Identify intervals on which the function is increasing, decreasing, or constant. g(x) = 4 - (x - 6)^2 ??

Answers

Answer 1

Taking the derivative will give you the velocity at any time.

g(x)=4-(x-6)^2

g(x)=4-(x^2-12x+36)

g(x)=4-x^2+12x-36

g(x)=-x^2+12x-32

dg/dx=-2x+12

So g(x) will be increasing when dg/dx>0

-2x+12>0

-2x>-12

x<6

So g(x) is increasing on the interval (-oo, 6)

g(x) will be decreasing when dg/dx<0

-2x+12<0

-2x<-12

x>6

So g(x) will be decreasing on the interval (6, +oo)

Related Questions

Find the length of the hypotenuse of a right triangle with legs of lengths 5 and 12. If necessary, round your answer to two decimal places

Answers

Let "c" be the hypotenuse

By the Pythagorean theorem:

c² = 5² + 12² = 25 + 144 = 169
с = √169 = 13 units ← answer

I need help please :( !!!

Answers

Number of cans donated the first week = 132
Number of cans donated the second week = 146
Number of cans donated the third week = c, where c is some positive number

Add up the three values (132, 146, and c) to get 132+146+c. I'm choosing not to simplify because each answer choice hasn't simplified either.

The expression of 132+146+c represents the total amount of cans donated for weeks 1 through 3. We want "at least 325 cans", so that means the expression is 325 or larger. That translates to this inequality

[tex]132+146+c \ge 325[/tex]

The "greater than or equal to" sign indicates we want that sum to be 325 or larger.

Now we solve for c

[tex]132+146+c \ge 325[/tex]
[tex]278+c \ge 325[/tex]
[tex]278+c-278 \ge 325-278[/tex]
[tex]c \ge 47[/tex]

So the amount of cans donated for week three needs to be 47 or larger. If you collect exactly 47 cans for week three, then you meet the goal of 325 total cans. If you collect more than 47 cans for week three, then you exceed the goal of 325 total cans.

------------------------------------

In summary we have the inequality
[tex]132+146+c \ge 325[/tex]
which solves to
[tex]c \ge 47[/tex]

Meaning that the answer is choice D

A liquid substance was left at the scene of the crime. Krisann uses a beaker that measures to the nearest tenth of a liter and finds that it is 4.9 liters. If there are five or more liters of the substance, it needs to be sent to the lab for testing. If it is less than five liters, the test can be done immediately. Does Krisann need to send the substance to the lab? Why or why not?

Answers

If the volume of the substance of 4.9 liters is from x rounded to the nearest tenth of a liter, that means 4.85 <= x < 4.95 then this does NOT leads to x > 5. Therefore the substance does not need to be sent to the lab.

a bowl contains 80 M&M candies If 15 are orange what fraction of the candies is NOT orange. Answer reduced to lowest terms

Answers

65/80 can be reduced to 13/16.

So, it says that there are 80 M&M candies in a bowl. 15 are orange, so that means the others aren't orange. So, then you would do (the total number of M&M candies in the bowl)-(the number of orange M&M candies)=The number of M&M candies that are not orange. So, 80-15=65.
So, they are 65/80 in the bowl that aren't orange. But we aren't done yet. We need to find the lowest term for 65/80. First, we'll need to find what can go into 65 and 80 evenly without leaving a remainder. Yes, you guessed it, five can go into 65 and 80 without leaving a remainder. So, 65 divided by 5=13 and 80 divided by 5=16. So, your final answer is 13/16.
13/16 is the final answer. This is the lowest possible term for the number pf candies that aren't orange.
65/80=13/16
13/16 are the number of M&M candies that aren't orange.
Hope I helped.

how can exponential and logarithmic functions be created to use in real world situations?

Answers

In realistic world there are so many examples which use exponential and logarithmic functions.

Use of Logarithmic function
We can find use of logarithmic function in measuring earthquake (Richter Scale) , the brightness of stars , and chemistry(pH balance , measure of acidity and alkalinity)

For example:
In Richter Scale , a logarithmic function that is used to measure the magnitude of earthquake.
If A = measure of amplitude of earthquake wave.
[tex]A_o[/tex] = Amplitude of smallest detectable wave.
From this we can find R the Richter scale measure of magnitude of earthquake.
[tex]R = log \frac{A}{A_o} [/tex]

Use of Exponential Function:

Exponential function may use in finding compound interest , population growth , radioactivity decay , etc.

For example :
As we know the formula for compound interest is
[tex]A = P(1+ \frac{r}{n})^{nt} [/tex]
Where P is principal amount , r = rate of interest(decimal) , n is the number of compounding period , t is time.

