cm, and the width is labeled as 6 cm. Perimeter = 50 cm, area = 155.25 cm2 Perimeter = 50 cm, area = 1,452 cm2 Perimeter = 154 cm, area = 155.25 cm2 Perimeter = 154 cm, area = 1,452 cm2
Answers
scale factor =5.5
the dimensions of the original rectangle are
length is 8 cm, and the width is 6 cm.
original perimeter=2*[8+6]-----> 28 cm
original area=8*6----> 48 cm²
perimeter of the larger rectangle=[scale factor]*original perimeter
perimeter of the larger rectangle=5.5*28-----> 154 cm
area of the larger rectangle=scale factor²*area original rectangle
area of the larger rectangle=5.5²*48-----> 1452 cm²
the answer is
perimeter=154 cm
area=1452 cm²
perimeter is 154 cm
area is 1452 cm^2
This means that the last option is the correct one
Explanation:
1- getting the new dimensions:
We are given that the scale factor is 5.5
This means that:
new length = old length * scale factor
new width = old width * scale factor
We are given that:
scale factor = 5.5
old length = 8 cm
old width = 6 cm
Therefore:
new length = 8 * 5.5 = 44 cm
new width = 6 * 5.5 = 33 cm
2- getting the perimeter:
perimeter of the rectangle can be calculated as follows:
perimeter = 2(length + width)
We have:
length = 44 cm
width = 33 cm
This means that:
perimeter = 2(44+33)
perimeter = 2(77)
perimeter = 154 cm
3- getting the area:
area of rectangle can be calculated as follows:
area = length * width
We have:
length = 44 cm
width = 33 cm
This means that:
area = 44 * 33
area = 1452 cm^2
Hope this helps :)
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(3, -2), B(6, -2), C(6, 5), and D(3, 5). What is the area of rectangle ABCD?
Answers
Answer:
21
Step-by-step explanation:
a = 6-3 = 3
b = 5 -(-2)= 7
Area = a*b = 3*7 = 21
The area of rectangle ABCD which is graphed in the coordinate plane with vertices A(3, -2), B(6, -2), C(6, 5), and D(3, 5) is 21 unit².
What is the area of a rectangle?Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,
[tex]A=a\times b[/tex]
Here, (a)is the length of the rectangle and (b) is the width of the rectangle.
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(3, -2), B(6, -2), C(6, 5), and D(3, 5).
The shortest distance(length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
[tex]D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]
The distance from A to B is the length of the rectangle. The distance of line segment AB is,
[tex]W= \sqrt{(3-6)^2 + (-2-(-2))^2}\\W = \sqrt{(-3)^2 + (0)^2}\\W=\sqrt{9}\\W=3\rm\; units[/tex]
The distance from B to C is the width of the rectangle. The distance of line segment BC is,
[tex]L = \sqrt{(6-6)^2 + (-2-5)^2}\\L = \sqrt{(0)^2 + (-7)^2}\\L=\sqrt{49}\\L=7\rm\; units[/tex]
Thus, the area of rectangle ABCD is,
[tex]A=7\times3\\A=21\rm\; unit^2[/tex]
Hence, the area of rectangle ABCD which is graphed in the coordinate plane with vertices A(3, -2), B(6, -2), C(6, 5), and D(3, 5) is 21 unit².
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Help ASAP!!
[tex]3 - 1 \times \frac{3}{5} = [/tex]
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1 2/5 or 1.4
what is the answer to Divide 2800 by 10
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Which relationship describes angles 1 and 2?
Select each correct answer.
adjacent angles
vertical angles
complementary angles
supplementary angles
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the gift shop at a science museum sells lollipops that are made to look like the plants. Each lollipop is shaped like a sphere and has a radius of 12 mm
What is the volume of each lollipop?
Answers
The answer is 2304pi
The volume of the lollipop having the radius of 12 mm is 7241.14 [tex]mm^{3}[/tex].
What is volume?Volume is the capacity of a container to hold something in its capacity. Like a drum can hold water.
How to calculate the volume of lollipop?The radius is given as 12 mm. The lollipop is having shape of sphere. The formula of volume of sphere is 4/3π[tex]r^{3}[/tex].
