Answer:
answer is 18 54 an 72 is 18
Sea grass grows on a lake. The rate of growth of the grass is ????????/???????? = ????????, where ???? is a constant.
a. Find an expression for ????, the amount of grass in the lake (in tons), in terms of ????, the number of years, if the amount of grass is 100 tons initially, and 120 tons after one year.
b. In how many years will the amount of grass available be 300 tons?
c. If fish are now introduced into the lake and consume a consistent 80 tons/year of sea grass, how long will it take for the lake to be completely free of sea grass?
Answer:
[tex](a)\ G(t) = 100 *e^{0.1823t}[/tex]
[tex](b)\ t = 6[/tex]
[tex](c)\ t = 1.7[/tex]
Step-by-step explanation:
Given
[tex]G_0 = 100[/tex] --- initial
[tex]G(1) = 120[/tex] --- after 1 year
[tex]r \to rate[/tex]
Solving (a): The expression for g
Since the rate is constant, the distribution of G follows:
[tex]G(t) = G_0 * e^{rt}[/tex]
[tex]G(1) = 120[/tex] implies that:
[tex]G(t) = G_0 * e^{rt}[/tex]
[tex]120 = G_0 * e^{r*1}[/tex]
Substitute [tex]G_0 = 100[/tex]
[tex]120 = 100 * e^{r[/tex]
Divide both sides by 100
[tex]1.2 = e^{r[/tex]
Take natural logarithm of both sides
[tex]\ln(1.2) = \ln(e^r)[/tex]
[tex]0.1823 = r[/tex]
[tex]r = 0.1823[/tex]
So, the expression for G is:
[tex]G(t) = G_0 * e^{rt}[/tex]
[tex]G(t) = 100 *e^{0.1823t}[/tex]
Solving (b): t when G(t) = 300
We have:
[tex]G(t) = 100 *e^{0.1823t}[/tex]
[tex]300 = 100 *e^{0.1823t}[/tex]
Divide both sides by 100
[tex]3 = e^{0.1823t}[/tex]
Take natural logarithm
[tex]\ln(3) = \ln(e^{0.1823t})[/tex]
[tex]1.099 = 0.1823t[/tex]
Solve for t
[tex]t = \frac{1.099}{0.1823}[/tex]
[tex]t = 6[/tex] --- approximated
Solving (c): When there will be no grass
Reduction at a rate of 80 tons per year implies that:
[tex]G(t) = 100 *e^{0.1823t}- 80t[/tex]
To solve for t, we set G(t) = 0
[tex]0 = 100 *e^{0.1823t}- 80t\\[/tex]
Rewrite as
[tex]80t = 100 *e^{0.1823t}[/tex]
Divide both sides by 100
[tex]0.8t = e^{0.1823t}[/tex]
Take natural logarithm of both sides
[tex]\ln( 0.8t) = \ln(e^{0.1823t})[/tex]
[tex]\ln( 0.8t) = 0.1823t[/tex]
Plot the graph of: [tex]\ln( 0.8t) = 0.1823t[/tex]
[tex]t = 1.7[/tex]
whats the area of a rectangle
:)
Answer:
Baguette. :)
Step-by-step explanation:
Answer:
I don't know you lollollollll
Write the following comparison as a ratio reduced to lowest terms. 169 inches to 13 feet
Answer:
14.0833333333 feet | 13 feet
Step-by-step explanation:
169 Inches is 14.0833333333 feet on calculator compared to 13 feet
and 1.08333333333 is 14.0833333333 divided by 13
if is not it, then 13/14.0833333333 is 0.92307692307
i guess that is the lowest terms in ratio
john had a bag of 10 marbles (2 Green, 4 Blue, 1 Yellow, 2 Red) What is the probability that john selects a green marble, replaced it, and then selects a green marble?
Answer:
2/9
Step-by-step explanation:
the question didnt say replaced it with another colour
the lengths of two sides of a right triangle are 12 inches and 15 inches.What is the difference between the two possible lengths of the third side of the triangle
Answer:10.2 inches
Step-by-step explanation:
we know that
In this problem we have two cases
First case
The given lengths are two legs of the right triangle
so
Applying the Pythagoras Theorem
Find the length of the hypotenuse
substitute
Second case
The given lengths are one leg and the hypotenuse
so
Applying the Pythagoras Theorem
Find the length of the other leg
substitute
Find the difference between the two possible lengths of the third side of the triangle
so
Answer:
The difference between the two possible lengths for the third side of the triangle is about 10.21 inches.
