Hello, Brainly community!
This question is for all of those Calculus people out there.
The volume of a swimming pool is changing with respect to time, such that the volume is given by W(t), where W(t) is measured in cubic centimeters and t is measured in seconds. A tangent line is shown for W(t) at t = 3 seconds. Determine the best estimate for the value of the instantaneous rate of change of W(t) when t = 3.
(I've narrowed down the answer choices to 2, and just really need to find the right way of thinking to find the answer)
(A) W(lim t) as t goes to 3.
(B) [W(3.1) - W(2.9)] / 0.2.
Thank you in advance!
Answer:
(B) [tex]\displaystyle \frac{W(3.1) - W(2.9)}{0.2}[/tex]
General Formulas and Concepts:
Calculus
Limits
Derivatives
The definition of a derivative is the slope of the tangent line.Derivative Notation
Instantaneous Rates
Tangent Line: [tex]\displaystyle f'(x) = \frac{f(b) - f(a)}{b - a}[/tex]Step-by-step explanation:
Since we are trying to find a rate at which W(t) changes, we must find the derivative at t = 3.
We are given 2 close answer choices that would have the same numerical answer but different meanings:
(A) [tex]\displaystyle \lim_{t \to 3} W(t)[/tex](B) [tex]\displaystyle \frac{W(3.1) - W(2.9)}{0.2}[/tex]If we look at answer choice (A), we see that our units would simply just be volume. It would not have the units of a rate of change. Yes, it may be the closest numerically correct answer, but it does not tell us the rate at which the volume would be changing and it is not a derivative.
If we look at answer choice (B), we see that our units would be cm³/s, and that is most certainly a rate of change. Answer choice (B) is also a derivative at t = 3, and a derivative tells us what rate something is changing.
∴ Answer choice (B) will give us the best estimate for the value of the instantaneous rate of change of W(t) when t = 3.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
Find the x-intercept of the graph of the linear equation y = −12x + 3.
Answer:
x-intercept = (1/4, 0)
Step-by-step explanation:
Just change the y to 0 if you want to find the x-intercept of a linear equation.
0=-12x+3
-12x=-3
x=1/4
y=0
x-intercept = (1/4, 0)
PLEASE HELP!!!!!!!!!
A car manufacturer does performance tests on its cars. During one test, a car starts from rest, and accelerates at a constant rate for 20 seconds. Another car starts from rest three seconds later, and accelerates at a faster constant rate. The equation that models the distance (d) in metres the first car travel travels is: d=1.16t^2, where t is time, in seconds, after the car starts. The equation for the second car is: d= 1.74(t-3)^2
a. In the context, what is a suitable domain for the graph of this system?
b. At what time will both cars have driven the same distance?
c. How far will they have driven at this time?
Answer:
15.66
Step-by-step explanation:
(NEED THIS ASAP)
Tests show that the hydrogen ion concentration of a sample of apple juice is 0.0003 and that of ammonia is 1.3 x 10-9. Find the approximate pH of each liquid using the formula pH = -log (H+), where (H+) is the hydrogen ion concentration The pH value of the apple juice is___ The pH value of ammonia is____
1.pH of apple juice
A. 8.11
B. 1.75
C. 3.5
D. 2.1
2. pH of ammonia
A. 1.1
B. 7.0
C. 5.4
D. 8.9
Answer: I believe but not 100% sure
1) C
2) B
Step-by-step explanation:
The pH value of the apple juice is 3.5, option C) is the correct answer.
The pH value of the ammonia is 8.9, option D) is the correct answer.
What is pH of solution?The pH of a solution is defined as the logarithm of the reciprocal of the hydrogen ion concentration [H+] of the given solution.
From the formular;
pH = -log[ H⁺ ]
Given the data in the question.
For the Apple juice;
hydrogen ion concentration H⁺ = 0.0003 pH of the apple juice pH = ?pH = -log[ H⁺ ]
pH = -log[ 0.0003 ]
pH = 3.5
The pH value of the apple juice is 3.5
Option C) is the correct answer.
For the ammonia;
hydrogen ion concentration H⁺ = 1.3 × 10⁻⁹pH of the ammonia pH = ?pH = -log[ H⁺ ]
pH = -log[ 1.3 × 10⁻⁹]
pH = 8.9
The pH value of the ammonia is 8.9
Option D) is the correct answer.
Learn more about pH & pOH here: brainly.com/question/17144456
#SPJ2
What is the largest prime number less than 200?
Answer:
199Step-by-step explanation:
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers.
A prime number is a number that has only two divisors: 1 and itself.
Exaples:
2, 3, 5, 7, 11, 13, 17, 19, 23 ...
We know: all primes except 2 are odd.
Let's check the number 199:
We know:
13² = 13 · 13 = 169 < 200
17² = 17 · 17 = 289 > 200
199 : 3 is not an integer
199 : 5 is not an integer
199 : 7 is not an integer
199 : 11 is not an integer
199 : 13 is not an integer
199 : 17 is not an integer
Therefore 199 is thelargest prime number less than 200.
please tell me the answer to this, thanks
Step-by-step explanation:
Hey there!
