If you know about the power rule,
d/dw (2w² + 1) = 2 d/dw (w²) = 2 • 2w = 4w
If you have to use the limit definition of the derivative, let f(w) = 2w² + 1. Then
[tex]f'(w)=\displaystyle\lim_{h\to0}\frac{f(w+h)-f(w)}h[/tex]
[tex]f'(w)=\displaystyle\lim_{h\to0}\frac{(2(w+h)^2+1)-(2w^2+1)}h[/tex]
[tex]f'(w)=\displaystyle\lim_{h\to0}\frac{2(w^2+2wh+h^2)-2w^2}h[/tex]
[tex]f'(w)=\displaystyle\lim_{h\to0}\frac{4wh+2h^2}h[/tex]
[tex]f'(w)=\displaystyle\lim_{h\to0}(4w+2h)=\boxed{4w}[/tex]
You score a 95% or your mouth quiz the quiz was out of 60 points how many points did you get
Answer:
It will be 57 points.
Step-by-step explanation:
The three consecutive terms
of an exponential sequence are
the second third and sixth terms
of a linear sequence. Find the
common ratio
the exponential
sequence.
Answer:
1Step-by-step explanation:
The nth term of an exponential sequence is expressed as ar^n-1
The nth term of a linear sequence is expressed as Tn = a + (n-1)d
a is the first term
r is the common ratio
d is the common difference
n is the number of terms
Let the three consecutive terms of an exponential sequence be a/r, a and ar
second term of a linear sequence = a +d
third term of a linear sequence = a + 2d
sixth term of a linear sequence = a + 5d
Now if the three consecutive terms of an exponential sequence are the second third and sixth terms of a linear sequence, this is expressed as;
a/r = a + d ..... 1
a = a + 2d ..... 2
ar = a+ 5d .... 3
From 2: a = a + 2d
a-a= 2d
0 = 2d
d = 0/2
d = 0
Substitute d = 0 into equation 1:
From 1: a/r = a + d
a/r = a+0
a/r = a
Cross multiply
a = ar
a/a = r
1 = r
Rearrange
r = 1
Hence the common ratio of the exponential sequence is 1
The student council at Summerfield High School is making T-shirts to sell for a fundraiser, at a price of $11 apiece. The costs, meanwhile, are $10 per shirt, plus a setup fee of $141. Selling a certain number of shirts will allow the student council to cover their costs. What will the costs be? How many shirts must be sold?
Answer:
$1551 needed to cover the costs and 141 shirts will be sold.
Step-by-step explanation:
If a shirt costs $10 and the council is selling the shirt for $1 more ($11), after selling 141 shirts, they would have made a profit of $1*141=$141. Since there is also a setup fee of $141, the profit would actually be $0. This is when the costs are covered.
C = 10s + 141 (C is cost and s in no. of shirts sold)
s = 141
C = 141*10 + 141 = 1551
Hope this helps!
Question 12
7 pt
Marcus bought school supplies for $42.00, not including tax. If the tax rate was 8.5%,
what was the total cost of the school supplies, including tax?
Answer:
$45.57
Step-by-step explanation:
First, calculate the dollar amount of the tax. This can be done by multiplying the price by the sales tax percentage
$42 × 8.5%= $3.57
Now, add the sales tax amount back to the price.
42 + 3.57 = 45.57
The value of a correlation coefficient, r, is 0.9841. What does the value of the correlation coefficient indicate? Group of answer choices There is weak or no correlation between Yumiko's exercise time and how far she runs. There is a causal relationship between Yumiko's exercise time and how far she runs. There is a strong positive correlation between Yumiko's exercise time and how far she runs. There is a strong negative correlation between Yumiko's exercise time and how far she runs.
Answer: There is a strong positive correlation between Yumiko's exercise time and how far she runs.
Step-by-step explanation:
The correlation Coefficient value measures the relationship between two variables in other it determine the strength of association between them. The Coefficient could take any value between - 1 to + 1 with negative r values depiction negative relationships while positive values means positive relationship. The closer the r value is to either 1 or - 1, the stronger the relationship between hen m
Find the mean, median, mode, and range of the data below:
1)
# Words in Book Titles
2
6
5
5
5
4
4
2
3
2
3
2 1 2
2
Answer:
6.75
Step-by-step explanation:
Find the mean of the set {2,5,5,6,8,8,9,11} .
There are 8 numbers in the set. Add them all, and then divide by 8 .
2 + 5 + 5 + 6 + 8 + 8 + 9 + 118=548=6.75
13 was subtracted form a number and that difference was then divided by 5. After which, that quotient was multiplied by 7. The resulting product was -7. What was the number?
