The critical number of the given function {g(t) = 3t ㏑t} is t = e⁻¹
What is critical number?Assume f(x) is a function with an open interval (a,b). If c is in the interval (a,b) and either f'(c) =0 or f'(c) does not exist, we say c is a critical number of f(x).
Each local minimum as well as maximum of f(x) must correspond to a critical number of f(x). The opposite is not truly the case: not all critical number of f(x) must correspond to a local maximum as well as minimum of f(x).
Now, as per the question;
It should be noted that the broadest possible domain of {g(t) = 3t ㏑t} is given in the set {t : t > 0} as ㏑t can not be defined for negative numbers of zero.
Now, differentiate the given function with respect to t.
[tex]g^{\prime}(t)=\frac{d}{d t}(3 t \ln t)[/tex]
Apply the product rule of differentiation;
[tex]\begin{aligned}&=\left[\frac{d}{d t}(3 t)\right] \ln t+3 t \frac{d}{d t}(\ln t) \\&=3 \ln t+3 t \frac{1}{t} \\&=3 \ln t+3 \\&=3(\ln t+1)\end{aligned}[/tex]
Now, put this value of g'(t) = 0 for finding the critical points.
0 = g'(t)
= 3(㏑t + 1)
Divide equation by 3.
0 = ㏑t + 1
㏑t = -1
Taking anti log;
t = e⁻¹ (critical value)
Therefore, the critical value obtained for the given function is t = e⁻¹.
To know more about the critical value of the function, here
https://brainly.com/question/5984409
#SPJ4
The complete question is-
how many critical numbers does {g(t) = 3t ㏑t} have? note: critical numbers must be within the domain of the function.
How many significant digits are in the given measurement:
6040.0050 m
7
0
8
4
Answer:
8 significant digits
Step-by-step explanation:
Let's count
6040.0050
⬇ ⬇⬇⬇.⬇ ⬇⬇ ⬇
1 234 567 8
therefore it's 8 significant figures
3. Select all the equations that match the diagram.
X+5\x+5\x+5
a.
x+5=18
b. 18÷3=x+5
C. 3(x+5)= 18
d. x+5=-18
e. 3x+5= 18
The equations that match the diagram are 18 ÷ 3 = x + 5 and 3(x + 5) = 18
How to select all the equations that match the diagram?The given parameters are
Expression = x+5\x+5\x+5
Value = 18
The above means that
Expression = Value
So, we have
x + 5 + x + 5 + x + 5 = 18
Evaluate the sum
So, we have
3x + 15 = 18
Factor out 3
So, we have
3(x + 5) = 18
Divide both sides by 3
So, we have
x + 5 = 18 ÷ 3
Hence, the equations that match the diagram are 18 ÷ 3 = x + 5 and 3(x + 5) = 18
Read more about equations at
https://brainly.com/question/13763238
#SPJ1
Best painters charges $100 to paint a room and $15 per can of paint used. Top Painters charges $75 to paint a room and $30 per can of paint used. Which equation could be used to find the number of cans of paint (p) for which the cost of the two companies is the same?
a) 45p = 175
b) p(100 + 15) = p(75 + 30)
c) 100p + 15 = 75p + 30
d) 15p + 100 = 30p + 75
d. 15p + 100 = 30p + 75
Please answer the 2 question in photo [ Brainliest + easy points ]
Translate abc with coordinates a(3,4) b(7,7) c( 8,1) 6 units left 7 units down
Answers:
A ' = (-3, -3)
B ' = (1, 0)
C ' = (2, -6)
=====================================================
Explanation:
To translate 6 units to the left, we subtract 6 from each x coordinate.
For point A, we have x = 3 become 3-6 = -3 as the new x coordinate.
Point A also goes down 7 units, in which we subtract 7 from the y coordinate. So the y coordinate of point A, which is 4, becomes 4-7 = -3 as the new y coordinate.