For

-13x=90-2y
-6x=48-2y

Answers

Final answer:

The solution to the system of equations is x = 6 and y = 84.

Explanation:

The given equations are:

-13x = 90 - 2y

-6x = 48 - 2y

To find the values of x and y, we can solve the system of equations. We can start by multiplying the second equation by -2 to eliminate the y variable. This gives us:

12x = -96 + 4y

Now we have two equations:

-13x = 90 - 2y

12x = -96 + 4y

We can add the two equations together:

-13x + 12x = 90 - 2y + (-96 + 4y)

-x = -6

Then, we can divide both sides of the equation by -1 to solve for x:

x = 6

Substituting the value of x back into one of the original equations, we can solve for y. Let's use the first equation:

-13(6) = 90 - 2y

-78 = 90 - 2y

-2y = -168

y = 84

Therefore, the solution to the system of equations is x = 6 and y = 84.

You unfold chicken wire to make a circular pen with a diameter of 2.9 meters. how many meters of chicken wire do you need?

Answers

circumference = PI x D

using 3.14 for PI

2.9 x 3.14 = 9.106 = 9.11 meters of chicken wire are needed.

Evaluate the function rule for the given value. Y=6*4 for x=-3

Answers

Because x does not appear anywhere in the equation y=6*4, evaluate the equation by simply multiplying the numbers on the right side.
y=24

A game involves tossing a biased coin that has a 60% probability of landing on heads. If a player wins $50 when heads appears, what is the expected value of a player's winnings?

Answers

Probability of winning = 0.6 , Probability losing = 1-0.6 = 0.4

Expected value = 50(0.6) - 1(0.4) = $29.6

The interpreation of this is that if you play many times you would expect a profit of $29.6.

This net folds into the cube shown beside it. On the cube, which letter will be on the side opposite D?

Answers

Final answer:

Without more information or a diagram, it's hard to give a specific answer. However, on a cube net, the face opposite 'D' is likely the one not directly connected to 'D' on the plane of the net.

Explanation:

Unfortunately, without a diagram or more context, it's difficult to provide a definitive answer to the question. However, typically on a cube net, sides that are opposite each other when the net is folded into a cube are adjacent (next to each other) on the net. For example, if 'D' were on a flat square in the center of the net, the squares directly connected to it (on the top, bottom, left, and right) on the plane of the net would end up being the sides adjacent to 'D' when the cube is formed. The square not connected directly to 'D' on the plane would be opposite 'D' once the cube is formed.

Learn more about Cube Net here:

https://brainly.com/question/12079637

#SPJ12

C =5/9(F-32). Covert 12 degrees Celsius to Fahrenheit. Round to nearest degree

Answers

12 = 5/9(F - 32)

F - 32 = 12 / 5/9 = 12 * 9/5 = 21.6

F = 32 + 21.6 = 53.6 = 54 to nearest degree

Which statement is true about the discontinuation of the function F(x)? F(x)=x+1/6x^2-7x-3

Answers

The answer to your question is:
there are holes at x= 3/2 and x=-1/3

Which graph correctly represents
x + 2y ≤ 4?

Answers

x + 2y < = 4
2y < = -x + 4
y < = -1/2x + 2

u will have a solid line (because there is an = sign in the problem)....the slope will be -1/2...so ur line is going down....u have a y int (where ur line crosses the y axis at (0,2).....u have an x int (where ur line crosses the x axis at (0,4)..ur line will be shaded below the line.

Step-by-step explanation:

[tex]x + 2y \leq 4[/tex]

To graph this inequality we replace <= symbol with = sign

[tex]x + 2y =4[/tex]

subtract x on both sides

[tex]2y =-x+4[/tex]

divide both sides by 2

[tex]y= \frac{-1}{2} x +2[/tex]

Graph the equation using a table

LEts assume some number for x and find out y

x [tex]y= \frac{-1}{2} x +2[/tex]

-2 3

0 2

2 1

Now graph the equation using points (-2,3) (0,2)(2,1)

use solid line for graphing

Now use test point (0,0) for shading

[tex]x + 2y \leq 4[/tex]

[tex]0 + 2(0) \leq 4[/tex]

[tex]0 \leq 4[/tex] true

So we shade the region that contains (0,0)

the graph is attached below

The key idea of the transformation called a reflection is _____.

the object moves the plane a certain angle measure
the object moves in a straight line movement
the object and its image have opposite orientations
the rotating of a plane about a fixed point

Answers

The object and its image have opposite orientations

Answer: The object and its image have opposite orientations

Step-by-step explanation:

A reflection is a type of rigid transformation in which the preimage is flipped across a line of reflection to produce the image, such that the figure and its image have opposite orientations.

