find the exact area between f(x) = 2x and g)x_ = 6 - x from the vertical axis to their point of intersecti0n
Answers
The area between the curves f(x) = 2x and g(x) = 6 - x from the vertical axis to their point of intersection is 3 square units.
To find the area between the curves, we need to determine the limits of integration, which will be the x-values where the curves intersect. Setting the equations equal to each other, we get:
2x = 6 - x
Solving for x, we get:
3x = 6
x = 2
So the curves intersect at x = 2. To find the area between them, we integrate the difference of the functions from 0 to 2:
A = ∫(6 - x - 2x)dx from 0 to 2
= ∫(6 - 3x)dx from 0 to 2
= [6x - (3/2)x^2] from 0 to 2
= [6(2) - (3/2)(2)^2] - [6(0) - (3/2)(0)^2]
= 6 - 3
= 3
Therefore, the exact area between the curves f(x) = 2x and g(x) = 6 - x is 3 square units.
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Related Questions
Steven and Anna start running from the school. Steven starts 15 seconds before Anna and runs at a rate of 3 feet per second. Anna runs at a rate of 4 feet per second. Which equation could you solve to find when Anna will catch up to Steven?
Answers
Answer:
Step-by-step explanation:
An application of linear equations can be found in distance problems. When
solving distance problems we will use the relationship rt = d or rate (speed) times
time equals distance. For example, if a person were to travel 30 mph for 4 hours.
To find the total distance we would multiply rate times time or (30)(4) = 120.
This person travel a distance of 120 miles. The problems we will be solving here
will be a few more steps than described above. So to keep the information in the
problem organized we will use a table. An example of the basic structure of the
table is blow:
Answer:
Step-by-step explanation:
Which is the larger amount?
A) 5 cups
B) 500 milliliters
Answers
Answer:
a
Step-by-step explanation:
we know that for a probability distribution function to be discrete, it must have two characteristics. one is that the sum of the probabilities is one. what is the other characteristic?
Answers
The other characteristic of a discrete probability distribution function is that each individual outcome has a probability greater than or equal to zero.
In other words, the probability assigned to each possible value in the distribution must be non-negative. This ensures that the probabilities are valid and that the distribution accurately represents the likelihood of each outcome occurring. So, the two characteristics of a discrete probability distribution function are: (1) the sum of the probabilities is one, and (2) each individual outcome has a probability greater than or equal to zero.
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What is the value of the x in the diagram ?
Answers
Answer:
138
Step-by-step explanation:
Angle ∠42 and vertical angle of ∠x are supplementary
∠42 + ∠x = ∠180
∠x = ∠180 - ∠42
∠x = 138
Draw a tape diagram to represent 8-2+2=8
Answers
A tape diagram to represent 8-2+2 will be:
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
^ ^
| |
| |
8-2 +2
| |
| |
v v
+-----+-----+ +-----+
| | | | |
+-----+-----+ +-----+
6 2
What is a tape diagram?A tape diagram is a rectangular visual model resembling a piece of tape, that is used to assist with the calculation of ratios and addition, subtraction, and commonly multiplication.
In this diagram, the first segment with 8 boxes represents the starting quantity of 8. Then, we subtract 2 from that by crossing out 2 boxes, leaving us with 6. Finally, we add 2 by drawing a new segment of 2 boxes, bringing us to a total of 8.
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You roll 2 dice. If the sum of the dice is: 2, 3, 4 you win $20. If the sum is 5, 6, 7, 8 you win $10. If the sum is 9, 10, 11 you lose $20. If the sum is 12 you lose $25. It costs $5 to play. Create a probability distribution of the random variable, "winnings" including the cost to play, for this game. What is the expected value of the "winnings" for this game? What is the variance for the "winnings" for this game? What is the standard deviation? Is this game a "fair game"? Why or why not?