Answer:the number is 8
Step-by-step explanation:
Step 1
Let x be the number 13 was subtracted from so that the difference becomes x-13
i. dividing the resulting difference by 5, then (x-13)/5
ii. Multiplying the quotient by 7 makes the expression become (x-13)/5 x 7
with the product coming to -7 we have our final equation as
(x-13)/5 x 7 = -7
Step 2 -----solving the equation
(x-13)/5 x 7 = -7
Ist divide both sides by 7,
(x-13)/5 =-1
cross multiplying gives
x-13=-5
x= -5+ 13
x=8
the number is 8
Casey started a puzzle yesterday and completed 63 of the pieces. Today, he is
continuing the puzzle and is laying down the pieces at a constant rate. After 13
minutes, he now has 115 pieces put together. After 21 minutes, he has 147 pieces in
total put together. At what rate is he putting this puzzle together today?
7 pieces/min
2 pieces/min
4 pieces/min
9 pieces/min
Answer:
4 pieces a minute
Step-by-step explanation:
115 minus 63 equals 52. 52 is what they did in 13 minutes so 52 divided by1 3 is 4 so 4.
I cant solve this question :(
Answer:
a) tan x = 1
b) tany = 4 + tanx /2tanx - 3
Step-by-step explanation:
a) Given the equation
2(sinx + 2cosx) = sinx +5cosx
Open the bracket
2sinx + 4cosx = sinx +5cosx
Collect like terms
2sinx - sinx = 5cosx - 4cosx
sinx = cos x
Divide both sides by cos x
sinx/cosx = cosx/cosx
tanx = 1
Hence the value of tan x is 1
b) Given the expression
sinxcosy + 3cosxsiny = 2sinxsiny - 4cosxcosy
We are to express tany in terms of tan x
Divide through by cosx cosy
sinxcosy/cosx cosy + 3cosxsiny/cosx cosy = 2sinxsiny/cosx cosy - 4cosxcosy/cosx cosy
sinx/cosx + 3siny/cosy = 2tanxtany - 4
tanx +3tany = 2tanxtany - 4
Collect like terms
tanx - 2tanxtany = -4 - 3tany
- 2tanxtany+3tany = -4 - tanx
tany (-2tanx+3) = -4 - tanx
tan y = -4 - tanx/-2tanx+3
tan y = -(4+tanx)/-(2tanx-3)
tany = 4 + tanx /2tanx - 3
Hence the function of tany in term of tan x is tany = 4 + tanx /2tanx - 3
The sides of four triangles are given...
Answer:
Triangle C is
Step-by-step explanation:
can i get brainliest answer pleaseeee
Evaluate f(-2) if f(x) = x2+ 3
Answer:
f(-2) = 7
Step-by-step explanation:
-2 squared would be a positive 4 then add 3
Answer:
f(-2) = 7
Step-by-step explanation:
becuase yes
Please answer!!!! And show work if possible!!!!!
Step-by-step explanation:
Triangles ABX and DCX are similar.
Since they are similar, AX/DX = AB/DC.
Hence AX/2.8 = 8/4 and AX = 5.6.
how many times will lines 3x+4y=8 and y-5x=2 intersect
Find the slope of a line parallel to each given line. y = − 1 4 x − 2
Identify the pair of points that can represent an increasing function that has a greater rate of change than that of the function Y=8/5x+ 3/5
Answer:
A general lineal equation is written as:
y = a*x +b
Where a is the slope (also called the rate of change) and b is the y-intercept-
For a line that passes through the points (x1, y1) and (x2, y2)
The slope will be:
a = (y2 - y1)/(x2 - x1)
For the line:
Y= (8/5)*x+ 3/5
The slope, or rate of change, is 8/5.
Then we want to find two points (x1, y1) and (x2, y2) such that the slope generated by them is larger to 8/5.
There are a lot of ways to finding these points, a simple way is:
We could define (x1, y1) = (0, 0)
And (x2, y2) = (5, 9)
Then the rate of change of the line that passes through these two points will be
a = (9 - 0)/(5 - 0) = 9/5
Which is larger than 8/5, as we wanted.
