[tex]\displaystyle \text{Find the summation given that } f(x) = x^3 \text{ and } \triangle x_i = 2 + \frac{i}{4}. \\ \\\[ \sum_{i = 1}^{4} x^3 \times \triangle x[/tex]
Answers
Answer:
Click the picture and u will see the answer.
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![[tex]\displaystyle \text{Find The Summation Given That } F(x) = X^3 \text{ And } \triangle X_i = 2 +](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/e9tK1OFDIlNljA6V6klEYtFpGw68BDme.jpeg)
The summation of the given function from 1 to 4 is 10.5x³.
The given parameters:
[tex]\Sigma \ x^3 \times \Delta x, \ \ \ \Delta x = 2 + \frac{i}{4} \\\\[/tex]
The summation of the given function from i = 1, to i = 4, is calculated as follows;
[tex]\Sigma \ x^3 \times \Delta x = x ^3 (2 + \frac{1}{4} ) + x ^3 (2 + \frac{2}{4} ) + x ^3 (2 + \frac{3}{4} ) + x ^3 (2 + \frac{4}{4} )\\\\= x^3(10\frac{1}{2} )\\\\=\frac{21}{2} x^3\\\\= 10.5x^3[/tex]
Thus, the summation of the given function from 1 to 4 is 10.5x³.
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Related Questions
A town’s population increases at a constant rate. In 2010 the population was 56,000. By 2012 the population had increased to 81,000. If this trend continues, predict the population in 2016.
Answers
The approximate population in 2016 is 91, 604 population
Let the time taken by the population to increase be "t"Let the number of the population be PThe exponential equation representing the statement is [tex]P=P_0e^t[/tex]
If in 2010 the population was 56,000, then at t = 0, P0 = 56000Substituting into the formula will give:
P = 56000If by 2012 the population had increased to 81,000, then:
81000 = 56000e^12k
81000/56000 = e^12k
1.4464 = e^12k
ln1.4464 = 12k
0.3691 = 12k
k = 0.3690/12
k = 0.03076
Get the prediction of the population in 2016.
[tex]P = 56000e^{16(0.03076)}\\P=56000e^{0.49213}\\P = 56000(1.6357)\\P = 91,603.70[/tex]
Hence the approximate population in 2016 is 91, 604 population
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Rewrite in simplest terms: (-9x + 7y) - (-9x + 5y)
Answers
Answer:
3y
Step-by-step explanation:
(-9x+7y)-(-9x+5y)
Distribute the negative(-)
-9x+7y+9x-5y
-9 and 9 cancel each other
3y
The simplest terms of the given expression (-9x + 7y) - (-9x + 5y) will be 2y.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
As per the given expression,
(-9x + 7y) - (-9x + 5y)
Open the bracket
-9x + 7y + 9x - 5y
Combined likely terms together
-9x + 9x + 7y - 5y
0 + 2y = 2y
Hence "The formula (-9x + 7y) - (-9x + 5y) will have 2y as its simplest terms".
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What percent of 111 is 94?
Answers
Answer:
I’d say 84.68%
A new health drink has 190% of the recommended daily allowance (RDA) for a certain vitamin. The RDA for this vitamin is 50 mg. How many milligrams of the vitamins are in the drink?
Answers
There is 95mg of vitamins in the drink
Percentages and proportionIf a new health drink has 190% of the recommended daily allowance (RDA) for certain vitamins and the RDA for this drink is 50mg.
The amount of milligrams of the vitamins in the drink is expressed as shown:
A = 190 % of 50mg
A = 1.9 * 50
A = 95mg
Hence there is 95mg of vitamins in the drink
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Answer:
There is 95mg of vitamins in the drink
Company A makes 20 notebooks in 4 hours. Company B make 28 notebooks in
3 hours. Write a statement comparing the number of notebooks made per
hour.
Answers
What of the following exponential functions is represented by the data in the table?