Volume =4/3π[tex]r^{3}[/tex].
Volume of lollipop is 4/3π[tex]12^{3}[/tex]
=4/3*22/7*576
=(88*1728)/21
=152064/21
=7241.14[tex]mm^{3}[/tex].
Hence the volume of lollipop having radius of 12 mm is 7241.14[tex]mm^{3}[/tex].
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Lee wants to cut this piece of canvas into two rectangles that are 3x2 and 3x5. He wants the sum of the two small rectangles to be the same as the area of the large rectangle. Can he do this? explain
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Cougar Park is shaped like a parallelogram and has an area of 1/10 square mile. It’s base is 3/8 mile. What is its height?
Answers
The formula for the area of a parallelogram is A=b*h. We plug in the information that we know and solve for the missing height.
[tex] \frac{1}{10}= \frac{3}{8}*h [/tex]
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[tex]\frac{8}{3}*\frac{1}{10}= h [/tex]
multiply the factions to get 8/30. 8 and 30 have common factors of 2 and can reduce to 4/15
What is the total cost or sale price to the nearest cent 20$ haircut; 15% tip
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The answer is $23.00
−2x+15y=−24
2x+9y=24
what do y and x equal?
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Hope this helps
what is 3.87 rounded to the nearest tenth
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Hope this helps
3.87 => 3.9
Solve for y 3/11 = 6/y
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Answer:
Khan academy says 22 is the correct answer
Step-by-step explanation:
It just does
Solve the quadratic equation by completing the square.
x^2 - 10x + 18 = 0
Answers
x² - 10x = -18
So then you add (b/2)², which is 25, to both sides, to get
x² - 10x + 25 = 7
After this, you factor.
(x-5)(x-5) = 7
Then you simplify.
(x-5)² = 7
Then you solve for x.
√(x-5)² = √7
x-5 = (+ or -)√7
~ x= 5 (+ or -)√7 ~
Hope this helps!
Sarah folds this pattern into a square pyramid. What is the surface area of Sarah's pyramid?
A. 161 sq. Inches
B.224sq.inches
C. 112sq.inches
D.273sq.inches
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A computer randomly selects a number from the given set.
{18, 47, 51, 60, 63, 65}
What is the probability that a number greater than 50 is selected?
Enter your answer as a fraction, in simplest form, in the box.
P(> 50) =
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using the distributive property to find the product (y-4)(y^2+4y+16) results in a polynomial of the form y^3 + 4y^2 + ay - 4y^2 - ay - 64 what is the value of a in the polynomial
Answers
y^3+4y^2+16y-4y^2-16y-64=y^3+4y^2+ay-4y^2-ay-64
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Answer: The value of a in the polynomial is 16
Answer:d
Step-by-step explanation:
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Hope this help
y = -3x - 3
Explanation:
The equation of line in slope-intercept form is:
y = mx + c
where:
m is the slope
c is the y-intercept
1- getting the slope:
To get the slope, we will need two points from the curve. I will choose points (-1,0) and (-2,3)
slope = (y2-y1) / (x2-x1) = (3-0) / (-2--1) = -3
The equation now is:
y = -3x + c
2- getting the y-intercept:
The y-intercept is the value of y at x = 0. From the graph, we can directly get this value.
y-intercept = c = -3
Based on the above, the equation of the line is:
y = -3x - 3
Hope this helps :)
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Beth’s final exam is worth 140 points. It consists of 40 questions. Each multiple choice question is worth 2 points, and each word problem is worth 5 points. How many of each kind of question are on the test?
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Two cars are traveling along the same highway. The distance, d, in miles, from San Francisco after h hours spent driving is described for each car below.
Car A:
d = 60h + 20
Car B: h d
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2 160
4 260
Select three statements that are true.
A.Car A is traveling at the same rate, in miles per hour, as Car B.
B.Car A is traveling at a faster rate, in miles per hour, than Car B.
C. Car A is traveling at a slower rate, in miles per hour, than Car B.
D.Car A is originally closer to San Francisco than Car B.
E .Car A is originally at the same distance from San Francisco as Car B.
F.Car A and Car B are at the same distance away from San Francisco after 4 hours.
