Find the sum of ∑3/k=0 k^2
Answer:
[tex]14[/tex]
Step-by-step explanation:
Given
[tex]\displaystyle \sum_{k=0}^3k^2[/tex]
Let's break down each part. The input at the bottom, in this case [tex]k=0[/tex], is assigning an index [tex]k[/tex] at a value of [tex]0[/tex]. This is the value we should start with when substituting into our equation.
The number at the top, in this case 3, indicates the index we should stop at, inclusive (meaning we finish substituting that index and then stop). The equation on the right, in this case [tex]k^2[/tex], is the equation we will substitute each value in. After we substitute our starting index, we'll continue substituting indexes until we reach the last index, then add up each of the outputs produced.
Since [tex]k=0[/tex] is our starting index, start by substituting this into [tex]k^2[/tex]:
[tex]0^2=0[/tex]
Now continue with [tex]k=1[/tex]:
[tex]1^1=1[/tex]
Repeat until we get to the ending index, [tex]k=3[/tex]. Remember to still use [tex]k=3[/tex] before stopping!
Substituting [tex]k=2[/tex]:
[tex]2^2=4[/tex]
Substituting [tex]k=3[/tex]:
[tex]3^2=9[/tex]
Since 3 is the index we end at, we stop here. Now we will add up each of the outputs:
[tex]0+1+4+9=\boxed{14}[/tex]
Therefore, our answer is:
[tex]\displaystyle \sum_{k=0}^3k^2=0+1+4+9=\boxed{14}[/tex]
Answer:
14
Step-by-step explanation:
∑3/k=0 k^2
Let k=0
0^2 =0
Let k = 1
1^2 =1
Let k =2
2^2 = 4
Let k = 3
3^2 = 9
0+1+4+9 = 14
use undetermined coefficient to determine the solution of:y"-3y'+2y=2x+ex+2xex+4e3x
First check the characteristic solution: the characteristic equation for this DE is
r ² - 3r + 2 = (r - 2) (r - 1) = 0
with roots r = 2 and r = 1, so the characteristic solution is
y (char.) = C₁ exp(2x) + C₂ exp(x)
For the ansatz particular solution, we might first try
y (part.) = (ax + b) + (cx + d) exp(x) + e exp(3x)
where ax + b corresponds to the 2x term on the right side, (cx + d) exp(x) corresponds to (1 + 2x) exp(x), and e exp(3x) corresponds to 4 exp(3x).
However, exp(x) is already accounted for in the characteristic solution, we multiply the second group by x :
y (part.) = (ax + b) + (cx ² + dx) exp(x) + e exp(3x)
Now take the derivatives of y (part.), substitute them into the DE, and solve for the coefficients.
y' (part.) = a + (2cx + d) exp(x) + (cx ² + dx) exp(x) + 3e exp(3x)
… = a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)
y'' (part.) = (2cx + 2c + d) exp(x) + (cx ² + (2c + d)x + d) exp(x) + 9e exp(3x)
… = (cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)
Substituting every relevant expression and simplifying reduces the equation to
(cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)
… - 3 [a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)]
… +2 [(ax + b) + (cx ² + dx) exp(x) + e exp(3x)]
= 2x + (1 + 2x) exp(x) + 4 exp(3x)
… … …
2ax - 3a + 2b + (-2cx + 2c - d) exp(x) + 2e exp(3x)
= 2x + (1 + 2x) exp(x) + 4 exp(3x)
Then, equating coefficients of corresponding terms on both sides, we have the system of equations,
x : 2a = 2
1 : -3a + 2b = 0
exp(x) : 2c - d = 1
x exp(x) : -2c = 2
exp(3x) : 2e = 4
Solving the system gives
a = 1, b = 3/2, c = -1, d = -3, e = 2
Then the general solution to the DE is
y(x) = C₁ exp(2x) + C₂ exp(x) + x + 3/2 - (x ² + 3x) exp(x) + 2 exp(3x)
help with 1 b please. using ln.
