Split up the interval [1, 9] into n subintervals of equal length (9 - 1)/n = 8/n :
[1, 1 + 8/n], [1 + 8/n, 1 + 16/n], [1 + 16/n, 1 + 24/n], …, [1 + 8 (n - 1)/n, 9]
It should be clear that the left endpoint of each subinterval make up an arithmetic sequence, so that the i-th subinterval has left endpoint
1 + 8/n (i - 1)
Then we approximate the definite integral by the sum of the areas of n rectangles with length 8/n and height [tex]f(x_i)[/tex] :
[tex]\displaystyle \int_1^9 (x^2-4x+6) \,\mathrm dx \approx \sum_{i=1}^n \frac8n\left(\left(1+\frac8n(i-1)\right)^2-4\left(1+\frac8n(i-1)\right)+6\right)[/tex]
Take the limit as n approaches infinity and the approximation becomes exact. So we have
[tex]\displaystyle \int_1^9 (x^2-4x+6) \,\mathrm dx = \lim_{n\to\infty} \sum_{i=1}^n \frac8n\left(\left(1+\frac8n(i-1)\right)^2-4\left(1+\frac8n(i-1)\right)+6\right) \\\\ = \lim_{n\to\infty} \frac8n \sum_{i=1}^n \left(1+\frac{16}n(i-1)+\frac{64}{n^2}(i-1)^2-4-\frac{32}n(i-1)+6\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \sum_{i=1}^n \left(64(i-1)^2-16n(i-1)+3n^2\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \sum_{i=0}^{n-1} \left(64i^2-16ni+3n^2\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \left(64\sum_{i=0}^{n-1}i^2 - 16n\sum_{i=0}^{n-1}i + 3n^2\sum{i=0}^{n-1}1\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \left(\frac{64(2n-1)n(n-1)}{6} - \frac{16n^2(n-1)}{2} + 3n^3\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \left(\frac{49n^3}3-24n^2+\frac{32n}3\right) \\\\= \lim_{n\to\infty} \frac{8\left(49n^2-72n+32\right)}{3n^2} = \boxed{\frac{392}3}[/tex]
12
Detroit, Michigan covers an area of 142.9 square miles. There are approximately
672,800 people living in Detroit. Grand Rapids, Michigan has an area of 45.3 square
miles and has a population of approximately 195,100 people. How many more
people, per square mile, live in Detroit verses Grand Rapids? Round to the nearest
person per square mile.
Answer:
401 more people per square mile
Step-by-step explanation:
Find how many people there are per square mile in both cities by dividing the number of people by the number of square miles:
672,800/142.9
= 4708 people per square mile (Detroit)
195,100/45.3
= 4307 (Grand Rapids)
Find how many more people per square mile live in Detroit by finding the difference between these two numbers:
4708 - 4307
= 401
So, there are 401 more people per square mile living in Detroit versus Grand Rapids.
1.3 is 10% of what number
Answer:
33.33 percent
Step-by-step explanation:
Answer:
13
Step-by-step explanation:
Make a proportion
part/whole = part/whole
1.3/x=10/100
130=10x
x=13
What is the circumference of a circle with a diameter of 9 cm?
Answer:
the answer=28.27cm
using formula
c=2πr
d=2r
solving for c
C=πd
=π.9
=28.27
hope it help you
Hot-dog buns come in packages of 10. Wieners come in
packages of 12. Barry would like to buy the smallest
number of hot-dog buns and wieners so that he will have
exactly 1 wiener per bun. How many packages of hot-dog
buns and wieners must he buy?
A 6 packages of buns, 5 packages of wieners
B 5 packages of buns, 5 packages of wieners
C 8 packages of buns, 7 packages of wieners
05 packages of buns, 4 packages of wieners
Answer:
A 6 Packages of buns and 5 packages of wieners.
Step-by-step explanation:
Because if you multiply 6x10 you get 60 and if you multiply 5x12 you get 60 exactly 1 wieners per bun
Find the product of 2x 3 xy and 5
Answer:
30x²y
Step-by-step explanation:
2x × 3xy × 5
= 2 × 3 × 5 × x × xy
= 30x²y
|x| = - |x| What can I write
Y= 3x-1
2x+6=y substitution method
Answer: (7, 20)
Concept:
There are three general ways to solve systems of equations:
EliminationSubstitutionGraphingSince the question has specific requirements, we are going to use substitution to solve the equations.