A) f(x)=(1/3)^3
B) f(x)=3^x
C) f(x)=x^3
D) f(x)=x1/3
Answers
Answer:
f(x) = ( 1/3) ^ (x)
Step-by-step explanation:
The function is
f(x) = (1/3) ^ (x)
When x = 1 f(x) = 1/3
when x=2 f(x) = 1/9
When x = -1 f(x) = ( 1/3) ^ -1 = 3/1 =3
Answer:
f(x)=(1/3)^x
Step-by-step explanation:
Plug in the given values of x in the function above and match the answers with f(x) which is y.
If a = 0.3 and b =0.5, what is the value of a+b?
A. [tex]\frac{8}{10}[/tex]
B. [tex]\frac{8}{9}[/tex]
C. [tex]\frac{80}{99}[/tex]
D. [tex]\frac{88}{100}[/tex]
Answers
Answer=
D
Step-by-step explanation
because of the dot/line at the top of the number it means it is a continuous same number
for example, 0.3 with a dot/line on top means it is 0.333333...
so 0.55...+0.33...=0.88...
and as it is a decimal that is in the range of 1-100 its like a percentage so it is 88/100
1
10
is for Internet service, and
2
9
is for utilities. If the rest of the total amount is for food, how much does Karen have for food?
In 2004 5,545 woman were participating in college lacrosse and in 2008 6,830 woman joined was is the rate of change
Answers
Answer:
321.25 per year
Step-by-step explanation:
In 2004 they had 5,545
In 2008 they had 6,830
Subtract them both and you get 4 years, 1285 people
Divide 1285 by 4 and get 321.25 per year.
what is equivalent to 1 and 5/6?? and what is 3 and 1/6 equivalent to?
Answers
Answer: 1.833 and 3.167
Step-by-step explanation:
1 and 5/6 is demonstrated with this equation:
[tex]1 + \frac{5}{6} , \\\\\frac{6}{6} + \frac{5}{6} = \frac{11}{6} = 1.833\\[/tex]
3 and 1/6 is demonstrated with this equation:
[tex]3 + \frac{1}{6}, \\\\\frac{18}{6} + \frac{1}{6} = \frac{19}{6} = 3.167[/tex]
Planet Q Is 3.6 x 10^6km
Planet R Is 1.6 x 10^7km
What Is The Shortest Distance Between Planet Q And R (Answer In Standard Form)
I've Been Stuck On This Question For A Vast Amount Of Time.
Answers
Answer:
1.64×10⁷ km
Step-by-step explanation:
We know this is a triangle rectangle, so we apply the Pythagorean Theorem
QR=sqrt(PR²+PQ²)
Solving it, we will encounter in
sqrt(2.56×10¹⁴+1.296×10¹³)
to solve it, we need to bring the two numbers at the same power of ten, so we move 1.296 of one place to the left:
sqrt(2.56×10¹⁴+0.1296×10¹⁴)
we can now add the two numbers:
sqrt(2.6896×10¹⁴)
to solve this, we do the square root of 2.6896 and divide 14 by two (the index of the root is 2, so for roots' properties we can divide 14 by 2 - the index)
which gives us
1.64×10⁷
A can has a radius of 1.5 inches and a height of 3inches. Which of the following best represents the volume of the can .
Answers
The expression which best represents the volume of the can in discuss as evaluated from the formula; V = π r² h and as required is; 6.75π.
What is the volume of the can as described?It follows from the task content that the volume of the can whose radius is; 1.5 inches and height is; 3 inches is to be determined.
It is noteworthy to know that the volume of a can often the shape of a cylinder is given by the formula;
Volume, V = π r² h.
where, radius, r = 1.5 in.
height, h = 3 in.
Therefore, we have that the volume of the can can be evaluated as;
Volume, V = π × ( 1.5 )² × 3
Volume, V = 6.75 π.
On this note, the best representation of the volume of a can having dimensions as described is; 6.75π.
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5. The combined perimeter of a circle and a square is 16. Find the dimensions of the circle and square
that produce a minimum total area.
Answers
The dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively
Represent the side length of the square with s, and the radius of the circle with r.
