Answers
Answer:
[tex]\large \boxed{\sf \ \ 35.805 \ \ }[/tex]
Step-by-step explanation:
Hello,
First of all we need to find the intersection points of y = 12 and
[tex]y=f(x)=e^x+e^{-x}[/tex]
We need to solve the following equation.
[tex]e^x+e^{-x}=12\\\\\text{*** We multiply by }e^x\text{ both side ***}\\\\\left(e^x\right)^2+1=12e^x\\\\\text{*** Let's note } X =e^x\text{, it comes *** }\\\\X^2-12X+1=0[/tex]
[tex]\Delta=b^2-4ac=12^2-4=140=2^2\cdot 35\\\\X_1=\dfrac{12-2\sqrt{35}}{2}=6-\sqrt{35}\\\\X_2=\dfrac{12+2\sqrt{35}}{2}=6+\sqrt{35}\\[/tex]
And, we take the greater solution to solve:
[tex]X=e^x=6+\sqrt{35}<=>\boxed{x=ln(6+\sqrt{5})}[/tex]
Let's note it a.
Let's compute the integral.
We need to compute the following (because 12-f(x) is pair the integral that we are looking for is)
[tex]\displaystyle 2\int\limits^a_{0} {\left(12-(e^x+e^{-x})\right)} \, dx =12*(2a)-2\int\limits^a_{0} {(e^x+e^{-x})} \, dx \\\\=24a-2[e^x-e^{-x}]_{0}^a=24a-2(e^a-e^{-a})[/tex]
We can replace a by the value we already found.
[tex]24\cdot ln(6+\sqrt{35})-2\left( 6+\sqrt{35}-\dfrac{1}{6+\sqrt{35}}\right)\\\\=24\cdot ln(6+\sqrt{35})-2\left(6+\sqrt{35}-\dfrac{\sqrt{35}-6}{(\sqrt{35}-6)(\sqrt{35}+6)}\right)\\\\=24\cdot ln(6+\sqrt{35})-2\left(\dfrac{29*6+29*\sqrt{35}-\sqrt{35}+6}{29}\right)\\\\\\=24\cdot ln(6+\sqrt{35})-2\left(\dfrac{180+28\sqrt{35}}{29}\right)\\\\[/tex]
= 59.46933...-26.66432...=35.8050...
So the answer is [tex]\boxed{\sf \ \ 35.805 \ \ }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Related Questions
HELP QUICK!
If your player is Erik, write an expression that shows all of the ways that Erik will win if Nita chooses 7. If your player is Nita, write an expression that shows all of the ways that Nita will win if Erik chooses 17.
Answers
Answer:
Eric will win if Nita chooses 7 and he chooses and number that is less than 17 (ex. n<17).
Nita will win if Eric chooses 17 and she chooses a number less than 8 (ex. n<8).
Golden Corral charges $11 for a buffet plus $1 for each drink. Western Sizzlin charges $9 for a buffet plus $2 for each drink. Which restaurant has the best deal? (I made up these prices!!) Graph the system of equations. (Show your x/y tables) **Use a ruler or your answer will not come out correctly** or Slope- intercept simulation copy and paste
Answers
Answer:
[see below]
Step-by-step explanation:
Equation 1:Using 'd' as per drink, and 't' as the total cost:
Golden Corral charges 11 dollars for the buffet. ( + 11 )
They also charge 1 dollar for each drink This could be represented by ' 1d' or 'd'.
So, the Golden Corral deal can be represented by:
t = d + 11
Equation 2:The Western Sizzlin restaurants charge 9 dollars for a buffet. ( + 9 )
They also charge 2 dollars for the drinks. This is represented by '2d'.
The Western Sizzlin deal can be represented by:
t = 2d + 9
Graphing the equations together, Golden Corral's line is less steeper then Western Sizzlin's line.
Therefore, Golden Corral is cheaper and should be the best deal compared to Western Sizziln'.
please help on this question I will mark you as brainlist
Answers
Answer:
7, 10, 15, 22, .... 106
3, 12, 27, 48, .... 300
Step-by-step explanation:
Plug n as 1, 2, 3, 4, and 10 to find the terms.
