Answer:
f(6) = 3
f'(6) = 1/6
Step-by-step explanation:
Remember that for a function f(x), we define f'(x) as the slope of the tangent line to the point (x, f(x))
We know that:
y = f(x) passes through the point (6, 3)
Then we already know that:
f(6) = 3.
Now we also know that the tangent at this point, also passes through (0, 2)
Remember that a line can be written as:
y = a*x + b
Where in this case, a = f'(6)
so we just want to find the slope of this line.
Remember that for a line that passes through (x₁, y₁) and (x₂, y₂) the slope is given by:
a = (y₂ - y₁)/(x₂ - x₁)
And we know that the tangent line passes through the points (0, 2) and (6, 3)
Then the slope is:
a = (3 - 2)/(6 - 0) = 1/6
Then we have:
a = f'(6) =1/6
Solve this question:Зх <-24
Answer:
x< - 8
Step-by-step explanation:
3x <-24
x < - 24
3
x< - 8
x < - 8
Step-by-step explanation:
3x < - 24
Divide 3 on both sides,
3x / 3 < - 24 / 3
x < - 8
WHAT IS X³-27 SIMPLIFIED
Answer:
It is (x - 3)³ - 9x(3 - x)
Step-by-step explanation:
Express 27 in terms of cubes, 27 = 3³:
[tex] = {x}^{3} - {3}^{3} [/tex]
From trinomial expansion:
[tex] {(x - y)}^{3} = (x - y)(x - y)(x - y) \\ [/tex]
open first two brackets to get a quadratic equation:
[tex] {(x - y)}^{3} = ( {x}^{2} - 2xy + {y}^{2} )(x - y)[/tex]
expand further:
[tex] {(x - y)}^{3} = {x}^{3} - y {x}^{2} - 2y {x}^{2} + 2x {y}^{2} + x {y}^{2} - {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3x {y}^{2} - 3y {x}^{2} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3xy(y - x) \\ \\ { \boxed{( {x}^{3} - {y}^{3} ) = {(x - y)}^{3} - 3xy(y - x)}}[/tex]
take y to be 3, then substitute:
[tex]( {x}^{3} - 3^3) = {(x - 3)}^{3} - 9x(3 - x)[/tex]
Does this appear to be a regular polygon? Explain using the definition of a regular polygon.
Answer:
yes it is. a polygon is any closed shape with at least 3 connected lines (eg. triangle, square, pentagon, hexagon, heptagon, octagon, etc)
Step-by-step explanation:
Write the equation of the sinusoidal function shown.
A) y = 2 sin(2x)
B) y = 2 sin x + 2
C) y = 2 cos x + 2
D) y = 2 cos(2x)
Answer:
2 sin(2x)
Step-by-step explanation:
sin x stretched vertically by a factor 2 and compressed horizontally by a factor 2.
The solution is : A. y = cos(x) - 2, is the equation of the sinusoidal function shown.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
The word "sinusoid" means the graph has a shape of the sine function that smoothly goes up and down.
so, we get,
However, the cosine function also has the same shape but the only thing is that it is horizontally translated. Thus, the cosine function is the sinusoid.
Hence, The solution is : A. y = cos(x) - 2, is the equation of the sinusoidal function shown.
To learn more on function click:
brainly.com/question/21145944
#SPJ7
What is the discriminat of 2x+5x^=1
Answer:
don't know...........
Wayne has a rectangular painting. The width of the painting is
5/6
of a foot, and the length is
3/4
of a foot. What is the area of the painting?
Answer:
5/8 ft^2
Step-by-step explanation:
The area of a rectangle is given by
A = l*w where l is the length and w is the width
A = 5/6 * 3/4
A = 3/6 * 5/4
A = 1/2 * 5/4
A = 5/8 ft^2
The equation of the line L is 2y-x=10.Find the coordinates of the point where L intersects the y-axis
Equation:- 2y-x=10
For L to intersects Y axis then X cordinate must be zero
so put value of X as zero (0)
2y=10
So Y cordinate is equal to 5
Cordinate:- (0,5)
The circle graph above shows the distribution of utility expenses for the Hierra family last year. If the family’s total utility expenses last year were $3,600, what were their expensive go water and sewer.
Water and sewer=X%
Electric=30%
Heating and gas=50%
Answer:
The correct answer is - $720 or 20%.
