The integral [tex]\int\limits^a_b {I (t)} \, dt[/tex]represents the total change in the charge from time t= b to t = a. Or in other words, it is the total amount of charge passed through between t = a and t = b.
What is the Net change Theorem?The ultimate value of a quantity, according to the net change theorem, equals the beginning value plus the integral of the rate of change when a quantity changes. Net change can be either a positive, negative, or zero number.
The Net Change Theorem: The integral of a rate of change is the net change.
[tex]\int\limits^a_b {F'(x)} \, dx[/tex] = F(b) − F(a)
[tex]\int\limits^a_b {I (t)} \, dt[/tex] & I(t) = Q'(t)
Consider the given integral,
[tex]\int\limits^a_b {I (t)} \, dt[/tex], where I(t) = Q'(t)
Now substitute the value I(t) = Q'(t) in [tex]\int\limits^a_b {I (t)} \, dt[/tex]. It becomes[tex]\int\limits^a_b {I (t)} \, dt[/tex] = [tex]\int\limits^a_b[/tex]Q'(t) by using the Net Change Theorem,
[tex]\int\limits^a_b[/tex] Q'(t) dt = Q(b)−Q(a)
[tex]\int\limits^a_b {I (t)} \, dt[/tex] = Q(b)−Q(a)
The integral [tex]\int\limits^a_b {I (t)} \, dt[/tex] represents the change in the charge from time b to a.
Therefore, [tex]\int\limits^a_b {I (t)} \, dt[/tex] represents the change in the charge from time t= b to t= a.
Learn more about Net change Theorum here:
https://brainly.com/question/15867119
#SPJ4
16
Which one of the following
sets of three lengths will form
a triangle
A. 3, 4, and a
B. 3, 5, and a
C. 3, 6, and a
D. 3, 7, and a
Answer:
A .........................
According to a survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of e-mails per day (Entrepreneur magazine website). Assume the number of e-mails received per hour follows a Poisson distribution and that the average number of e-mails received per hour is five. a. What is the probability of receiving no e-mails during an hour (to 4 decimals)
Answer:
the probability is 0.0067
Step-by-step explanation:
The computation of the probability of receiving no e-mails during an hour is shown below;
Let us assume x be the number of emails received during an hour
Now the probability of receiving no e-mails is
= e^-5 × 5^0÷ 0!
= e^-5 × 1 ÷ 1
= e^-5
= 0.00674
= 0.0067
Hence, the probability is 0.0067
Sue receives a monthly salary of $500. She also receives a sales commision of
8% of her total sales. Her total sales this week were $2,500. Find her
commission and total sales.
Answer:
2000 because you got to subtract
The domain of y = f(x) = _ is
(a) R - {0}
(b) R
(c) (-2,1)
(d) (-1.1)
Answer:
The domain of a function is the set of all possible x values that satisfy the equation. We cannot answer this question without first knowing what the equation for f(x) is.
Step-by-step explanation:
Take for example the function y = f(x) = [tex]x^{2} +3[/tex]. Here, you can plug in literally any value for x and still get our a real number. Thus, the domain of f(x) is (-∞, ∞).
However, if your function is y = f(x) = [tex]\frac{2}{\sqrt{x+3} }[/tex] , not every x value is acceptable. First, we cannot have the denominator (bottom part) of the fraction be zero, because division by zero is undefined. Thus, x = -3 is not an acceptable value for x.
We also cannot take the square root of a negative number. Thus, we have the rule that x + 3 must be greater than or equal to zero.
[tex]x+3 > 0\\\\x > -3\\[/tex]
Normally we would use greater than or equal to zero, but because this is in the denominator, we don't want it to equal zero (and thus x = -3 is not acceptable).
So, the domain of x is (-3, ∞). The parenthesis tell us we do not include the negative three and we do not include infinity. In other words, the domain of x is all numbers greater than -3 but less than infinity.
So, first look at your equation for f(x), then see which values of x don't break the rules of math like division by zero or square roots of negative numbers. Good luck!
-29= x + 8
what is x
Answer:
x=-37 (the answer should have a negative sign.)Step-by-step explanation:
To solve this problem, isolate the value of x from one side of the equation.
First, switch sides.
-29=x+8
x+8=-29
Then, subtract by 8 from both sides.
x+8-8=-29-8
Solve.
-29-8=-37
x=-37
Therefore, the final answer is x=-37.
Please answer soon
(2x+5)37 what is x
Answer:
74 x + 185
Step-by-step explanation:
Step-by-step explanation:
(2x+5)+37 - multiply 37 by 2x and then 37 by 5
which gives you a answer of 74x+185
The sum of x and y is 280. If x + 8 is y, when will the value of x be the same for both equations?
