Find the average velocity of the function over the given interval.
y = 3/x - 2 (4,7)
a. -3/50.
b. 7.
c. 2.
d. 1/3.
Answer:
Average velocity of the function over the given interval
= [tex]log(\frac{7}{4} ) -2[/tex]
Step-by-step explanation:
Explanation:-
Given function y = 3/x -2 ...(i)
The average velocity of the function over the given interval
Average velocity = [tex]\frac{1}{b-a} \int\limits^b_a {(\frac{3}{x} -2)} \, dx[/tex]
= [tex]\frac{1}{7-4} \int\limits^7_4 {(\frac{3}{x} -2)} \, dx[/tex]
now integrating
= [tex]\frac{1}{3}( \int\limits^7_4 {(\frac{3}{x} )} \, dx-2\int\limits^7_4 {1} \, dx )[/tex]
= [tex]\frac{1}{3} (3 (log x) - 2 x )_{4} ^{7}[/tex]
= [tex]\frac{1}{3}( (3 (log 7) - 14 )-(3 log 4 -8))[/tex]
by using formulas
log a-log b = log(a/b)
on simplification , we get
= [tex]\frac{1}{3}( (3 (log 7) -3 log 4 ) - \frac{1}{3} (6)[/tex]
= [tex]log(\frac{7}{4} ) -2[/tex]
Average velocity of the function over the given interval
= [tex]log(\frac{7}{4} ) -2[/tex]
A florist has 60 tulips and 72 daffodils. The florist will make bouquets with the same number of tulips and the same number of daffodils in each using all the flowers. What is the greatest number of bouquets the florist can make?
Answer:
12
Step-by-step explanation:
No of tulips = 60
No of daffodils = 72
We need to find the greatest number of bouquets the florist can make if the florist will make bouquets with the same number of tulips and the same number of daffodils in each using all the flowers.
It would mean that we need to find the HCF of 60 and 72
Prime factorisation of 60 = 2×2×3×5
Prime factorization of 72 = 2 x 2 x 2 x 3 x 3
Highest common factor or HCF = 2×2×3 = 12
So, the florist can make 12 bouquets as maximum number.
A 2 level 5 factor experiment is being conducted to optimize the reliability of an electronic control module. In a full factorial experiment, how many treatment combinations will there be
Answer:
32
Step-by-step explanation:
In a full factorial experiment, there are usually 32 or 2⁵ treatments. This implies that there are usually 2 levels and 5 factors. From the description below, there is a list of the 32 treatments.
Factor A Factor B Factor C Factor B Factor E
lo hi hi hi hi
hi low hi hi hi
hi hi low hi hi
hi hi hi low hi
hi hi hi hi low
lo lo hi hi hi
lo hi lo hi hi
lo hi hi lo hi
A painter paints a wall in x hours, so the fraction of the wall that she paints in 3 hours is
Need Help?
Read It
Answer:
3/x
Step-by-step explanation:
1 wall - x hours
y wall - 3 hours
y = (1*3)/x=3/x
The fraction of the wall that she paints in 3 hours is 3/x.
Here,
A painter paints a wall in x hours.
We have to find, the fraction of the wall that she paints in 3 hours.
What is fraction?
A fraction simply tells us how many parts of a whole we have.
Now,
Here, A painter paints a wall in x hours
1 wall = x hours
Let number of walls is z when she paints in 3 hours.
z wall = 3 hours
Hence, The fraction of the wall that she paints in 3 hours =( 1 x 3)/x
= 3/x
Learn more about the fraction visit:
https://brainly.in/question/5112127
#SPJ2
Can you please help me with this question and i will give you a Brain list
Answer:
- A reflection can be done on a point, shape, or object
- A reflection flips a shape across a line
Step-by-step explanation:
A reflection is a rigid transformation, meaning that the object that you are reflecting does NOT change size or shape. A reflection is when you graphically "flip" an image across a line such as the x-axis or the y-axis.
A company increased the number of its employees from 320 to 400. What was the percent increase in employees?
Answer:
25% increase.
Step-by-step explanation:
What does algebra mean?
A. The Gate to the Unknown
B. The Gate to the unknown and all possibilities
C. I don’t know
Using the slope formula, find the slope of the line through the given points
(9,9) and (7,1)
Answer:
Step-by-step explanation:
(1 - 9)/(7 - 9)= -8/-2 = 4 is the slope
convert 5 2/5 into an improper fraction
Step-by-step explanation:
To write 5 as a fraction with a common denominator, multiply by 55 . Combine 5 and 55 . Combine the numerators over the common denominator. Simplify the numerator.
The convert of the mixed fraction into an improper fraction is [tex]\frac{27}{25}[/tex]
Important information:The mixed fraction is [tex]5 \frac{2}{5}[/tex]Calculation:[tex]= 5\frac{2}{5}\\\\ = \frac{27}{25}[/tex]
Learn more about the fraction here: https://brainly.com/question/24584039
Alyssa had 59 dollars to spend on 6 books. After buying them she had 11 dollars. How much did each book cost
A farmer feeds her four horses 64 bales of hay each week. How many bales of hay would the farmer need in order to feed six horses for a week?
Answer:
96 bales
Step-by-step explanation:
[tex]\frac{64}{4}[/tex] = [tex]\frac{x}{6}[/tex]
You must multiply 6 by 64, which is 384.
Then you divide that by 4, which is 96.
Therefore, the answer is 96.
Also, I lined up the bales in the same row and horses in the same row, so this way can help. It can also help if it's in the same column though, but I hope this helped you!
Answer:
96
Step-by-step explanation:
2 Look at the open number line in
Problem 1. How would you change the
numbers to show 9 + 5?
Answer:
i need the number line
Step-by-step explanation:
lol
Which of the following is an odd function? f(x) = 3x2 + x f(x) = 4x3 + 7 f(x) = 5x2 + 9 f(x) = 6x3 + 2x
The odd function from the following function is f(x) = 6x³ + 2x.
What is an odd function?The function f(x) is said to be an odd function if the output value of f(-x) is the same as the negative of f(x) for all values of x in the domain of f.
f(-x) = -f(x)
The functions are given below.
f(x) = 3x² + x
f(x) = 4x³ + 7
f(x) = 5x² + 9
f(x) = 6x³ + 2x
f(x) = 3(-x)² + (-x) = 3x² - x
f(x) = 4(-x)³ + 7 = -4x³ + 7
f(x) = 5(-x)² + 9 = 5x² + 9
f(x) = 6(-x)³ + 2(-x) = -6x³ - 2x = - (6x³ + 2x)
Learn about the odd function;
brainly.com/question/14264818
#SPJ2
Answer:
D f(x) = 6x3 + 2x
Step-by-step explanation:
A= 5,000 (1+.002*10)
Toss 3 dice. What's the probability that a 4 will come up exactly twice?
Answer:
[tex]\bold{\dfrac{1}{12}}[/tex]
Step-by-step explanation:
The dice is rolled 3 times.
To find:
The probability that a 4 will come up exactly twice = ?
Solution:
Let 4 comes up exactly twice, let the third number be [tex]x[/tex].
The possible outcomes can be:
([tex]x[/tex], 4, 4) where [tex]x[/tex] can be any number between 1 to 6 , so 6 outcomes.
(4, [tex]x[/tex], 4) where [tex]x[/tex] can be any number between 1 to 6 , so 6 outcomes.
(4, 4, [tex]x[/tex]) where [tex]x[/tex] can be any number between 1 to 6 , so 6 outcomes.
So, the total number of favorable outcomes possible = 6 + 6 + 6 = 18
Total number of outcomes that can be possible at roll of 3 dice:
6 [tex]\times[/tex] 6 [tex]\times[/tex] 6 = 216
Formula for probability of an event E is given as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
[tex]P(\text{exact 2 fours}) = \dfrac{18}{216}\\\Rightarrow \bold{P(\text{exact 2 fours}) = \dfrac{1}{12}}[/tex]
Please guys help me when I take a picture of the question it always say something went wrong try again later I got a test seeing please help me
4.2(5.1x+6.8) Simplify the expression
Answer:
21.42x+28.56
Step-by-step explanation:
Expand: 4.2×5.1×x+4.2×6.8
4.2×5.1×x to (21.42)x
Simplify: 21.42x+4.2×6.8
4.2×6.8 = 28.5628.56
21.42x+28.56
Which pair of variables would most likely have a negative correlation?
A. the time spent driving in a car and the number of miles driven
B. the height of a dog in inches and the number of ounces of food the dog eats per day
C. the number of sit-ups completed and the number of calories burned during a workout
D. the time spent reading a book and the number of pages remaining to be read in the book
Answer: D
Step-by-step explanation:
The pair of variables that will most likely have a negative correlation are D. the time spent reading a book and the number of pages remaining to be read in the book.
Negative CorrelationThis means that the variables involved move in the opposite direction from each other. Means that as one variable increases, the other decreases and vice versa.If you spend a longer time reading a book, you would read more pages which would reduce the number of pages left to be read. The time taken to read the book is therefore negatively correlated with the number of pages left.
In conclusion, option D is correct.
Find out more on negative correlation at https://brainly.com/question/2476038.
what is the point slope form for 2x + 3y = 1,470
Each side of a square field is 50m long. A barricade is to be placed along the diagonal of the field. Find the length of the barricade.
Answer:
70.71m
Step-by-step explanation:
In order to find the diagonal, we can use Pythagiras theorem by splitting the field in half and creating a right angled triangle.
A^2+B^2=C^2
50^2+50^2=C^2
5000=C^2
Square root 5000= 70.71m (2dp)
Hope this helped!
Since there is a barricade placed along the diagonal sq field, let's focus on one side of the triangle.
A pythagoras theorem formula can be used for right angle triangle.
So now we let the barricade be X.
By Pythagoras Theorem,
X² = 50² + 50²
X = sq root (50² +50²)
= 70.711 m ( 5sf)
= 70.7 m ( 3sf)
Therefore, the length of barricade is 70.7 m
7:00PM For dinner, you decide to go out to eat at a restaurant with your significant other. The bill is $32.43, and you would like to leave a 20% tip for your waiter. What will the amount of the tip be and what is the final amount of your bill? Remember to round all values to the nearest cent.
Answer:
Tip amount: $6.49
Final amount of the bill: $38.92
Step-by-step explanation:
We need to calculate the tip amount which is 20% of $32.43.
Then we will add the tip amount to $32.43.
To find a percent of a number, change the percent to a decimal by dividing the percent by 100 and multiply by the number.
20% of $32.43 =
= 0.2 * $32.43
= $6.486
We round off the tip amount to the nearest cent, $6.49
The tip amount is $6.49
To find the final amount of the bill, we add the tip amount to the bill amount.
$32.43 + $6.49 = $38.92
Which statement is true about the expression 12 minus 7 + 3? The expression is equivalent to 12 minus (7 + 3) because of the associative property. The expression is equivalent to 12 + 3 + (negative 7) because of the associative property. The expression is equivalent to 12 minus 3 + 7 because of the commutative property. The expression is equivalent to 12 + 3 + (negative 7) because of the commutative property.
Answer:
The Expression is equivalent to 12+3+ negative 7
Step-by-step explanation:
When you sub tract something for example 5-3 the three can be looked at as a negative number. 5-3=2 but 5+ (-3)=2 as well
The associative property indicates that the true statement about the expression is the option;
''The expression is equivalent to 12 + 3 + (negative 7) because of the associative property''
What is the associative property?
