Answers
Answer:
7.5 -ln(0.25)
Step-by-step explanation:
We can first graph this function. Looking at the graph, we can separate this into two ranges -- from x=0.25 to x=1 and from x=1 to x=4.
From x=0.25 to x=1, we want to find the area above y=1/x and below y=4. To do this, we can take the integral of y=4 from x=0.25 to x=1 to encompass the whole area under y=4 from that range. Then, we subtract the area under y=1/x as we don't need that (we only want what's above it). Therefore, we have
[tex]\int\limits^{1}_{0.25}{4} \, dx - \int\limits^{1}_{0.25} {1/x} \, dx \\= 4(1) - 4 (0.25) - (ln(1) - ln(0.25))\\= 4 - 1 - ln(1) + ln(0.25)\\= 3 - ln(1) + ln(0.25)[/tex]
Next, we know that ln(x/y) = ln(x) - ln(y), so ln(0.25) - ln(1) = ln(0.25/1) = ln(0.25), so we have
3 - ln(0.25)
For x=1 to x=4, we want to find the area above y=x and below y=4. We can apply a similar strategy, subtracting the area below y=x from the area below y=4 to get
[tex]\int\limits^{4}_{1}{4} \, dx - \int\limits^{4}_{1} {x} \, dx \\ \\= 4(4) - 4(1) - (4^{2} /2 - 1^2/2)\\= 16 - 4 - 8 + 0.5\\= 4.5[/tex]
Add these two areas up to get
3-ln(0.25) + 4.5 = 7.5 -ln(0.25)
Related Questions
The normal blood glucose level is between 70 mg/dL and 130 mg/dL. Write a compound inequality to represent the values at which blood glucose is not normal.
Answers
Let the input be x
x is greater than or equal to 70mg/dl.x is less than or equal to 130mg/dl.[tex]\\ \rm\Rrightarrow x\geqslant 70mg/dl[/tex]
[tex]\\ \rm\Rrightarrow x\leqslant 130mg/dl[/tex]
Now
[tex]\\ \rm\Rrightarrow 70mg/dl\leqslant x\leqslant 130mg/dl[/tex]
Or
[tex]\\ \rm\Rrightarrow 130mg/dl\geqslant x\geqslant 70mg/dl[/tex]
Answer:
70 ≤ x ≤ 130
130 ≥ x ≥ 70
Step-by-step explanation:
We know that a persons glucose level can only be equal to or between 70 and 130 mg/dL. We can create an inequality to represent this;
70 < x < 130
This means that anything in between will work but anything less or more will not. You can also write this inequality as 130 > x > 70.
In word form you would say this:
A humans glucose level can only be more than or equal to 70 and less than or equal to 130.Best of Luck!
Which of the
following numbers
falls between 8 and 9
on the number line
square root of 75 or square root of 100?
Answers
Answer: [tex]\sqrt{75}[/tex]
================================================
Explanation:
Square both 8 and 9 to get
8^2 = 8*8 = 649^2 = 9*9 = 81Since 75 is between 64 and 81, this means [tex]\sqrt{75}[/tex] is between 8 and 9
Put another way, we can say this:
[tex]64 < 75 < 81\\\\\sqrt{64} < \sqrt{75} < \sqrt{81}\\\\\sqrt{8^2} < \sqrt{75} < \sqrt{9^2}\\\\8 < \sqrt{75} < 9\\\\[/tex]
Or we could use a calculator to find that:
[tex]\sqrt{75} \approx 8.66[/tex] [tex]\sqrt{100} = 10[/tex]Which is another way to see why [tex]\sqrt{75}[/tex] is between 8 and 9.
What is the range with steps? f(x)=x^2+8x+8
Answers
Answer:
[-8, ∞)Step-by-step explanation:
Given function:
f(x)=x² + 8x + 8This is a quadratic function with positive leading coefficient, therefore it is an increasing function with its minimum at vertex. It has no maximum value.
The vertex is at x = -b/2a:
x = -8/2 = -4The minimum value is:
f(-4) = (-4)² + 8(-4) + 8 = 16 - 32 + 8 = -8The range of the function is:
[-8, ∞)f(x)=x^2+8x+8
Find vertex to x[tex]\\ \sf\longmapsto \dfrac{-b}{2a}[/tex]
[tex]\\ \sf\longmapsto \dfrac{-8}{2(1)}[/tex]
[tex]\\ \sf\longmapsto \dfrac{-8}{2}[/tex]
[tex]\\ \sf\longmapsto -4[/tex]
Find value of function at -4[tex]\\ \sf\longmapsto f(-4)[/tex]
[tex]\\ \sf\longmapsto (-4)^2+8(-4)+8[/tex]
[tex]\\ \sf\longmapsto 16-32+8[/tex]
[tex]\\ \sf\longmapsto -16+8[/tex]
[tex]\\ \sf\longmapsto -8[/tex]
The range is
[tex]\\ \sf\longmapsto (8,\infty)[/tex]
Solve the simultaneous
equation log(x+2) +log2=2log y and log(x-3y+3)=0
Answers
Answer:
that's is my answer for the question
order these numbers in ascending order. -11, 11.8 9.42 ,10
Answers
Answer:
-11,9.42,10,11.8
-11<9.42<10<11.8
Answer:
I think the answer is
-11, 9.24 ,10, 11.8
Maggies brother is 4 years younger than three times her age the sum of there ages is 28 how old is maggie
Answers
Answer:
24
Step-by-step explanation:
Find the perimeter and area of a rectangle of cardboard measuring 11.3 cm by 14.8 cm.