Answer:
x = 136, y = 144
Step-by-step explanation:
x+y = 280
y = x +8
use substitution
x + x+8 = 280
2x = 272
x = 136
y= 136+8 = 144
Answer:
the answer is x=136
Step-by-step explanation:
x + y = 280
x + 8 = y (substitute this expression for y)
x + (x + 8) = 280
2x + 8 = 280
2x = 272 -> x = 136
to find y:
x + 8 = y
136 + 8 = y
144 = y
CHECK:
136 + 144 = 280
yes
Simplify the expression. 9√3(8√3+9√5)
Answer:
B
Step-by-step explanation:
first of all we have to multiply 9√3 for each members in the brackets. For do this we have to multiply number x number and roots x roots
(9x8) = 72
(√3)^2 = 3
72 x 3 = 216
9 x 9 = 81
√3 x √5 = √15
81√15
now we have to added up the two results
216 + 81√15
wiil give crown if right Winston bought an encyclopedia priced at $42. Shipping and handling cost anadditional 30% of the price. What was the total cost of the encyclopedia, in cluding shipping and handling?
Answer:
42.3
Step-by-step explanation:
Turn 30% into decimal=0.30 then add both numbers=42.3
Hope it's correct if not sorry, but you can mark other person brainliest now! :)
Kianna started her homework at 4:30 pm. She finished at 5:05 pm. How many SECONDS did it take her to finish her homework? *
1 point
Answer:
2100 second
Step-by-step explanation:
4:30 pm to minutes
4 × 60 + 30 = 240 + 30
= 270 minutes
5:05 to minutes
5 × 60 + 5 = 300 + 5
= 305
4:30 to 5:05
305 - 270
= 35 minutes
35 minutes to second
35 × 60
= 2100 second
Answer:
2100
Step-by-step explanation:
25 minutes you need to know that 60 sec =1 hour.35x60=2100
A rectangular prism has a volume of 72 cubic units. How many unit cubes will fill the rectangular prism exactly?
a.12 unit cubes
b.36 unit cubes
c.24 unit cubes
d.72 unit cubes
1. Sam rolls a fair dice and flips a fair
coin. What is the probability of
obtaining an odd number and a head?
Use a sample space diagram to help.
See below for an example.
Answer:
Mark brainliest pls
Step-by-step explanation:
People have given you correct answers but not explained why, perhaps because it seems so obvious.
One of Bayes laws of probability says that if two events e1 and e2 are independent (unrelated), then the probability of both happening together is the product of their individual probabilities.
The die and the coin are independent events. Each is a 50% chance (odd number on a die, heads on a coin). Thus the probability of both happening together is 50% * 50% = 25%.
The probability of obtaining an odd number and a head is 1/4.
What is probability?Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.
For the given situation,
Let A be Sam rolls a fair dice.
Sample space, s = { [tex]1,2,3,4,5,6[/tex] }
⇒ [tex]n(s)=6[/tex]
An event A is obtaining an odd number, e = { [tex]1,3,5[/tex] }
⇒ [tex]n(e)=3[/tex]
The probability of A is obtaining an odd number,
[tex]P(A)=\frac{n(e)}{n(s)}[/tex]
⇒ [tex]P(A)=\frac{3}{6}[/tex]
⇒ [tex]P(A)=\frac{1}{2}[/tex]
Now, let B be Sam flips a fair coin.
Sample space, s = { [tex]H,T[/tex] }
⇒ [tex]n(s)=2[/tex]
An event B is getting a head, e = { [tex]H[/tex] }
⇒ [tex]n(e)=1[/tex]
The probability of B is getting a head,
[tex]P(B)=\frac{1}{2}[/tex]
Both A and B are independent events.
Thus the probability of obtaining an odd number and a head is
[tex]P(e)= P(A)P(B)[/tex]
⇒ [tex]P(e)=(\frac{1}{2})( \frac{1}{2} )[/tex]
⇒ [tex]P(e)=\frac{1}{4}[/tex]
Hence we can conclude that the probability of obtaining an odd number and a head is 1/4.
Learn more about probability here
https://brainly.com/question/11455301
#SPJ3
If y = 2/3x^2– 5x, what is the
value of x = 6
Please
Answer:
y=-29.98
Step-by-step explanation:
y=2/3(6)^2-5(6)
y=2/108-30
y=1/54-30
54y=1-1620
y=-1619/54
y=-29.98
I need help with my math assignment please
Answer:
angles 1 and 6
Step-by-step explanation:
Answer:
C. angle 2 and angle 7
Step-by-step explanation:
hope this helps, have a nice day :)
Solve the following equation: *
Answer:
Step-by-step explanation:
x/3 + 6 = 17
Bringing like terms on one side
x/3 = 17 - 6
x/3 = 11
Dividing by 3 on both sides
x = 11/3
The number N of bacteria present in a culture at time t (in hours) obeys the equation N = 1000e^0.01t After how many hours will the population equal 1500? 2000?
Answer: N(t) = (2^t)*1500
Step-by-step explanation:
Let's define the hour "zero" as the initial population.
So if N(t) is the number of bacteria after t hours, then:
N(0) = 1500.
Now, we know that the population doubles every hour, so we will have that after one hour, at t = 1
N(1) = 2*1500 = 3000
after two hours, at t = 2.