This is how we can write out the work shown for moving point A
[tex](\text{x},\text{y})\to(\text{x}-6,\text{y}-7)\\\\(3,4)\to(3-6,4-7)\\\\(3,4)\to(-3,-3)[/tex]
Point A is at (3,4) and moves to A ' which is at (-3, -3)
Do similar steps for points B and C to get the answers shown above.
10. Two of the greatest rainfalls ever recorded were on, July 4, 1956.
In Unionville, Maryland it rained 1.23 in. in 1 min. In Curtea-de-
Arges, Romania on July 7, 1889 it rained 8.1 in. in 20 min. If it
had rained for 20 min in Unionville at its same record pace, what
would be the difference between the two rainfall amounts?
Answer:
The difference would be Unionville would have had 24.6 in. of rain and Arges only had 8.1 in
Step-by-step explanation:
find f(-2)
i need help
Answer:
f(-2) = -1
Step-by-step explanation:
wwwwwwwwwwww
Answer: f(-2) = 5
Step-by-step explanation: In this piecewise function, when x is less than -1, the equation is -3x-1. -2 is less than -1 so we use the first equation. -3(-2)-1= 6-1 = 5.
Which graph shows the function f(x) = x with an input of f ?
A coordinate plane with a line passing through (negative 4, negative 1), (negative 3, 0), and (0, 3).
A coordinate plane with a line passing through (negative 2, negative 5), (0, negative 3), and (3, 0).
A coordinate plane with a line passing through (negative 1, negative 3), (0, 0), and (1, 3).
A coordinate plane with a line passing through (negative 3, negative 2), (0, 0), and (3, 1).
Using translation concepts, the graph that shows that function f(x) = x with an input of f(x - 3) is given by:
A coordinate plane with a line passing through (negative 2, negative 5), (0, negative 3), and (3, 0).
What is the missing information?The input of the function, of f(x - 3), is missing.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For this problem, the function is:
f(x) = x.
The translation is in the input, f(x - 3), meaning that the function is shifted 3 units right and defined by:
f(x - 3) = x - 3.
Hence three points on the graph are:
x = -2, f(x) = -5.x = 0, f(x) = -3.x = 3, f(x) = 0.Hence the correct description is:
A coordinate plane with a line passing through (negative 2, negative 5), (0, negative 3), and (3, 0).
More can be learned about translation concepts at https://brainly.com/question/4521517
#SPJ1
Answer:
D
Step-by-step explanation:
Enlarge triangle A by scale factor 1.5 with centre (0,2)
Scale factor 1.5
Let O (0,2) as the centre of enlargement
A (0, 0)
B (-2, 0)
C (-2, 4)
Step 1:
First draw lines from point O through A, B and C, as shown in the image attached below
Step 2:
Measure the length O A and multiply it by 1.5 to get the distance from O of the image point A';
<=> O A' = 1.5 × O A.
<=> OA' = 1.5 * [tex]\sqrt{2^2}[/tex]
<=> OA' = 1.5*2
<=> OA' = 3
Mark the point A' on the diagram
Step 3:
The images B' and C' can then be marked in a similar way and the enlarged triangle A' B' C' can then be drawn.
OB' = 1.5OB
<=> OB' = 1.5 *[tex]\sqrt{( 2^2+2^2}[/tex]
<=> OB' = 1.5*2[tex]\sqrt{2}[/tex]
<=> OB' = 3[tex]\sqrt{2[/tex]
OC' = 1.5*[tex]\sqrt{2^2+2^2}[/tex]
<=> OC' = 1.5*2[tex]\sqrt{2[/tex]
<=> OC' = 3[tex]\sqrt{2}[/tex]
learn more of triangle here https://brainly.com/question/16446634
#SPJ9
Find the measure of ∠ b ?
Answer:
38 degrees
Step-by-step explanation:
Angle 38 and b are the same.
which two cards show reflection, rotation, or translation?
