TODAY'S BRAIN TEASER
Solve it and gain 50 points plus BRAINLIEST
Solve any two questions out of three
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GOOD LUCK
Answers
Answer:
Question 3
Find the range of the function for the domain 2 < x < 3
[tex]f(2)=(2)^2-1=3[/tex]
[tex]f(3)=(3)^2-1=8[/tex]
Therefore, the range of [tex]f(x)=x^2-1[/tex] is [tex]3 < f(x) < 8[/tex] with domain 2 < x < 3
This means that for the function to be continuous, when the domain is x=3, f(x) = 8
[tex]f(3)=2a(3)=6a[/tex]
[tex]\implies 6a=8\implies a=\dfrac43[/tex]
Similarly, when the domain is x > 3, f(x) > 8
[tex]f(3)=b(3)-4=3b-4[/tex]
[tex]\implies 3b-4 > 8 \implies b = 4[/tex]
Therefore, [tex]a=\dfrac43[/tex] and b = 4
Question 5
[tex]\textsf{let}\:u=\ln (x)[/tex]
[tex]\implies \dfrac{du}{dx}=\dfrac{1}{x}\implies dx=x\:du[/tex]
[tex]x=1\implies u=0[/tex]
[tex]x=3 \implies u=\ln 3[/tex]
[tex]\implies \displaystyle \int\limits_{1}^{3} \dfrac{\ln x \sin (\ln x)}{x} \,\:dx=\displaystyle \int\limits_{0}^{\ln 3} \dfrac{u \sin u}{x} \, \cdot x\:du=\displaystyle \int\limits_{0}^{\ln 3} (u \sin u) \, \:du[/tex]
Use integration by parts:
[tex]\displaystyle \int u\dfrac{dv}{dx} \, dx=uv- \displaystyle \int v \dfrac{du}{dx} \, dx[/tex]
[tex]\textsf{where}\:u=u\:\textsf{and}\:\dfrac{dv}{dx}=\sin u[/tex]
[tex]\implies \dfrac{du}{dx}=1\:\textsf{and}\:v=\int \sin u=-\cos u[/tex]
[tex]\implies \displaystyle \int\limits_{0}^{\ln 3} (u \sin u) \, \:du=-u \cos u- \int\limits_{0}^{\ln 3}-\cos u \,\:du[/tex]
[tex]\begin{aligned}\implies \displaystyle \int\limits_{0}^{\ln 3} (u \sin u) \, \:du & =\left[-u \cos u+ \sin u\right]_{0}^{\ln 3}\\ & =[- (\ln 3) \cos (\ln 3)+ \sin (\ln 3)]-[-0 \cos (0)+ \sin (0)]\\\\ & =[- (\ln 3) \cos (\ln 3)+ \sin (\ln 3)]-0\\\\ & = 0.3908925527...\end{aligned}[/tex]
Related Questions
Financial- One of the main differences between a Roth IRA and a traditional IRA is that:
A. You can withdraw money at different ages.
B. The amount you can contribute depends on your age.
C. A Roth IRA is offered by banks, while a traditional IRA is offered by an employer.
D. Contributions are taxed differently.
Answers
The difference between Roth IRA and a traditional IRA is that Contributions are taxed differently. That is option D.
What is Individual Retirement Account (IRA)?An Individual Retirement Account (IRA) is an account that has tax advantages which is used for financial saving for a long term.
In Roth IRA, taxes are being paid while the individual is still working.
In traditional IR, taxes are being paid after retirement.
Therefore, the difference between Roth IRA and a traditional IRA is that Contributions are taxed differently.
Learn more about tax here:
https://brainly.com/question/25783927
The main difference between a Roth IRA and a traditional IRA is that D. Contributions are taxed differently.
What is IRA?It should be noted that IRA simply means an individual retirement account. They're usually not taxed until retirement.
In this case, the main difference between a Roth IRA and a traditional IRA is that the contributions are taxed differently.
Therefore, the correct option is D.
Learn more about IRA on:
https://brainly.com/question/27445373
Amy and Julie are going camping.
Each of them both has a bag of marshmallows. The bag of marshmallows has 60 marshmallows inside. The girls also bring crackers. If Amy and Julie make 15 s'mores, how many crackers did they use?
Answers
Need help or the answer for these two someone help please!!
Answers
Answer:
1) 287.97; 2) 75.396 [in³].
