The volume of the solid generated by revolving the region bounded by the curves y = 3x, y = x, and y = 9 about the y-axis can be found using the washer method.
First, let's find the points of intersection between the curves. Setting y = 3x and y = x equal to each other, we get:
3x = x
2x = 0
x = 0
So, the curves intersect at the point (0, 0).
Next, we'll find the limits of integration. The region r is bounded between y = x and y = 9. The lower limit of integration is x = 0, and the upper limit of integration is x = 3.
Now, let's consider a vertical slice of the region at a given x-value. The radius of the outer circle (larger radius) is y = 9, and the radius of the inner circle (smaller radius) is given by the equation of the line y = x. The thickness of the washer is dx.
The volume of each washer can be calculated using the formula V = π(R^2 - r^2)dx, where R is the radius of the outer circle and r is the radius of the inner circle.
For the given problem, the volume can be calculated as follows:
V = ∫[0,3] π((9)^2 - (x)^2)dx
Evaluating this integral, we get:
V = π∫[0,3] (81 - x^2)dx
= π[(81x - (x^3)/3)]|[0,3]
= π[(81(3) - (3^3)/3) - (81(0) - (0^3)/3)]
= π[243 - 9]
= 234π
Therefore, the volume of the solid generated is 234π cubic units.
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By , cos(θ) = StartFraction x Over r EndFraction, and by , sin(θ) = StartFraction y Over r EndFraction. Multiplying both sides of the above equations by r, we get that x = r cos(θ) and y = r sin(θ). The states that x2 + y2 = r2. By , we have [r cos(θ)]2 + [r sin(θ)]2 = r2. Applying the , the equation can be written as r2 cos2(θ) + r2 sin2(θ) = r2. Dividing both sides of the equation by r2 results in cos2(θ) + sin2(θ) = 1.
Answer:
-Definition of cosine
-Definition of sine
-Pythagorean theorem
-Substitution
-Laws of exponents.
Step-by-step explanation:
Jason and David each decide to collect baseball cards. Jason has 37 cards and David has 42 cards to begin with. Jason decides to buy 4 more cards each week and David decides to buy 3 each week. A - (blank 1) Write an expression for the number of cards that Jason has, given the number of weeks (w) that he collects. B - (blank 2) Write an expression for the number of cards that David has, given the number of weeks (w) that he collects. C - (blank 3) How long (in weeks) will it take for Jason and David to have the same number of baseball cards?
How frequently does John typically receive account statements from bias bank?
A. Daily
B. Weekly
C. Monthly
D. Annually
John typically receives account statements from bias bank on a monthly basis.Bias bank is an American banking organization which provides customers with various banking services.
Account statements refer to a document that is produced by the bank which shows a summary of all the transactions that have been made by an account holder over a certain period of time.
The answer to the given question is that John typically receives account statements from bias bank on a monthly basis.
Therefore, option C.
Monthly is the correct answer. John may also request for account statements more frequently than the standard monthly statement.
It is important to review these account statements regularly to ensure that all the transactions have been made correctly, and to identify any errors or fraudulent activity that may have occurred.
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Find three functions named f(x), h(x) and g(x) that when combined the expression equals x2-5x+12. You must use two different operations.
Write two functions f(x) and g(x) such that f(g(x))= -4. What did you let x equal?
The volume of wood in a tree varies jointly as the height of the tree and the square of the distance around the tree trunk. If the volume of wood is 15.84 cubic feet when the height is 22 feet and the distance around the trunk is 3 feet, what is the volume of wood obtained from a tree that is 32 feet tall having a measurement of 4 feet around the trunk?
Answer:
64
Step-by-step explanation:
Answer:
solve for k: 31 - 3k = 10
Answer:
k = 7
Step-by-step explanation:
Step 1: Write equation
31 - 3k = 10
Step 2: Solve for k
Subtract 31 on both sides: -3k = -21Divide both sides by -3: k = 7Step 3: Check
Plug in k to verify it's a solution.
31 - 3(7) = 10
31 - 21 = 10
10 = 10
factor 144abc−108ab . if the expression cannot be factored, write cannot be factored.
The factored form of the expression 144abc - 108ab is 36ab(4c - 3).
To factor the expression 144abc - 108ab, we can first identify the common factors of the terms.