The equation is: 2x + 3y -12=0 (i)
From the given equation;
Slope (m) = (-coeff.of X)/(coeff.of y)
m = -2/3
Now; Let the missing component be "a".
The equation also can be written in;
The equation also can be written in;(y-8) = -2/3(x-a) (using one point formula)
3y - 24 = -2x + 2a
2x +3y -2a -24 = 0………(ii)
Since both equation are made from same coordinates, equating equation (i) and (ii).
2x + 3y -12= 2x +3y -2a -24
Cancel like terms,
-2a - 24 = -12
or, -2a = 12
or, a = -6.
Therefore, the missing value is -6.
Check:
Putting the value "a" in equation (ii).
2x + 3y -2(-6) -24 = 0
or, 2x+3y -12 = 0 (which is equal to equation (i).
Hope it helps!
The owner of a coffee shop compared the amount of hot coffee per day, in fluid ounces, sold and the daily high temp. In degrees f per day, 5.9x+850=
The question is not complete as the scatter plot is missing.
Thus, I have attached the complete question showing the scatter plot.
Answer:
D: On a day with a high temperature of 0°C, the shop can expect to sell about 850 fluid ounces of hot coffee
Step-by-step explanation:
From the attached image showing the question and scatter plot, we can see that the scatter plot is modeled by the line; y = -5.9x + 850
Where;
x is the high temperature in °F
y is the amount of fluid ounces sold
Let's try x = 0°F
Thus;
y = 0 + 850
y = 850 fluid ounces
Let's try x = 10°F
Thus;
y = -5.9(10) + 850
y = 850 - 59
y = 791
This means for every increase in temperature of 10°F, the amount sold is approximately 60 fluid ounces lesser.
Looking at the options in the attached file, the only correct one that corresponds to our answer is option D where it says;. On a day with a high temperature of 0°C, the shop can expect to sell about 850 fluid ounces of hot coffee
What is the slope of the line represented by the equation y-6 = 5(x-2)?
O A. 6
O B. 5
O C. -5
O D. 2
Answer:
B
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
y - 6 = 5(x - 2) ← is in point- slope form
with slope m = 5 → B
Which rates are equal? Choose 2.
A. 630 miles per 9 hours
B. 1,320 miles
per 24 hours
C. 1,170 miles per 18 hours
D. 455 miles per 7 hours
E. 840 miles per 14 hours
Answer:
C. 1170 miles per 18 hours
D. 455 miles per 7 hours
Step-by-step explanation:
1170/18=65
455/7=65
find the value of m. (-3/4)-⁴×(-3/4)-¹¹ = (-3/4)^m
Answer:
m = - 15
Step-by-step explanation:
Using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] , then
[tex](-\frac{3}{4}) ^{-4}[/tex] × [tex](-\frac{3}{4}) ^{-11}[/tex] = [tex](-\frac{3}{4}) ^{m}[/tex] , that is
[tex](-\frac{3}{4}) ^{(-4-11)}[/tex] = [tex](-\frac{3}{4}) ^{m}[/tex]
[tex](-\frac{3}{4}) ^{-15}[/tex] = [tex](-\frac{3}{4}) ^{m}[/tex]
Equating exponents gives
m = - 15
Which equation in slope-intercept form represents a line that is parallel to y=-4x-5 and passes through the points (0,0)?
Answer:
y = 0x
Step-by-step explanation:
y=-4x-b
0 = -4(0) + b
0 = 0 + b
0
It took Sarah 4 days to write a paper, she wrote 12 pages on day 1, 15 pages on day 2 and 9 pages on day 3. If she wrote 12 pages per day , how many pages did she write on the fourth day ?
Answer:
Option A
Step-by-step explanation:
Sarah took 4 days to write a paper.
She wrote 12 pages per day, so total number of pages she wrote in 4 days = 12 × 4
= 48 pages
On day 1, she wrote number of pages = 12
On day 2, she wrote number of pages = 15
On day 3, she wrote number of pages = 9
On day 4, she wrote number of pages = P
She wrote total number pages in 4 days = 12 + 15 + 9 + P
= 36 + P
Therefore, P + 36 = 48
P = 48 - 36
P = 12
She wrote 12 pages on day 4.
Option A is the answer.
2.1 One Step Equations
1) 4p = 68
2)x - 1 = -9
3) -25 = K - 17
4) 20n = 300 5) -17 + x = -196) 10b = -10
7)r - 11 = -27 8) -11n = -55
9) -120 = -8x
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
I
A 4-column table with 4 rows. Column 1 is labeled number of friends with entries 3, 5, 7, 9. Column 2 is labeled Carnival Cost with entries 51.5, 75.5, 99.5, 123.5. Column 3 is labeled Aquarium Cost with entries 43.5, 72.5, 101.5, 130.5. Column 4 is labeled Wave Pool Cost with entries 50.25, 61.25, 85.75, 110.25.
Gale wants to compare the cost of the events.
Aquarium: $14.50 each ticket
Carnival: c = 15.5 + 12f
Wave pool: $16.75 each, but $12.25 each for groups larger than 4
Which of the claims Gale makes is true?
The table represents all possibilities.
The carnival always costs the least.