Answers
Answer:
1) The expected value of the "winnings" is $(-0.97\(\overline 2\))
2) The variance for the "winnings" is $0.57966
3) The standard deviation for the "winnings" is$0.761354
4) The game is not a fair game because one is expected to lose $0.97\(\overline 2\)
Step-by-step explanation:
1) The probability of having a sum of 2 = 1/6×1/6 = 1/36
The probability of having a sum of 3 = 1/6×1/6 = 1/36
The probability of having a sum of 4 = 1/6×1/6 + 1/6×1/6 = 1/18
The probability of having a sum of 5 = 1/6×1/6 + 1/6×1/6 = 1/18
The probability of having a sum of 6 = 1/6×1/6 + 1/6×1/6 + 1/6×1/6 = 1/12
The probability of having a sum of 7 = 1/6×1/6 + 1/6×1/6 + 1/6×1/6 = 1/12
The probability of having a sum of 8 = 1/6×1/6 + 1/6×1/6 + 1/6×1/6 = 1/12
The probability of having a sum of 9 = 1/6×1/6 + 1/6×1/6 = 1/18
The probability of having a sum of 10 = 1/6×1/6 + 1/6×1/6 = 1/18
The probability of having a sum of 11 = 1/6×1/6 = 1/36
The probability of having a sum of 12 = 1/6×1/6 = 1/36
The values are;
For 2, we have 1/36 × (20 - 5) = 0.41\(\overline 6\)
For 3, we have 1/36 × (20 - 5) = 0.41\(\overline 6\)
For 4, we have 1/18 × (20 - 5) = 0.8\(\overline 3\)
For 5, we have 1/18 × (10 - 5) = 0.2\(\overline 7\)
For 6, we have 1/12 × (10 - 5) = 0.41\(\overline 6\)
For 7, we have 1/12 × (10 - 5) = 0.41\(\overline 6\)
For 8, we have 1/12 × (10 - 5) = 0.41\(\overline 6\)
For 9, we have 1/18 × (-20 - 5) = -1.3\(\overline 8\)
For 10, we have 1/18 × (-20 - 5) = -1.3\(\overline 8\)
For 11, we have 1/36 × (-20 - 5) = -0.69\(\overline 4\)
For 12, we have 1/36 × (-25 - 5) = -0.69\(\overline 4\)
The expected value of the winnings is given as follows;
0.41\(\overline 6\) + 0.41\(\overline 6\) + 0.8\(\overline 3\) + 0.8\(\overline 3\) + 0.8\(\overline 3\) + 0.41\(\overline 6\) + 0.41\(\overline 6\) + -1.3\(\overline 8\) -1.3 - 0.69\(\overline 4\) - 0.69\(\overline 4\) = -0.97\(\overline 2\)
Therefore, the expected value = $-0.97\(\overline 2\), which is one is expected to lose $0.97\(\overline 2\)
2) Using Microsoft Excel, we have;
The variance for the "winnings", σ² = $0.57966
3) The standard deviation for the "winnings" = √σ² = √(0.57966) ≈ $0.761354
4) The game is not a fair game because one is expected to lose $0.97\(\overline 2\)
can someone pls help me
Answers
Answer:
B
Step-by-step explanation:
This ones pretty simple, all you need to do is write the two varible equations for how many fruits they bought and how much it cost.
In the first one there are 3 apples and 4 oranges, x represents the price of the apples and y represents price of the number of oranges, so the equation would be written like this:
3x+4y=
Then after the equal sign you put how much the total price was in total, which is 4.25 in the first one so
3x+4y=4.25
On the second equation there are 5 apples and 2 oranges, again x will be the price of the apples, and y will be the price of the oranges. The total price of both apples and oranges is 4.75 for this one, so the equation would be written like this:
5x+2y=4.75
Both equations together would be
3x+4y+4.25
5x+2y=4.75
This is the anwser
How to solve 1000/11 via long divison… pls help with full working out
Answers
The number that is being divided is called the dividend, and the number that it is being divided by (in this case, 11) is called the divisor. The result of the division is the quotient.
See attached picture.
Step 1 - set up for long division
Step 2 - 11 divides into 100 (9 times)
9 x 11 = 99
Subtract and you have 1
Step 3 - drop the remaining number (0)
11 does not divide into 10 so it goes
(0) times for the answer 90 R 10.
The second example is if you wanted to take your division further into a decimal. In this case, you add a decimal at the end of your dividend and a decimal into your answer at the same place, and perform the same steps. In this case it’s a non terminating repeating decimal and it would continue on forever.
What is the equation of the line that is perpendicular to
the given line and passes through the point (3, 0)?
Answers
Answer:
y=-0.6x+1.8
Step-by-step explanation:
Since the line is perpendicular to that line, it has the same slope. So, the slope is -3/5. Also, it passes through the point 3, 0. So, y=-3/5x + b. To find the y intercept, lets solve the equation with the value of x being the x intercept. 0=-3/5(3)+b. 0=-9/5+b. Add 9/5 to both sides. b=1 4/5 So, the answer is y=-0.6x+1.8
If the mpc increases in value, what will happen to the slope of the consumption function?