(a)
1² + 6
1 + 6 = 7
2² + 6
4 + 6 = 10
3² + 6
9 + 6 = 15
4² + 6
16 + 6 = 22
10² + 6
100 + 6 = 106
(b)
3(1)²
3(1) = 3
3(2)²
3(4) = 12
3(3)²
3(9) = 27
3(4)²
3(16) = 48
3(10)²
3(100) = 300
Answer:
a) n²+6
U1 = 1²+6 = 1+6=7
U2= 2²+6 = 4+6 = 10
U3= 3³+6= 9+6= 15
U4= 4²+6= 16+6 = 22
U10= 10²+6 = 100+6= 106
So= 7, 10, 15, 22,... 106
b) 3n²
U1= 3(1)²= 3(1)= 3
U2= 3(2)²= 3(4) = 12
U3= 3(3)²= 3(9)= 27
U4= 3(4)²= 3(16)= 48
U10= 3(10)²= 3(100)= 300
So= 3, 12, 27, 48,..., 300
WILL MARK BRAINLIEST! Which of the following is a discrete random variable? a) length of time you play in a baseball game b) length of a car c) volume of water in a tank d) number of candies in a box
Answers
Answer:
d.which is number of candle's in a box
Answer:
number of candies in a box
Step-by-step explanation:
Kina is cleaning the tiles inside her pool today. The pool was 4/7 full of water at the
start of the day. She decided to drain half of the water out of the pool before she
started cleaning the tiles.
1) How full was the pool after Kira drained out half of the water?
2) If there was 1,000 gallons of water left in the pool, how many gallons did
Kina drain out of the pool?
3) How many total gallons of water can the pool hold?
Answers
Answer:
1)2/7
2) 500
3) 1,000
hope you like this answer
stay at home stay safe
keep rocking
2. 500
3. 1,750
Select the correct answer.
Molly rewrote the equation as shown:
-50 + 11 =8-30
50 +11+30=8-30-30
Which property did she use to rewrite the equation?
Answers
[tex]\text{Molly used the addition property of equality}\\\\\text{In the equation shown in the question, you can see that Molly is trying}\\\text{to find the value of "d"}\\\\\text{In order to do this, she must get the "d" variable by itself}\\\\\text{To do this, she adds "3d" to both sides to get the "d" variable on one side}\\\\[/tex]
30 points will give brainliest if correct Please Answer an industrial copy machine
Answers
Answer:
f(x) = 16 * ( 3/4) ^x
Step-by-step explanation:
y = a ( b) ^x
where a is the initial value and b is the growth rate
We know when x =0 y = 16
and when x = 1 y = 12
16 = a * b^0
16 = a * 1
a = 16
So the initial value is 16
12 = 16 * b^ 1
Divide each side by 16
12/16 = b^1
3/4 = b
y = 16 * ( 3/4) ^x
Greetings from Brasil...
In the statement are given 2 moments:
X = 0 ⇒ F(0) = 16
and
X = 1 ⇒ F(1) = 12
F(X) = a . bˣ
F(0) = a . b⁰
16 = a . 1
a = 16
F(X) = a . bˣ
F(1) = a . b¹ a=16 calculated above
12 = 16 . b
b = 12/16
b = 3/4 = 0,75
so,
F(X) = 16 . (3/4)ˣThe senior class at High School A and High School B is planning seperate trips to the local museum. The senior class at High School A rented and filled 13 vans and 1 bus with 184 students. High School B rented and filled 10 vans and 10 buses with 520 students. Every van and every bus had the same number of students in it. How many students can a van carry? How many students can a bus carry?