Step-by-step explanation:
1) the rule:
V=1/3 *πhr²;
2) according to the formula above:
V₁=1/3 *3.1415*11*5²=287.97 [in³];
V₂=1/3 *3.1415*8*3²=75.396 [in³].
The following list shows how many brothers and sisters some students have:
3
,
4
,
4
,
5
,
5
,
2
,
5
,
4
,
6
,
3
,
6
,
5
,
3
State the mode.
Answers
Answer:
5
Step-by-step explanation:
So we have the set of numbers: 3,4,4,5,5,2,5,4,6,3,6,5,3.
Mode just means the most repeated number so let's sort them into groups.
(2) (3,3,3) (4,4,4) (5,5,5,5) (6,6).
the most repeated number is 5 which we see in the sequence about 4 times.
Multiply: (x−4)(x+5)
Simplify and write your answer in Standard Form.
HINT
Standard Form: ax2+bx+c
Answers
Answer:
x^2 + x -20
Step-by-step explanation:
First, Multiply
(x)(x) + (x)(5) + (-4)(5) + (-4)(x)
Second, Add The Like Terms Together
X^2 + x + -20
Answer: Its x^2 + 9x -20
Step-by-step explanation:
I did the test and got it wrong
-2.2y - 3.4y -1(-5.7y) + 8.2y
Answers
Answer:
8.3y
Step-by-step explanation:
-2.2y - 3.4y -1(-5.7y) + 8.2y
Apply rule -(-a) = a:
⇒ -2.2y - 3.4y + 5.7y + 8.2y
Factor out common term y:
⇒ y(-2.2 - 3.4 + 5.7 + 8.2)
Carry out operations in the parentheses:
⇒ y(8.3)
Write in standard form:
⇒ 8.3y
Emily got a new fish tank for her pet betta fish.
The tank is shaped like a rectangular prism that
is 48 centimeters long, 30 centimeters wide,
and 30 centimeters high. She is filling the tank
with water from a faucet flowing at a rate of 7.2
liters, or 7,200 cubic centimeters, per minute.
How many minutes will it take Emily to fill the
tank?
Write your answer as a whole number or
decimal. Do not round.
Answers
Explanation:
To start off, we'll need the volume of the fish tank.
Volume of a rectangular block = (length)*(width)*(height)
V = L*W*H
V = 48*30*30
V = 43,200
The volume of the tank is 43,200 cubic cm.
Divide this over the flow rate of 7200 cubic cm per minute to get
(43,200)/(7200) = 6
It will take Emily 6 minutes to completely fill the tank.
A train travels at an average rate of 40 mph and travels for 110 miles . Write an equation
Answers
Answer:
the equation is 40/1 = 110/x hours
Step-by-step explanation:
It would take (2 hours and 45 min) for the train to travel this far
1. The Rock has an 88-gallon fish tank. When it needs to be cleaned, it can be drained at a rate of 6 gallons per minute. Handwritten. Show all work. Complete sentence for each question. (a) Assuming the tank was full, write a function in the form y=mx + b that represents the amount of water in the tank, Y, after X minutes. You will need to know the initial value and the rate of change. (b) How long has the tank been draining for if it has 34 gallons left?
Answers
Using linear function concepts, it is found that:
a) The function is y = 88 - 6x.
b) The tank has been draining it for 9 minutes.
What is a linear function?
A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Item a:
The full volume of the tank is of 88 gallons, hence the y-intercept is of b = 88.The volume can be drained at a rate of 6 gallons per minute, hence the slope is of m = -6.Thus, the equation is given by:
y = 88 - 6x.
Item b:
This is x for which y = 34, hence:
y = 88 - 6x
34 = 88 - 6x
6x = 54
x = 9.
The tank has been draining it for 9 minutes.
More can be learned about linear function concepts at https://brainly.com/question/24808124
The amount of water in the tank is given by y = -6x + 88, it would take 9 minutes for the water to remain 34 gallons.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let y represent the amount of water after x minutes.
The Rock has an 88-gallon fish tank which can be drained at a rate of 6 gallons per minute. Hence:
m = -6, b = 88
y = -6x + 88
For 34 gallons:
34 = -6x + 88
x = 9
The amount of water in the tank is given by y = -6x + 88, it would take 9 minutes for the water to remain 34 gallons.
Find out more on equation at: https://brainly.com/question/2972832
Add the mixed numbers.