Since, it preserves distance.

Therefore, the points of the image have the same distance from the line as the points of pre-image on the opposite side of the line.

Hence, the right option is "the object and its image have opposite orientations".

Vera and her roommates ate 1 1/3 pints of ice cream on Friday night and 1 1/6 pints of ice cream on Saturday night. How many pints did they eat in all

Answers

1 1/3 + 1 1/6

add the 1 +1 = 2

add 1/3 + 1/6 ( find common denominator, which in this case is 6)

so 1/3 becomes 2/6

2/6 + 1/6 = 3/6 which reduces to 1/2

they ate 2 1/2 pints total

Use the change of base formula to evaluate log4 20.

Answers

your calculator probably only evaluates in base 10 (ln is base e but we won't use that today)

so
[tex]log_a(b)=\frac{log_c(b)}{log_c(a)}[/tex]
where c is the new base
so if you wanted in base 10
[tex]log_4(20)=\frac{log_{10}(20)}{log_{10}(4)}[/tex]
using calculator, that is about 2.16096

What is the vertex of y=-6(2.5-x)(x-5.5)?

Answers

hello :

y=-6(2.5-x)(x-5.5) = -6(2.5x -13.75 -x² +5.5x)
y = -6(-x²+8x -13.75)
y = 6x²-48x+82.5
note :
if f(x) = ax²+bx +c the vertex is the point : ( -b/2a ; f(-b/2a))
a=6 b=-48 c = 82.5 .......calculate
-b/2a = -(-48)/2(6)= 4
f(4) =6(4)²-48(4)+82.5 =96 - 192 +82.5 = -13.5

How many roots do the following equations have?

-12x2 - 25x + 5 + x3 = 0

A. 4

B. 5

C. 3

D. 2

Answers

the answer is C. ( 3 )

Last year the profit for a company was $560,000. This year's profit decreased by 7.1%. Find this year's profit.

Answers

Profit this year is
560,000−560,000×0.071
=520,240

What is 2/3x = 4/15?

Answers

2/3x = 4/15 =

x = 4/15 / 2/3 = 4/15 x 3/2 = 12/30 = 2/5

x = 2/5

all i know is x=25 its hard for me to explain.

For which value of m does the graph of y = 18x2 + mx + 2 have exactly one x-intercept?

Answers

this will be a parabola which will just touch the x access and will be a perfect square The discrimant b^2 - 4ac will be = 0 so we have

m^2 - 4*18*2 = 0
m^2 = 144

m = +/-12

so its m = 12 or -12

Answer:

Step-by-step explanation:

Kyra is using rectangular tiles of two types for a floor design. A tile of each type is shown below: Two rectangular tiles, rectangle PQRS with vertices at P 5, 7. Q is at 9, 7. R is at 9, 12. S is at 5, 12 . Rectangle JKLM with vertices J 4, 5. K is at 6, 5. L is at 6, 10. M is at 4, 10. Which statement is correct?

Answers

Since there is no picture shown, I just plotted the given data points myself. That is shown in the attached picture. The blue rectangle is rectangle PQRS while the orange one is rectangle JKLM. I believe there are some choices for this question but you forgot to include. Nevertheless, I will give my observations from the given figure.

The tile PQRS is bigger than tile JKLM. A rectangle is a two-dimensional shape that has two sets of equal parallel planes. Thus, its area is equal to the length multiplied by its width.

tile PQRS = (9-5)*(12-7) = 20 units²
tile JKLM = (6-4)*(10-5) = 10 units²

Tile PQRS is larger by 10 units².

Find the factorization of the polynomial below.

2x²+7x+6

A. (2x+2)(x+4)
B. (2x+2)(x+3)
C. (2x+3)(x+1)
D. (2x+3)(2x+2)

Answers

Using slip and slide
2x^2+7x+6
x^2+7x+12
(x+3)(x+4)
(2x+3)(x+2)
The best answer is none of the above.
When foiling the answer choices,
A: 2x^2+10x+8
B: 2x^2+8x+6
C: 2x^2+5x+3
D: 4x^2+10x+6

Answer:

(2x+3)(x+2)

Step-by-step explanation:

i hope this helps

Vivian measured 2/5 cup of onions, 1/3 cup of celery, and 1/2 cup of carrots. How many cups of vegetables did Vivian measure out for her vegetable soup?