The associative property is related to the grouping of the numbers in an operation. According to the associative property changing the grouping of numbers does not change the result of addition and multiplication.
The associative property allows us to change the grouping of the addition operation, so we can rewrite the expression as follows; (12 + 3) + (negative 7), which simplifies to 15 + (negative 7) or 8. The commutative property on the hand, allows us to change the order of the addition operation. However, with regard to the question, it is not relevant because the expression involves addition and subtraction
Learn more on the associative property here: https://brainly.com/question/17214533
#SPJ6
HELLO HELP PLSS
Identify the line(s) of symmetry for kite ABCD.
A)Line BD
B)Line AC
C)line EF
D)no line of symmetry
Answer:
C) line BD
Step-by-step explanation:
If you fold along the line the sides of the shape should line up perfectly. the only answer listed that fits the criteria is C
26 = 8 + v 2) 3 + p = 8
Answer:
1)26=8+v
v=26-8
v=18
2)3+P=8
P=8-3
P=5
please mark me as BRAINLIST
(-9a? +12a - 10)+(9a? +10)
I need help with this test
Answer:
12a
Step-by-step explanation:
Because -9a and 9a would get rid of themselves the only "a-value" left is 12a. 10 and -10 also cancel each other out so 12a is all that is left.
If you need more help let me know, have a great day!
1/2 n + 3 = 6 please the answer thank u
Answer:
Step-by-step explanation:
1/2 n + 3 = 6
-3 -3
1/2 = 3
Answer is 1.5=n
Answer:
n = 18
Step-by-step explanation:
(1/2)*n-3 = 6 // - 6
(1/2)*n-6-3 = 0
1/2*n-9 = 0 // + 9
1/2*n = 9 // : 1/2
n = 9/1/2
n = 18
n = 18
PLZ GIVE ME BRAINLIEST
If AB=BC,AB=4=4x-2,andBC=3x+3,fine the length of AB
Answer:
18
Step-by-step explanation:
First, I'm assuming AB=4=4x-2 was a typo and it's supposed to be AB = 4x - 2
AB=BC
AB = 4x - 2 BC = 3x + 3
4x - 2 = 3x + 3
Solve for x Add 2 to each side
4x - 2 = 3x + 3
4x - 2 + 2 = 3x + 3 + 2
4x = 3x + 5 Subtract 3x from each side.
4x - 3x = 3x- 3x + 5
4x - 3x = 5
x = 5
Now plug back in to the original equations
AB = 4x - 2 BC = 3x + 3
AB = 4 (5) - 2 BC = 3(5) + 3
AB = 20 - 2 BC = 15 + 3
AB = 18 BC = 18
So AB is 18
please help!! I don't understand this
Step-by-step explanation:
(f○g)(-3)
= f(g(-3))
g(-3) =
[tex] \frac{2}{2( - 3) - 1} [/tex]
g(-3) = -2/7
f(-2/7) = (-2/7)^2 + 2(-2/7) -4
= 4/49 - 4/7 - 4
= 4/49 - 28/49 - 196/49
= -220/49
please check again ^-^
4+y when y = 18 would the answer be 22
Answer:
22
Step-by-step explanation:
4+18=22 if y is solved for 18 in the equation 4+y= the answer would be 22.
Answer:
22
Step-by-step explanation:
Evaluate y + 4 where y = 18:
y + 4 = 4 + 18
Hint: | Evaluate 4 + 18 using long addition.
| 1 |
| 1 | 8
+ | | 4
| 2 | 2:
Answer: 22
The table below shows the number of students who attend various after-school activities. After-School Activities Activity Number of Students Spanish Club 19 Basketball 24 Drama 15 Homework Help 17 Soccer 20 Which ratio compares the number of students in the Spanish club to the total number of students? a.19:95 b.20:95 c.95:24 c.95:19
Answer:
C. 95:19
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
because the total number of students is 95 and those who play Spanish club is 19