N(2) = 2*(2*1500) = (2^2)*1500
After three hours, at t = 3
N(3) = 2*(2^2)*1500 = (2^3)*1500
So we already can see the pattern, the number of bacteria after t hours will be:
N(t) = (2^t)*1500
You started a dog walking business. You spent $45 in start up costs and charge $12 per hour of
dog walking. How many hours must you walk before you have a minimum of $117?
Answer:
7
Step-by-step explanation:
Hakim is making birdhouses. Each birdhouse uses 7/8 yard of wood. What is the total length of wood Hakim will need to build 5 birdhouses.
Answer: 4 3/8 yards of wood
Step-by-step explanation:
It would be 5 times the ammount needed for one birdhouse so it would be-
7/8 x 5= 35/8 or 4 3/8
Abdul uses 15 1/2 cups of flour to make 3 loaves of bread. At that rate, how many cups of flour would Abdul need to make 4 loaves of bread?
NO ANSWERS FROM UNKNOWN FILES OR I'LL REPORT IT!!!
An ant population began with 30 ants. From this point, the population
continuously increased by 4% each hour. Based on this model, how many
hours will it take the population to reach 100 ants?
Answer:about 5.3
Step-by-step explanation:
HELP ASAP!! I will give brainlist!! THANK YOU!
Answer:
dont trust me but i think its subtraction or division
Step-by-step explanation:
at time t, the position of a body moving along the s-axis is s=t^3 - 12t^2 + 36t m. Find the total distance traveled by the body from t=0 to t=3.
Answer:
27 m
Step-by-step explanation:
The position of a body is given by :
[tex]s=t^3 - 12t^2 + 36t[/tex]
We need to find the total distance traveled by the body from t=0 to t=3.
At t = 0,
[tex]s=0^3 - 12(0)^2 + 36(0)=0\ m[/tex]
At t = 3 s,
[tex]s=(3)^3 - 12(3)^2 + 36(3)\\\\=27\ m[/tex]
So, the total distance from t=0 to t=3 is equal to 27 m.
Jayden is filling his 290 gallon pool with a garden hose. The garden hose produces 29 gallons of water per hour. How long will it take for Jayden to fill up his pool?
Answer:
10 hours
Step-by-step explanation:
290 divided by 29 = 10
check to see if its correct 29 multiple by 10 is 290
please help asap ! no scam links or scam comments for points or reported.
Answer:
C
Step-by-step explanation:
it is -25x X= each time he goes rock climbing
You recently obtained a job with a sports analytics firm, and your first assignment is to write a report evaluating early evidence behind predictions for the 2019-20 NBA season. You will use your knowledge of hypothesis testing to assess the predictions. When conducting a hypothesis test for the population mean, you will not know the population standard deviation, so you will have to use the sample standard deviation instead. How will this affect the process
Answer:
It will affect the process in the sense that the sample population size will be unknown due to the fact that we don't know the population standard deviation.
Step-by-step explanation:
We are told that you do not know the population standard deviation. Thus, the sample population will not be able to be calculated because this sample standard deviation given will not suffice and we need the population standard deviation to be able to calculate the sample population size.
The absence of population standard deviation will result in performing the one mean t test. The one mean t test gives an insight of the deviation of values from the mean.
For the approval or rejection of the null hypothesis, hypothesis testing has been performed. For performing a test, a hypothesis has been assigned based on the results we wish to obtain. The rejection of null hypothesis leads to acception of the alternate hypothesis, while the approval of the null hypothesis results in the rejection of the alternate hypothesis.
For performing the null hypothesis test, there has been the first step to be the requirement of the hypothesis. The hypothesis has been tested based on the population size. And the test has been performed.
The absence of population standard deviation will result in performing the one mean t test.
The one mean t test gives an insight of the deviation of values from the mean. It has been used for the determination of random data sample, normal distribution, range of sampling.
For more information, refer to the link given below:
https://brainly.com/question/22687297
Is the graph increasing, decreasing, or constant?
O A. Constant
B. Decreasing
C. Increasing
Answer:
Decreasing because the line is going down meaning it is decreae
Alana has $80 in a savings account. The interest rate is 5% per year and is not compounded. How much interest will she earn in 1 year?
Answer:
Answer:
I = $ 1,937.50
Step-by-step explanation:
Equation:
I = Prt
Calculation:
First, converting R percent to r a decimal
r = R/100 = 3.875%/100 = 0.03875 per year,
then, solving our equation
I = 10000 × 0.03875 × 5 = 1937.5
I = $ 1,937.50
The simple interest accumulated
on a principal of $ 10,000.00
at a rate of 3.875% per year
for 5 years is $ 1,937.50.
I hope this is correct and hope it helps!
Answer and explain deeply thank you so much! I’ll mark brainliest
Find the measurement of the angle labeled X
PLEASE IM REALLY BAD AT THESE QUICK!!!!!!!!!!!!!
Answer:
b.
42+x+90+8=180° linear pair
x=180-140=40°
x=40°
c.
10+x+90+3x=180 linear pair
4x=180-100
x=80/4=20
x=20°
Please please help!!!
Answer:
pretty sure its A
Step-by-step explanation: