Answer:
(i) The derivative of the function is [tex]f' = \frac{1}{10}[/tex].
(ii) The domain of all first order polynomials (linear functions) is the set of all real numbers. That is:
[tex]Dom\{f(x)\} = \mathbb{R}[/tex]
The domain of all zero order polynomials (constant functions) is the set of all real numbers. That is:
[tex]Dom\{f'\} = \mathbb{R}[/tex]
Step-by-step explanation:
(i) Find the derivative of the function using the definition of derivative:
The derivative is defined by the following limit:
[tex]f' = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex] (1)
If we know that [tex]f(x) = \frac{1}{10}\cdot x - \frac{1}{3}[/tex], then the definition of derivative is expanded:
[tex]f' = \lim_{h \to 0} \frac{\frac{1}{10}\cdot (x+h) - \frac{1}{3}-\frac{1}{10}\cdot x +\frac{1}{3}}{h}[/tex]
[tex]f' = \lim_{h \to 0} \frac{\frac{1}{10}\cdot h }{h}[/tex]
[tex]f' = \lim_{h \to 0} \frac{1}{10}[/tex]
[tex]f' = \frac{1}{10}[/tex]
The derivative of the function is [tex]f' = \frac{1}{10}[/tex].
(ii) State the domain of the function and the domain of its derivative:
The domain of all first order polynomials (linear functions) is the set of all real numbers. That is:
[tex]Dom\{f(x)\} = \mathbb{R}[/tex]
The domain of all zero order polynomials (constant functions) is the set of all real numbers. That is:
[tex]Dom\{f'\} = \mathbb{R}[/tex]
Algebra 2
Help me pls
Answer:
log (150)=2.176091259
Answer:
log104=2.107
log150=2.176
log1025=3.011
log10570=4.024
log7=0.845
Step-by-step explanation:
To solve these questions, you can just plug them into your calculator:
log104=2.107033339≈2.107
log150=2.176091259≈2.176
log1025=3.010723865≈3.011
log10570=4.024074987≈4.024
log7=0.84509804≈0.845
C С 154 -Y Х 2 3 5 w 4 6 7 Z D
Answer:
m<1 = 26°
m<2 = 154°
m<3 = 26°
m<4 = 26°
m<5 = 154°
m<6 = 154°
m<7 = 26°
Step-by-step explanation:
What is required was not stated, however, let's find the value of every angle labelled in this diagram.
✔️m<1 = 180° - 154° (linear pair theorem)
m<1 = 26°
✔️m<2 = 154° (vertical angles theorem)
m<2 = 154°
✔️m<3 = m<1 (vertical angles theorem)
m<3 = 26° (substitution)
✔️m<4 = m<3 (alternate interior angles theorem)
m<4 = 26° (substitution)
✔️m<5 = m<2 (alternate interior angles theorem)
m<5 = 154° (substitution)
✔️m<6 = m<5 (vertical angles theorem)
m<6 = 154° (substitution)
✔️m<7 = m<4 (vertical angles theorem)
m<7 = 26° (substitution)
Tommy has blue, green, and red
marbles. The number of blue marbles
and green marbles combined total 25.
The number of blue and red marbles
combined total 30. There are twice as
many red marbles as green marbles.
How many green marbles does
Tommy have?
A. 5
B. 10
C. 15
D. 20
Answer:
The correct answer is 5.
Step-by-step explanation:
Find the following bases.
a. 8% of ? = 20
b. 75% of ? = 30
c. 20% of ? = 45
d. 150% of ? = 36
Answer:
a.. 8% of ? = 20 240
b.75% of ? = 30 40
c. 20% of ? = 45 225
d. 150% of ? = 36 24
The steps of answer is in attached file
Hope it helps..
Have a great day : )
Help me and if the answer is correct and neat I will give you brainliest. Its about line plots.
Answer:
Step-by-step explanation:
Pls help me
5 ( a - b ) , if a = -4, b = -2
Answer:
-10
Step-by-step explanation:
5(a - b) =
= 5(-4 - (-2))
= 5(-4 + 2)
= 5(-2)
= -10
Find the value of each expression using the given information cot∅=8, csc<0
find sin ∅
9514 1404 393
Answer:
sin(∅) = -√65/65
Step-by-step explanation:
The identities that relate the cotangent, the cosecant, and the sine are ...
csc² = 1 +cot²
sin = 1/csc
_____
For the given values, we find ...
csc(∅)² = 1 +cot(∅)² = 1 +8² = 65
csc(∅) = -√65 . . . . . . . . . . . . . . . . square root with attention to sign
sin(∅) = -1/√65 = (-√65)/65
Simplify: 17b + 82c + 90 + e - 18 - 10c - b
The difference between three times a number and 5 is 10.
Answer:
Equation: 3x-5=10
Answer: X=5
Step-by-step explanation:
3 times a number (represented as X) and 5 (means subtract by 5)
3x-5=10
Add 5 on both sides
3x=15
X=5
Answer:
3(5) - 5 = 10
15 - 5 = 10
10 = 10 x = 5
Step-by-step explanation:
Three times a number is 3x because you do not know the number.
Add five to both sides of the equation.
Divide both sides of the equation by 3 and the solution is x = 5
The ratio of cups of sugar to cups of water
Answer:
yes
Step-by-step explanation:
Sugar and water amounts used change proportionately.
What is the measure of
Answer:
Just Plus the 2 Given and Minus in the 360 Because 360 It has a Fourside The Answer is 168degrees
Branliest to correct answer explain how you solved it please
Answer:
0.03
Step-by-step explanation:
.25% for the tails times .5 for the odd number on the dice times 0.25 for the clubs because it is a 13/52 chance you will pull a clubs and put that all together and you get 0.03125 simplified and you get 0.03
Answer:
0.03
Step-by-step explanation:
The probability of landing on 1 tail is 1/2, since it is 1 out of 2 options, a tail or a head. If you want the probability of two tails, it would be 1/2 * 1/2 = 1/4.
Next we can take the probability of rolling an odd number on a fair die. A fair die has 3 even numbers: 2,4,6; and 3 odd numbers: 1,3,5. Since 3/6 or 1/2 of the numbers are odd, there is a 50% chance that it would roll an odd number.
Finally, drawing a club out of standard deck of cards is 1/4, since there are 4 choices: hearts, spades, clubs, or diamonds. You now get the idea, and you can figure out that the probability would be 1/4.
Our last step is to multiply all the answers we get, since to get all of them at once would lower your chances. 1/4 * 1/2 * 1/4 = 1/32 = 0.03125; rounded to 0.03.
Use the slope formula to find the slope of the line through the points (2,1) and (8,7)
Answer:
m = 1
Step-by-step explanation:
(2,1) and (8,7)
m = (y2-y1)/(x2-x1)
m=(7-1)/(8-2)
m=6/6
m = 1
the dimensions of the lawn shaped like trapezoid are given in meters what is the area of the lawn in square meters
Answer:
Where are the dimensions?
How many groups of 1/4 are in 3. Draw a tale diagram
Answer:
12.
Step-by-step explanation:
In the figure, angle D measures 31 degrees and angle A measures 27 degrees.
The measurement of angle B is:
59, 63, or 90
Angle F is:
59, 63, or 90
Answer:
Angle B = 63° Angle F = 59°Step-by-step explanation:
C = 90° (right angle)
A = 27°
3 angles are added to result in 180° (property of triangle)
Therefore B =
180 - (90 + 27) =
180 - 117 =
63°
Angle B = 63° ✅E = 90° (right angle)
D = 31°
3 angles are added to result in 180° (property of triangle)
Therefore F =
180 - (90 + 31) =
180 - 121 =
59°
Angle F = 59° ✅____________________
#IndonesianPride - kexcvi
Answer:
B= 63
F= 59
Step-by-step explanation:
a+ b+ c= 180
27+b+ 90=180
117+b=180
180-117=b
B= 63
D+E+F=180
31+ 90+ F=189
121 +F=180
180-121= F
F= 59
Pleasee helpp Which one??
Answer:
Constant
Step-by-step explanation:
there numbers with no variables next to them and coefficient's do. :)
Answer:
constant
Step-by-step explanation:
what is the volume of the rectangular prism ?
Answer:V=whl
Step-by-step explanation:
all you have to do is multiply width times length times height
1 1/2 × 1 1/2 × 1 1/2= 3/2 × 3/2 × 3/2 = 27/ 8
simplify to
3 3/8
hope this was helpful:)
Find the value of 5⁰ X 7⁰ X 3⁰
plz help asap
Answer:
5⁰ × 7⁰ × 3⁰ = 1
Step-by-step explanation:
5⁰ × 7⁰ × 3⁰ = ?
5⁰ = 1
7⁰ = 1
3⁰ = 1
1 × 1 × 1 = 1
Identify the equation as either Linear, Quadratic, or Exponential: *
f (x) = 2x
A. Linear
B. Quadratic
C. Exponential
Answer:
It's A.) linear
Step-by-step explanation:
The power of x is equal to one, making it linear [ f(x) = 2x^1 ]
21 ≤ 2x + 3 =
How do you work this out? And what is the answer? :)
Answer:
9
Step-by-step explanation:
21≤2x+321-3≤2x18≤2xdivide both side by 2therefore the answerx≥9Identify the vertex of the graph. Tell whether it is a minimum or a maximum.
The vertex needs to be in ordered pair.
Answer:
Vertex = (-1, 2)
Maximum
Step-by-step explanation:
The middle point of the graph is at x coordinate -1 and the point is at the top while the graph slopes down so it is a maximum point and not a minimum point.
Please mark Brainliest if this was helpful :)
How many cuboids of size 4m x 3cm X 2cm. Can be made from a cuboid of size 12cm x 9cm x 6 cm ?
Answer:
Lets find volume of smaller cubiod first.
Volume = l x b x h = 24 cm³
Again,
Lets find volume of bigger cuboid.
Volume = l x b x h = 648cm³
Now,
The no. of cuboids that can be made from the bigger cuboid is
= Volume of bigger cuboid / volume of smaller cuboid
= 648/ 24
= 27 cuboids
A water storage tank has a cylindrical shape. The base has a diameter of
18 m and the tank is 32 m high. How much water, to the nearest cubic
unit, can the tank hold?
Answer:
Rounded to the nearest cubic unit, the tank can hold 8,139 cubic meters of water.
Step-by-step explanation:
Given that a water storage tank has a cylindrical shape, and the base has a diameter of 18 m and the tank is 32 m high, to determine how much water can the tank hold, the following calculation must be performed, knowing that the volume of a cylinder is obtained by multiplying the number pi by the radius squared of the cylinder, and this result by its height:
V = Pi x (radius x radius) x height
Radius = 1/2 diameter = 9
V = 3.14 x (9 x 9) x 32
V = 3.14 x 81 x 32
V = 254.34 x 32
V = 8,138.88
Thus, rounded to the nearest cubic unit, the tank can hold 8,139 cubic meters of water.
does anyone know the answer to this
17y -19 =219
Question 1 ) The population of Jackson Heights is 125% of the population of Elmhurst. If Elmhurst has 80,000 people, how many people live in Jackson Heights?
Question 2 ) The population of Jackson Heights is 125% of the population of Elmhurst. If Jackson Heights has 80,000 people, how many people live in Elmhurst?
Answer:
1) Jackson Heights population = 100,000
2) Elmhurst population = 64,000
Step-by-step explanation:
1) 80,000 x 1.25 = 100,000
2) 80,000/1.25 = 64,000
y
45°
X 100°
y = [ ? 1°
Step-by-step explanation:
x+100°=180°{being straight angle}
x=180-100
x=80°
again,
45°+x+y=180°{sum of angle of triangle}
45+80+y=180
y=180-125°
y=55°
hope it helps.
A desk drawer is shaped like a rectangular prism. The height of the drawer is 7 inches. The bottom of the drawer has an area of 210 square inches.
What is the volume of the desk drawer?
pls help Ill give you brainiest and pic for your profile
Answer:
1470
Step-by-step explanation:
You should stay real close to Jesus
Keep that bottle at your hand, my man
Find your way back to my bed again
Sing me like a Bible hymn
We should go back to Arkansas
Trade this body for the can of Gin
Like a little piece of heaven
No more candle in the wind
[Verse 1]
You should come back to our place, baby
Don't be afraid of our love
On the second floor, darling
In a second flat, hurry up
'Cause down in Arkansas the stores are all closed
The kids in their hoodies, they dance super slow
We're white-hot forever and only God knows
[Chorus]
You should stay real close to Jesus
Keep that bottle at your hand, my man
Find your way back to my bed again
Sing me like a Bible hymn
We should go back to Arkansas
Trade this body for the can of Gin
Like a little piece of heaven
No more candle in the wind
[Post-Chorus]
We'll be white-hot forever
White-hot forever
White-hot forever
And ever and ever, amen
[Verse 2]
Could I come back to the ranch, baby?
I had to get away for a while
Just to rest my nerves, darling
Can I make you laugh with a smile?
You knew when you chose me
I was nothing but ordinary
And now the wind's blowing, reminding you of what you know
[Chorus]
You should stay real close to Jesus
Keep that bottle at your hand, my man
Find your way back to my bed again
Sing me like a Bible hymn
We should go back to Arkansas
Trade this body for that can of Gin
Like a little piece of heaven
No more candle in the wind
[Post-Chorus]
We'll be white-hot forever
White-hot forever
White-hot forever
And ever and ever, the end
White-hot forever
White-hot forever
White-hot forever
And ever and ever, amen
[Outro]
You should stay real close to Jesus
If you don't pray, you'll never learn
Keep that bottle at your hand, my man
You know what I'm sayin'?
Find your way back to my bed again
Sing me like a Bible hymn
We should go back to Arkansas
I like living here
Trade this body for the can of Gin
Like a little piece of heaven
No more candle in the wind
Answer:
AMEN
Step-by-step explanation:
.
simplify by distributive property 8-3(7m-3p)