What is the minimum value of the function over the interval -5 < x < 5?

h(x) = log[(x – 3)^2 + 2]

Answers

Answer 1

Answer: ln(2)

Step-by-step explanation:

In order to minimize ln[(x – 3)^2 + 2], we have to minimize [(x – 3)^2 + 2] since natural log is an increasing function

For that, it suffices to minimize (x – 3)^2, which is non-negative for all real numbers x

As such, the minimum value is achieved when x - 3 = 0; - 5 < 3 < 5

Substitute x = 3 in the original equation to get ln(2)


Related Questions

There are 6 brownies to share with 4 children.
How many brownies does each child get?

Answers

Answer:

SO evry child gets 1 then you go around again and there will be 2 more, so all you hae to 2 is split hose into halfs and it will be equal :)

Step-by-step explanation:

Evaluate an expressions: 4a + 3b + c if a = 8, b=-2 and c = 4


For 25 points 7th grade math

Answers

Answer:

4 x 8= 32

3 x 2= 6

32 + 6 + 4= 42

Therefore your answer would be 42.

Step-by-step explanation:

Hope this is helpful :)

A projectile is launched from ground level with an initial velocity of v0 feet per second. Neglecting air resistance, its height in feet t seconds after launch is given s=-16t^2+v0t. Find the tim(s) that the projectile will (a) reach a height of 128 ft and (b) return to the ground when v0 is 64 feet per second​

Answers

Answer:

22

Step-by-step explanation:

HELPPPPPPPP PLEASEEEEEEE!!!!!!

Answers

X=40
Y=70.
Z=70. They must add up to 180

Answer:

A. 40°

Step-by-step explanation:

As we can see it is an isosceles triangle because two sides are equal. so Base angles of an isosceles triangle are equal. Then Now.,

70° + 70° + <X = 180° {Being sum of angles of triangle }

140° + < X = 180°

< X = 180° - 140°

< X = 40°

Hope it will help :)❤

solve : -2 1/3-(-5) = 0

Answers

Answer:

2 2/3

Step-by-step explanation:

Answer:

2 2/3

Step by Step

Joe wants to buy a $180 number that's on is on sale the snowboard is 30% off what is the sale price of the snowboard (show work)

Answers

Answer:

Step-by-step explanation:

Assuming that the Skateboard is $180, and you are asking for the price when it is 30% off.

180 * .70 = $126

Another way of solving the question is finding 10 % of 180, which is 18. And you are looking for 30% less, so 18 * 3 = 54, which is 30% of 180.

180 - 54 = 126

54 is the correct answer

1. Caleb has a bike rental agency. He has 26 vehicles available, 19 are ack bikes. What is the relative frequency probability that a randomly selected vehicle will be a black bike?​

Answers

Answer:

Probability of 7%

Step-by-step explanation:

Use the distributive property to find an expression that is equivalent to 2(x + 7) - (3x + 1)

Answers

This is the answer it will help you

A salesperson at a jewelry store earns a 4​% commission each week. Last​ week, Jarrod sold $640 worth of jewelry. How much did he make in​ commission? How much did the jewelry store make from his ​sales?

please help!

Answers

Answer: 19.2

Step-by-step explanation:

Plz give brainlest

Answer:$51.20 commission

Step-by-step explanation:

can I get some help ???

Answers

Answer is D. 288 . i am glad to help

tia is swimming at a constant rate in a lake

Answers

Answer:

Step-by-step explanation:

If you wanted to figure out how long it would take her to get there it would be the distance she swims divided by her speed.

if you wanted to figure out how much her speed is, it would be the distance she swims divided by her speed.

If you wanted to figure out how long the distance is, you would multiply her speed and how long it took to get their.

May someone help me on question 7 please

Answers

it’s literally c these are so easy n it’s shouldn’t be that hard.

30 POINTS
Simplify.

−5x4(−3x2+4x−2)

Answers

Answer:

15 x ^6 − 20 x ^5 + 10 x ^4

Step-by-step explanation:

Answer:

15x^6 - 20x^5 + 10x^4

Step-by-step explanation:

−5x^4(−3x^2+4x−2)

15x^6 - 20x^5 + 10x^4

write the standered equation of the circle (0,7)

Answers

Answer:

C

Step-by-step explanation:

WILL GIVE BRAINLIEST! NEED ANSWER FAST!

Anthropologists approximate the height of a primate by the size of its humerus (the bone from the elbow to the shoulder) using the equation

H = 1.2L + 27.8,

where L is the length of the humerus and H is the height, in inches, of the primate.