Step-by-step explanation:
We are given that the lengths of two sides of a right triangle is 12 inches and 15 inches.
And we want to find the difference between the two possible lengths of the third side.
In the first case, assume that neither 12 nor 15 is the hypotenuse of the triangle. Then our third side c must follow the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
Substitute in known values:
[tex](12)^2+(15)^2=c^2[/tex]
Solve for c:
[tex]c=\sqrt{12^2+15^2}=\sqrt{369}=\sqrt{9\cdot 41}=3\sqrt{41}[/tex]
In the second case, we will assume that one of the given lengths is the hypotenuse. Since the hypotenuse is always the longest side, the hypotenuse will be 15. Again, by the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
Substitute in known values:
[tex](12)^2+b^2=(15)^2[/tex]
Solve for b:
[tex]b=\sqrt{15^2-12^2}=\sqrt{81}=9[/tex]
Therefore, the difference between the two possible lengths for the third side is:
[tex]\displaystyle \text{Difference}=(3\sqrt{41})-(9)\approx 10.21\text{ inches}[/tex]
A motor boat travels 60 miles down a river in 3 hours but takes 5 hours to return upstream. Find the rate of the boat in still water and the rate of the current.
Step-by-step explanation:
Given that,
A motor boat travels 60 miles down a river in 3 hours but takes 5 hours to return upstream,
We know that,
Speed = distance/time
The rate while moving downstream[tex]=\dfrac{60}{3}=20\ mph[/tex]
The rate while moving upstream [tex]=\dfrac{60}{5}=12\ mph[/tex]
The rate of the boat in still water is the average of these:
[tex]v_s=\dfrac{20+12}{2}=16\ mph[/tex]
The rate of the current is the difference between the boat speed and actual speed = 16 mph - 12 mph = 4 mph
Hence, this is the required solution.
Calculate the total population increase of South Africa from 2001 Difference You may use the following formula: Increase = 2001 Population Calculate the total population of KZN in 2021. Identify the province with the lowest population in 2011. Write down the 2011 total population of South Africa in words.
The figure below is made of 2 rectangular prisms.
What is the volume of this figure?
Answer:
6536 cubic in
Step-by-step explanation:
1. Split both the prisms apart- In doing so, you can simplify the problem.
2. Put in the #'s for the formula which in this case is V=L*W*H, we will start with the formula for the front one, V=7*8*1 or V=7*8
3. answer for the front is 56 cubic in, now we solve for the other half.
4. V=9*1*90 or V=9*90 which is 6480 cubic in.
5. add 6480 and 56 and your answer is 6536 cubic in as your answer.
Hope this helped ;D
HCF of the numbers divisible be
3 between 21 and 30 is ___
Answer:
3
Step-by-step explanation:
Numbers between 21 and 30 divisible by 3 are 24 and 27. so you get the HCF of the two.
A card is picked from a standard deck of 52 cards. Determine the odds against and the odds in favor of selecting a 4.
Answer:
1 : 12
Step-by-step explanation:
P(4) = 4 cards out of 52 = 1/13
P(4') = 48 cards out of 52 = 12/13
Odds in favour of selecting a four
Probability "for" : Probability "against" = P(4) : P(4') = 1/13 : 12/13 = 1 : 12
Simplify ratio to the simplest integers.
a motor pumps out 6704.76 liters of water in 6 hours how many litres of water will it pump in one hour?
Answer:
Amount of water pumped out by the motor = 1117.46 liters
Step-by-step explanation:
Amount of water pumped out by the motor pump = 6704.76 liters
Time taken by the motor to pump the water = 6 hours
Rate at which the motor pumps out the water = [tex]\frac{\text{Amount of water pumped out}}{\text{Time taken to pump the water}}[/tex]
= [tex]\frac{6704.76}{6}[/tex]
= 1117.46 liters per hour
Therefore, amount of water pumped out by the motor = 1117.46 liters
Please help will mark BRAINLIEST! This is pt.1
Answer:
See below.
Step-by-step explanation:
Problem 1.
1. QU
2. QW
3. UW
Given
4. QUW
Problem 2.
1. CB
2. <1, <2
Given
3. BD, BE
Given
4. ABD, CBE
SAS
The perimeter of a rectangle is 58 inches and the area is 180 square inches. Find the dimensions of the rectangle.
Answer:
width = 9 inches
length= 20 inches
perimeter of the rectangle=2(9+20)
2w +2L= 2×29
=58 inches
area of the rectangle=w×L
=9×20=180 inch²
the area of a tennis court is 2000m2 . a rugby pitch has a legnth of 45m and width of 45m . which has the biggest area?