Based on my answer, each van can carry students and each bus can carry students
Answers
Answer:
Number of students van can carry = 11
Number of students bus can carry = 41
Step-by-step explanation:
Given the following :
HIGH SCHOOL A:
Number of students = 184
Number of vans(v) = 13
Number of buses(b) = 1
Mathematically,
13v + 1b = 184 - - - - (1)
HIGH SCHOOL B:
Number of students = 520
Number of vans(v) = 10
Number of buses(b) = 10
Mathematically,
10v + 10b = 520 - - - - (2)
Multiply (1) by 10 and (2) by 1
130v + 10b = 1840 - - - (3)
10v + 10b = 520 - - - (4)
Subtract (4) from (3)
120v = 1320
v = 11
Substitute v = 11 into (1)
13(11) + 1b = 184
143 + b = 184
b = 184 - 143
b = 41
Number of students van can carry = 11
Number of students bus can carry = 41
PLS HELP : D Each new triangle shown below has one more dot per side than the previous triangle. What is the total number of dots on the 200th triangle of this sequence?
Answers
Hey there!
Let's look for some patterns here.
In the first triangle, we see that there are six dots in total.
In the second triangle, there are nine dots in total.
And, for the third one, we see that there are 12 dots in total.
So, we see that it is counting up by threes because there is one more added to each side.
This is an arithmetic sequence, which means that there is a pattern of adding or subtracting from a base over and over again. There is a specific formula for calculating a certain term in a sequence and you can find proofs of it out there on the internet, but here is the formula.
To find a certain number in a sequence (in our case, 200), you
STEP 1: Take that certain number and subtract 1
200-1=199
STEP 2: You multiply this by the common difference, which is what you add or subtract to make the series. Since we keep on adding 3, our common difference is 3.
199×3=597
STEP 3: You add the first term in the series. In our case, this is the number of dots on the first triangle, which is six.
597+6=603
Therefore, the total number of dots on the 200th triangle of this sequence is 603 dots.
Now you can find a certain term in an arithmetic sequence! Have a wonderful day! :D
the population of weston is 4320. the towns records shot that 45% of the population are males, and 2/3 of these males are married. how many males in weston are married?
Answers
Answer:
1296 males
Step-by-step explanation:
Males in Weston: 4320*0.45 = 1944
Married Males in Weston: 1944*2/3 = 1296
Answer:
Answer is 1296 (For me if I add commas it would mark my answer wrong)
Step-by-step explanation:
SOMEONE PLEASE HELP A GIRL OUT BRAINLIEST! The diameters of Breaburn apples are normally distributed with a mean of 8.2cm and a standard deviation of 2.8cm. If you had a shipment of 2000 apples, how many apples would have a diameter: a) smaller than 5.9cm? b) larger than 10.2cm?
Answers
Answer:
a. 0.2061*2000 apples = 412.20 or about 412 apples.
b. 0.2389*2000 apples = 477.8 or about 478 apples.
Step-by-step explanation:
We have to find the corresponding probabilities using the standard normal table (or also we can use statistics software for doing this).
The parameters for this normal distribution are (without using units):
The mean, [tex] \\ \mu = 8.2[/tex].
The standard deviation, [tex] \\ \sigma=2.8[/tex]
We need to use z-scores, given by:
[tex] \\ z = \frac{x-\mu}{\sigma}[/tex]
For a diameter smaller than 5.9cm, we have:
[tex] \\ z = \frac{5.9-8.2}{2.8}[/tex]
The value for z:
[tex] \\ z = -0.82142 \approx -0.82[/tex]
Then, find the cumulative probability for this z, P(z<-0.82), using the standard normal table (for this, use -0.8 (in right column), and -0.02 in the first row of the table).
Then, P(z<-0.82) = 0.2061
How many apples would have a diameter: a) smaller than 5.9cm?
The answer is 0.2061*2000 apples = 412.20 or about 412 apples.
How many apples would have a diameter: b) larger than 10.2cm?
We can proceed similarly as before. Calculate z, find the cumulative probability using the standard normal table.
[tex] \\ z = \frac{10.2-8.2}{2.8}[/tex]
[tex] \\ z = 0.71428 \approx 0.71[/tex]
Then, P(z<0.71) = 0.7611
But we are asked for P(z>0.71), then (because of the symmetry of the normal distribution):
P(z>0.71) = 1 - P(z<0.71)
P(z>0.71) = 1 - 0.7611
P(z>0.71) = 0.2389
The answer is 0.2389*2000 apples = 477.8 or about 478 apples.
Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer.
Answers
Answer:
72cm2 (2 means squared)
Step-by-step explanation:
you add all the sides once you get the are for each side. To do that you multiply l(w)
Answer:
The surface area of the rectangular prism is [tex]136cm^{2}[/tex]
Step-by-step explanation:
What is surface area?
Surface area is the amount of space covering the outside of a three-dimensional shape.
What is rectangular prism?
A rectangular prism can be defined as a 3-dimensional solid shape which has six faces that are rectangles. A rectangular prism is also a cuboid.
Given, length l= 7cm
breadth b=6cm
height h=2cm
The surface area of the cuboid is,
=2(lb+bh+lh)
=2(7*6+6*2+2*7)
=2(42+12+14)
=2*68
=136 [tex]cm^{2}[/tex]
To know more about surface area, rectangular prism here
https://brainly.com/question/21226782
#SPJ2
which equation is correct?
arccsc(x)=1/cos(x)
Answers
Answer:
arccsc(x)=1/cos(x)
Step-by-step explanation:
Answer:
the answer to your question is D
Step-by-step explanation:
The perimeter of a rectangle is 38 inches. If the length is 3 inches more than the width, find the width.
Answers
Answer:
8 inches
Step-by-step explanation:
For this the length is 11 inches, and when u subtract 3 from that you get 8. 11×2 is 22, 8×2 is 16
22+16=38
Answer:
8 inches
Step-by-step explanation:
P = 2w + 2l
l = w + 3
38 = 2w + 2(w + 3)
38 = 2w + 2w + 6
38 - 6 = 4w
4w = 32
w = 32 : 4
w = 8 inches
Simplify the inequalities and match them with the graphs that represent them. x + 1 15 7x 12 arrowRight arrowRight arrowRight arrowRight Reset Next
Answers
Answer:
I dont quite understand the inequalities, I think it might be the way is shows up, bit the first graph represents x equals all numbers less than 6. The second graph is all numbers greater than 6. Third graph is all numbers less than 7. forth graph is all numbers greater than 7.
Step-by-step explanation:
If you want to give me a better representation of the inequalities, I would be more than happy to help you more!! :)
Hope this helps!!
The graph represents measurements that Mack took in science class. Which units of measure could be related to this graph? A) x = yards and y = feet B) x = cups and y = ounces C) x = feet and y = inches D) y = pounds and y = ounces
Answers
Answer:
it's too late it's been 2years
Given the table of values, determine the base for the exponential function. x y −2 −1 0 1 1 9 2 81
Answers
Answer:
81
Step-by-step explanation:
Find the area of the shaded polygons:
Answers
Answer:
9
Step-by-step explanation:
You could divide this into several smaller shapes, such as triangles and trapezoids. But with this one, it might be simpler to count the full squares, half squares, and partial squares.
Full square - 4
Half squares - 3 ( for an area of 1.5)
Two squares divided in half - 2
Three squares divided in half - 1 (for an area of 1.5)
4+1.5+2+1.5=9
Answer:
9
Step-by-step explanation:
A simpler way of doing this is using pick's theorem.
Pick's theorem is:
i + b/2 - 1 which translates to: interior points + boundary points/2 - 1
Interior points: There is 5 interior points
Boundary points: There is 10 boundary points
---> 5 + 10/2 - 1
= 9
What is the product?
(4x+2)(5x^2+10x+3)
Answers
Answer:
20x³ + 50x² + 32x + 6Step-by-step explanation:
[tex](4x + 2)(5 {x}^{2} + 10x + 3)[/tex]
Multiply the second parentheses by each term from the first parentheses
[tex]4x( {5x}^{2} + 10 x + 3) + 2(5 {x}^{2} + 10x + 3) [/tex]
Distribute 4x through the parentheses
[tex]20 {x}^{3} + 40 {x}^{2} + 12x + 2(5 {x}^{2} + 10x + 3)[/tex]
Distribute 2 through the parentheses
[tex]20 {x}^{3} + 40 {x}^{2} + 12x + 10 {x}^{2} + 20x + 6[/tex]
Collect like terms
[tex]20 {x}^{3} + 50 {x}^{2} + 32x + 6[/tex]
Hope this helps...