Answers
If the mpc increases in value, the consumption function will become steeper.
What is MPC ?
MPC is an advanced method of process control that is used to control a process while satisfying a set of constraints. In economics, the marginal propensity to consume is a metric that quantifies induced consumption, the concept that the increase in personal consumer spending occurs with an increase in disposable income. The proportion of disposable income which individuals spend on consumption is known as propensity to consume. MPC is the proportion of additional income that an individual consumes.
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Select the correct answer. rational functions v and w both have a point of discontinuity at x = 7. which equation could represent function w? a. w(x) = v(x − 7) b. w(x) = v(x 7) c. w(x) = v(x − 7) 7 d. w(x) = v(x) 7
Answers
The following equation could be used to represent a function w:
= w(x)=v(x-7)+7
According to the information provided,
The point of discontinuity of rational functions is at x=7.
When a rational function has a point of discontinuity, it generally occurs when,
q(x) = r(x-a), where x = a
In this case, we must pay attention to the following relationship, which is a combination of a parent rational function and a vertical translation:, (2)
If we know that a=7 and k=7.
The equation which can represent w is as follows,
w(x) = v ( x-7 ) + 7
A rational function can be represented as a polynomial split by another polynomial. Because polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros in the denominator.
Example: x = f(x) (x - 3). The denominator, x = 3, has only one zero. Rational functions are no longer defined when the denominator is zero.
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if r(x) = 3x – 1 and s(x) = 2x + 1, which expression is equivalent to ?
a. 3 (6)-1/2(6) +1
b. (6)/ 2(6)+1
c. 36-1/26+1
d. (6)-1/(6)+1
Answers
If the expression \(r(x) = 3x - 1\) and the expression \(s(x) = 2x + 1\) , then the expression equivalent to \(\frac{r}{s} (6)\) is (a) \(\frac{3(6)-1}{2(6) +1}\) .
What are Algebraic Expression ?
The algebraic Expression are defined as the expressions that are written with the combination of variables and constants joined by mathematical operators , For Example : \(3x+7\) .
Here the two expressions are given as \(r(x) = 3x - 1\) and \(s(x) = 2x + 1\) ;
we have to find equivalent expression for \(\frac{r}{s} (6)\) ;
By the Division Property of Algebraic Expression ;
it can be written as : \(\frac{r(6)}{s(6)}\) ;
So , Substituting \(x=6\) , in r(x) ,
we get ; \(r(6) = 3(6) - 1\) , ......equation(1)
On Substituting \(x=6\) , in s(x) ,
we get ; \(s(6) = 2(6)+1\) , ....equation(2) ;
Substituting the values of r(6) and s(6) from equation(1) and equation(2) in \(\frac{r(6)}{s(6)}\) ;
we get ;
⇒ \(\frac{r(6)}{s(6)} = \frac{3(6)-1}{2(6) +1}\) ;
Therefore , the expression equivalent to \(\frac{r}{s} (6)\) is \(\frac{3(6)-1}{2(6) +1}\) .
The given question is incomplete , the complete question is
If r(x) = 3x - 1 and s(x) = 2x + 1, which expression is equivalent to r/s(6) ?
(a) \(\frac{3(6)-1}{2(6) +1}\)
(b) \(\frac{(6)}{2(6)+1}\)
(c) \(\frac{36-1}{26+1}\)
(d) \(\frac{(6)-1}{(6)+1}\)
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I'm solving polynomial inequalities and I need to know (-4-x)(x+7)(x-3) > 0
Answers
Given the inequalities
(-4 -x)(x+7)(x-3) >0
Step 1: Find the zeros of the polynomials
For (-4 -x)
\(\begin{gathered} (-4-x)=0 \\ -4\text{ -x =0} \\ -x=4 \\ x\text{ = -4} \end{gathered}\)For (x+7)
\(\begin{gathered} x\text{ +7 = 0} \\ x\text{ = 0 - 7} \\ x\text{ = -7} \end{gathered}\)For (x-3)
\(\begin{gathered} x-3\text{ =}0 \\ x\text{ = 0+ 3} \\ x\text{ = 3} \end{gathered}\)Step 2: Draw the range of values on a number line
Step 3: Construct a table to test the range
The table tests the ranges that were obtained from the number line
column 1 shows the range
The values are then tested for each range.