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Car A is traveling faster at the checkpoint because it must go past the speed of car B to reach the same distance.
Explanation:Car A is traveling faster at the checkpoint because it must go past the speed of car B to reach the same distance.
To determine which car is traveling faster at the checkpoint, we need to compare their velocities. Car A has a positive, constant acceleration, which means its velocity is increasing. Car B, on the other hand, travels at a constant speed, which means its velocity remains the same.
Therefore, Car A is traveling faster at the checkpoint than Car B.
a 56 inch board is to be cut into three pieces so that the second piece is three times as long as the first piece and a third piece is four times as long as the first piece if x represents the length of the first please find the length of all three pieces
Answers
8x = 56
x = 7
The shortest piece is 7 inches
The middle piece is 7*3 = 21 inches.
The longest piece is 4*7 = 28 inches
Check
7 + 21 + 28 = 56 It does check and the lengths are correct.
The line plot shows the number of hours two groups of teens spent studying last week.
How does the data compare for the two groups of teens?
A)The range for the hours spent studying last week for the 13- to 15-year olds is the same as the range for the hours spent studying last week for the 16- to 18-year olds.
B)The median value for the hours spent studying last week for the 13- to 15-year olds is greater than the median value for the hours spent studying last week for the 16- to 18-year olds.
C)The mode for the hours spent studying last week for the 13- to 15-year olds is less than the mode for the hours spent studying last week for the 16- to 18-year olds.
D)The 13- to 15-year olds spent an average of 14 hours studying last week.
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I took this test☺
Hope this helps if it did plz mark brainliest so I can help more people.☺
6x+8=7x+13
one solution
infinite solution
no solution
which one?
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The simplification 6x + 8 = 7x + 13 is one solution. The correct option is A.
What is one solution?There is just one correct answer to some equations. There is only one value for the variable in these equations that causes the equation to be true.
If you solve an equation and the result is a variable equal to a number, the equation has just one solution. There is only ever one real number solution to a quadratic problem. A system is deemed consistent if it has at least one solution.
A consistent system is independent if it only has one solution. A consistent system is dependent if there are an endless number of possible solutions. Both equations show the same line on a graph when you plot the equations.
Therefore, the correct option is A, one solution.
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If 4/5 X a= 2/5, what is a?
Answers
--
2
I really hope this helps
any variable with nothing
in front of it is always 1
The ratio of the corresponding linear measures of two similar cans of fruit is 4 to 7. The smaller can has a surface area of 220 square centimeters. Find the surface area of the larger can
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How many unit cubes are in the rectangular prism?
A)
12 cm3
Eliminate
B)
15 cm3
C)
20 cm3
D)
60 cm3 What is the BEST estimate for the capacity of a bath tub?
A)
50 fluid ounces
B)
50 gallons
C)
50 cups
D)
50 pints
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The two triangles below are similar. Which pair are corresponding sides?
LN and MN
MN and QR
LM and QR
LM and PQ
Answers
Answer:
2) MN correspond to QR .
Step-by-step explanation:
Given : The two triangles below are similar.
To find : Which pair are corresponding sides
Solution : We have given that Triangle LMN is similar to triangle PQR.
Then Sides
MN correspond to QR .
Therefore, 2) MN correspond to QR .
In the figure, lines a, b, and c are parallel and m∠4=48° .
Drag and drop the correct angle measure for each angle.
Answers
m<1 = m∠4=48°
m<2 = 180 - 44 = 132
m<3 = m<2 = 132
m<5 = m∠4=48°
The values of each angle are:
∠1 = 48
∠2 = 132
∠3 = 132
∠5 = 48
We have,
∠4 = 48
∠4 and ∠5 are corresponding angles.
so,
∠5 = 48
Now,
∠3 and ∠4 make a straight angle.
So,
∠3 + ∠4 = 180
∠3 = 180 - 48
∠3 = 132
Now,
∠2 and ∠3 are alternate angles.
So,
∠2 = ∠3 = 132
Now,
∠1 and ∠2 make a straight angle.
So,
∠1 + ∠2 = 180
∠1 = 180 - 132
∠1 = 48
Thus,
∠1 = 48
∠2 = 132
∠3 = 132
∠5 = 48
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