Solve:
Given equations
y = 3x - 1
2x + 6 = y
Substitute the y value since both equations has isolated [y]
2x + 6 = 3x - 1
Add 1 on both sides
2x + 6 + 1 = 3x - 1 + 1
2x + 7 = 3x
Subtract 2x on both sides
2x + 7 - 2x = 3x - 2x
[tex]\boxed{x=7}[/tex]
Find the value of y
y = 3x - 1
y = 3(7) - 1
y = 21 - 1
[tex]\boxed{y=20}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Which numbers are 9 units from −5 on this number line?
Drag and drop all of the numbers that are 9 units from −5 to their correct position on the number line.
-14,-5 -4 4 5 9
Answer:
-14 and 4
Step-by-step explanation:
To find the values subtract 9 from -5, as well as add 9 to -5
-5-9= -14
-5+9= 4
HELP! I really need the answer quick!!!!!!!
Answer:
139°
Step-by-step explanation:
8x+51+6x-25=180
14x+26=180
14x=180-26
14x=154
x=154/14
x=11
<AOB= 8x+51 = 8(11)+51 = 88+51 = 139
Suppose that one state’s license plates consist of 1 digit followed by 4 letters followed by 2 digits. How many such plates can the state issue?
Answer:
The state can issue 456,976,000 license plates.
Step-by-step explanation:
For digits, it is assumed that we can use 0-9. Thus, there are 10 options for each slot with a digit.
For letters, it is assumed that we can use the 26 letters of the alphabet (i.e. A through Z). Thus, there are 26 options for each slot with a letter.
For this particular problem, the slot method can be used. Assuming that repetition of letters/digits is allowed:
[tex]\frac{10}[/tex] [tex]\frac{26}[/tex] [tex]\frac{26}[/tex] [tex]\frac{26}[/tex] [tex]\frac{26}[/tex] [tex]\frac{10}[/tex] [tex]\frac{10}[/tex]
= 10*26*26*26*26*10*10
=456,976,000.
Therefore, the state can issue 456,976,000 license plates.
I need help with the answer
Answer:
Option B, x ≈ -2.25
Step-by-step explanation:
3^x-2=(x-1)/(x^2+x-1)
or x ≈ -2.21166
so it's closest to the answer of the 2nd option
I) Find the volume in terms of pie
ii) curved surface area in terms of pie
iii) capacity in litres (correct to nearest litre)
Answer:
i) pi×4500 cm³
ii) pi×600 cm²
iii) 14 liters
Step-by-step explanation:
in general : the diameter is 30 cm, the radius is half of that (15 cm)
i)
the volume of a cylinder is base area times height.
Vc = pi×r²×h = pi×15²×20 = pi×225×20 = pi×4500 cm³
ii)
similar to volume, the side "mantle" area of the cylinder is the circumference of the base area times height.
surface area of the cylinder mantle is
Scm = 2×pi×r×h = 2×pi×15×20 = pi×30×20 = pi×600 cm²
iii)
for this we need now to do the multiplication with pi and then convert the cm³ to liters.
1 liter = a cube of 10 cm side length = 10×10×10 = 1000 cm³
pi×4500 = 14137.17 cm³ = 14.13717 liters or rounded 14 liters
Find the smallest number from which 3 is to be subtracted so that the difference is exactly divisible 18,24,36
Answer:
72
Step-by-step explanation:
look at the prime factors of each number.
18 = 2*3^2
24 = 2^3*3
36 = 2^2*3^2
The most factors of 2 in any of these numbers is 3: 2^3
The most factors of 3 in any of these numbers is 2: 3^2
2^3*3^2 is 8*9 or 72.
72 is the lowest number exactly divisible by 18, 24, and 36.
factorise completely 4x^(2 )(x + 1) - 6x (x+1)
Answer:
[tex] {4x}^{2} (x + 1) - 6x(x + 1) \\ = (x + 1)(4 {x}^{2} - 6 x ) \\ = (x + 1)(2x)(2x - 3)[/tex]
explanation:
first choose the common factor by observation, it is (x + 1):
factorise it out:
= (x + 1)(4x² - 6x)
by observation in (4x² - 6x), common factor is 2x.