Best regards!!
The sum of two numbers is 20 more than one of the numbers and 18 more than the other number. What are the two numbers?
Answers
Answer:
18 , 20Step-by-step explanation:
Let the numbers be x and y
Sum = x + y
Sum = one number + 20
[tex]x + y = x + 20[/tex]
Cancel equal terms on both sides of the equation.
[tex]y = 20[/tex]
Again,
Finding another number
Sum = other number + 18
[tex]x + y = y + 18[/tex]
Cancel equal terms on both sides of the equation
[tex]x = 18[/tex]
Hence, The two numbers are 18 and 20.
Hope this helps..
Best regards!
PLZ I WILL GIVE BRAINLIEST AND IT HAS 20 POINTS The volume of a cylinder is approximately 72 feet cubed. Which is the best approximation of the volume of a cone with the same base and height as the cylinder? 24 feet cubed 216 feet cubed 24 pi feet cubed 216 pi feet cubed
Answers
Answer:
24 feet cubed
Step-by-step explanation:
When comparing the volume formula for a cone and the volume formula for a cylinder, a cone is 1/3 of a cylinder. Therefore, divide 72 by 3 to get the volume of a cone with the same base and height. It would not be 24 pi feet cubed because 72 feet cubed is already multiplied by the pi.
Answer:
24 feet cubed
Step-by-step explanation:
Volume formula:
V cylinder = BhV cone = 1/3BhThe ratio:
V cylinder / V cone = Bh ÷ 1/3BhV cylinder / V cone = 3 ÷ 1Plugging in the value of cylinder to find the value of cone:
72 ÷ x = 3 ÷ 1x= 72 ÷ 3x= 24 ft³24 feet cubed is the best estimate
60 is what percent of 90?
Answers
Answer:
[tex]\boxed{66.67\%}[/tex]
Step-by-step explanation:
[tex]\frac{60}{90}[/tex]
[tex]=\frac{2}{3}[/tex]
[tex]\approx 66.67\%[/tex]
60 is 66.67 percent of 90.
66,(6) %
Step-by-step explanation:90 ............... 100%
60 ....................X%
X = 60×100/90 = 600/9 = 66,(6) %
Plz help me plzzzzzz 64=8c
Answers
Answer:
c=8
Step-by-step explanation:
do find c, we do 64/8=8. We can check our work by doing 8*8 which is in fact 64
24 ÷ [ 33- (1+2)^2] = ?
21 + 3 (2-2^2) = ?
[(14+[tex]\sqrt 4[/tex])÷2^3] - 14 = ?
20 + [18÷(4+1)] - (3^2 + 2) = ?
please simplify the expressions using the proper order of operations.
Answers
Answer:
Below in bold.
Step-by-step explanation:
24 ÷ [ 33- (1+2)^2]
= 24 / ( 33 - 3^2)
= 24 / 24 = 1.
21 + 3 (2-2^2)
= 21 + 3(2 - 4)
= 21 + 3 * -2
= 21 - 6
= 15.
[(14+√4)÷2^3] - 14
= [ (14 + 2) / 8] - 14
= 16/8 - 14
= 2 - 14
= -12.
20 + [18÷(4+1)] - (3^2 + 2)
= 20 + [18÷ 5] - (9 + 2)
= 20 + 3.6 - 11
= 23.6 - 11
= 12.6.
Please help will mark brainly
Answers
Answer:
$3.50
Step-by-step explanation:
23.6÷4=5.90 5.90-2.40=3.50
Answer:
$3.50
Step-by-step explanation:
cost of beads - $2.40
cost of pendant - x
2.40(4) + 4x = $23.60
9.60 + 4x = $23.60
4x = $14
x = $3.50
Each pendant costs $3.50.
Hope this helps.
Suppose a poll of 700 voters says that 45% of the voters will vote for Candidate A for president. Compute the 99% confidence interval
Answers
Answer: (0.4016, 0.4984).