In this case, we can see that both terms have a common factor of 36ab:
144abc - 108ab = 36ab(4c - 3)
So, the expression can be factored as 36ab(4c - 3).
This means that the expression is not prime and can be simplified further by factoring out the common factor.
By factoring out the common factor of 36ab, we obtain the simplified form of the expression as 36ab times the binomial (4c - 3).
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Please I need help please find the exponent for “3”
Answer:
53
Step-by-step explanation:
Answer:
the exponent is 3 and 4 because the exponents is suppose to be on top of the base.
Step-by-step explanation:
3x2+(2y+z3) if x=4, y=5, and z=3
Answer:
43 or 25
Step-by-step explanation:
Plug all of the numbers into the equation.
(i'm not sure if the 3x2 is a letter or not, so i'll just solve it anyways for both.)
3(4)(2) + (2(5) +(3)(3) = 43
If it's not a letter then
3x2 + (2(5)+3(3)) = 25
what is the total weight of 7 basketballs that weigh 23 ounces each?
Answer:
10.0625 pounds exactly. I'm assuming that's what this question is asking, or 161 ounces.
Step-by-step explanation:
First, multiply 7 by 23, we get 161 ounces. Assuming the question is asking for pounds, and then we divide by 16. As there are 16 ounces in a pound. 161/16 = 10.0625.
Not sure the rounding so this is the number you get from a calculator exactly.
Please show all working.
b 2. Supppose a = 0, b = 0 and = a b A) 2015 B) 2016 = 2017. Find the value of C) 2017 b+c a+b' (D) 2018 E) 2019
Given the values a = 0, b = 0, and c = a + b, we are asked to find the values of expressions involving these variables: C = 2017(b + c), D = 2018, and E = 2019.
Given a = 0 and b = 0, we can substitute these values into the expressions involving c.
Since c = a + b, we have c = 0 + 0, which simplifies to c = 0.
Now we can evaluate the expressions:
A) 2015: No information is provided to determine the value of 2015. We cannot evaluate this equation.
B) 2016: Similarly, no information is provided to determine the value of 2016. We cannot evaluate this expression.
C) 2017(b + c): Substituting c = 0, we have C = 2017(b + 0) = 2017b.
D) 2018: This expression has a constant value of 2018.
E) 2019: This expression has a constant value of 2019.
In summary, the values of the expressions are as follows: C = 2017b, D = 2018, and E = 2019. The values of A and B cannot be determined without additional information.
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D Question 13 3 pts [True or False] For a standardized normal distribution, Z, the probability that Z is greater than 1.50 is less than the probability that Z is greater than 2.50. True O False < Prev
For a standardized normal distribution, Z, the probability that Z is greater than 1.50 is less than the probability that Z is greater than 2.50. False, is the correct statement regarding the given statement.
In statistics, the standardized normal distribution is a normal distribution with a mean of zero and a standard deviation of one. It is also known as the standard normal distribution. The distribution is entirely defined by its mean and standard deviation. For example, any normal distribution can be standardized by subtracting its mean and dividing by its standard deviation.This distribution is a continuous probability distribution.
A continuous probability distribution is a probability distribution that assigns probabilities to an infinite number of possible outcomes that are not countable. These probabilities are expressed as the area under the curve in a continuous probability distribution. The total area under the curve of a continuous probability distribution is always equal to one.
The statement given "For a standardized normal distribution, Z, the probability that Z is greater than 1.50 is less than the probability that Z is greater than 2.50" is false.
This is because the normal distribution curve is a symmetrical curve and the probability of being greater than a value of 1.50 or 2.50 is the same.
Therefore, the probability of Z being greater than 1.50 is the same as the probability of Z being greater than 2.50. The answer is False.
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a submarine was approximately 625 feet below sea level if it descends another 250 feet what is its new positions write your answer as an integer
Answer:
875
Step-by-step explanation:
625 feet + 250 feet = 875 feet
HELP WILL MARK YOU BRAINLIEST NO GUESSES PLZ!!!!
x° + 90° + 52.6 = 180°
because a triangle adds up to 180° and that specific triangle is a right angle triangle which means that it consists of angle adding up to 90°
A tuxedo rental service charges a $150 flat fee for a suit plus $50 per additional day. Write and solve an equation to determine the cost of renting the tuxedo for 4 days.