Answer:
The area of a rugby pitch is more as compared to the area of the tennis court.
Step-by-step explanation:
Given that,
The area of a tennis court is 2000 m².
The length and width of a rugby pitch are 45 m and 45 m.
The area of a rugby pitch is given by :
A = lb
So,
A = 45×45
A = 2025 m²
So, it is clear that the area of a rugby pitch is more as compared to the area of the tennis court.
A family uses 15 gallons of milk every 3 weeks. At that rate, about how many gallons of milk will they need to purchase in a year’s time?
Give your answer as a whole number.
They will need to purchase
Answer:
15 gallons of milk at 3 week
15/3= 5
for a month 5 * 4 =20
in a year 12 * 20 = 240
Step-by-step explanation:
Can you help me with this please (finals)
Answer:
around 90 cm because that measure is equal to 180 you divide into 2 so the answer is 90
I’m suppose to find the measure of each angle. Thank you
Answer:
E) π/9
Step-by-step explanation:
The angles are complementary meaning they add up to 90°.
Convert radians to degrees:
7π/18 · 180/π = 70°
Now we know that we need the radian equivalent of 20°.
Convert degrees to radians:
70 · π/180 = π/9
Therefore, the measure of the missing degree is π/9.
A brick staircase has a total of 17 steps The bottom step requires 131 bricks. Each successive step requires 5 less bricks than the prior one. How many bricks are required to build the staircase?
Answer: 1547 bricks are required to build the staircase.
Step-by-step explanation:
We are given:
Number of bricks in the first step, [tex]a_1[/tex] = 131
Number of bricks in the second step, [tex]a_2[/tex] = 131 - 5 = 126
Number of bricks in the third step, [tex]a_3[/tex] = 126 - 5 = 121
Sequence become:
131, 126, 121, .....
These are in arithmetic progression where a = 131 and d (common difference) = -5
To calculate the sum of an AP, we use the formula:
[tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]
where,
n = number of terms = 17
Putting values in above equation, we get:
[tex]S_n=\frac{17}{2}[2(131)+(17-1)(-5)]\\\\S_n=\frac{17\times 182}{2}=1547[/tex]
Hence, 1547 bricks are required to build the staircase.
How many dimensions does a plane have?
O
A. Three
о
B. Zero
O C. Two
D. One
A Plane does not have one dimensions.
What is Plane?A plane is a doubly ruled surface in two dimensions that is spanned by two linearly independent vectors. A hyperplane is a generalisation of the plane to higher dimensions. The dihedral angle is the angle formed by two intersecting planes.
A plane doesn't only have one dimension, though. The two dimensions of a plane.
A plane is a flat, infinitesimally long two-dimensional surface.
The plane can occasionally be extended into three dimensions.
Consequently, a plane has more than one dimension.
Learn more about Plane here:
https://brainly.com/question/1962726
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d) The Princess was allowed to climb trees.
e)
Hector lived a lonely life in the King's castle.
Answer these questions in one or two words only.
a) Who first discovered that the Princess had climbed up a tree?
Hector is the one who discovered
PLEASE HELP!! graph the circle whose equation is (x-6)^2 + (y+2)^2 =4
Answer:
Y= -x^2+12x-36
Step-by-step explanation:
Which best explains whether a triangle with side lengths 2 in., 5 in., and 4 in. is an acute triangle?
The triangle is acute because 22 + 52 > 42.
The triangle is acute because 2 + 4 > 5.
The triangle is not acute because 22 + 42 < 52.
The triangle is not acute because 22 < 42 + 52.
9514 1404 393
Answer:
The triangle is not acute because 2² + 4² < 5²
Step-by-step explanation:
The square of the hypotenuse of a right triangle with the given short sides would be 2² +4² = 20. So, that hypotenuse would be √20, about 4.47. The long side of this triangle is longer than that, so the angle opposite is larger than 90°. The triangle with sides 2, 4, 5 is an obtuse triangle.
The triangle is not acute because 2² + 4² < 5²
The triangle is not acute because 22 + 42 < 52.
Option C is the correct answer.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
To determine if a triangle is acute, we need to check whether all three angles of the triangle are acute angles (less than 90 degrees).
Pythagorean theorem,
- If the square of the length of the hypotenuse is greater than the sum of the squares of the other two sides, then the triangle is acute.
- If the square of the length of the hypotenuse is less than the sum of the squares of the other two sides, then the triangle is obtuse.
Now,
The triangle with side lengths 2 in., 5 in., and 4 in. is not a right triangle.
