Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and values of the rate at two hour time intervals are shown in the table. Find lower and upper estimates for the total amount of oil that leaked out.
t (h) 0 2 4 6 8 10
r(t) (L/h) 8.8 7.6 6.8 6.2 5.7 5.3
V=_____ upper estimate
V= ______lower estimate
Answers
The exact amount of oil that leaks out for 0 ≤ t ≤ 10 is given by the integral,
[tex]\displaystyle\int_0^{10}r(t)\,\mathrm dt[/tex]
Then the upper and lower estimates of this integral correspond to the upper and lower Riemann/Darboux sums. Since r(t) is said to be decreasing, this means that the upper estimate corresponds to the left-endpoint Riemann sum, while the lower estimate would correspond to the right-endpoint sum.
So you have
• upper estimate:
(8.8 L/h) (2 h - 0 h) + (7.6 L/h) (4 h - 2h) + (6.8 L/h) (6 h - 4h) + (6.2 L/h) (8 h - 6h) + (5.7 L/h) (10 h - 8 h)
= (2 h) (8.8 + 7.6 + 6.8 + 6.2 + 5.7) L/h)
= 70.2 L
• lower estimate:
(7.6 L/h) (2 h - 0 h) + (6.8 L/h) (4 h - 2h) + (6.2 L/h) (6 h - 4h) + (5.7 L/h) (8 h - 6h) + (5.3 L/h) (10 h - 8 h)
= (2 h) (7.6 + 6.8 + 6.2 + 5.7 + 5.3) L/h)
= 63.2 L
Related Questions
Find the measure of the missing angles.
WILL GIVE BRAINLIEST
Answers
Answer:
h= 60
g= 120
m= 147
k= 33
Step-by-step explanation:
We know that all three lines are straight an continuous, so, at any given point the angles should add up to 180 degrees.
This immediately helps with angle h:
120 + h = 180
h = 60
As well as m:
33 + m = 180
m = 147
There are two ways to solve the next part:
First and most familiar way:
h + g = 180
60 + g = 180
g = 120
and:
m + k = 180
147 + k = 180
k = 33
The other way that I prefer is that the angles opposite of each other when two lines intersect are equal. I don't know if that makes sense, it's hard to explain in this format.
Which of the following best describes a type of growth that is exponential at
first but slows as the amount reaches a certain maximum value?
A. Exponential decay
B. Exponential growth
C. Linear growth
D. Logistic growth
Answers
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Answer:
D. Logistic growth
Step-by-step explanation:
The logistic growth function models a situation where the rate of growth is jointly proportional to the population and to the difference between the population and the carrying capacity.
Attached is an example of such a function.
Determine whether the three points are colinear (0,-4),(-3,-18),(2,6) are the three points colinear?
Answers
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Answer:
they are not collinear
Step-by-step explanation:
A graph shows that a line through points A and C misses point B, so the points are not collinear.
__
If the points are collinear, then the slope of the segment between the first pair would be the same as the slope of the segment between the second pair.
m = (y2 -y1)/(x2 -x1)
m = (-18 -(-4))/(-3 -0) = -14/-3 = 14/3 . . . . slope of AB
__
m = (6 -(-18))/(2 -(-3)) = 24/5 . . . . slope of BC ≠ slope of AB
The points are not collinear.
_____
Additional comment
With about the same amount of computational effort, you can find the area of the triangle bounded by the three points. If it is zero, then the points are collinear. Here, it is 1 square unit, so the points are not collinear.
I am need help and an explanation on how to read these graphs.