Answer:
150+50*4=350
Step-by-step explanation:
hope it helped sorry if it's not what you wanted.
Answer: 150 + 50(d) = a
It would cost $350 to rent the tuxedo for four days
Steps: 150 + 50(d)
d = days = 4
a = total amount
Plz mark brainliest:)
Can someone awsner this for me honestly I’m sorry but I really need these awsner but I need the answers for these 3 to
1. 50 + 20x = 240
2. 85% so more than 75%
3. 25.9% so about 26%
Hope this helps and please consider marking branliest if this helped you
A system of linear equations is given by the tables. One of the tables is represented by the equation y = - 1/3x + 7. x y 0 5 3 6 6 7 9 8 x y -6 9 -3 8 0 7 3 6 The equation that represents the other equation is y = x + . The solution of the system is ( , )
The solution of the system is (- 3, 8).
A system of linear equations is given by two tables. The first table is represented by the equation y = - 1/3x + 7, while the second table is not represented by any equation.
However, we can determine the equation of the second table by finding the slope of the line that passes through the points (0, 5) and (3, 6).slope = change in y/change in x= (6 - 5)/(3 - 0)= 1/3
Since the slope of the line is 1/3 and it passes through the point (0, 5), we can use point-slope form to find the equation of the line. Using point-slope form,
the equation of the second table is:y - 5 = 1/3(x - 0)y = 1/3x + 5To solve the system of equations, we can use substitution. We can substitute y = - 1/3x + 7 into the equation y = x + 5:y = x + 5- 1/3x + 7 = x + 5- 1/3x = - 2x = 6x = - 3
The solution for x is x = - 3. We can use this value to find the solution for y by substituting into either of the equations. Using y = - 1/3x + 7, we get:y = - 1/3(- 3) + 7= 1 + 7= 8
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Find the measure of angle MKN.
Answer:
m∠MKN = 61°
Step-by-step explanation:
Since KN is a perpendicular bisector, m∠NKM and m∠MKJ have to add up to 90°.
Step 1: Set up equation
6x + 7 + 3x + 2 = 90
Step 2: Solve for x
Combine like terms: 9x + 9 = 90Subtract 9 on both sides: 9x = 81Divide both sides by 9: x = 9Step 3: Find m∠MKN
m∠MKN = 6x + 7
m∠MKN = 6(9) + 7
m∠MKN = 54 + 7
m∠MKN = 61°
Answer:
61
Step-by-step explanation:
Since JKL is a straight line, it equals 180
JKM + MKN + NKL = 180
3x+2 + 6x+7 + 90 = 180
Combine like terms
9x+99 = 180
Subtract 99 from each side
9x+99-99= 180-99
9x =81
Divide each side by 9
9x/9 = 81/9
x=9
We want MKN
6x+7 = 6*9 +7 = 54+7 = 61
Whats the solution X3=9
Answer:
x=2.080084
Step-by-step explanation: take cube root
Answer:
Forgive me if i am incorrect but i am pretty sure if i am not mistaken x=3*3=9
Step-by-step explanation:
When you look at it x is attach to the 3 thus making it multiplication but you would have to do the opposite. Which is division so 9 divide by 3 is 3.
Hope this help you
what is 2+2-5×6? ill mark brainliest
Answer:
-26
Step-by-step explanation:
2+2−(5)(6)=
-26
Answer:
-26
Step-by-step explanation:
2+2-5×6 = 2+2- -2630 = 4-30 = -26
A truck can be rented from Acme
Truck Rental for $80 per week plus $0.28 per mile.
How many miles can be driven if you have at most $100 to spend on truck rental.
Answer: 71.429 miles
Step-by-step explanation:
The charge for the rental truck can be represented by the equation: y= 0.28m+80
m is the miles driven
y is the total cost
Plug in 100 for y because that’s how much you have to spend
100=0.28m+80
-80 -80
20=0.28m. Divide both sides by 0.28
71.429 miles
You can round it again if you want
71.43 or 71.4 or 71
0.3401224 ÷ 0.717
divide, and then round the answer to two decimal places
Answer: .47
Step-by-step explanation:
question in link below
Answer:
105
Step-by-step explanation:
2x17=34
17x2.5=42.5
1.5x17=25.5
1/2x2x2x1.5=3
34+42.5+25.5+3=105
Answer Po Ba Ay 11.33?