Step-by-step explanation:
Given:
Total expense = 3600
Electric=30%
Heating and gas=50%
Water and sewer=X%
Solution:
For electric: 3600*30/100 = 1080
for heating and gas: 3600*50/100 = 1800
Left money for expense of water and shower = total - (electric and heating)
= 3600-1880
= 720
Percentage of water and shower = 720*100/3600
= 20%
Answer:
Correct!
Step-by-step explanation:
Thank you this is correct :) I took the test
A particle is moving with the given data. Find the position of the particle.
a(t) = [tex]t^{2}[/tex] − 4t + 5, s(0) = 0, s(1) = 20
How do I find s(t)=?
Recall that
[tex]\dfrac{dv(t)}{dt} = a(t) \Rightarrow dv(t) = a(t)dt[/tex]
Integrating this expression, we get
[tex]\displaystyle v(t) = \int a(t)dt = \int(t^2 - 4t + 5)dt[/tex]
[tex]\:\:\:\:\:\:\:= \frac{1}{3}t^3 - 2t^2 + 5t + C_1[/tex]
Also, recall that
[tex]\dfrac{ds(t)}{dt} = v(t)[/tex] or
[tex]\displaystyle s(t) = \int v(t)dt = \int (\frac{1}{3}t^3 - 2t^2 + 5t + C_1)dt[/tex]
[tex]\:\:\:\:\:\:\:= \frac{1}{12}t^4 - \frac{2}{3}t^3 + \frac{5}{2}t^2 + C_1t + C_2[/tex]
Next step is to find [tex]C_1\:\text{and}\:C_2[/tex]. We know that at t = 0, s = 0, which gives us [tex]C_2 = 0[/tex]. At t = 1, s = 20, which gives us
[tex]s(1) = \frac{1}{12}(1)^4 - \frac{2}{3}(1)^3 + \frac{5}{2}(1)^2 + C_1(1)[/tex]
[tex]= \frac{1}{12} - \frac{2}{3} + \frac{5}{2} + C_1 = \frac{23}{12} + C_1 = 20[/tex]
or
[tex]C_1 = \dfrac{217}{12}[/tex]
Therefore, s(t) can be written as
[tex]s(t) = \frac{1}{12}t^4 - \frac{2}{3}t^3 + \frac{5}{2}t^2 + \frac{217}{12}t[/tex]
Determine if the table below represents a linear function. If so, what's the rate of change?
A) No; it's a non-linear function.
B) Yes; rate of change = 4
C) Yes; rate of change = 2
D) Yes; rate of change = 3
Answer:
A
Step-by-step explanation:
Its not a linear function; there is no consistent rate of change between each of the points.
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
18x + 3y = -18
Answer:
y = -6x -6
Step-by-step explanation:
The general form of the equation of a line in the slope-intercept form may be given as
y = mx + c where
m is the slope and c is the intercept
Hence given the equation
18x + 3y = -18
subtract 18x from both sides
3y = -18x - 18
Divide both sides of the equation by 3
y = -6x -6
This is the equation in the slope - intercept form with -6 as the slope and -6 as the intercept
which of the following
is not
a fraction equivalent to 3/4?
a) 6/8
b) 9/12
c) 12/18
d) 21/28
e) 27/36
Answer:
c
Step-by-step explanation:
12/18 = 2/3
Answer:c
Step-y-step explanat:c
After simplification, how many terms will be there in 4x3 + 9y2 - 3x + 2 - 1?
3
6
5
4.
Answer:
Correct answer is 4 because the last 2 terms can be combined:
Step-by-step explanation:
4x3 + 9y2 – 3x + 2 – 1 = 4x3 – 3x + 9y2 + 1.
I need help answering this ASAP
Answer:
x=13
Step-by-step explanation:
f(x) = sqrt(x-11)
The square root must be greater than or equal to zero
sqrt(x-11)≥0
Square each side
x-11≥0
x ≥11
The only answer that is greater than or equal to 11 is
x=13
Write an explicit formula for the sequence.
-4,7,-10,13,-16
Step-by-step explanation:
Sequence is
4
,
7
,
10
,
13
,
16
,
.
.
.
a
1
=
4
,
a
2
=
7
,
a
3
=
10
,
.
.
.
If it is Arithmetic sequence,
a
2
−
a
1
=
a
3
−
a
2
=
a
4
−
a
3
& so on
In the given sum,
a
2
−
a
1
=
7
−
4
=
3
a
3
−
a
2
=
10
−
7
=
3
a
4
−
a
3
=
13
−
10
=
3
Since the difference between the successive terms is same and
hence
common difference
d
=
3
Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.438.43 and a standard deviation of 1.51.5. Using the empirical rule, what percentage of American women have shoe sizes that are between 6.936.93 and 9.939.93
Answer:
The right solution is "68%".
Step-by-step explanation:
The empirical rule is:
[tex]X\sim N(8.43, 1.5)[/tex]
According to the question,
= [tex]P(6.93< \mu < 9.93)[/tex]
= [tex]P(\frac{6.93-8.43}{1.5} < \frac{\mu -8.43}{1.5} < \frac{9.93-8.43}{1.5} )[/tex]
= [tex]P(z(1)-P(z(-1))[/tex]
= [tex]68[/tex] (%)
Thus the above is the right solution.
Write and solve a word problem involving a $145.00 price and a 5.5% sales tax.
Your question is not complete but I guess you want to know the total price to be paid. This will be:
= $145 + (5.5% × $145)
= $145 + (0.055 × $145)
= $145 + $7.975
= $152.975
Match the property with its correct name
match the property to its correct name
A} additive inverse property
B} multiplicative inverse property
C} commutative property of multiplication
D} multiplicative identity
E} commutative property of complement
F} ascending property of multiplication
G} distributive property
H} associative property of multiplication
I} additive identification property
J} zero property
{1} x+(y-z)=(x+y)+z
2} (pq) * 1 = pq
3} (5x)y-5(xy)
4} a+5b = 5b + a
5} a+0=a
6} gh - hg
7} 8 + (-8)=0
8} x * 0 = 0
9} 5 * (1/5)=1
10} 2(a+h)=2a * 2b
Answer:
see below
Step-by-step explanation:
{1} x+(y-z)=(x+y)+z associative property of addition
2} (pq) * 1 = pq D multiplicative identity
3} (5x)y-5(xy) H associative property of multiplication
4} a+5b = 5b + a commutative property of addition
5} a+0=a I additive identification property
6} gh - hg C commutative property of multiplication
7} 8 + (-8)=0 A additive inverse property
8} x * 0 = 0 J zero property
9} 5 * (1/5)=1 B multiplicative inverse property
10} 2(a+b)=2a * 2b G distributive property
Let's see
#a
x+(y-z)=(x+y)+z
Associative property (Addition)#b
(pq) * 1 = pq
Identity property multiplication#c
(5x)y-5(xy)
Associative property of multiplication#d
a+5b = 5b + a
Commutative property of addition#e
a+0=a
identity property of addition#f
gh - hg
Commutative property of multiplication#g
8 + (-8)=0
additive inverse property#h
x * 0 = 0
Zero property#i
5 * (1/5)=1
Inverse property of multiplication#j
2(a+h)=2a * 2b
Distributive propertythank you for the help every one
Answer:
1. 1.66in
2. 6.66in
3. 3.33in
4. 1inch
Step-by-step explanation:
the area of a rectangle is found by multiplying the length times width or the two sides.
5 x 1/3 is about 1.66 inches
5 x 4/3 is about 6.66 inches
5/2 x 4/3 is about 3.33 inches
and 7/6 x 6/7 is 1 inch
WILL GIVE BRAINLIEST TO THE FIRST CORRECT ANSWER!!!
Find the total surface area.
A. 731 cm²
B. 770 cm²
C. 649 cm²
D. 900 cm²
Answer:770
Step-by-step explanation:
There are a total of 6 faces, so we shall calculate the area of each face then add them
=(11×12) +(11×12) +(11×11)+(11×11)+(11×12)+(11+12)
=770cm^2
The total surface area of the given box will be 770 cm² hence correct option will be option (B).
What is surface area?The quantity of space enclosing a three-dimensional shape's exterior is its surface area.
In another meaning, if we say side square then it is an area of the square but for a cuboid, there are 6 faces so the surface area will be external to all 6 surfaces area.
Given that the box has 6 faces with sides
2 face has dimension = 11cm and 12 cm
2 face has dimension = 11cm and 11cm
2 face has dimension = 11cm and 12 cm
Total surface area = 2(11 × 12) + 2(11 × 11) + 2(11 × 12) = 770 cm²
Hence, the total surface area will be 770 cm².
To learn more about surface area,
https://brainly.com/question/2835293
#SPJ2
?????????????please help
Answer:
ok so you take m time h then like you count to h like a b c d e f g h and tgen with that you count 1 2 3 4 5 6 7 till h than you multiply that with 3
find the value of trigonometric ratio
Step-by-step explanation:
tan Z=p/b
=48/14
=24/7
Keep smiling and hope u are satisfied with my answer.Have a good day :)
can anybody help me with this?