Answers
Area of rectangle = Length * Width
Length = 11.3 cmWidth = 14.8 cmArea = 11.3 cm * 14.8 cm
Area = 167.24
PerimeterPerimeter of rectangle = 2 (L + W)
Length = 11.3 cmWidth = 14.8 cmPerimeter = 2 (11.3 cm + 14.8 cm)
Perimeter = 2 (26.1 cm)
Perimeter = 52.2 cm²
Final AnswerArea of rectangle is 167.24 cm²
Perimeter of rectangle is 52.2 cm²
I need help solving this question please with an explanation.
Answers
Answer:
if he work 3 hours and earn 40.50
then the money he earn per hour is 40.50/3=13.5 ans
Someone please help me with 13 and 14 I’m really struggling
Answers
Answer:
Step-by-step explanation:
Danny got a raise and now makes $58,965.95 a year. Round this number to the
nearest:
a) dollar
b) thousand dollars
c) ten thousand dollars
Answers
Answer:
c) ten thousand dollars
Step-by-step explanation:
HW #3 review
I will give brainliest to whoever gets it right
Answers
Hi there!
The numbers you have written there are correct.
[tex]-5<x<0[/tex] is true for any value of x that is greater than -5 or less than 0.
When a number is less than 0, we know that it has to be negative.
However, it cannot be more negative than -5. It cannot be -5 either.
So, x could be -1, -2, -3, -4, -1/2, -2.3, -4.9, the list goes on.
I hope this helps!
7(6-4) distribitive property
Answers
Answer:
14
Step-by-step explanation:
Multiply 7 and 6, then 7 and -4: 42-28=?
Subtract: 42-28=14
For the following set of sample data: {10, 50, 60, 70, 75 79, 85, 90, 91, 95, 100, 110} Find the sample mean.
Answers
Answer:
76.25
Step-by-step explanation:
17/3x + 17 - 2/3x - 15
Answers
Kelly works two jobs. She usually works at a retail store for 5 hours during the day and is paid $7.18 per hour by the store. In the evening she works at a restaurant as a
manager for 7 hours and is paid $20.68 per hour. How much does she make on average per hour for the day?
Answers
Answer:
Think of two or three jobs with which you are familiar, perhaps a teacher, a retail worker, a nurse, or a police officer.
In each case, indicate why the employment contract is necessarily incomplete. What important parts of the person’s job—things that the employer would like to see the employee do or not do—cannot be covered in a contract, or if they are, cannot be enforced?
Step-by-step explanation:
The expression 1/x+y
is equal to which quantities?
(1/x) + y
1/x + y
1/(x + y)
Answers
The equivalent form of the given expression is 1 /(x + y)
The given expression:
[tex]\frac{1}{x+y}[/tex]
To find:
the equivalent form of the expression:The equivalent form of the expression can be written as follows:
[tex]\frac{1}{x+y} = 1 /(x + y)[/tex]
For example, if x = 1 and y = 2, the inverse of the expression can be written as;
[tex]\frac{1}{x + y} = \frac{1}{(1 + 2)} = \frac{1}{3}[/tex]
Also, if x = 2 and y = 3, the inverse of the expression can be written as;
[tex]\frac{1}{x + y} = \frac{1}{(2 + 3)} = \frac{1}{5}[/tex]
Thus, the equivalent form of the given expression is 1 /(x + y)
Learn more here: https://brainly.com/question/15469690
Is [tex]2 \frac{2}{3} [/tex]
a rational number
Answers
simplify. (3st)^2
a.6s^2t*2
b. 9s^2t^2
c. 3st^2
d. 2s^2t^2
Answers
Answer:
b. 9s^2 t^2
Step-by-step explanation:
If (x*y) ^ 2 = multiple of x and y then power 2
(x * y) ^2 is equal to (x^2 * y^2)
That makes 9s^2t^2
Answer:
Option B. 9s^2t^2 is the correct answer.
Step-by-step explanation:
I just completed it.
What is the relationship between the 6s in 675,002 and 385,621
Answers
Answer:
The value of 6 in 675,002 is 1,000 times greater than the value of 6 in 385,621.