Step-by-step explanation:
Calc
set up a proportion and use cross multiplication to solve.
100 is 250% of____
Answer:
25
Step-by-step explanation:
What is the equation? Been trying for 20minutes
Answer:
y = x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2. 0) and (x₂, y₂ ) = (0, 2) ← 2 points on the line
m = [tex]\frac{2-0}{0+2}[/tex] = [tex]\frac{2}{2}[/tex] = 1
the line crosses the y- axis at (0, 2 ) ⇒ c = 2
y = x + 2 ← equation of line
Please help me with these three answers. It’s solving systems of equations.
Can someone please help me solve [tex]|b|\ \textless \ 3[/tex]
9514 1404 393
Answer:
-3 < b < 3
Step-by-step explanation:
The inequality is equivalent to two inequalities.
For b ≥ 0, this is ...
b < 3
Together with the restriction that b ≥ 0, the solution to this is ...
0 ≤ b < 3
__
For b ≤ 0, this is ...
-b < 3
b > -3 . . . . multiply by -1
Together with the restriction that b ≤ 0, the solution to this is ...
-3 < b ≤ 0
__
The solution is the 'or' of these two solutions. They can be expressed as the single compound inequality ...
-3 < b < 3
_____
Comment on absolute value inequalities
When the inequality is of the form ...
|p| < q
It can be written as the equivalent compound inequality ...
-q < p < q
as we showed above.
Which expression is equivalent to 5(2+7)?
0 205+7)
O2+7(5)
05(2)+7
05(2)+5(7)
Answer:
4
5(2)+5(7)
Step-by-step explanation:
4. The 3 x 3 matrix B given below, in terms of a scalar constant k. k 0 1 B = -11 k-3 9 -11 0 k (a) Given that B is singular, find the value of k. (b) Given instead that λ = 2 is an eigenvalue of B, determine the value of k on thi occasion.
(a) The value of k for which the matrix B is singular is k = -2.
(b) When λ = 2 is an eigenvalue of B, the value of k is not uniquely determined.
(a) To determine the value of k for which the matrix B is singular, we need to find when the determinant of B is equal to zero. The determinant of B is given by:
[tex]|B| = (k)((k)(9) - (-11)(0)) - (0)((-11)(9) - (k)(-11)) + (1)((-11)(0) - (k)(-11))[/tex]
Simplifying the determinant expression and setting it equal to zero, we get:
[tex](k)(9k + 11k) + (11)(-11) = 020k^2 - 121 = 0[/tex]
Solving this quadratic equation, we find two possible values for k: k = -11/4 and k = 11/4. However, for B to be singular, the determinant must be zero, which means the value of k is k = -11/4.
(b) To determine the value of k when λ = 2 is an eigenvalue of B, we need to find the values of k that satisfy the equation Bv = λv, where v is the eigenvector corresponding to λ. Substituting the given values, we have:
Bv = 2v
Expanding the equation, we get:
[tex](k)(v1) + (0)(v2) + (1)(v3) = 2v1\\(-11)(v1) + (k)(v2) + (0)(v3) = 2v2\\(0)(v1) + (-11)(v2) + (k)(v3) = 2v3[/tex]
Simplifying these equations, we find that there are multiple solutions for k that satisfy the given conditions. The value of k on this occasion is not uniquely determined.
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can u guys please help me
with this question??!!! 10 points and brainy will be awarded PLEASE!?
Answer:
The answer is the last option.
Step-by-step explanation:
What is the value of x in the product of powers below?
6 Superscript 9 times 6 Superscript x = 6 squared
Negative 11
negative 7
7
11
Answer:
Step-by-step explanation:
We can start by simplifying the left side of the equation using the product of powers rule, which states that when we multiply two powers with the same base, we can add their exponents.
6^9 * 6^x = 6^2
Now we can use the rule to add the exponents on the left side of the equation:
6^(9+x) = 6^2
Since the bases are the same, we can equate the exponents:
9 + x = 2
Subtracting 9 from both sides gives us:
x = -7
Therefore, the value of x in the product of powers equation is -7.