So, the perimeter (P) and the area (A) of the shape are:
[tex]P =4s + 2\pi r[/tex]
[tex]A =s^2 + \pi r^2[/tex]
The perimeter is 16. So, we have:
[tex]4s + 2\pi r = 16[/tex]
Divide through by 4
[tex]s + 0.5\pi r = 4[/tex]
Make s the subject
[tex]s = 4 - 0.5\pi r[/tex]
Substitute [tex]s = 4 - 0.5\pi r[/tex] in [tex]A =s^2 + \pi r^2[/tex]
[tex]A = (4 - 0.5\pi r )^2 + \pi r^2[/tex]
Expand
[tex]A = 16 - 4\pi r + 0.25(\pi r)^2 + \pi r^2[/tex]
This gives
[tex]A = 16 - 4\pi r + (0.25\pi^2 + \pi )r^2[/tex]
Differentiate with respect to r
[tex]A' = 0 - 4\pi + 2(0.25\pi^2 + \pi )r[/tex]
[tex]A' = - 4\pi + 2(0.25\pi^2 + \pi )r[/tex]
Set to 0
[tex]- 4\pi + 2(0.25\pi^2 + \pi )r =0[/tex]
Add 4pi to both sides
[tex]2(0.25\pi^2 + \pi )r =4\pi[/tex]
Divide both sides by 2
[tex](0.25\pi^2 + \pi )r =2\pi[/tex]
Make r the subject
[tex]r =\frac{2\pi}{(0.25\pi^2 + \pi )}\\[/tex]
Factor out pi
[tex]r =\frac{2\pi}{\pi(0.25\pi + 1 )}[/tex]
Cancel out the common factors
[tex]r =\frac{2}{0.25\pi + 1 }[/tex]
Express pi as 3.14
[tex]r =\frac{2}{0.25\times 3.14 + 1 }[/tex]
[tex]r =\frac{2}{1.785}[/tex]
Divide
[tex]r =1.12[/tex]
Recall that:
[tex]s = 4 - 0.5\pi r[/tex]
This gives
[tex]s =4 -0.5 \times \pi \times 1.12[/tex]
This gives
[tex]s =4 -0.5 \times 3.14 \times 1.12[/tex]
[tex]s =2.24[/tex]
Hence, the dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively
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Pure acid is to be added to a 10% acid solution to obtain 90L of 81% solution. What amounts of each should be used?
How many liters of 100% pure acid should be used to make the solution?
Answers
Answer:
Step-by-step explanation:
let X be the quantity of 100% acid
let Y be the quantity of 10% acid
X + Y = 90
Y = 90 - X
X(100) + Y(10) = 90(81)
X(100) + (90 - X)(10) = 90(81)
100X + 900 - 10X = 7290
90X = 6390
X = 71 L
Elton has 2 jobs and can work at most 32 total hours per week. He makes $9.00 per hour as a dog walker and $10.00 per hour as a store clerk. He wants to earn a minimum of $200 per week. Which is system of inequalities can be solved to find the possible combination of hours worked at each job that will help him to reach his goal?
Answers
Answer:
3-4 days
Step-by-step explanation:
So, if Elton works at each job for 5 hours, he will get $95. He would keep on doing this for 2-3 days. He would get $190 in total. The next day, he could get his $10 for being a store clerk. 190 + 10 = 200. And that's how Elton would make $200 in less than one week!
A triangular prism is 18 centimeters long and has a triangular face with a base of 12 centimeters and a height of 8 centimeters. The other two sides of the triangle are each 10 centimeters.
What is the surface area of the triangular prism?
Answers
Answer:
672 sq cm
Step-by-step explanation:
Each triangular base is 1/2 (12 * 8) or 48, making them = 96.
One of the sides is 12 x 18 = 216
The other 2 sides are 10 x 18 = 180 x 2 = 360
Add them all together to get 672 sq cm
Which triangle is a 30°-60°-90° triangle?
Answers
Answer:
-90
Step-by-step explanation:
it's right
Answer:
The first one.