Answer:
1 & 4
Step-by-step explanation:
because 3 & 5 is a reflection, 2 & 6 is a translation.
solve the inequality |x +4|-4>0
The inequality form of the given expression is:
x < -8 or x > 0
The interval notation is : (−∞,−8)∪(0,∞)
Given, the expression is |x + 4| - 4 > 0
An inequality is a relationship that shows a non-equal comparison between two numbers or mathematical expressions.
Isolate the variable by dividing each side by factors that don't contain the variable.
⇒ |x + 4| - 4 > 0
⇒ |x + 4| > -4
Remove mod.
⇒ x + 4 > -4 or x - 4 > -4
⇒ x > -4 -4 or x > -4 +4
⇒ x <-8 or x > 0
Hence the internal notation is :
(−∞,−8)∪(0,∞)
The required graph is plotted.
Learn more about Inequality here:
brainly.com/question/25275758
#SPJ9
Get 15 points and 1 Thanks if ur answer is correct.
Answer:
1 3/4
Step-by-step explanation:
OK but what if brainliest instead
Answer:1 3/4
Step-by-step explanati
ar travels on a straight, level road. (a) Starting from rest, the car is going 38 ft/s (26 mi/h) at the end of 4.5 s. What is the car's average acceleration in ft/s²?
The car's average acceleration is 8.44 ft/s².
Acceleration is defined as the rate of change of velocity per unit time. It is usually denoted by the letter a.
Here, we are given that a car travels on a straight road. Starting from rest, the car is going at 38 ft/s (26 mi/h) at the end of 4.5 s.
Acceleration of an object can be calculated using the given formula-
acceleration = velocity/ time
Here, the velocity of the car will be 38 ft/s
and the time is equal to 4.5 seconds.
Thus, putting these formulas in the equation, we get-
acceleration of the car = 38/ 4.5
= 380/ 45
= 8.44
Thus, the car's average acceleration is 8.44 ft/s².
Learn more about acceleration here-
https://brainly.in/question/571983
#SPJ9
PLEASE ANSWER FAST
How many times larger is 7 x 10^5 than 2 x 10^3?
Answer:
698,000
Step-by-step explanation:
7×10^5=700000
2×10^3=2000
700,000-2000=698,000
The given 7 * [tex]10^5[/tex] is 3.5*10² times larger than 2 * 10³.
Given that,
To determine, how many times larger is 7 x 10^5 than 2 x 10^3.
What is the Ratio?The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
We have two values, here we have to determine the relationship between the two values.
[tex]ratio = 7*10^5 / 2 * 10^3\\Ratio = 3.5 * 10 ^2[/tex]
Implies,
[tex]7*10^5 = 3.5*10^2 (2 * 10^3)[/tex]
Thus, the given 7 * [tex]10^5[/tex] is 3.5*10² times larger than 2 * 10³.
Learn more about Ratio here:
brainly.com/question/13419413
#SPJ2
Given negative four and one sixth times negative three and fifteen hundredths, determine the product.
The resulting product of the expression is 13 1/8
Product of fractionsFractions are written as a ratio of two integers
Given the following expression
-4 1/6 * -3 15/100
Convert to improper fraction to have:
-25/6 * -315/100
-1/6 * -315/4
315/24
13 1/8
Hence the resulting product of the expression is 13 1/8
Learn more on product of expression here: https://brainly.com/question/4344214
#SPJ1
The circumference is 25 ft I have to find what X is for my radius
R= -4x-5
The value of x based on the information given about the circumference is 2.24.
How to illustrate the information?It should be noted that the circumference is calculated as:
= 2πr
where
π = 3.142
r = radius = 4x - 5.
Circumference = 25
Therefore, circumference = 2πr.
(2 × 3.142)(4x - 5) = 25
6.284(4x - 5) = 25.