Answer:
Option (a)
Step-by-step explanation:
[tex]\sqrt[6]{1000m^{3} n^{12} } = \sqrt[6]{10^{3} } \sqrt[6]{m^{3} } \sqrt[6]{n^{12} } =\\\sqrt{10} \sqrt{m} n^{2} = n^{2} \sqrt{10m}[/tex]
Consider the geometric series modeling Pete's total and the formula for finding the sum of a series. Use this
information to determine the total amount of allowance Pete will be paid over the 16 weeks.
Type the correct answer in the box. Use numerals instead of words.
Over the span of 16 weeks, Pete will be paid a total of $
in allowance.
Answer:
655.35
Step-by-step explanation:
got it right on edmentum
Write seventy-one and one hundred sixty-four thousandths as a decimal number.
Answer:
0.0071164
Step-by-step explanation:
What is the sum of the geometric sequence 1, 3, 9, ... if there are 10 terms? (5 points)
Answer:
[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]
Step-by-step explanation:
There's a handy formula we can use to find the sum of a geometric sequence, and here it is
[tex]S_n = \frac{a_1 (1 - r^n)}{1 - r}[/tex]
The value n represents the amount of terms you want to sum in the sequence. The variable r is known as the common ratio, and a is just some constant. Let's find those values.
First lets visualize this sequence
[tex]n_1 = 1\\n_2 = 1 + 3\\n_3 = 1 + 3 + 3^2\\n_4=1+3+3^2+3^3\\...[/tex]
Okay so there's clearly a pattern here, let's write it a bit more concisely. For each n, starting at 1, we raise 3 to the (n-1) power, add it to what we had for the previous term.
[tex]S_n = \sum{3^{n-1}} = 3^{1 - 1} + 3^{2 - 1} + 3^{3-1} ...[/tex]
Our coefficients of r, and a, are already here! As you can see below, r is just 3, and a is just 1.
[tex]S_n = \sum{a*r^{n-1}}[/tex]
To finish up lets plug these coefficients in and get our sum after 10 terms.
[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]
help pls, i have to get this correct
Answer:
Table C
Step-by-step explanation:
r = j+3
In table A
j = 12 so r = 12+3 = 15 not true so it does not fit the equation
In table B
j = 3 so r = 3+3 = 6 not true so it does not fit the equation
In table C
j = 6 so r = 9+3 = 9 this could be the table
In table D
j = 27 so r = 27+3 = 30 not true so it does not fit the equation
How much bigger is the Sum of first 50 even numbers than the sum of first 50 odd numbers?
Answer:
50
Step-by-step explanation:
Sum Even numbers
n = 50
d = 2
a1 = 2
The last number is
an = a1 + (n-1)d
an = 2 + (50 - 1)*2
an = 2 + 49 * 2
an = 2 + 98
an = 100
Sum of the even numbers
Sum = (a1 + a50)*n/ 2
Sum = (2 + 100)*50/2
sum = 102 * 25
sum = 2550
Sum of the first 50 odd numbers
a1 = 1
n = 50
d = 2
l = ?
Find l
l = a1 + (n - 1)*2
l = 1 + 49*2
l = 99
Sum
Sum = (1 + 99)*50/2
Sum = 2500
The difference and answer is 2550 - 2500 = 50
Rose walks 2 2/3 km in three-fifths of an hour. If her speed remains unchanged, how many kilometres can she walk in one and three quarters of an hour? Express your answer as a mixed number in lowest terms
Answer:
Distance = 7 7/9 Km
Step-by-step explanation:
Given the following data;
Distance = 2⅔ = 8/3 Km
Time = ⅗ hour
First of all, we would find her speed;
Speed = distance/time
Speed = (8/3)/(3/5)
Speed = 8/3 * 5/3
Speed = 40/9 km/h
Next, we would find the distance covered when time = 1¾ hours
Distance = speed * time
Distance = 40/9 * 1¾
Distance = 40/9 * 7/4
Distance = 10/9 * 7
Distance = 70/9
Distance = 7 7/9 Km
find the perimeter of 6 CM 6 CM 6 CM 6 CM
Answer:
P = 24
Step-by-step explanation:
Since all the sides are the same length, the shape is a square.
Multiply all sides by 6.
6 cm x 4 sides = 24