6 1/12
+ 3 1/3
The sum is ___
Answers
Answer:
9 5/6
Step-by-step explanation:
6 1/2 + 3 1/3
= (6 + 3) + (1/2 + 1/3)
= 9 + 1 * 3/ 2 * 3 + 1 * 2/ 3*2
= 9 + 3/6 + 2/6
= 9 + 3+2/6
= 9 + 5/6
= 9 5/6
Hey there!
6 1/12 + 3 1/3
= 73/12 + 10/3
= 73/12 + 40/12
= 73 + 40 / 12 + 0
= 113 / 12
= 9 5/12
Therefore, your answer is:
• 113/12
OR
• 9 5/12
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
3827 x 8/8 lees than equal to or greater than 3827 asap
Answers
Answer:
It's equal to itself. Here are the two ways to do this problem. ↓
[tex](3,827 * 8) / 8 = 3,827[/tex][tex]3,827 * 100~percent(8/8) = 3,827[/tex]7u<42
solve the inequality for U
Answers
Answer: u<6
Step-by-step explanation:
Isolate u by dividing both sides of the inequality by 7
[tex]\frac{7u}{7} < \frac{42}{7} \\u < 6[/tex]
u<6
Solution:In order to solve this inequality, we need to divide both sides by 7.Remember, our goal is to find the value of u.We know that 7u is less than 42.So, divide both sides by 7:u<6So u is less than 6.This also means that the numbers less than 6 will satisfy the inequality (make it true).Hope it helps.
Do comment if you have any query.
The following are ages of 16 of the signers of the Declaration of Independence.
43, 62, 35, 45, 42, 46, 39, 31, 60, 37, 39, 47, 35, 36, 35, 40
Send data to calculator
Find 10th and 75th percentiles for these ages.
(a)
The 10th
percentile: 0
(b)
The
75th
percentile: 0
Х
5
?
Answers
Mr. and Mrs. Doran have a genetic history such that the probability that a child being
born to them with a certain trait is 0.61. If they have four children, what is the
probability that at most two of their four children will have that trait? Round your
answer to the nearest thousandth.
Answers
Using the binomial distribution, it is found that there is a 0.011 = 1.1% probability that exactly one of their four children will have that trait.
For each children, there are only two possible outcomes, either they have the trait, or they do not. The probability of a children having the trait is independent of any other children, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X=x)=C_{n,x.}p^x.(1-p)^{n-x}[/tex]
[tex]C_{n,x}=\frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
85% probability of a children having the trait, hence [tex]p=0.85[/tex].They have four children, hence [tex]n=4[/tex]The probability is P(X = 1), hence:
[tex]P(X=x)=C_{n,x.}p^x.(1-p)^{n-x}[/tex]
[tex]P(X=1)=C_{4,1*}(0.85)^1.(0.15)^3=0.011[/tex]
0.011 = 1.1% probability that exactly one of their four children will have that trait.
A similar problem is given at https://brainly.com/question/24863377
Help help help help math math
Answers
Answer:
x> 2
Step-by-step explanation:
Multiply by 6
2x6=12
5x+2>12
Move the 2 and make it subtraction
5x>12-2
Subtract 12-2=10
5x>10 divide by 5
X>2
V
Playing with Numbers
5. Test the divisibility of the following numbers by 8:
(iii) 36712
Answers
Answer:
Last 3 digits 712 is divisible by 8 so 36712 is divisible by 8
Step-by-step explanation:
A circle passes through the point (5,2) and touches the line y + x = 9 at the point (3.6). Find the coordinates of the center and the radius of the circle. Hence, state the standard equation of the circle
Answers
Step-by-step explanation:
solution is attached
MARK ME AS BRAINLISTEspanol
- 9
1
2
P4
8
3
5
6
A triangle is placed in a semicircle with a radius of 3 yd, as shown below. Find the area of the shaded region.
Use the value 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.
Answers
Answer: 5.13 square cm
Step-by-step explanation:
Simplify the radical expression.
Answers
Answer:
-8√(6n).
Step-by-step explanation:
-√(8n) * 2√12
= -√4*√(2n) * 2√4√3
= -2√(2n)*4√3
= -8√(6n)
Helpppp me tell me the fraction
Answers
Answer: [tex]\frac{5}{6}[/tex] of a yard
=========================================================
Explanation:
The longest is [tex]\frac{6}{6}[/tex] yard and the shortest is [tex]\frac{1}{6}[/tex] of a yard.