An anthropologist estimates the height of a primate to be 60 in. What is the approximate length of the humerus of this primate? Round to the nearest tenth of an inch.

in

Answers

Answer:

26.83

Step-by-step explanation:

H=1.2L + 27.8

60=1.2x+27.8

minus 27.8 from both sides

32.2=1.2x

divide both sides by 1.2

x=26.83

Chang types at a rate of 12 words per minute. How many words does he type in 3 minutes?

Answers

Answer: 2,160 words

Step-by-step explanation:

Simplify each expression. 3.3(x + 4)

Answers

Answer:

33 • (x + 4)

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

       10  

Step-by-step explanation:

(1): "3.3" was replaced by "(33/10)".

STEP 1:

                 33

Simplify   ——

                 10

Equation at the end of step 1:

 33

 ---   • (x + 4)

 10

STEP 2:

Final result :

 33 • (x + 4)

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

       10  

I hope I helped, and I always appreciate Brainliest!!! :)

100 time 100 minus 200

Answers

Answer:

9800

Step-by-step explanation:

Answer:

9800

Step-by-step explanation:

(100 x 100) - 200

PLEASE I NEED HELP ON THIS T^T
An online media service offers video and music downloads. Each download of a song costs $1. Each download of a video costs 5 times as much as the song download. You have a credit of $70. How many songs can you purchase after buying 12 videos?

Answers

Answer:

10

Step-by-step explanation:

we can solve this using basic algebra

We set up the equation using the info that each video costs $5 and that we but 12 of them

12(1 * 5) + x = 70

(Please note: 1x = x)

12(5) + x = 70

60 + x = 70

60 - 60 + x = 70 - 60

x = 10

Can someone please explain this to me?

Answers

G)

g(x) = (x+18)(x-3)
g(x) = x2 + 18x - 3x - 54
g(x) = x2 + 15x - 54

Determine whether y=2x^3 represents an exponential function.

Answers

Answer:

This is not an exponential function.

Step-by-step explanation:

x would have to be the exponent for it to be an exponential function.

25 students in class A did a science exam.
30 students in class B did the same science exam.

The mean mark for the 25 students in class A is 67.8
The mean mark for all the 55 students is 72.0

Work out the mean mark for the students in class B.

Answers

Answer:

class B

Step-by-step explanation:

f(x) = 3x - 1; Find x = 3

Answers

Answer
8
You’re welcome
f(3)=3(3)-1

f(3)=9-1

f(3)=8

Please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

B

Step-by-step explanation:

The orthocenter of a triangle is the point of intersection of the three altitudes of the triangle.

In an obtuse triangle, two altitudes are completely outside the triangle; therefore, the three altitudes cannot possibly intersect inside the triangle.

Answer: B

3(4x + 2) +2(x-1) please help me with this equation

Answers

Answer:

14x + 4

Step-by-step explanation:

3(4x+2) + 2(x-1)

Distribute by multiplying into the bracket

=12x + 6 + 2x - 2

Group like terms by adding and subtracting

= 14x + 4

Answer:

1) Multiply and expand the brackets:

12x + 6 + 2x - 2

2) Combine like terms (combine terms that have an x together, and those that don't together.)

14x + 4

If the question wanted you to simplify the expression, then 14x + 4 is your answer. However, to solve for x, you could equate the expression to 0, but I'm not too sure of this part.

14x + 4 = 0

14x = - 4

x = - 4/14

x = - 2/7

The area of a rectangular park is 3500sq.m.If its width is 50m,then find the
cost of its fencing at the rate of Rs.100per meter​

Answers

Deez nu-tz gottem
I looked it up

How many square feet of clear grass will be needed for the window? (Please Provided Explanation of Answer)

Answers

Answer:

40 sq ft

Step-by-step explanation:

A= bh

A= (4)(10)

A= 40

3 in.
3 in.
4 in.
6 in.
7 in.
11 in.
What is area of the shaded region in the figure shown?

Answers

Answer:

9 + 8 + 12 = 29

Step-by-step explanation:

Please help me need ASAPp

Answers

It is the 4th option 0

HELP ASAP 10 POINTSSS

Answers

Answer:

Complementary angles, adjacent angles

Step-by-step explanation:

Which relationships describe angles 1 and 2?

Options: Complementary angles, vertical angles, supplementary angles, adjacent angles

Angles 1 and 2 are opposite to the 90° angle. So, the angles' relationship to that angles is a vertical angle, meaning that the two add up to 90°.

Complementary angles add up to 90°, so this option is correct.

Vertical angles are the pairs of opposite angles formed by two intersecting lines. Because the two angles do not follow this definition, this option is incorrect.

Supplementary angles add up to 180°. However, we know that the two add up to 90°, so this option is incorrect.

Adjacent angles are angles that are next to each other, so this option is correct.

I hope this helps! Feel free to ask any questions!

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