Answers
Answer:
i think its b
Step-by-step explanation:
If x+y=6 and xy =2find x³+y³(please help me fast with explanation also please) T^T
Answers
Answer: x³+y³=180
Step-by-step explain: let's remember the formula x³+y³=(x+y)(x²-xy+y²) and also x³+y³=(x+y)³-3xy(x+y) then [tex]\displaystyle\boldsymbol{ x^3+y^3=\underbrace{(x+y)^3}_{6}-3\underbrace{xy}_{2}\underbrace{(x+y)}_6}=\\\\6^3-3\cdot 2\cdot 6=216-36=180[/tex]
I need help with this
Answers
Answer:
A. More students prefer Model A1 calculators than the Model C3 calculators.
please help me please help me
Answers
14. largest 9510
15. smallest 1000000
16. n+6=22 —> n=22-6 —>n = 16
17. Add : 204 + 38429= 38633
Question 4 4 pts Lori buys a $1500 certificate of deposit (CD) that earns 6% interest that compounds monthly. How much will the CD be worth in: 5 years? 10 years? 486 months?
Answers
Answer:
Step-by-step explanation:
5 years
[tex]1500(1+\frac{.06}{12})^{12*5}=2023.275229[/tex]
10 years
[tex]1500(1+\frac{.06}{12})^{10*12}=2729.095101[/tex]
486 months:
[tex]1500(1+\frac{.06}{12})^{486}=16935.47074[/tex]
round those as you please
A professor has learned that nine students in her class of 35 will cheat on the exam. She decides to focus her attention on ten randomly chosen students during the exam. a. What is the probability that she finds at least one of the students cheating
Answers
Answer:
[tex]\frac{73,331}{75,516}\approx 97.11\%[/tex]
Step-by-step explanation:
The probability that she will find at least one student cheating is equal to the probability that she finds no students cheating subtracted from 1.
Each time she randomly chooses a student the probability she will catch a cheater is equal to the number of cheaters divided by the number of students.
Therefore, for the first student she chooses, there is a [tex]\frac{9}{35}[/tex] chance that the student chosen is a cheater and therefore a [tex]\frac{26}{35}[/tex] chance she does not catch a cheater. For the second student, there are only 34 students to choose from. If we stipulate that the first student chosen was not a cheater, then there is a [tex]\frac{9}{34}[/tex] chance she will catch a cheater and a [tex]\frac{25}{34}[/tex] chance she does not catch the cheater.
Therefore, the probability she does not catch a single cheater after randomly choosing ten students is equal to:
[tex]\frac{26}{35}\cdot \frac{25}{34}\cdot \frac{24}{33}\cdot \frac{23}{32}\cdot \frac{22}{31}\cdot \frac{21}{30}\cdot \frac{20}{29}\cdot \frac{19}{28}\cdot \frac{18}{27}\cdot \frac{17}{26}[/tex]
Subtract this from one to get the probability she finds at least one of the students cheating after randomly selecting nine students. Let event A occur when the professor finds at least one student cheating after randomly selecting ten students from a group of 35 students.
[tex]P(A)=1-\frac{26}{35}\cdot \frac{25}{34}\cdot \frac{24}{33}\cdot \frac{23}{32}\cdot \frac{22}{31}\cdot \frac{21}{30}\cdot \frac{20}{29}\cdot \frac{19}{28}\cdot \frac{18}{27}\cdot \frac{17}{26},\\\\P(A)=1-\frac{2,185}{75,516},\\\\P(A)=\boxed{\frac{73,331}{75,516}}\approx 0.97106573441\approx \boxed{97.11\%}[/tex]
what is the slope intercept equation of the line below?
Answers
Answer:
[tex]{ \tt{slope, \: m = \frac{1 - ( - 1)}{1 - 0} }} \\m = 2 \\ y - intercept : y = mx + c \\ { \tt{1 = (2 \times 1) + c}} \\ c = - 1 \\ { \boxed{ \bf{y = 2x - 1}}}[/tex]
Write a linear equation in point slope form that passes through the points (-2,18) and (1,9)
Answers
Answer:
y-18=-3(x+2)
Step-by-step explanation:
The Slope-intercept form is -3x+12
expand and simplify √3(√3-1)
Answers
Answer:
[tex]3 - \sqrt{3} [/tex]Step-by-step explanation:
[tex] \sqrt{3} ( \sqrt{3} - 1)[/tex]
[tex] = \sqrt{3} \times \sqrt{3} - \sqrt{3} \times 1[/tex]
[tex] = 3 - \sqrt{3} (ans)[/tex]
help I was never taught how to do this im confused
Answers
Answer:
36
Step-by-step explanation:
Area of a triangle = (bh)/2
Where b = base length and h = height
Given base length: 18ft
Given height: 4ft
This being known let's define the variables
b = 18
h = 4
Now to find the area we simply plug in these values into the formula
Area = (18)(4)/2
Simplify multiplication 18 * 4 = 72
Area = 72/2
Simplify division
Area = 36
19/3+[14/3 ÷{10-3(3+1/2-1/4)×1/3}]
Answers
Answer:
= 3 11/20
Sorry I am not doing the step by step.