25.136x - 31.42 = 25
Collect like terms
25.136x = 25 + 31.42
25.136x = 56.42
x = 56.42 / 25.136
x = 2.24
Therefore, the value of x based on the information given about the circumference is 2.24.
Learn more about circumference on:
brainly.com/question/27447563
#SPJ1
A parallelogram has an AREA of 7 square units. If the height that corresponds to a base is 14 units, what is the base?
Answer:
b = 0.5
Step-by-step explanation:
a = b x h
7 = 14b Divide both sides by 14
0.5 = b
during math class, you find the length of a right triangle's hypotenuse with a theorem created long ago. who do you have to thank for that theorem?
The length of a right triangle's hypotenuse with a theorem created long ago is c² = a² + b², where 'c' = the hypotenuse of the right triangle and 'a' and 'b' are the other two legs.
We need to find the length of a right triangle's hypotenuse with a theorem created long ago.
What is a Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
The Pythagoras theorem equation is expressed as, c² = a² + b², where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs. Hence, any triangle with one angle equal to 90 degrees produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.
Therefore, the length of a right triangle's hypotenuse with a theorem created long ago is c² = a² + b², where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs.
To learn more about the Pythagoras theorem visit:
https://brainly.com/question/343682.
#SPJ4
Please answer this math equation.
The table that represents the linear function is table (B)
How to determine the linear function?As a general rule, a linear function is any function that has a constant rate of change
This means that as the function independent value changes by a constant, the function dependent value changes by a constant
In other words, as the function x value changes by a constant, the function y value changes by a constant
Using the above as a guide, we can see the table B represents a linear function
This is so because, as x increases by 3, the y value decrease by -2
Hence, the table that represents the linear function is table (B)
Read more about linear functions at:
https://brainly.com/question/15602982
#SPJ1
Can yall help me with this
Answer:
8 feet
Step-by-step explanation:
Since it is 2 inches and 1 inch is equal to 4 feet, you just multiply 2 inches by 4 feet which will give you 8 feet.
Hope that helps
if angle 2 equals (2x+5)degrees and angle 3 equals 85degrees, what is the value of x
Based on the information given, the value of x is 40 degrees
What are corresponding angles?Corresponding angles are defined as any pair of angles which on the same side of one or two lines, there is a cut through by a transversal.
It is also important to note that when a transversal intersects two parallel lines, the corresponding angles of the lines would be equal.
Given the angles;
Angle 2 equals (2x+5) degrees Angle 3 equals 85 degreesWe have that;
Angle 2 = Angle 3
Substitute the values
2x + 5 = 85
collect like terms
2x = 85 - 5
2x = 80
Make 'x' the subject by dividing both sides by 2
2x/ 2 = 80/ 2
x = 40 degrees
Thus, the value of x is 40 degrees
Learn more about corresponding angles here:
https://brainly.com/question/2009183
#SPJ1
The measure of an angle is 56.3°. What is the measure of its complementary angle?
Answer:
33.7
Step-by-step explanation:
Complementary angles are angles that when added, sum up to 90*
First, make the equation, x being the missing angle
90*= x + 56.3
Rewrite the equation to find the missing angle
90 - 56.3 = x
x= 33.7
Answer:33.7°
Step-by-step explanation:
To find the complement of an angle, subtract that angle's measurement from 90 degrees. The result will be the complement
90° - 56.3°
=33.7°
find the indicated value for the given function. f(4) =|2x-7|
Answer: 1
I did this problem a couple times and got 1 every time
Let g(x) = {2x + 4 if x < −1, x + 4 if x ≥ −1.