The Aquarium always costs the most.
(7, 101.5) is an ordered pair used to represent the aquarium cost.
Answer:
D.(7, 101.5) is an ordered pair used to represent the aquarium cost.
Hope it helps :)
Step-by-step explanation:
Answer: it is d - (7, 101.5) is an ordered pair used to represent the aquarium cost
Step-by-step explanation: got it right on edge 2022
Which of the following are integers?
100
78
35
5
There can be more than one
Express your answer as a decimal (to the nearest hundredth).
What part of an hour is 20 minutes?
0.25
0 0.375
0.50
0.33
Answer:
0.33
Step-by-step explanation:
An hour is 60 minutes. 20 goes into 60 three times, so it is 1/3 of an hour or 0.333333333333, etc. As a percent, 20 minutes is 33.33%. Converted to a decimal, it is 0.33 or 1/3 of an hour
PLEASE HELP NEED HELP W ALGEBRA 2 QUESTION!!
the graph of f(x) = 3 sqr root x+8 is shown which statement is true
1. The function is only increasing x > -8
2. The function is only increasing when x > 0
3. The function is always decreasing
4. The function is always increasing
Pls say what number choice in your answer! Thanks!
Answer:
2. increasing when x > 0
the result of root is a positive number
and since there is no value of neg number in roots so it's increasing when x>0
plus in zero it self has a positive number (0,8)
but u cannot find either it's increasing or decreasing in zero bcoz in first derivative test
when x =0
y= not defined
A company uses two vans to transport
workers from a free parking lot to the
workplace between 7:00 and 9:00 a.m.
One van has 6 more seats than the other.
The smaller van makes two trips every
morning while the larger one makes only
one trip. The two vans can transport 57
people, maximum.
How many seats does the larger van have?
Answer:
The larger van has 23 seats
Step-by-step explanation:
Create a system of Equations:
1. Define variables.
> let x=small van and y=larger van
2. create 2 equations based on the information given.
> y = 6 + x
> 2x + y = 57
3. Use any method to solve
Substitution: 2x + (6 + x) = 57. x=17
now plug x in to the original equation to solve for y (the larger van)
y = 6 + 17 and y = 23
Elimination: 2y = 12 + 2x
y = 57 - 2x
3y = 69 and y = 23
PLEASE HELP.
if v1….
PLEASE HELP I'LL MARK BRANLIEST!
Activity Gina is playing dominoes with her family. She and her brother, Greg, are playing as a team (team A) against their parents (team B). The table shows how many points the two teams have scored in each round. Gina is keeping track of the scores and wants to know which measures of center and spread best represent each team’s data.
Team A: 15 20 15 5 10 15 10 15 5 20
Team B: 20 15 25 30 20 25 0 15 25 30
Part B What is the mean score for team A? Show your calculation.
Answer:
Mean of team A is 13
Step-by-step explanation:
I hope it helps:)
A soccer team made $575.75 from selling popcorn at a concession stand during a tournament. The popcom cost the
team $65.00. What is the amount of money earned for each player if the profit is divided equally among the 15
players? Round to the nearest cent.
O S34.05
0 $42.72
57.661.25
59.611.25 hurry I'm being timed!
Answer:
$34.05
Step-by-step explanation:
please answer
HCF of 16 and 40
Answer:
8
Step-by-step explanation:
Hello can someone help me with this problem
The width of this rectangle is measured as 19.4 correct to 1 decimal place. What is the lower bound for the area of the rectangle
Answer:
:D
Step-by-step explanation:
19.35 = 7062.75 mm²
Which is the value of this expression {jk^-2/j-1k-3}3, when j=-2 and k=-1?
Answer:
-9
Step-by-step explanation:
{-2*-1^-2/-2-1*-1-3}3
= -9
Answered by GAUTHMATH
GIVING 15 POINTS PLS HELP!!!
Part A: factor 2x^2b^2 + 5xb^2 + 2b^2. Show your work.
Part B: factor x^2 - 8x + 16. Show your work.
Part C: factor x^2 - 49. Show your work.
Answer:
the picture I've given is an answer
PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS ANSWERRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR
Answer:
ssssssssssssssssssssssssssssssssssssssssssssssss
Answer:
¼. 1000
Step-by-step explanation:
25% = 25/100
= 1/4
Therefore,
25% of 1,000 is the same as
1/4. 1000
Simplify the expression 7(9 + k).
Answer:
The answer is 63+7k. :))
Answer:
7k+63
Step-by-step explanation:
Distribute the 7 into the expression 9+k
so 7*9=63
and 7*k=7K
The following figures are not drawn to scale but AB and CD are straight lines. Find x.
Answer:
x=60
Step-by-step explanation:
solve, 180-(90+x) = 180-(30+2x)
Help please
If the measure of angle 6 is 140 degrees and the measure of angle 7 is (x + 30) degrees, what value of x will guarantee n ∥ m?
Answer:
x = 10
Step-by-step explanation:
If n // m , then angle 6 and angle 7 are co interior angles and they are supplementary.
∠6 + ∠7 = 180
140 + x +30 = 180
x + 170 = 180
x = 180 - 170
x = 10