Answer:
[tex]\displaystyle \frac{dy}{dx} = \frac{1}{(x - 2)^2\sqrt{\frac{x}{2 - x}}}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Terms/CoefficientsFactoringExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Algebra II
Natural logarithms ln and Euler's number eLogarithmic Property [Exponential]: [tex]\displaystyle log(a^b) = b \cdot log(a)[/tex]Calculus
Differentiation
DerivativesDerivative NotationImplicit DifferentiationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
*Note:
You can simply just use the Quotient and Chain Rule to find the derivative instead of using ln.
Step 1: Define
Identify
[tex]\displaystyle y = \sqrt{\frac{x}{2 - x}}[/tex]
Step 2: Rewrite
[Function] Exponential Rule [Root Rewrite]: [tex]\displaystyle y = \bigg( \frac{x}{2 - x} \bigg)^\bigg{\frac{1}{2}}[/tex][Equality Property] ln both sides: [tex]\displaystyle lny = ln \bigg[ \bigg( \frac{x}{2 - x} \bigg)^\bigg{\frac{1}{2}} \bigg][/tex]Logarithmic Property [Exponential]: [tex]\displaystyle lny = \frac{1}{2}ln \bigg( \frac{x}{2 - x} \bigg)[/tex]Step 3: Differentiate
Implicit Differentiation: [tex]\displaystyle \frac{dy}{dx}[lny] = \frac{dy}{dx} \bigg[ \frac{1}{2}ln \bigg( \frac{x}{2 - x} \bigg) \bigg][/tex]Logarithmic Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle \frac{1}{y} \ \frac{dy}{dx} = \frac{1}{2} \bigg( \frac{1}{\frac{x}{2 - x}} \bigg) \frac{dy}{dx} \bigg[ \frac{x}{2 - x} \bigg][/tex]Chain Rule [Basic Power Rule]: [tex]\displaystyle \frac{1}{y} \ \frac{dy}{dx} = \frac{1}{2} \bigg( \frac{1}{\frac{x}{2 - x}} \bigg) \bigg[ \frac{2}{(x - 2)^2} \bigg][/tex]Simplify: [tex]\displaystyle \frac{1}{y} \ \frac{dy}{dx} = \frac{-1}{x(x - 2)}[/tex]Isolate [tex]\displaystyle \frac{dy}{dx}[/tex]: [tex]\displaystyle \frac{dy}{dx} = \frac{-y}{x(x - 2)}[/tex]Substitute in y [Derivative]: [tex]\displaystyle \frac{dy}{dx} = \frac{-\sqrt{\frac{x}{2 - x}}}{x(x - 2)}[/tex]Rationalize: [tex]\displaystyle \frac{dy}{dx} = \frac{-\frac{x}{2 - x}}{x(x - 2)\sqrt{\frac{x}{2 - x}}}[/tex]Rewrite: [tex]\displaystyle \frac{dy}{dx} = \frac{-x}{x(x - 2)(2 - x)\sqrt{\frac{x}{2 - x}}}[/tex]Factor: [tex]\displaystyle \frac{dy}{dx} = \frac{-x}{-x(x - 2)^2\sqrt{\frac{x}{2 - x}}}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = \frac{1}{(x - 2)^2\sqrt{\frac{x}{2 - x}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
please help! 50 points!
Answer:
a) forming a bell
b) 5
c) 4.7
d) mean
is the correct answer
pls mark me as brainliest
A manufacturer of industrial solvent guarantees its customers that each drum of solvent they ship out contains at least 100 lbs of solvent. Suppose the amount of solvent in each drum is normally distributed with a mean of 101.8 pounds and a standard deviation of 3.76 pounds.
Required:
a. What is the probability that a drum meets the guarantee? Give your answer to four decimal places.
b. What would the standard deviation need to be so that the probability a drum meets the guarantee is 0.99?
Answer:
The answer is "0.6368 and 0.773".