This is because 6 is the largest numerator and 1 is the smallest numerator.
Subtract the two fractions:
[tex]\frac{6}{6} - \frac{1}{6} = \frac{6-1}{6} = \frac{5}{6}[/tex]
We subtract the numerators while the denominator stays the same at 6 the entire time.
This is the difference between the longest and shortest ribbon, and the unit is in yards.
Determine the equation of the circle graphed below.
Answers
Answer:
(x+6)^2+(y-5)^2 = 3.1622^2
Step-by-step explanation:
The equation for a circle can be represented by (x+_)^2+(y+_)^2 = r^2
So, we already can find this portion of the equation knowing the center of the circle:
(x+6)^2+(y-5)^2= r^2
Next, we find the distance between the two given points to find the radius.
6-5 = 1
-3--6 = 3
1^2+3^2 = c^2
1+9= c^2
10=c^2
3.1622...
So, now we know the full equation.
(x+6)^2+(y-5)^2 = 3.1622^2
the area of a parallelogram measures 171 cm the base of the parallelogram is 18 cm in length which of the following best represents the height of the parallelogram A. 11cm B. 9.5 C. 13.5 D. 8cm give step by step explanation
Answers
Answer:
A=bxh
171 cm=18cmxh
h=171/18
= 9.5 cm
which is B no.
A temperature of 35 degrees Fahrenheit is as cold as a temperature of -35 degrees Fahrenheit.
Answers
Answer:yes
Step-by-step explanation:
What is the equation of this line?
Answers
Answer:
y = 2x
3
Step-by-step explanation:
From the graph, y=4 when x= 6
And
y= -4 when x= -6
So, we can deduce the relationship between x and y.
If i have 3 apples then i lose 1 and get 2000 more then give half to a friend? how many apples do i have.
Answers
Answer:
1001
Step-by-step explanation:
You lose an apple, so now have 2You buy 2000 (you must be rich), so now have 2002You give half to your friend, so divide by 2That gives you 1001 applesfor charles the great please help
Answers
Answer:
119
Step-by-step explanation:
23 plus 64 plus 32
I think I just did this question
Jack dining room room is 5 inches wide and 12 inches long. He wants to install wooden trim around the top of the room. The trim cost 5$ per inch. How much will it cost him to buy enough trim?
Answers
Answer:
$170
Step-by-step explanation:
since he wants to put it around the top and not fill it, it will be a perimeter problem. 5+12+5+12 is 34, and 34 x $5 is 170.
How many milliliters are in 5 liters?
500 mL
5,000 mL
50,000 mL
50 mL
Answers
Answer:
5,000 is the correct answer
This is correct
Multiply and reduce to lowest terms. Convert into a mixed number if necessary.
I will give you brainliest if you answer
Answers
Answer: 1 3/12
Step-by-step explanation: You can multiple straight accross and
5 is equivelant to 5/1 so we would do
5/1 * 3/12 = 15/12 which can get simplified into 1 3/12
Hopt this helps :D
Find the equation of a line that passes through the points (-4,-2) and (6, 3).
Answers
Answer:
[tex]y = \frac{x}{4} [/tex]
Step-by-step explanation:
we find the slope which also represented as m by the formula
[tex] m = \frac{(y2 - y1)}{(x2 - x1)} [/tex]
where from point (-4, -2) the x1 is -4 and the y1 is -2 and also from point (6, 3) the x2 is 6 and the y2 is 3.
so we substitute
[tex] \frac{(3 - ( - 2))}{(6 - ( - 4))} = \frac{(3 + 2)}{(6 + 4)} = \frac{5}{10} = \frac{1}{2} [/tex]
[tex]m = \frac{1}{2} [/tex]
after we have the slope, we calculate the equation of the line by using the formula
[tex](y - y1) = m(x - x1)[/tex]
but for now, we only have y1, m and x1 so can substitute
[tex](y - ( - 2)) = \frac{1}{2} (x - ( - 4))[/tex]
we have to get rid of the fraction 1/2 so we multiply it through by the denominator 2
[tex]2(y + 2) = 2 \times \frac{1}{2}(x + 4) [/tex]
we get
[tex]2(y + 2) = 1 \times (x + 4)[/tex]
so now we expand the brackets
[tex]2y + 4 = x + 4[/tex]
we make y stand alone by grouping liked terms.
[tex]2y = x + 4 - 4[/tex]
we get
[tex]y = \frac{x}{4} [/tex]