Answer:
d. Definite integral can be used to calculate area under a curve in a given interval
General Formulas and Concepts:
Calculus
Integration
IntegralsArea of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
Step-by-step explanation:
We know that by definition, an integral is an antiderivative.
Also by definition, an integral is also the area under the curve. This can be extended to area between 2 curves.
We have a formula specifically to find an area under a curve (region), as listed above.
∴ our answer is D.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
si la pendiente es negativa, la linea no es recta?
En matemáticas, la pendiente de una línea ( m ) se describe cómo rápidamente o lentamente cambiar se está produciendo y en qué dirección, ya sea positiva o negativa. Funciones-aquellos lineales cuya gráfica es una línea recta-tienen cuatro posibles tipos de pendiente: positivos , negativos, cero , e indefinido. Una función con una pendiente positiva está representada por una línea que sube de izquierda a derecha, mientras que una función con una pendiente negativa se representa por una línea que va hacia abajo de izquierda a derecha. Una función con pendiente cero está representado por una línea horizontal, y una función con una pendiente indefinida está representada por una línea vertical.
La pendiente se expresa normalmente como un valor absoluto. Un valor positivo indica una pendiente positiva, mientras que un valor negativo indica una pendiente negativa. En la función y = 3 x , por ejemplo, la pendiente es positiva 3, el coeficiente de x .
En estadística, un gráfico con una pendiente negativa representa una correlación negativa entre dos variables. Esto significa que como una variable aumenta, la otra disminuye, y viceversa. Correlación negativo representa una relación significativa entre las variables x e y , que, dependiendo de lo que son el modelado, puede entenderse como entrada y salida , o causa y efecto .
¿Cómo encontrar la pendiente
pendiente negativa se calcula igual que cualquier otro tipo de pendiente. Lo puede encontrar dividiendo la subida de dos puntos (la diferencia a lo largo del eje y vertical u) por la carrera (la diferencia a lo largo del eje x). Sólo recuerda que la “subida” es en realidad una caída, por lo que el número resultante será negativo.
m = (y2 - y1) / (x2 - x1)
Una vez que se representa gráficamente la línea, verá que la pendiente es negativa porque la línea bajará de izquierda a derecha. Incluso sin dibujar un gráfico, usted será capaz de ver que la pendiente es negativa, simplemente calculando m utilizando los valores dados para los dos puntos.
Por ejemplo, la pendiente de una línea que contiene los dos puntos (2, -1) y (1,1) es:
m = [1 - (-1)] / (1 - 2)
m = (1 + 1) / -1
m = 2 / -1
m = -2
Una pendiente de -2 significa que por cada cambio positivo en x , habrá el doble de cambio negativo en y .
= Pendiente negativa correlación negativa
Un negativo pendiente demuestra una correlación negativa entre los siguientes:
las variables x e y
entrada y salida
variable independiente y la variable dependiente
causa y efecto
Correlación negativa se produce cuando las dos variables de un movimiento función en direcciones opuestas. A medida que el valor de x aumenta, el valor de y disminuye. Del mismo modo, como el valor de x disminuye, el valor de Y aumenta. Correlación negativa, entonces, indica una clara relación entre las variables, es decir, uno afecta al otro de una manera significativa.
En un experimento científico, una correlación negativa mostraría que un aumento en la variable independiente (el manipulado por el investigador) causaría una disminución en la variable dependiente (la medida por el investigador). Por ejemplo, un científico podría encontrar que a medida que los depredadores se introducen en un entorno, el número de presas se hace más pequeño. En otras palabras, existe una correlación negativa entre el número de depredadores y número de presas.
Ejemplos del mundo real
Un ejemplo sencillo de pendiente negativa en el mundo real está bajando una colina. Cuanto más lejos esté de viaje, cuanto más abajo se le cae. Esto puede ser representado como una función matemática, donde x es igual a la distancia recorrida y Y es igual a la elevación.
Otros ejemplos de pendiente negativa demuestran la relación entre dos variables:
Sr. Nguyen bebe café con cafeína dos horas antes de su hora de dormir. Los más tazas de café bebe (entrada), el menor número de horas que van a dormir (salida).
Aisha es la compra de un billete de avión. El menor número de días entre la fecha de compra y la fecha de salida (entrada), más el dinero Aisha tendrán que gastar en pasajes de avión (salida).
John está gastando una parte del dinero de su último cheque de pago en regalos para sus hijos. Cuanto más dinero gasta John (entrada), menos dinero John tendrá en su cuenta bancaria (de salida).