Factorise 2x out:
= (x + 1)[2x(2x - 3)]
Answer:
(4x2-6x) (x+1)
now common factor is (x+1) ,so,(4x2-6x) (x+1)
If each pen costs ₹7 and Joseph has a total of ₹410, for how many of his classmates would he be able to buy pens if the shopkeeper gives him a discount of ₹20 on the total bill at most?
Answer:
what is that corency
Step-by-step explanation:
An athletic club charges a monthly membership
fee of $65. Members can also take classes for an
additional $15 per class. For this month only, the
club has a special that includes two free classes for
all new members. Which of the following functions
expresses the cost for the month for new members
who take x classes this month, where x > 2?
(A) C(x) = 2x + 65
(B) C(x) = 15x + 65
(C) C(x) = 2(x - 15) + 65
(D) C(x) = 15(x - 2) + 65
Solve for
x. Round to the nearest tenth of a degree, if necessary.
Answer:
[tex]\displaystyle x \approx 30.8[/tex]
Step-by-step explanation:
Note that the figure is a right triangle, and that we are given the length of the side adjacent to x and the hypotenuse of the triangle.
Therefore, we can use the cosine ratio. Recall that:
[tex]\displaystyle \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}[/tex]
The adjacent side is 8.5 and the hypotenuse is 9.9. Therefore:
[tex]\displaystyle \cos x = \frac{8.5}{9.9}[/tex]
We can take the inverse cosine of both sides:
[tex]\displaystyle x = \cos^{-1} \frac{8.5}{9.9}[/tex]
Use a calculator. Hence:
[tex]\displaystyle x \approx 30.8[/tex]
helppfind the value of x and y
I know tje answer
x+6kkkkkkkk
Answer:
X=75°;AND Y=30°
Step-by-step explanation:
Angle( x+75°)+(y)=180°
Angle(2x)+(y)=180°
[by subtracting both the equation we get;]
-1x=-75
x=75°
Now,value of y;
2x+y=180
2×75+y=180
150+y=180
y=180-150
y=30°
Sam is shopping for clothes. There's a 9% sales tax where he lives. Select the expression that gives the price of clothes after including the sales tax, where c is the original cost of the clothes.
1c + 0.9c
Incorrect Response
1.09c + 0.09c
Correct Answer
1.09c
Answer:
1.09c
Step-by-step explanation:
The clothes cost c before tax.
The tax is 9% of the price of the clothes, or 9% of c.
To find a percent of a number, change the percent to a decimal and multiply by the number.
9% as a decimal is 0.09
9% of c = 9% * c = 0.09c
The amount of tax is 0.09c.
Now we add the amount of tax to the original price, c.
c + 0.09c = 1.09c
Answer: 1.09c
if A(-1;10) B(0 ;-1) C (-3;2) ,determine whether AB is perpendicular to AC
Answer:
No, they aren't perpendicular
Step-by-step explanation:
Two lines are perpendicular if the product of their slope is - 1. The slope of line AB=(-1-10)/(0-(-1))=-11 and the slope of the line AC=(2-10)/(-3-(-1))=4. Since the product of their slope isn't - 1. They aren't perpendicular.
5√6 multiple 5√6 is equal
(a) 5√36
(b) 5√6×0
(c) 5√6
(d) 5√12
step by step
for brainlist.
solve :-
[tex]\\ \sf\longmapsto 5\sqrt{6}\times 5\sqrt{6}[/tex]
a×a=a^2[tex]\\ \sf\longmapsto (5\sqrt{6})^2[/tex]
[tex]\\ \sf\longmapsto 25\times 6[/tex]
[tex]\\ \sf\longmapsto 150[/tex]
But,
[tex]\\ \sf\longmapsto \sqrt{36}=6[/tex]
So
[tex]\\ \sf\longmapsto 5\sqrt{6}\times 5\sqrt{6}[/tex]
[tex]\\ \sf\longmapsto 5\sqrt{6\times 6}[/tex]
[tex]\\ \sf\longmapsto 5\sqrt{36}\checkmark[/tex]
If you need value then It is 150 but for your question its option aThe perimeter of a picture frame is
24 inches. If the width of the picture
frame is 5 inches, what is the length of
the picture frame?