So we can't use the Pythagorean theorem directly.
Now,
We can check if the sum of the squares of the two shorter sides is greater than the square of the longest side.
2² + 4² = 4 + 16 = 20
5² = 25
Since 20 < 25, we know that the triangle is not acute.
Therefore,
The triangle is not acute because 22 + 42 < 52.
Learn more about triangles here:
https://brainly.com/question/25950519
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A person walks 1/6 mile in 1/18 hour.
The person's speed is _ miles per hour.
This Is What I Got!
Hope This Helps! :)
Have A Good Day!!
And If You Can I Wouldn't Mind A Brainliest! :))
Answer:
Divide 1/6 miles to 1/12hour since u wanna find our miles per hour
So it’ll be : 1/6 / 1/12
= 1/6 x 12/1
= 2 miles
How much is six dimes, 8 nickels, and three one-dollar bills? *
Answer:
.60 + .40 + 3.00 = 4.00
Step-by-step explanation:
Answer:
$ 4
Step-by-step explanation:
six dimes (.10 each) = .60
8 nickels (.05 each)= .40
3 dollars (1.00 each) = 3.
Add together
Solve for x. 8x = 35
Answer:
[tex]x = \frac{35}{8} [/tex]
Step-by-step explanation:
Divide both sides by 8:
[tex] \frac{8x}{8} = \frac{35}{8} \\x= \frac{35}{8} [/tex]
calculate the volume of each cone. Use 3.14 for π. Round answers to the nearest hundredth if necessary.
Answer:
πr of length
»» 3.14 x (5)²
»» 3.14 x 30 = 94.2cm²
πr of base
»» 3.14 x (4)²
»» 3.14 x 16 = 50.24cm²
Length x base
»» 94.2cm² x 50.25cm²
A= 4733.55cm²
[tex]\color{yellow}{}[/tex][tex]\color{yellow}{}[/tex][tex]\color{yellow}{}[/tex][tex]\color{yellow}{}[/tex][tex]\color{yellow}{}[/tex]
Which expression are greater than 1/2? Choose all the apply
Answer:
25/30
5/8
Step-by-step explanation:
Which fraction is it out of all of these 6/14,5/8,25/30,or 3/6?
to determine which fractions are greater than 1/2, convert the fractions to decimals
to convert to decimals, divide the numerator by the denominator
1/2 = 0.5 less than half
6/14 = 0.43 less than half
5/8 = 0.625 greater than half
25 / 30 = 0.83 greater than half
3 / 6 = 0.5 equal to half
Analyze the graph below and complete the instructions as follows.
Answer:
Option A:
x^2 + (y - 2)^2 = 9
Step-by-step explanation:
We know that the equation for a circle centered in the point (a, b) and of radius R is given by:
(x - a)^2 + (y - b)^2 = R^2
So the first thing we need to find is the center of the circle.
We can see that the center is at:
x = 0
y = 2
Then the center is at the point (0, 2)
Now we want our circle to pass through point 2, located at a distance of 2 units from the radius of the first circle.
So the distance between the center and point 2 is 2 units plus the radius of the smaller circle:
And the radius of the smaller circle is one unit.
Then, the radius of a circle centered at (0, 2) that passes through point 2 is:
R = 1 + 2 = 3
Then we have a circle centered at (0, 2) and of radius R = 3
Replacing these in the equation for a circle we get:
(x - 0)^2 + (y - 2)^2 = 3^2
x^2 + (y - 2)^2 = 9
The correct option is A
In Act I, scene ii, Claudius’s mention of Fortinbras raises the issue of _____. the cause of King Hamlet’s death how Fortinbras is better than Hamlet an external threat to Denmark corruption in Denmark’s government
Answer:
the answer to this is D "an external threat to Denmark"
Step-by-step explanation: just did the assignment :)
What is the slope of the line?
Hi there!
»»————- ★ ————-««
I believe your answer is:
m = (7/4)
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{The slope formula is rise over run.}}\\\\m=\frac{\text{Rise}}{\text{Run}}\\\\m=\frac{y_2-y_1}{x_2-x_1}\\-------------\\(x_1,y_1) \text{ and } (x_2,y_2) \text{ are two points that are on the line.}[/tex]
⸻⸻⸻⸻
The line passes through the points (3,4) and (-1, -3).
⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the Slope:}}\\\\\rightarrow m = \frac{-3-4}{-1-3}\\\\\rightarrow m=\frac{-7}{-4}\\\\\rightarrow m=\boxed{\frac{7}{4}}[/tex]
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.