Step-by-step explanation:
I took the quiz and got a 100, hope this helps :))
Nadia is a stockbroker. She earns 12% of commission each week. Last week, she sold 4,500 worth of stocks. How much did she make last week in commission? If she averages that same amount each week, how much did she make in commission in 2011?
Answers
Answer:
540 last week
52X540.=$28,080 a year
Step-by-step explanation:
Un
número formado por 22 centenas,
515 unidades 1765 décimas, ¿cuantas
milésimas tiene?
Answers
Hay cero milésimas en los parámetros dados.
El valor posicional se refiere al valor representado por un dígito en un número sobre la base de su posición en el número.
De los parámetros dados:
22 centenas ⇒ 2200515 unidades ⇒ 5151765 décimas ⇒ 176.5Si sumamos los valores juntos, podremos determinar la cantidad de milésimas que tenemos:
= 2200+515+176.5
= 2891.5
Por tanto, podemos concluir que hay cero milésimas en los parámetros.
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Elements that do not belong to a set belong to its
Answers
Answer:
What do you mean for this question?
Step-by-step explanation:
Give specific details
Suppose a 5-digit number is formed using the digits from 1 to 9 (without replacement). What is the probability that it will be an even number?
Answers
Answer:
First take 5 empty. Digits.The no of digits are 9 (1-9).The last no must be even so . The total no of even no’s . Are 4 (2,4,6,8)The probability of last digit is 4There are remaing 8 digits so. Place them where. U required. The probability are. 8, 7,6,5(no reputations)The final answer is 4*8*7*6*5=6720 waysAnswer:
0.444 (44.4%)
Step-by-step explanation:
All possible ending: 1,2,3,4,5,6,7,8,9 ... 9
ending with 2,4 6,8 to make even number: 4
___ ___ ___ ___ ___
even number : 8 * 7 * 6 * 5 * 4
All 5 digit without repeating: 8 * 7 * 6 * 5 * 9
possibility = (8*7*6*5*4) / (8*7*6*5*9)
= 4/9
= 0.444 (44.4%)
_______________________________________________
(4 * ₈P₄) / (9 * ₈P₄) = 4/9
How many terms does the expression 14 + 9 have? What are they? Explain how you know.
Answers
Answer:
23, so 1. i know because i added 14+9 and got 23. im sorry if you meant like a definition term, please comment if thats what you meant. because i'll help you then.
Step-by-step explanation:
Find m
∠
J
L
K
∠JLK.
Answers
Answer:
m∠JLK° = 62°
Step-by-step explanation:
∠JLK = ∠KJL
SO
56°+2(∠JLK)° = 180°
2(∠JLK)° = 180-56
2(∠JLK)° = 124
∠JLK° = 62°
so m∠JLK° = 62°
Answer:
m∠JLK = 62°
Step-by-step explanation:
180 - 56 = 124
124 ÷ 2 = 62
Put the following capacities in order from smallest to largest. 0.1 l 0.5 l 1000 ml 10 ml 15 cl
Answers
Answer:
10 ml, 0.1 l, 15 cl, 0.5 l, 1000 ml
Step-by-step explanation:
m is an SI prefix for milli-, meaning 1/1000.
c is an SI prefix for centi-, meaning 1/100.
Expressed in liters, these volumes are ...
0.10 l
0.50 l
1000/1000 l = 1.00 l
10/1000 l = 0.01 l
15/100 l = 0.15 l
In order from smallest to largest, they are ...
0.01 l, 0.10 l, 0.15 l, 0.50 l, 1.00 l
In the original units, the order is ...
10 ml, 0.1 l, 15 cl, 0.5 l, 1000 ml
A square is a quadrilateral with four equal sides and four 90 degree angles. Is quadrilateral ABCD a square?