Step-by-step explanation:
The manufacturer of organic compounds guarantees that its clients have at least 100 lbs. of solvent in every fluid drum they deliver. [tex]X\ is\ N(101.8, 3.76)\\\\P(X>100) =P(Z> \frac{100-101.8}{3.76}=P(Z>-0.47))[/tex]
For point a:
Therefore the Probability =0.6368
For point b:
[tex]P(Z\geq \frac{100-101.8}{\sigma})=0.99\\\\P(Z\geq \frac{-1.8}{\sigma})=0.99\\\\1-P(Z< \frac{-1.8}{\sigma})=0.99\\\\P(Z< \frac{-1.8}{\sigma})=0.01\\\\z-value =0.01\\\\area=-2.33\\\\ \frac{-1.8}{\sigma}=-2.33\\\\ \sigma= \frac{-1.8}{-2.33}=0.773[/tex]
Answer as soon as you can. a. 162 comes just after b. What comes just before 182. lies in between 99 and 101. c.
Answer:
a. 161
b. 181
c. 100
Step-by-step explanation:
a. 162 comes just after 161 (160, 161, 162, 163...)
b. 181 comes just before 182 (180, 181, 182, 183...)
c. 100 is between 99 and 101 (98, 99, 100, 101, 102...)
If 8x+5(3+x)-a=15+5x, then a = ?
Answer:
a = 8x
if you want to find x also, then x = a/8
Step-by-step explanation:
PLEAZE HELPPPPPPPSPPSPAP
Answer:
Step-by-step explanation:
345ftyfthftyft.plk,k,
Answer:
Hello,
Anwser is C
Step-by-step explanation:
[tex]y=log_9(12x)\\\\9^y=12x\\\\9^x=12y\ inverting \ x \ and \ y \\\\y=\dfrac{9^x}{12} \\[/tex]
What does si mean in temperature
Answer:
The kelvin (abbreviation K), also called the degree Kelvin (abbreviation, o K), is the SI unit of temperature. One Kelvin is 1/273.16 (3.6609 x 10 -3 ) of the thermodynamic temperature of the triple point of pure water (H 2 O). The ampere (abbreviation, A) is the SI unit of electric current.
Answer:
kelvin is si unit of tempreature
Help me please thanks guys
Answer:
B, D, F
Step-by-step explanation:
In a rational exponent, the numerator is an exponent, and the denominator becomes the index of the root.
[tex]a^{\frac{m}{n}} = \sqrt[n] {a^m}[/tex]
Answer: B, D, F
Terrell loves to listen to music, so he buys a subscription to a music-streaming service. He pays $4.99 each month. How much does the streaming service cost per year?
PLEASE HELP
Solve the equation for y. Identify the slope and y-intercept then graph the equation.
-3y=3x-9
Y=
M=
B=
Please Include a picture of the graph and show your work if you can
9514 1404 393
Answer:
y = -x +3
m = -1
b = 3
Step-by-step explanation:
To solve the given equation for y, divide by the coefficient of y.
(-3y)/(-3) = (3x -9)/(-3)
y = -x +3
__
The slope is the x-coefficient, M = -1.
__
The y-intercept is the added constant, B = 3.
__
Both equations are graphed in the attachment. Texture has been added to the original so you can see the graphs are the same line.
Need the answer please, soon as possible
9514 1404 393
Answer:
(d) 27.4%
Step-by-step explanation:
The desired percentage is ...
(juniors for Kato)/(total juniors) × 100%
= 129/(129 +194 +147) × 100%
= (129/470) × 100% ≈ 27.4%
About 27.4% of juniors voted for Kato.
What is the volume of the cylinder below?
Height 4
Radius 7
Answer:
V ≈ 615.75
r Radius 7
h Height 4
Calls to a customer service center last on average 2.3 minutes with a standard deviation of 2 minutes. An operator in the call center is required to answer 76 calls each day. Assume the call times are independent.
What is the expected total amount of time in minutes the operator will spend on the calls each day?
What is the standard deviation of the total amount of time in minutes the operator will spend on the calls each day? Give your answer to four decimal places.
What is the approximate probability that the total time spent on the calls will be less than 166 minutes? Give your answer to four decimal places. Use the standard deviation as you entered it above to answer this question.
