1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
MArishka [77]
3 years ago
15

AP Calculus Help Please!

Mathematics
1 answer:
ivanzaharov [21]3 years ago
4 0
4. By the fundamental theorem of calculus,

\displaystyle\frac{\mathrm dg(x)}{\mathrm dx}=\frac{\mathrm d}{\mathrm dx}\int_{-2}^xf(t)\,\mathrm dt=f(x)

g(x) is increasing on those intervals where g'(x)=\dfrac{\mathrm dg(x)}{\mathrm dx}>0. So you have

g'(x)=f(x)=\begin{cases}3&\text{for }-3\le x

which is clearly positive for x\in[-3,0), and in the second interval you have

-x+3>0\implies x

Together, this means g'(x)>0 for all x\in[-3,3).

5. When 0\le x\le6, f(x) reduces to -x+3, so you have

g(x)=\displaystyle\int_{-2}^xf(t)\,\mathrm dt=\int_{-2}^03\,\mathrm dt+\int_0^x(-t+3)\,\mathrm dt
g(x)=6+\left(3t-\dfrac12t^2\right)\bigg|_{t=0}^{t=x}
g(x)=6+3x-\dfrac12x^2
You might be interested in
An ice cream shop offers 5 different types of ice cream, 6 different toppings and the option of having a small, medium or large.
prohojiy [21]

Answer:

90 possible outcomes.

Step-by-step explanation:

In order to find the total number of combinations possible you simply need to multiply the total number of each options with one another. For example, the number of options in each category are the following

types: 5

toppings: 6

size: 3  (small, medium, large)

Now we simply need to multiply all three of these numbers together to find the total number of possible outcomes.

5 * 6 * 3 = 90 possible outcomes.

5 0
3 years ago
<img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B%20-%20%20%5Cfrac%7B7%7D%7B216%7D%20%7D%20%5Ctimes%20%20%5Csqrt%7B42%7D%20%20" id
Natalija [7]

Answer:

IM GOING TO THIS but what do I gotta do evaluate? simplify?

6 0
3 years ago
What is the minimum value of the function g(x) = x2 - 6x – 12?<br> -21<br> 3-21<br> 3<br> 3+21
balandron [24]

Answer:

- 21

Step-by-step explanation:

The minimum value occurs at the vertex of the function

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

Given

f(x) = x² - 6x - 12

add/ subtract ( half the coefficient of the x- term)² to x² - 6x

f(x) = x² + 2(- 3)x + 9 - 9 - 12

     = (x - 3)² - 21

with vertex = (3, - 21 )

The minimum is the value of k, that is minimum value = - 21

4 0
3 years ago
Which classification describes the following system of equations? inconsistent and dependent consistent and dependent consistent
sveta [45]

The system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.

<h3>What is a linear equation?</h3>

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have three linear equations in three variables:

x - y - z = 0 ..(1)

2x - y + 2z = 1 ..(2)

x - y + z = -2 ..(3)

From the equation (1):

\rm x=y+z

Plug this value in the equation (2) and (3):

\rm 2\left(y+z\right)-y+2z=1\\\\ y+z-y+z=-2

After solving we get:

z = -1

y = 5

Plug the above two values in equation (1) we get:

x = 4

Thus, the system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ1

5 0
2 years ago
I need to "find the Indicated values" of each problem and I am very confused.
kotegsom [21]

sorry i dunno i really dont i just need to finish my test lol

5 0
4 years ago
Other questions:
  • What is the measure of X?
    14·1 answer
  • -7 times what equals 2? i’ll give brainliest
    14·1 answer
  • The perimeter p of a rectangle is given by the formula p=2L+2w, where L is the length of the rectangle and w is the width. Which
    15·1 answer
  • 3)
    5·2 answers
  • Why doesn’t my ex get back with me already ?
    8·2 answers
  • Which relation is not a function?
    15·1 answer
  • Which of the four triangles was formed by a translation of triangle POR?<br> A <br> B<br> C<br> D
    13·2 answers
  • Point B is between Q and R on Q through R. BR = 16.9 and QR = 51.5. Sketch to determine the length of QB. A. QB = 34.6 c. QB = 1
    10·1 answer
  • Can someone help a bab with geometry?
    14·1 answer
  • QUICK !!! FAST 15 POINTS <br> I NEED HELP!!!!!
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!