fill in each blank with a true statement
Answers
Answer:
See below.
Step-by-step explanation:
7.)
Supplementary angles add up to 180°. ∠B's supplement is 22°. This means ∠B is 158°. Since ∠A ≅ ∠B, the m∠A = 158°.
8.)
Again, supplementary angles add up to 180°. ∠P is a right angle meaning it is 90°. Therefore, the m∠Q is 90° as well.
9.)
Complementary angles add up to 90°. In order for ∠S and ∠T to be complementary, they both need to angle measurements less than 90° meaning they both need to be acute angles.
Now that we know that ∠T is acute, the only way ∠U can be its supplement is if it has an angle measure greater than 90°. Therefore, ∠U is an obtuse angle.
10.)
Similar to question 9, if an angle is obtuse, its supplement must be an acute angle.
it’s question number 3 and i know the answer but i need someone to explain to me how to get the answer the answer is B. pls can hurry i need the explanation soon
Answers
Answer:
2+6=8
Step-by-step explanation:
Start at 2
Then since we are adding 6 move 6 units to the right
A golf ball is hit from ground level. Its path is modelled by the relation h(t) = -4.9 t2 + 27.2t , where h is the ball’s height above the ground, in meters, and t is the time, in seconds. Determine the time the ball is in the air.
Answers
determine a simplified expression
Answers
Answer:
For Task B: [tex]3x^4 - 2x^3[/tex]
Step-by-step explanation:
Given that Volume = l*w*h, we can plug in the values on the diagram, so we get the equation (3x-2)([tex]\frac{1}{2}x[/tex])([tex]2x^2[/tex]) = [tex](\frac{3}{2} x^2 - x)(2x^2) = 3x^4-2x^3[/tex]. Hope this helps!!!
Last question pls help me
Answers
Answer:
Step-by-step explanation:
684 dollars
If there is a song that is 2 minutes and 58 seconds long and it plays 40 times how long does it play convert answer into seconds.
Answers
Answer: I got 7120 seconds
Step-by-step explanation:
There's 178 seconds in the song (for more context, I just converted the 2 minutes into seconds and added it with 58) then I multiplied it by the total amount of times it played (in this case, 40)
Hope this helps
A cube has an edge of 8cm. Calculate its Volume.
Answers
Answer:
512cm³
Step-by-step explanation:
to get the volume the formula is Base area x height
BA X H
=8x8x8 because all sides of a cube are equal
=512cm³
At a store, 2 gallons of milk cost $6.
Which is the value of the ratio of dollars to gallons of milk?
0.33
per gallon
$3 per gallon
Answers
Answer:
B
Step-by-step explanation:
$3 per gallon
that is the procedure above
What is a40
a
40
of the arithmetic sequence for which a8=60
a
8
=
60
and a12=48
a
12
=
48
?
Answers
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Answer:
-36
Step-by-step explanation:
Using the expression for the general term, you can fill in the known values and solve for the parameters of the sequence.
an = a1 +d(n -1)
a8 = a1 + d(8 -1) = 60
a12 = a1 + d(12 -1) = 48
The difference of these equations is ...