What is the value c such that the approximate probability that the total time spent on the calls each day is less than c is 0.95? Give your answer to four decimal places. Use the standard deviation as you entered it above to answer this question.
Answer:
The expected total amount of time in minutes the operator will spend on the calls each day is of 174.8 minutes.
The standard deviation of the total amount of time in minutes the operator will spend on the calls each day is of 17.4356 minutes.
0.3085 = 30.85% approximate probability that the total time spent on the calls will be less than 166 minutes.
The value c such that the approximate probability that the total time spent on the calls each day is less than c is 0.95 is [tex]c = 203.4816[/tex]
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
n instances of a normally distributed variable:
For n instances of a normally distributed variable, the mean is:
[tex]M = n\mu[/tex]
The standard deviation is:
[tex]s = \sigma\sqrt{n}[/tex]
Calls to a customer service center last on average 2.3 minutes with a standard deviation of 2 minutes.
This means that [tex]\mu = 2.3, \sigma = 2[/tex]
An operator in the call center is required to answer 76 calls each day.
This means that [tex]n = 76[/tex]
What is the expected total amount of time in minutes the operator will spend on the calls each day?
[tex]M = n\mu = 76*2.3 = 174.8[/tex]
The expected total amount of time in minutes the operator will spend on the calls each day is of 174.8 minutes.
What is the standard deviation of the total amount of time in minutes the operator will spend on the calls each day?
[tex]s = \sigma\sqrt{n} = 2\sqrt{76} = 17.4356[/tex]
The standard deviation of the total amount of time in minutes the operator will spend on the calls each day is of 17.4356 minutes.
What is the approximate probability that the total time spent on the calls will be less than 166 minutes?
This is the p-value of Z when X = 166.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
For this problem:
[tex]Z = \frac{X - M}{s}[/tex]
[tex]Z = \frac{166 - 174.8}{17.4356}[/tex]
[tex]Z = 0.5[/tex]
[tex]Z = 0.5[/tex] has a p-value of 0.6915.
1 - 0.6915 = 0.3085.
0.3085 = 30.85% approximate probability that the total time spent on the calls will be less than 166 minutes.
What is the value c such that the approximate probability that the total time spent on the calls each day is less than c is 0.95?
This is X = c for which Z has a p-value of 0.95, so X = c when Z = 1.645. Then
[tex]Z = \frac{X - M}{s}[/tex]
[tex]1.645 = \frac{c - 174.8}{17.4356}[/tex]
[tex]c - 174.8 = 1.645*17.4356[/tex]
[tex]c = 203.4816[/tex]
The value c such that the approximate probability that the total time spent on the calls each day is less than c is 0.95 is [tex]c = 203.4816[/tex]
Can someone please help me with this math problem
We have [tex]f\left(f^{-1}(x)\right) = x[/tex] for inverse functions [tex]f(x)[/tex] and [tex]f^{-1}(x)[/tex]. Then if [tex]f(x) = 2x+5[/tex], we have
[tex]f\left(f^{-1}(x)\right) = 2f^{-1}(x) + 5 = x \implies f^{-1}(x) = \dfrac{x-5}2[/tex]
Then
[tex]f^{-1}(8) = \dfrac{8-5}2 = \boxed{\dfrac32}[/tex]
express 111 as a sum of two primes
Answer:
2 + 109 = 111
Step-by-step explanation:
.............
What is the dimension of the null space Null (A) of A =
Answer:
the nullity of a matrix A is the demision of its null space:nullity A = dim (n(A).
Find the area of the shape shown below.
Answer:
28 units²
Step-by-step explanation:
Area of trapezoid =
2(8 + 4)/2 = 12
Area of rectangle =
2 x 8 = 16
16 + 12 = 28
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
There is 3m wide path around a circular cricket ground having the diameter of 137 m. Find the area of the path.