Column 6 shows the product of all the values gotten
The solution to the polynomial is that which was accepted
Since the inequality sign is that of a greater sign, we will accept those that are positive
Hence the solution is
\(\begin{gathered} x\text{ < -7 } \\ \text{and} \\ -4
Can someone help me ASAP it’s due tomorrow. I will give brainliest if it’s all done correctly. Show work.
Answers
The probability that he will reach out into his pocket and pull out a $10 bill each time is 1/7. The correct option is the second option 1/7
Calculating the Probability of pulling out a $10 billFrom the question, we are to determine the probability of William pulling out a $10 bill twice without replacement
The probability of pulling out a $10 bill on the first draw is 3/7, since William has three $10 bills out of a total of seven bills in his wallet.
Since William does not replace the first bill when he pulls out the second one, there will be one less bill in the wallet for the second draw. Therefore,
The probability of pulling out another $10 bill on the second draw is 2/6 (since there will be two $10 bills left out of six bills in the wallet).
Thus,
The probability that he will reach out into his pocket and pull out a $10 bill each time is
P(two $10 bill) = 3/7 × 2/6
P(two $10 bill) = 3/7 × 1/3
P(two $10 bill) = 1/7
Hence, the probability is 1/7
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HELP I NEED HELP PLEASE I NEED TO FINISH THIS RIGHT NOW ITS URGENT. WILL BE OFFERED BRAINLIEST
Answers
Answer:
102
Step-by-step explanation:
4=51 + 51= 102
And make sure to add those dot things at the top. Lol I forgot what there called haha how this helps!
The diameter of a sphere is 4 centimeters. Which represents the volume of the sphere? StartFraction 32 Over 3 EndFractionπ cm3 8π cm3 StartFraction 64 Over 3 EndFractionπ cm3 16π cm3
Answers
Answer:
The volume of the sphere is 32 π /3 cm^3
Step-by-step explanation:
Mathematically, the volume of a sphere can be calculated using the formula below;
V = 4/3 * pi * r^3
Now since we have the radius and diameter = 2 * radius
radius = diameter/2 = 4/2 = 2
Substituting this value into the volume equation;
V = 4/3 * pi * 2^3 = 32pi/3
Answer:
The correct answer is A
Step-by-step explanation:
Rearrange the equation
a = 1/2 (b-c)
to make b the subject.
Answers
Answer:
b = 2a + c
Step-by-step explanation:
Given
a = \(\frac{1}{2}\) (b - c)
Multiply both sides by 2 to clear the fraction
2a = b - c ( add c to both sides )
2a + c = b
After the rearrangement, the equation as b the subject b = 2a + c.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given that the equation;
a = 1/2 ( b - c)
Rearranging the equation;
a = 1/2 ( b - c)
Multiplying 1/2 to the the terms of brackets,
a = (b/2) - (c/2)
b/2 = a + (c/2)
Divide by 2 on both sides of the equation;
b = 2a + c
Therefore, the equation as b the subject b = 2a + c.
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Aubrey jarred 24 liters of jam after 4 days. How much jam did Aubrey jar if she spent 5 days making jam? Assume the relationship is directly proportional.
? liters
I NEED HELP PLZ I WILL GIVE MORE POINTS I NEED 20 MORE POINTS TO GET FROM A 64 TO AN 80
Answers
your welcome
A fair die is cast four times. Calculate
the probability of obtaining at least two
6's.
Round to the nearest tenth of a
percent.
Answers
Answer:
That's incredible. I have that exact problem on my website.
Here is my explanation.
My website says probability = 0.131944444444445
https://www.1728.org/occupncy8.htm
Step-by-step explanation:
A holiday company offer a 12% discount if you book before 31st March. How much
would you pay today for a holiday to France if the full price is £1,245?
Answers
You would have to pay £1,095.6.
Please Help. What expression is equivalent to 6( t - 5 ) + 3
A. 6t - 2
B. 6t - 12
C. 3 ( 2t - 11 )
D. 3 ( 2t + 9 )
Answers
Explanation: The simplified version of 6(t-5)+3 is 6t+27, and D gives us the same answer.
Domain-Functions
state the domain and range of the function
Answers
The domain of the function is [-2, 2] and the range of the function is [-1, 2].
If there is a function y = x + a, then the domain is the set of all values that x can take and the range is the set of all the values that y can take for the function to exist.
Here, we are given a function as shown in the graph.
As we can see the function is defined only for the given points, that is, it has 2 endpoints.
Just by looking at the graph we can see that x can take values from -2 to 2. Thus, the domain of the function is [-2, 2].