(a1 +7d) -(a1 +11d) = (60) -(48)
-4d = 12
d = -3
Substituting into the first equation, we have ...
a1 +7(-3) = 60
a1 = 81 . . . . . . . . . add 21
Then the 40th term is ...
a40 = 81 -3(40 -1) = 81 -117
a40 = -36
Convert the following fraction to a decimal.
1/3
A. 0.3
B. 0.03
C. 0.303
D. 3.9
Answers
Answer:
Option A, 0.3
Step-by-step explanation:
Step 1: Convert the fraction into a decimal
Technically, 1/3 is an irrational number meaning that it never ends. However, if we round it, it would round to 0.3 since 1/3 = 0.3333333.....
Answer: Option A, 0.3
If a square root parent function is vertically compressed by a factor of 1/6,
what is the equation of the new function, G(x)?
O A. G(x)=1/6square root of x
B. G(x) = Square root of 6x
C. G(x) = 6 square root of x
D. G(x) = -6 square root of x
Answers
Answer:
the answer could be B i think cause that makes total sense
PLEASE HEP ME
PLEASE HELP AND BE CORRECT BEFORE ANSWERING
Answers
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Answer:
TrueTrueStep-by-step explanation:
The center of dilation (point D) is a point that doesn't move. Any line not through that point will be moved to a parallel location when a dilation factor is applied.
Any line through the center of dilation will still go through the center of dilation. Its slope does not change, so the line will appear to be the same.
AB ║ A'B' — True
AD ≅ A'D' — True
_____
You can see these relationships in the attached figure.
The degree of this expression 2x+3y=4
Answers
Answer:
1st degree
Step-by-step explanation:
You look at the largest exponet, right here, there are none so it would be 1st degree.
Answer:
1
Step-by-step explanation:
The degree of an expression with multiple exponents is the highest exponent in it. In this expression, there is no expression, so the answer will be 1 because there is no exponent and every variable and number has an invisible 1 as its exponent.
Hope this helps.
Owens Orchards sells apples in a large bag by weight. A sample of seven bags contained the following numbers of apples: 23, 19, 26, 17, 21, 24, 22. a. Compute the mean and median number of apples in a bag. (Round your answers to 2 decimal places.)
Answers
Answer:
The mean and median number of apples in a bag are 21.71 and 22 respectively.
Step-by-step explanation:
The mean is the arithmetic mean of a set of numbers. In other words, the mean is the average value of all my data.
The mean is calculated by adding all the values and dividing the sum by the total number of values. In this case:
[tex]Mean=\frac{23+19+26+17+21+24+22}{7}[/tex]
[tex]Mean=\frac{152}{7}[/tex]
Mean= 21.71
The median of a set of numbers is the average number in the set, that is, it is the value that occupies the central place of all the values.
The median can be calculated by putting the numbers in ascending order and then:
if the quantity is numbers it is odd: the median is the number in the center of that distribution. if the number of numbers is even: the median is the mean of the two middle numbers.In this case:
Putting the numbers in ascending order: 17, 19, 21, 22, 23, 24, 26
Since the quantity is odd numbers, the median is the number in the center of that distribution. So Median= 22
The mean and median number of apples in a bag are 21.71 and 22 respectively.
A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 5 tables is $53. The total cost to rent 8 chairs and 3 tables is $42. What is the cost to rent each chair and each table?
Answers
Answer:
c=cost of one chair rental
t=cost of one table rental
8c+3t=42
2c+5t=53
multiply the second equation, each term on both sides, by -4
8c+3t=42
-8c-20t=-212
add the two equations
-17t=-170
divide both sides by -17
t=$10 to rent one table
substitute t=10 into either original equation
2c+5(10)=53
2c+50=53
2c=3
c=$1.50 to rent one chair
Catriona spotted a major problem having to do with patient billing. A number of people may have received the wrong bills. When should she have told her boss? O a) When she was evaluating how to alert the patients O b) After she sent patient notices out c) When she first noticed the problem O d) After she decided on a communication plan
Answers
Answer:
C
Step-by-step explanation:
When she first noticed the problem