Find the value of g^-1(-1)
The inverse of a function when x = -1 is g^-1(-1) = -5/2
Inverse of a functionLinear functions are function that has a leading degree of 1. Given the expression below;
g(x) = 2x + 4
Determine the inverse
y = 2x + 4
Replace y with x
x = 2y + 4
Make y the subject of the formula
2y = x - 4
y = (x-4)/2
g^-1(x) = (x-4)/2
Substitute x = -1 into the equation
g^-1(x) = (-1-4)/2
g^-1(-1) = -5/2
Hence the inverse of a function when x = -1 is g^-1(-1) = -5/2
Learn more on inverse of a function here: https://brainly.com/question/3831584
#SPJ1
which expression shows the prime factorization of 36? 2 × 2 × 3 2 × 2 × 3 2 × 3 × 3 2 × 3 × 3 2 × 2 × 2 × 3 × 3 2 × 2 × 2 × 3 × 3 2 × 2 × 3 × 3
Answer:
36 = 2 x 2 x 3 x 3
Answer:
2 2/3 * 2 2/3 = 64/9 = 7 1/9 ≅ 7.1111111
Step-by-step explanation:
The result:
2 2/3 * 2 2/3 = 64/
9
= 7 1/
9
≅ 7.1111111
Spelled result in words is sixty-four ninths (or seven and one ninth).
How do we solve fractions step by step?
Conversion a mixed number 2 2/
3
to a improper fraction: 2 2/3 = 2 2/
3
= 2 · 3 + 2/
3
= 6 + 2/
3
= 8/
3
To find a new numerator:
a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/
3
= 6/
3
b) Add the answer from previous step 6 to the numerator 2. New numerator is 6 + 2 = 8
c) Write a previous answer (new numerator 8) over the denominator 3.
Two and two thirds is eight thirds
Multiple: 8/
3
* 8/
3
= 8 · 8/
3 · 3
= 64/
9
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(64, 9) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - eight thirds multiplied by eight thirds is sixty-four ninths.
HOPE THIS HELPS!
I Did It On Another Website And Had To Re-Write It So If You Don't Understand It LMK!
[Thanks] Are Appreciated!
[High Rates] Are Also Really Appriciated
Have A Nice Day!
What is the equation of the line?
y=-12+1
Oy=2x-1
O y=-2z+1
Oy=-z-1
Answer:
y = -1/2 x + 1.
Step-by-step explanation:
The slope is -1/2.
The y intercept is at y = 1
So, it's
y = -1/2 x + 1.
your friend says that you can write any equation in slope-intercept form. is your friend correct? explain.
Answer:
almost.
Step-by-step explanation:
You can write almost every linear equation in slope-intercept form.
Slope-intercept form is:
y = mx + b
So every line except a vertical line can be written in the form y=mx+b.
This form cannot be used when m is undefined.
write an equation of the line . through (1,-2);parallel to 2x=3y+4
Answer:
y = 2/3x - 8/3
or 2x = 3y + 8
Step-by-step explanation:
2x = 3y + 4
3y = 2x - 4
y = 2/3x - 4/3
If two lines are parallel, their slopes are equal
if m = 2/3, y = -2, x = 1
y = mx + b
-2 = 2/3(1) + b
-2 = 2/3 + b
b = -2 - 2/3 = -8/3
y = 2/3x - 8/3
or 3y = 2x - 8
or 2x = 3y + 8
Prove the following inequality.
The proof of the inequality → (a + b)²/2 ≥ 2ab, is given below -
We have the following inequality -
(a + b)²/2 ≥ 2ab
We have to prove it.
What is inequality ?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
According to the question, we have -
Inequality -
(a + b)²/2 ≥ 2ab
Proof -
Starting from the inequality - (a - b)² ≥ 0
(a - b)² ≥ 0
a² + b² - 2ab ≥ 0
a² + b² - 2ab + 2ab ≥ 2ab
a² + b² ≥ 2ab
Add - 2ab on both sides, we get -
a² + b² + 2ab ≥ 4ab
(a + b)² ≥ 4ab
Divide both sides by 2, we get -
(a + b)²/2 ≥ 2ab
Hence Proved.
To solve more questions on Proving inequalities, visit the link below-
https://brainly.com/question/13260153
#SPJ1