Answers
Answer: yes
Step-by-step explanation:
A line with a slope of 3 passes through the point (0, -10). What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{-10})\qquad \qquad \stackrel{slope}{m}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-10)}=\stackrel{m}{3}(x-\stackrel{x_1}{0}) \\\\\\ y+10=3x\implies \stackrel{\textit{slope-intercept form}}{y=3x-10}[/tex]
Help me with writing a check please
Answers
Answer: pay to the order of: Price Chopper.... $145.19.... next line: One hundred forty-five and 19/100.... bottom left line: whatever the money is for.... next line: signature. 5. fifty-four and 68/100 dollars 6. One hundred seventeen and 92/100 dollars 7. twenty dollars
Step-by-step explanation:
How many times do 5 go into 32
Answers
Answer:
6 times or 6.4
6 times
Explanation
32/5 = 6.4
12 POINT HURRY PLEASE
Answers
Answer:
• As x approaches -∞, g(x) approaches -∞; and as x approaches ∞, g(x) approaches ∞.
Step-by-step explanation:
[tex]{ \tt{g(x) = \frac{ {x}^{2} + 5x}{3x} }} \\ [/tex]
If x approaches -∞;
[tex]{ \tt{g( {}^{ - } \infin}) = \frac{ {( {}^{ - } \infin)}^{2} + {}^{ - } \infin}{ {}^{ - } \infin} } \\ \\ { \boxed{ \tt{g( {}^{ - } \infin) = {}^{ - } \infin }}}[/tex]
If x approaches +∞;
[tex]{ \tt{g( {}^{ + } \infin) = \frac{ {( \infin)}^{2} + \infin}{ \infin} }} \\ \\ { \boxed{ \tt{ g( {}^{ + } \infin) = {}^{ + } \infin }}}[/tex]
Note: I'm taking my infinite value to be 1,000
Find all numbers that satisfy the given condition. 1. Three less than twice the sum of a number and 6 is at most 13. 2. Five less than 3 times the sum of a number and 4 is at most 10. 3. Five times the sum of a number and 3 is at least 5. 4. Three times the difference between a number and 2 is at least 12. 5. The sum of 3 times a number and 8 is between 2 and 20. 6. Eight less than twice a number is between -20 and -8. 7. Four subtracted from three times some number is between -4 and 14. 8. Nine subtracted from 5 times some number is between 1 and 11.
Answers
Number be x
#1
[tex]\\ \sf\hookrightarrow 2(x+6)-3\leqslant=13[/tex]
#2
[tex]\\ \sf\hookrightarrow 3(x+4)-5\leqslant 10[/tex]
#3
[tex]\\ \sf\hookrightarrow 5(x+3)\geqslant 5[/tex]
#4
[tex]\\ \sf\hookrightarrow 3(x-2)\leqslant 12[/tex]
#5
[tex]\\ \sf\hookrightarrow 2\leqslant 3x+8\leqslant 20[/tex]
#6
[tex]\\ \sf\hookrightarrow -20\leqslant 2x-8\leqslant -8[/tex]
#7
[tex]\\ \sf\hookrightarrow -4\leqslant 3x-4\leqslant 14[/tex]
2x+7y+7x=18
Find the value of Y
Answers
Answer:
y=−9/7x+18/7
Step-by-step explanation:
2x+7y+7x=18
9x+7y=18
Step 1: Add -9x to both sides.
9x+7y+−9x=18+−9x
7y=−9x+18
Step 2: Divide both sides by 7.
7y/7=−9x+18/7
y=−9/7x+18/7
Given :
2x + 7y + 7x = 18To Find :
The value of ySolution :
[tex]\qquad { \dashrightarrow \: { \sf{2x + 7y + 7x = 18}}}[/tex]
Adding the like terms :
[tex]\qquad { \dashrightarrow \: { \sf{ 7y + 9x = 18}}}[/tex]
Transposing 9y to the other side which then becomes negative :
[tex]\qquad { \dashrightarrow \: { \sf{ 7y = 18 - 9x}}}[/tex]
Dividing both sides by 7 :
[tex]\qquad { \dashrightarrow \: { \sf{ \dfrac{7y}{7} = \dfrac{18 - 9x}{7} }}}[/tex]
[tex]\qquad { \dashrightarrow \: { \sf{ y = \dfrac{18 - 9x}{7} }}}[/tex]
⠀
Therefore, the value of y = 18 – 9x/7 .