Answer:
7 in
Step-by-step explanation:
perimeter = 2length + 2width
Input the given info:
24 = 2length + 2(5)
24 = 2L + 10
14 = 2L
14/2 = L
l = 7
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
what is the absolute value of -5/9
Answer:
5/9
Step-by-step explanation:
In short, the absolute value of a number turns that number into a positive value no matter what. Here is a small representation:
Negative -> Positive
Positive -> Positive
Since we are working with a negative value, it will turn positive.
Best of Luck!
Your boss asked you to prepare a company party for 20 employees with a budget of Rs. 50, 000.00. You have a choice of ordering a dinner at Rs. 3, 000.00 (Package 01) from “X-Hut Restaurant” per person or a dinner at Rs. 2,500.00 (Package 02) per person from the same place (Delivery charges also included in the price of the meal). i. How many numbers (From package 01 & 02) can you order for the party by using up the budget? ii. How many numbers (From package 01 & 02) can you order for the party if the budget increases to Rs. 55, 000.00?
Step-by-step explanation:
........... ................
Write the quadratic equation whose roots are 2 and -4 and whose leading coefficient is 2
Answer:
2x^2+4x-16
Step-by-step explanation:
The quadratic can be written as
f(x) = a(x-z1)(x-z2) where z1 and z2 are the roots
f(x) = a (x-2)(x- -4)
a is the leading coefficient
f(x) = 2(x-2)(x+4)
= 2(x^2 -2x+4x-8)
= 2(x^2 +2x-8)
= 2x^2 +4x-16
F(x)=x^2 what is g(x)
Answer:
stop spamming
Step-by-step explanation:
1. Write a survey question for which you would expect to collect numerical
data.
2. Write a survey question for which you would expect to collect categorical
data.
Answer:
How many siblings do you have?
I hope this helps you out :)
A. The interquartile range is 55
B.Three fourths of the data is less than 65
C. The median of the upper half of the data is 65
D. The median if the data is 55.
Answer:
d the median if the data is 55
1) A 22-ft ladder is leaning against a building. If the base of the ladder is 6 ft from the base of the building, what is the angle of elevation of the ladder? (Round your answer to one decimal place.)
2)How high does the ladder reach on the building? (Round your answer to the nearest whole number.)
Answer:
21.9 ft
Step-by-step explanation:
Answer:
Part A)
About 74.2°.
Part B)
About 21 feet.
Step-by-step explanation:
A 22 feet ladder is leaning against a building, where the base of the ladder is six feet from the base of the building.
This is shown in the diagram below (not to scale).
Part A)
We want to determine the angle of elevation of the ladder. That is, we want to find the value of θ.
Since we know the values adjacent to θ and the hypotenuse, we can use the cosine ratio. Recall that:
[tex]\displaystyle \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}[/tex]
The adjacent is 6 and the hypotenuse is 22. Thus:
[tex]\displaystyle \cos \theta = \frac{6}{22} = \frac{3}{11}[/tex]
Take the inverse cosine of both sides:
[tex]\displaystyle \theta = \cos^{-1}\frac{3}{11}[/tex]
Use a calculator. Hence:
[tex]\displaystyle \theta = 74.1733...\approx 74.2^\circ[/tex]
The angle of elevation is approximately 74.2°
Part B)
We want to find how high up the ladder reaches on the building. In other words, we want to find x.
Since x is opposite to θ and we know the adjacent side, we can use the tangent ratio. Recall that:
[tex]\displaystyle \tan \theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]
The opposite side is x and the adjacent side is 6. The angle θ is cos⁻¹(3/11) (we use the exact form to prevent rounding errors). Thus:
[tex]\displaystyle \tan \left(\cos^{-1}\frac{3}{11}\right) = \frac{x}{6}[/tex]
Solve for x:
[tex]\displaystyle x = 6 \tan \left(\cos^{-1}\frac{3}{11}\right)[/tex]
Use a calculator. Hence:
[tex]x = 21.1660... \approx 21\text{ feet}[/tex]
The ladder reaches about 21 feet up the building.
PRECAL QUESTION - please help thanks
Answer:
203/169 -183i/169
"A"
Step-by-step explanation:
[tex]\frac{9-19i}{12-5i}[/tex]
[tex]\frac{9-19i}{12-5i}[/tex] * [tex]\frac{12+5i}{12+5i}[/tex]
12^2 - (5i)^2 = 144 + 25 = 169
FOIL: 108 +45i - 228i + 95
203 -183