Answer:
1320 m^2
Step-by-step explanation:
area of ground = π r ^2
= (22/7) × (137/2)^2
= 14,747.0714286 m^2
area of ground and path
=( 22/7)(143/2)^2
= 16,067.0714286 m^2
area of path
=16,067.0714286 -14,747.0714286
= 1320 m^2
note :
r = radius = diameter /2
area of a circle = π r^2
diameter of circle created with path and ground = 137 + 2 × width of path
= 137 + 2× 3 = 143 m
what is the area of the triangle ://
Answer:
The area of a triangle is:
Area = 1/2(bh)
Area = 1/2(70)
Area = 35 square inches
Let me know if this helps!
Coefficient and degree of the polynomial
Answer:
The leading coefficient is -8 as it is a mix of x and cardinal, if it was x alone then it wouldn't be the coefficient, we would use the next number shown.
If it was just a number and no x then it would still be the coefficient.
The degree is 9 as it is the highest power shown.
Step-by-step explanation:
See attachment for examples
What is the sum of the infinite geometric series?
Answer:
-6
Step-by-step explanation:
a1= -3
r= -(3/2)/-3 = 0.5
r>-3
s= a1/1-r
= -3/1-0.5
=-6
Question 17 of 25
Solve the inequality. Enter the answer as an inequality that shows the value of
the variable; for example f>7, or 6 < w. Where necessary, use <= to write s
and use >= to write .
V-(-5) <-9
Answer here
I
SUBMIT
Answer:
v-(-5)<-9
v- remove brackets -5
v- -5= -4 +5 ( opposite operation)
v- = -4
v< -4
The figure shows an equilateral triangle with its sides as indicated. find the length of each side of the triangle .
I Will Mark Brainliest
Answer:
21
Step-by-step explanation:
All three sides are equal
2x-7 = x+y-9 = y+5
Using the last two
x+y-9 = y+5
Subtract y from each side
x+y-9-y = y+5-y
x-9 = 5
Add 9 to each side
x -9+9 = 5+9
x=14
We know the side length is
2x-7
2(14) -7
28-7
21
The side length is 21
please help I have 3 mins left
Answer:
the first one is 3.7 x 10^-4
and the second one is 3.7 x 10^4
explanation:
when we have decimals we are going backward,
therefore "0.00037" would be a negative number
to find the scientific notation form, we have to move the decimal over to the left untill we get 3.7
it took 4 moves to the right to get to 3.7, and since were dealing with decimals it will be negative,
so the first one is 3.7 x 10^4
the second one however is not a decimal so it will be a positive exponent.
now remember that there is always a decimal after a number we might just not see it.
so, going from the very end of the number it takes us 4 moves to the left to get to 3.7
so,
the second one will be 3.7 x 10^4
hope this helped :)
The sum of 'n' terms of an arithmetic sequence is 4n^2+3n. What is the first term, the common difference, and the sequence?
Answer:
d=8 and a=7
Step-by-step explanation:
The sum of a arithmetic sequence is given by (n/2)*(2a+(n-1)d). Comparing coefficients with the given Sn, we have; a-d/2=3 and d/2=4, d=8 and a=7. The sequence is 7, 15, 23, 31, 39
7. Solve for x: x/6 - y/3 = 1
Please give steps!
What year was it when I was a freshman if I graduated this year(2021)?
Answer:
2019
Step-by-step explanation:
I am assuming you mean graduated from high school. If that's the case it's 2019. Sophmore year means 9th grade. which is 2019!
Here's the result of this question
The point (-2,7) has undergone the following transformations:
1. Translated 1 unit up and 4 units left
Then
2. Reflected about the c-axis
Then
3. Rotated 90° anticlockwise about the origin
A) Its final coordinates are (3,-1)
B) Its final coordinates are (8,-6)
C) Its final coordinates are (-8,6)
D) Its final coordinates are (-3,1)
Answer:
B) Its final coordinates are (8,-6)
Step-by-step explanation:
1. Translated 1 unit up and 4 units left
(-2,7) becomes (-6, 8)
2. Reflected about the x-axis
(-6,8) becomes (-6, -8)
3. Rotated 90° anticlockwise about the origin
(-6, -8) becomes (8, -6) because when rotating 90 degrees anticlockwise about the origin, point A (x,y) becomes point A' (-y,x). In other words, switch the x and y and make y negative.