We use closed brackets as x can be -2 and 2 as well. Similarly, we can see that y can take values from -1 to 2.
Thus, the range of the function is [-1, 2].
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If f(x)=4x-16andtheDomainis{-2,-1,0,3,6},findtheRange of the function. Show all work.
Answers
Answer:
R={-24,-20, -16, -4, 8}
Step-by-step explanation:
f(x)=4x-16
f(-2)=4(-2)-16
f(-2)=-8-16
f(-2)=-24
f(x)=4x-16
f(-1)=4(-1)-16
f(-1)=-4-16
f(-1)=-20
f(x)=4x-16
f(0)=4(0)-16
f(0)=0-16
f(0)=-16
f(x)=4x-16
f(3)=4(3)-16
f(3)=12-16
f(3)=-4
f(x)=4x-16
f(6)=4(6)-16
f(6)=24-16
f(6)=8
Hannah says that 3.33 is a rational number. Gus says that 3.33 is a repeating decimal. Who is correct and why?
a. Gus is correct because 3.33 has two numbers that repeat.
b. Hannah is correct because 3.33 can be written as a fraction.
Gus is incorrect because 3.33 cannot be written as a fraction
d. Hannah is incorrect because 3.33 should have a repeating bar
What is the answer
Answers
Answer:
B
Step-by-step explanation:
you can write 3.33 as 10/3
If a b c are positive numbers othe than 1 show that
Log b a x log c b x log a c = 1
Answers
For any positive numbers a, b and c other than 1, it is shown that Log_b(a) * Log_c(b) * Log_a(c) is equal to 1.
We need to show that the expression Log_b(a) * Log_c(b) * Log_a(c) equals 1, given that a, b, and c are positive numbers other than 1.
Let's start by using the logarithmic identities to simplify the expression.
Using the property Log_b(a) = 1 / Log_a(b), we can rewrite the expression as:
(1 / Log_a(b)) * (1 / Log_b(c)) * (1 / Log_c(a))
Now, let's simplify further by multiplying the three fractions:
1 / (Log_a(b) * Log_b(c) * Log_c(a))
Next, we can use the change of base formula, Log_a(b) = Log_c(b) / Log_c(a), to rewrite the expression as:
1 / ((Log_c(b) / Log_c(a)) * (Log_c(c) / Log_a(c)) * (Log_a(a) / Log_b(a)))
Simplifying, we get:
1 / (Log_c(b) * Log_a(c) * Log_b(a))
Now, we can observe that Log_c(b) * Log_a(c) * Log_b(a) is equal to 1 according to the multiplicative property of logarithms.
Therefore, the expression simplifies to:
1 / 1
which equals 1.
Hence, we have shown that Log_b(a) * Log_c(b) * Log_a(c) is equal to 1 for positive numbers a, b, and c other than 1.
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3х + 8 = 19
Are they Equivalent
Answers
Answer:Equivalent Fractions for 8/19: There are infinity equivalent fractions to 819. See some examples: 819, 1638, 2457, 3276, 4095, 48114, 56133, 64152, 72171, 80190, 88209, 96228, 104247, 112266, 120285, 128304, 136323, 144342, 152361, 160380
Answer:
When x equals 8/3 they are
Step-by-step explanation:
8/3*3+8=19
someone help me right away
Answers
Explanation:
15x+300 =20x
-15x -15x
—————————
300= 5x
—— ——
5 5
60=x
9.How much interest do you earn when you deposit $100 at 25% for 2 years?
10.In question #9, how much does the bank owe you at the end of those two years?
Answers
Answer:
For simple interest: $50, for compound interest: $56.25
Step-by-step explanation:
Year 1) 100+100(.25) = 125
Year 2) 125+125(.25) = 125+31.25 = $156.25
156.25 - 100 = $56.25
25 x 2
=50
helppppppppppppp pls 15 = 2 + 4 - d
Answers
Answer:
d=-9
Step-by-step explanation:
Answer:
15=6-d
-d=15+6=9
d=-9
Step-by-step explanation:
PLEASE help me. I am stuck on this question for a long time. This is a graph problem
Answers
Answer:
plot 2
Step-by-step explanation:
put number in order from least to highest:
1 ,3,4,5,8,8,9,11,11,11,14,15,15,18,19,19,19,21,22,23,
from 1 to 5 4 terms
5 to 10 3 terms
from 10 to 15 4 terms (since you can put the 15 in either 10 to 15 or 15to 20)
from 15 to 20 6 terms
from 20 to 25 3