April has five times as many clear marbles as blue marbles she has 4 times as many blue marbles as red marbles she has three red marbles how many blue and clear marble does she have altogether
Answer:
12 blue marbles
60 clear marbles
Step-by-step explanation:
From the information given:
Let the red marble be = r
the blue marble = b; & the clear marbles be c
April has five times as many clear marbles as blue marbles.
i.e
5c as b
She has 4 times as many blue marbles as red marbles;
i.e. 4b as r
She has 3 red marbles
i.e. r = 3
If r = 3
Then; 4 times as many blue as r will be:
= 4 × 3
= 12 blue marbles
If b = 12; then 5 times as many clear marbles as blue marbles will be:
= 5 × 12
= 60 clear marbles
Does Anyone Know This
Answer:
1 g-h
2 g^2-h
3 gh
4 g+h
5 h-g
6 g+h^2
Step-by-step explanation:
The local Farm Market sells peppers at five for $2.25. Complete the rate table.
The proportionality is 0.45, then the equation is C = 0.45 n. The number of peppers you buy for $20 will be 44.44. Then the table is completed below.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
Let 'C' be the cost and 'n' be the number of peppers. Then the proportionality is given as,
C ∝ kn
At n = 5, the cost C = 2.25, then we have
2.25 = k (5)
k = 2.25 / 5
k = 0.45
Then the equation is given as,
C = 0.45 n
The number of peppers you buy for $20 will be given as,
20 = 0.45 n
n = 44.44
Then the table is completed below.
Number of peppers Cost
1 $0.45
2 $0.90
3 $1.35
4 $1.80
5 $2.25
10 $4.50
15 $6.75
20 $9
100 $45
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
#SPJ2
What numbers are prime numbers?
Answer:
C
Step-by-step explanation:
all four numbers in c do not have any other factors other than 1 and itself. All quotients of the number are not whole numbers.
expanded form of 54.98
[tex]x^a=y^b=z^c \\xyz=1\\ab+bc+ca=?[/tex]
Answer:
ab+bc+ca=0
Step-by-step explanation:
We are given:
[tex]x^a=y^b=z^c[/tex]
xyz=1
Separating equations:
[tex]x^a=z^c[/tex]
[tex]y^b=z^c[/tex]
Solving the first equation for x:
[tex]\displaystyle x=z^\frac{c}{a}[/tex]
Solving the second equation for y:
[tex]\displaystyle y=z^\frac{c}{b}[/tex]
Substituting in
xyz=1:
[tex]\displaystyle z^\frac{c}{a}z^\frac{c}{b}z=1[/tex]
Adding the exponents:
[tex]\displaystyle z^{\frac{c}{a}+\frac{c}{b}+1}=1[/tex]
Since [tex]1=z^0[/tex]:
[tex]\displaystyle z^{\frac{c}{a}+\frac{c}{b}+1}=z^0[/tex]
The base is z on both sides so we get rid of them:
[tex]\displaystyle \frac{c}{a}+\frac{c}{b}+1=0[/tex]
Multiplying by ab:
bc+ac+ab=0
Reordering:
ab+bc+ca=0
if
f(x)=3x+1 and f^-1= x-1/3,
then f(2)=
Answer:
f(2) = 7Step-by-step explanation:
f(x) = 3x + 1 ⇒ f(2) = 3×2 + 1 = 6 + 1 = 7
Pls help I'm in 4th grade and I was sick when we learned this pls pls help :( PLS
Answer:
He needs to cut 20.
Step-by-step explanation:
Help me please !!!!!
Answer:
a = 1
Step-by-step explanation:
[tex]\frac{2}{3} (9x - 3) = 2(3x - a)[/tex]
One must simplify this expression, by distributing. In order to find a solution, where x has infinite solutions, one must make this equation an identity. That means that the equation will hold true, no matter what value of x is plugged in.
[tex]\frac{2}{3} (9x - 3) = 2(3x - a)[/tex]
Distribute;
6x - 2 = 6x - 2a
Inverse operations;
6x - 2 = 6x - 2a
-6x -6x
-2 = -2a
1 = a
For this equation to be true no matter what, a must equal 1.
Answer:
1
Step-by-step explanation:
can anyone help me please? thanks ^^
Answer:
bruh im learning this right now, im pretty sure its ASA
what is the average of 110 and 93 ??????
Answer:
101.5
Step-by-step explanation:
Pleaseeeee helppp !!!!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
26
Step-by-step explanation:
just add a few points
does anyone know what the. distance would be ?? plz answer asap only if you are correct:)
Answer:
6 units :)
Step-by-step explanation:
Write an express for the perimeter of the figure shown by combing like terms.
Answer:
21w+3
Step-by-step explanation:
1) 9w+5+5w+7w-2
2) 9+5+7=21.
3) 5-2=3
I’ll give brainlest to you if you answer this question correctly!
Answer:
Step-by-step explanation:
we can take any value as its two variable equation.
(-3,0) (0,9) (-2,3)
put these numbers on a graph
I hope this helps