Step-by-step explanation:
Let p be the proportion of voters will vote for Candidate A for president.
Formula for confidence interval for proportion:
[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
, here [tex]\hat{p}[/tex]= sample proportion
n= sample size.
z* =two-tailed critical z- value.
As per given, we have
n= 700
[tex]\hat{p}[/tex] = 0.45
Critical two-tailed z-value for 99% confidence interval = 2.576
Then, the required 99% confidence interval for p would be:
[tex]0.45\pm (2.576)\sqrt{\dfrac{0.45(1-0.45)}{700}}\\\\=0.45\pm(2.576)\sqrt{0.000353571428}\\\\=0.45\pm (2.576)(0.0188035)\\\\=0.45\pm0.04844\\\\=(0.45-0.048437,\ 0.45+0.048437)\\\\=(0.401563,\ 0.498437)\approx(0.4016,\ 0.4984)[/tex]
Hence, the required confidence interval (0.4016, 0.4984).
Please help will mark brainliest
the bearing from Canada to Atlanta is 040 degrees. Calculate the bearing from Atlanta to Canada
Answers
Answer:
The bearing from Atlanta to Canada is 220 degrees
Step-by-step explanation:
Given
Represent Canada with C and Atlanta with A
Bearing from C to A = 040
Required
Determine the bearing from A to C
This concept is referred to as Back Bearing and it's calculated as follows.
Because the front bearing is less 180 (040, to be precise), we have to add it to 180 to get the back bearing;
Hence,
[tex]A\ to\ C\ =\ 180\ + C\ to\ A[/tex]
Substitute 040 for C to A
[tex]A\ to\ C\ =\ 180\ + 040[/tex]
[tex]A\ to\ C\ =\ 220[/tex]
Hence, the bearing from Atlanta to Canada is 220 degrees
(CORRECT ANSWER GETS BRAINLIEST) Drag each object to show whether distance is proportional to time in the situation represented.
Answers
Answer:
a horse running around a race track and
a person running down a field to score a touchdown
DONT HAVE ENOUGH INFORMATION
the two graphs are proportional to time and
a dog jumping at a constant speed for 20min and
a truck passing through 4 cities at a constant speed are not proportional to time because they are constant
Step-by-step explanation:
10. The easily accessible part of an emergency fund is
O cash
O credit cards
O savings
O CDs
Answers
Answer:Si está tratando de ahorrar dinero a través de un presupuesto pero todavía acarrea una deuda grande, comience por la deuda. ¿No está convencido? Sume cuánto gasta por mes en la manutención de la deuda y rápidamente se dará cuenta. Una vez que esté libre de pagar intereses sobre su deuda, ese dinero puede ahorrarse fácilmente. Una línea de crédito personal es solo una opción para consolidar la deuda, para poder cancelarla mejor.
Step-by-step explanation:
Answer: A. Cash
Cash is the most liquid, meaning that it can be accessed quickly and (nearly) everyone accepts it as payment. Though there are some vendors who only accept credit cards.
CD stands for Certificate of Deposit. This is like a savings account but with a higher interest rate. The catch is that the money must be locked into the account for a certain length of time. You cannot withdraw the money unless you want to incur a penalty.
HELP PLZZ!! Joe performed an experiment with a spinner. He spun the spinner and recorded the results in the frequency table. The spinner and the frequency table are given below. Find the experimental probability of the spinner landing on yellow or orange.
Answers
Answer:
7/13
Step-by-step explanation:
add all outcomes: 8 + 6 + 5 + 7 = 26
landing yellow or orange: 8 + 6 = 14
14/26 simplified 7/13
The Experimental probability of the spinner landing on yellow or orange is 7/13.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Yellow= 8
Orange = 6
Red= 5
Blue = 7
Total = 8+6+5+7= 26
So, the Experimental probability of the spinner landing on yellow or orange.
= 8/26 + 6/16
= 14/16
= 7/13
Learn more about Probability here:
https://brainly.com/question/30034780
#SPJ6