Mike tiene un examen al final de la semana. Desafortunadamente, él prefiere pasar su tiempo viendo deportes en la televisión que estudiar para el examen. Cuanto más tiempo pasa viendo la televisión Mike (entrada), la puntuación del Mike menor será en el examen (de salida). (En contraste, la relación entre el tiempo dedicado al estudio y la puntuación de examen estaría representada por una correlación positiva, ya que un aumento en el estudio conduciría a una mayor puntuación.)
PLEASE HELP!!! In the diagram, line AB is a perpendicular bisector of segment CD. What is the length of CD?
Answer:
12
Step-by-step explanation:
AD is 6. a bisector splits a line in half. X would equal 6 meaning AD would equal 12.
water flows into a reservoir at a rate of 1500+7t^2 gallons/hour. Since there is a tiny hole in the reservoir, the water leaks out at a rate of 4t+t^2 gallons/hour. What is the net change in the amount of water in the reservoir over the time interval of [1,5]
9514 1404 393
Answer:
6200 gallons
Step-by-step explanation:
The rate of change of volume is the difference between the inflow rate and the outflow rate.
v'(t) = (1500 +7t^2) -(4t +t^2) = 6t^2 -4t +1500
The change in volume over the time interval of interest is the integral of this expression over that interval:
[tex]\displaystyle\Delta V=\int_1^5{(6t^2-4t+1500)}\,dt=\left.(2t^3-2t^2+1500t)\right|^5_1\\\\=2(5^3-1^3)-2(5^2-1^2)+1500(5-1) = 2\cdot124-2\cdot24+1500\cdot4\\\\\boxed{\Delta V=6200\qquad\text{gallons}}[/tex]
The amount of water in the reservoir increases by 6200 gallons over the time interval.
Alfonso can do a certan job in 1 hour. His brother can do the same job in 1 hour however, their older sister Josefa can do this jobin 45 minute. If all three work together, how long will it take them to do the job?
Answer: About 13 minutes. Not entirely sure if I'm correct
Convert 45°C to Fahrenheit
Answer:
113
Step-by-step explanation:
it right trust
What does > mean. Greater than or less than.
Answer:
less than
Step-by-step explanation:
If f(x) = x2 – 7x - 13 ; find the following.
find f(10)
I need help with this
9514 1404 393
Answer:
4
Step-by-step explanation:
Dilation centered at the origin multiplies each individual coordinate by the scale factor. Considering the x-coordinates of W and W', we have ...
scale factor = Wx'/Wx = -12/-3 = 4
The dilation scale factor is 4.
PLEASE HELP ASAP. GIVE ANSWER AND BRIEF EXPLANATION.
The graph is attached
Determine whether the function shown in the graph is even or odd.
A. The function is even because it is symmetric with respect to the y-axis.
B. The function is odd because it is symmetric with respect to the y-axis.
C. The function is even because it is symmetric with respect to the origin.
D. The function is odd because it is symmetric with respect to the origin.
Please Help Meee!!
11. A Fruit punch recipe contains 8 ounces of pineapple juice and makes enough punch for 20 servings
(a) If 150 servings need to be prepared for a party, how many ounces of pineapple juice are needed?
(b) How many servings will 20 ounces of pineapple juice produce?
Thien and her friends earned $80 washing cars. Thien received $30 from this amount.
What is Thien's share as a percentage of the total amount earned?
Dilations: Triangle RST with vertices R(-5,1), S(-3,4), and T(2,-1): k=2
Answer:R’ (-10,2) S’(-6,8) T’(4,-2)
Step-by-step explanation:
Did it in class
After dilation of ΔRST with the given scale factor we have vertices of ΔR'S'T' as R'(-10, 2), S'(-6, 8) and T'(4, -2).
Given that, ΔRST with vertices R(-5,1), S(-3,4), and T(2,-1).
What is a dilation?Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.
Given, scale factor is k=2.
So, with using scale factor
R(-5,1)→2(-5, 1)= R'(-10, 2)
S(-3,4)→2(-3,4)=S'(-6, 8)
T(2,-1)→2(2,-1)=T'(4, -2)
Therefore, after dilation of ΔRST with the given scale factor we have vertices of ΔR'S'T' as R'(-10, 2), S'(-6, 8) and T'(4, -2).
To learn more about the dilation visit:
https://brainly.com/question/13176891.
#SPJ2
Mr. Rodriguez has owned his truck for 3 months. In that time, he has driven the truck a total of 45 miles.
How many miles has Mr. Rodriguez driven his truck in the 3 months?
Answer:
45 miles
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
45 divided by 3 is 15
sorry, i'm not all that good when it comes to explaining things. just kept it simple:)
Decrease 400 by 17% I need help
on coordinate grid, point p is at (5,8) and point r is at (-1,-3). points q and a are a reflection of both points across the x-axis. what are the coordinates of Q and S?
Answer:
q(5,-8) s(-1,3)
Step-by-step explanation:
you just have to add a negative to the y-axis point, if you reflect across the x-axis
If your car gets 34 miles per gallon, how much does it cost to drive 370 miles when gasoline costs $3.30 per gallon?
The cost is $
nothing.
(Simplify your answer. Round to the nearest cent as needed.)
Answer:
Cost = 2.5*(380/33) = $28.79
Step-by-step explanation:
A grocery store sells avocados for $1.25 each. The graph shows the cost for different numbers of avocados.
Drag each list, statement, or equation below to show whether it describes the independent quantity, the dependent quantity, or neither.
Answer:
A grocery store sells avocados for $1.25 each. The graph shows the cost for different numbers of avocados.
Drag each list, statement, or equation below to show whether it describes the independent quantity, the dependent quantity, or neither.
Step-by-step explanation:
True or false that a fraction is never a rational
Answer:
false
Step-by-step explanation:
hope it helps!
have a good day!
what is the percent of 2is 0.5
Answer:
0.01
Step-by-step explanation:
Answer:
25
0.5 is what percent of 2 = 25.
Hope this helped! :)
May i have brainliest!
What is the zero of r(x)=8/3
- 16?
Answer:
pretty sure it's no solution unless you wrote the equation wrong
Step-by-step explanation:
if you replace y with 0 (to find the roots or zeros) and solve for x then there is not a solution
anyone wanna be friends boys or girls:)
Answer:
sure follow my insta uknow.dan28
Step-by-step explanation:
The shoe store’s clerks are paid on commission. If the clerk receives a 12% commission on total purchase amounts before tax is applied, how much would the commission be for Isaac’s purchase with and without a coupon? (2 points)
plss show work I will mark brainliest
Answer:
a) 37 + 42 =79
=7/100 x 79
=553/100
=5.53
Isaac's total bill = 79 + 5.53 = $84.53
b) 25/100 x 79
= 19.75
= 79 - 19.75
= $59.25 (before tax)
7/100 x 59.25
= 414.75/100
= 4.15
= 59.25 + 4.15
= $63.4 (after adding tax)
First we have to take out the percentage of discount and minus it from the total cost . To find the discounted price with tax, we have to take out the percentage of the tax from the discounted amount and add it to the discounted amount to get the total cost.
what is the distance between the points (-6,7) and (-1,1)?
Answer:
8
Step-by-step explanation:
The user above is correct. The square root of 61 is equal to 7.810249676 which can be rounded up to 8.
I don't know what it means
Answer: x + 1 = 15
Step-by-step explanation:
solve -
x= 15 - 1
x = 14
x is a variable so it's not fix value in math
Carlos can run 5 miles in 45 minutes, Kelly can run 10 miles in 80 minutes, and Mick can run 30 miles in 170 minutes
Answer:
60 min
Step-by-step explanation:
Answer:
what is the question please
Which ordered pair is a solution to the system of linear equations?
Can you please help me? I will mark biggest brain if correct. Thank you.
Answer:
can u give me ur Intro..........
At a university, 60% of the students who apply. Of the students the university accepts, 25% actually enroll If 2000 students apply, how many actually enroll?
Answer:
300 students are enrolled.
Step-by-step explanation:
As the university accepts 60% of the students who apply.
As 2000 students apply, it means that:
2000 × 60% ⇒ 2000 × 0.6 = 1200 students are accepted
Out of these 1200, 25% enrolled
1200 × 25% ⇒ 1200 × 0.25 = 300 students are enrolled
Therefore, 300 students are enrolled.
4.1 Unit Rates
Find each unit rate. Round to the nearest hundredth, if nece
1. $140 for 18 ft?
Answer: 17.5
Step-by-step explanation:
round 861 to the nearest ten. Enter your answer in the box below.
860. Round down, since your ones place contains a 1.
please mark brainliest and have a great day
Answer:
860
Step-by-step explanation:
because it's rounding to the nearest ten and its only 1 you round it to 60
A child weighs 83 pounds. Given that 1 pound is equal to 16 ounces, how many ounces does the child weigh? A. 1,228 ounces B. 1,328 ounces 1,411 ounces D. 1,584 ounces C. A ir 100% of what numhor?