Answers

First find the lowest common denominator for 5, 3 and 2. LCD = 5 x 3 x 2 = 30. Then change 2/5, 1/3 and 1/2 so that they have the LCD as their denominator. For example 1/2 = 15/30. 1/3 = 10/30 and 2/5 = 12/30. Then you all all 3 fractions. 12/30 + 10/30 + 15/30 = 37/30. That is an improper fraction. Convert it to a mixed number. 37/30 = 1 7/30

what is the radius of a circle given by the equation x^2+(y-3)^2=21

Answers

The radius is 4.583, just take the square root of 21

What are the vertex, focus, and directrix of the parabola with the equation x^2+8x+4y+4=0

Answers

We are given the function x^2+8x+4y+4=0. To determine the characteristics of this function, we need to write it in the standard form as follows:

x^2+8x+4y+4=0
4y = -x^2 - 8x - 4
y = (-1/4)x^2 - 2x - 1

To determine the vertex and the focus of the parabola, we write it in the form (y+k)^2 = x+h by completing the square method.

y + 1 = (-1/4)x^2 - 2x
y +1 = (-1/4)(x^2 + x/2)
y +1 - 1/64 = (-1/4)(x^2 + x/2 + 1/16)
y + 15/16 = (-1/4) (x + 1/4)^2

The vertex would be at point ( -1/4, -15/16)
The focus would be determined as follows:
4p=-1/4 so p=-1/8
focus = (-1/4+(-1/8),-15/16) = (-3/8,-15/16)

Directrix = x = h - p
x = -1/4 - -1/8 = -1/8

Answer:

Vertex=(-4,3)

Focus=(-4, 2)

Directrix: y=4

Step-by-step explanation:

Given the equation

[tex]x^2+8x+4y+4=0[/tex]

we have to find the vertex, focus, and directrix of parabola.

[tex]x^2+8x+4y+4=0[/tex]

[tex]y=\frac{-x^2}{4}-2x-1[/tex]

[tex]h=\frac{-b}{2a}=\frac{2}{2(\frac{-1}{4})}=-4[/tex]

Now, k can be calculated by putting x=4 and y=k in given equation

[tex]k=-1-\frac{16}{4}-2(-4)=-1-4+8=3[/tex]

The vertex is (h,k) i.e (-4,3)

[tex]y=\frac{-x^2}{4}-2x-1[/tex]

[tex]y=\frac{1}{4}(-x^2-8x-4)[/tex]

[tex]=\frac{1}{4}(-x^2-8x-16+16-4)[/tex]

[tex]y=\frac{1}{4}(-(x+4)^4+12)[/tex]

[tex]y=\frac{-1}{4}(x+4)^2+3[/tex]

which is required vertex form [tex]4p(y-k)=(x-h)^2[/tex]

gives p=-1

Focus=(-4, 3+(-1))=(-4,2)

Now directrix can be calculated as

y=3-p=3-(-1)=4

The simple interest formula is I = Prt, where I represents simple interest on an amount, P, for t years at a rate of r. The equation solved for P is P = . What is the amount of money, P, that will generate $40 in interest at a 10% interest rate over 5 years? $60 $80 $90 $100

Answers

40=P x 10 x 5 / 100, use the solve function on the CAS calculator to find P

we know that

The simple interest formula is equal to

[tex]I=Prt[/tex]

where

I represents simple interest

P is the Principal amount of money to be invested

r is the rate of interest

t is Number of Time Periods

in this problem we have

[tex]t=5\ years\\ P=?\\ I=\$40\\r=0.10[/tex]

[tex]I=Prt[/tex]

Solve for P

[tex]P=I/(rt)[/tex]

substitute the values

[tex]P=40/(0.10*5)=\$80[/tex]

therefore

the answer is

[tex]\$80[/tex]

solve the equation 2x^2-1x=5x

Please enter any square root values using "sqrt" or the decimal answer rounded to the nearest hundredth (i.e. / = sqrt(2) or 1.41).

Answers

2x² - 1x = 5x
2x² - 1x - 5x = 0
2x²-6x=0
2x(x-3)=0
2x = 0 or x-3 = 0
x = 0 x = 3

Answer: x=0, x=3

Answer:

x=0, x=3

Step-by-step explanation:

The original value of the car is $18,000 it depreciates by 15% every year what is the value of the car after three years

Answers

The formula is
A=p (1-r)^t
A the value of the car after 3 years ?
P current value 18000
R rate of depreciation 0.15
T time 3 years
A=18,000×(1−0.15)^(3)
A=11,054.25

Evaluate: 3 x 5 3x5 when x=2 x=2 . Select one: a. 486 b. 96 c. 30 d. 7,776

Answers

3x^5...when x = 2

3(2^5) =
3(32) =
96 <==

3x^5 x = 2

3(2)^5

3(32)

96

The answer is b

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