Simplify the following expression. 2p – 10 – 4p – 7
Answers
Answer:
the answer is-2p-3
hope is helpful
Answer:
2p – 10 – 4p –7
–2p –17
I hope I helped you^_^
Josephine enlarged a picture using a photocopier the original photo was 3.5 inches by 5 inches the copy was 8.5 by 12.5 inches . What is the scale factor of the dilation?
Answers
Answer:
the answer is 1 : 2.4 because for every 1 inch on the original image there are 2.4 inches on the modified image.
Step-by-step explanation:
Step 1:
Measure the change in X and Y of a single length of the original image.
X1 = 3.5
Y1 = 5
Step 2:
Measure the change in X and Y of the same length on the modified image.
X2 = 8.5
Y2 = 12.5
Step 3:
use formula SF = X2/X1 = Y2/Y1
(SF = Scale Factor Dilation)
(X2 and Y2 = change in X and Y of the same length on the modified image.)
(X1 and Y1 = change in X and Y of a single length of the original image.)
X2 = 8.5
8.5/X1
X1 = 3.5
8.5/3.5
8.5/3.5 = 2.4
2.4
1 : 2.4
John has an account balance of $20. He receives his weekly paycheck
for work at his part-time job in the amount of $110. He can't find
a bike he wants, so he buys some comic books for $40. Then John
finds his dream bike priced as shown. If he buys the bike now, what
will his account balance be?
Answers
Step-by-step explanation:
Accounts balance=$20
Part time job salary=$110
Total balance
\begin{gathered}\\ \sf\longmapsto 110+20=130\$\end{gathered}
⟼110+20=130$
Now
Price of comics=$40
Price left for bike
\begin{gathered}\\ \sf\longmapsto 130-40=90\$\end{gathered}
⟼130−40=90$
After buying the dream bike, John's account balance will be -$110.
Let's calculate John's account balance after each transaction step by step:
1. Initial balance: $20
2. Weekly paycheck: +$110
Account balance = $20 + $110 = $130
3. Buys comic books: -$40
Account balance = $130 - $40 = $90
4. Buys dream bike: -$200
Account balance = $90 - $200 = -$110
After buying the dream bike, John's account balance will be -$110. This means he will have a negative balance of $110, indicating that he owes the bank or whoever manages the account. It's important to be cautious with negative balances as they can result in overdraft fees or other penalties depending on the account type and the bank's policies.
To know more about account:
https://brainly.com/question/6975956
#SPJ3
What is a rational number between -1/5 and -2/5?
Answers
Answer:
-1/4
Step-by-step explanation:
-0.25
what is the value of the 2 in 3,261? the 3? the 1?
Answers
Answer:
The 2 is 200
The 3 is 3000
The 1 is 1
And if needed
The 6 is 60
Step-by-step explanation:
2 is in hundredths place
3 is in thousand place
6 is in tens place
1 is in ones place
hope this helps
A waiter receives tips from each customer. On average, the tip is 15% of the customer’s bill. At this rate, which of the following is closest to the tip the waiter can expect when a customer has a bill that is $78.20?
A) $8.00
B) $10.00
C) $12.00
D) $14.00
(Pls add in the step-by-step explanation)
Answers
Answer:
C) $12.00
Step-by-step explanation:
Take the price of the bill
78.20
Find 10 %
78.20 * .1
7.82
Take half ( which is 5%)
3.91
Add the two amounts together
7.82+3.91
11.73
Rounding to the nearest dollar
12.00
OR
Round the bill to 80.00
Take 15%
80 * .15
12.00
Please help due tomorrow
Answers
The scaled factor is 3 for all of them.
Jasmine bought 3500g of flour. She used 3/7 of it to bake some tarts and 700g of it to bake a cake. Find the ratio of the amount of flour used for baking the cake to the amount of flour used for baking the tarts to the remaining amount of flour.
Answers
Answer: 15:13
Step-by-step explanation: 7/7=3500
1/7=3500÷7=500500x3=15001500+700=22003500-2200=13001500:130015 : 13 (if there is a need to simplify the ratio)How to determine open interval on which the function is increasing?
Answers
Answer:
To find when a function is increasing, you must first take the derivative, then set it equal to 0, and then find between which zero values the function is positive. Now test values on all sides of these to find when the function is positive, and therefore increasing.
A board of wood measures 58 inches thick. If you stack the boards 6212 inches high, how many boards are in the stack
Answers
Answer:
107 full and .103 of another
Step-by-step explanation:
6212/58 =
In a well-shuffled, standard 52 card deck, what is the probability that a card is a Queen, given that it is a black card
Answers
If instead you know you pulled a black card from the deck and you’re wondering what the probably is that it’s a queen, then it’s 2/26, since there are still 2 black queens, but only 26 black cards.
Answer:
2/52
Step-by-step explanation:
