Find the area between the curve
y
=
x
3
, the axis of
y
and the lines
y
=
1
and
y
=
8
Answers
Answer:
(d) 11 1/4 units²
Step-by-step explanation:
You want the area bounded by the x-axis, the lines y=1 and y=8, and the curve y=x^3.
AreaSince the y-axis is one bound it works well to use a differential of area that is (x2 -x1)dy, where x1 = 0, and x2 = ∛y. The limits of the integration will be the boundary lines y=1 and y=8. The power rule is used for integration.
[tex]\displaystyle A=\int_{1}^{8}{y^{\frac{1}{3}}}\,dy=\left.\dfrac{3}{4}y^{\frac{4}{3}}\right|_{1}^8=\dfrac{3}{4}(16-1)=\dfrac{45}{4}=\boxed{11\dfrac{1}{4}\text{ units}^2}[/tex]
__
Additional comment
The given curve is y=x³. Solving for x, we find x=∛y. This is the boundary curve we used for integration.
The attachment also shows the integral over x. For that, the region is divided into two parts: a rectangle to the left of x=1, and the region bounded on the bottom by y=x³ to the right of x=1. The x-value corresponding to y=8 is x=2, so that is the limit of integration for the part of the region to the right of x=1.
Related Questions
What will be the new position of the given point (3, –5) after reflection across the y-axis?
Answers
a jar contains 100 tickets for a drawing. Among those tickets are 7 winning tickets. what are the odds in favor of winning 7:937:10093:793:100
Answers
From the statement, we know that:
• a jar contains 100 tickets for a drawing,
,• among those tickets are 7 winning tickets.
We must find the odds in favour of winning.
The odds in favour of winning are:
Odds in favour = Number of successes : Number of failures
In this case, we have:
• Number of successes = 7,
,• Number of failures = 100 - 7 = 93.
So we have:
[tex]\text{ Odds in favour }=7:93.[/tex]Answer7:93
Jim's gas tank is 1/3 full. After he buys 9 gallons of gas it is 5/6 full. How many gallons can Jim's tank hold?
Answers
tank is 1/3 full
after he buys 9 gallons of gas it is 5/6
How many gallons can Jim's tank hold?
[tex]\frac{5}{6}-\frac{1}{3}=\frac{1}{2}[/tex]9 gallons = 1/2 tank
18 gallons is the capacity of the tank
Erica and Naomi are both pledging study hours as they prepare for theirAlgebra 1 EOC next week. Erica says that she is going to study fifteen minutesthe first night of this week and then double how much she studies every dayfor the next seven days. Naomi says she is going to study 3 hours the first daythis week and then is going to add on thirty minutes each day for the nextseven days.Part A: Write a recursive and explicit formula for each girl’s study pledge. Erica:Naomi:
Answers
we know that
Erica
The sequence in minute is
15,30,60,120,240,480,960
This is a geometric sequence
where
r=30/15=2 ----> common ratio
the recursive formula For n>1 is equal to
[tex]\begin{gathered} a_n=a_{(n-1)}*r \\ a_n=a_{(n-1)}*2 \end{gathered}[/tex]Find out the explicit formula
[tex]a_n=a_1*r^{(n-1)}[/tex]where
a1=15
r=2
[tex]a_n=15*2^{(n-1)}\text{ ----> explicit formula}[/tex]Naomi
we have the sequence in hours
3 3.5 4 4.5 5 5.5 6
This is an arithmetic sequence
where
d=3.5-3=0.5 ----> the common difference
the recursive formula For n> 1 is equal to
[tex]\begin{gathered} a_n=a_{(n-1)}+d \\ a_n=a_{(n-1)}+0.5 \end{gathered}[/tex]Find out the explicit formula
[tex]a_n=a_1+d(n-1)[/tex]where
a1=3
d=0.5
substitute
[tex]\begin{gathered} a_n=3+0.5(n-1) \\ a_n=3+0.5n-0.5 \\ a_n=0.5n+2.5\text{ ----> explicit formula} \end{gathered}[/tex]On a coordinate plane, how are the locations of the points (3, -7) and (-3, 7) related?
Answers
The number of tiles needed for a bathroom floor is proportional to the area of the bathroom floor. Five tiles cover an area of 90 square inches. The bathroom floor has a total area of 3,024 square inches. Let n be equal to the total number of tiles needed for the floor. Set up and solve a proportion to find the value of n.( Show your work)
Answers
Given:
5 tiels cover the area 90square inch.
bathroom floor area is 3024
[tex]\begin{gathered} 5\text{ tiles covers the area = 90} \\ 1\text{ tiles cover the area = }\frac{90}{5} \\ \text{ =18} \end{gathered}[/tex]1 tiles cover the area is 18 square inch.
Let n tiles cover 3,024 square inch then:
[tex]\begin{gathered} n\times18=3024 \\ n=\frac{3024}{18} \\ n=168 \end{gathered}[/tex]So 168 tiels required for cover the bathroom floor.
help meee pleasee!!!
thank you <3
Answers
Answer:
y = -800x + 294000
286,000
Step-by-step explanation:
To write the equation, you need the slope and the y-intercept.
The slope is -800
You find the slope by the change in y over the change in x
[tex]\frac{288400 - 294000}{7 - 0}[/tex] = [tex]\frac{15600}{7}[/tex] = -800
Now we will find the y -intercept. I will use the slope and the point (0, 294,000) to find this. I could have used the other point given. They will both work.
slope (m) = -800
x = 0
y = 294000
y = mx + b
294000 = -800(0) = b
294000 = b
The equation is
y = mx + b
y = -800x + 294000
2014
y = -800x + 294000
y = -800(10) + 294000
y =-8000 + 294000
y = 286,000
Determine whether the graph represents a function.
Answers
polynomials: adding and subtracting polynomials find each sum or differenceplease do minimum steps
Answers
A die is rolled 200 times with the following results. Outcome 1 2 3 4 5 6 Frequency 32 36 44 20 30 38 What is the experimental probability of rolling the given result? a number more than 3
Answers
The experimental probability of rolling such that the number is more than 3 is 0.44.
The proportion of outcomes where a specific event occurs in all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.
When a dies is rolled 200 times, the results are:
Frequency Outcome
1 32
2 36
3 44
4 20
5 30
6 38
Therefore,
The experimental probability that a number is more than 3 after rolling will be:
= The sum of outcome above 3 / total outcome
= ( 20 + 30 + 38 ) / ( 32 + 36 + 44 + 20 + 30 + 38 )
= 88/ 200
= 0.44
Hence, the probability that the number is more than 3 is 0.44.
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Thirteen million, three hundred and two thousand, six hundred and forty? In numbers
Answers
33,300 is standard form of the given question .
What does basic math standard form mean?
Writing down extremely large or extremely small numbers simply is possible using standard form. 103 = 1000, so 4 × 103 = 4000 . Therefore, 4000 can be expressed as 4 103. Even bigger numbers can be easily recorded in standard form using this method. The conventional form of small numbers is also an option.Definition of Standard Form?
A standard form is a way of expressing a certain mathematical idea, such as an equation, number, or expression, in a way that adheres to a set of norms. The standard form is used to concisely represent very big or very small values. For instance, 4,500,000,000 years is how 4.5 billion years is written.Thirteen million, three hundred = 33,300
Two thousand, six hundred and forty = 2640
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Find the sum of a number 2 units to the left of 16?
Answers
2 units left of 16 is 14
The sum is:
16 + (-2) = 16 - 2 = 14
Question 5(Multiple Choice Worth 5 points)
(08.02 MC)
Which of the following tables shows the correct steps to transform x2 + 10x + 24 = 0 Into the form (x-p)² = q?
Ip and q are integers]
Step 1 x²+ 10x + 24-1-0-1
Step 2
x2²+ 10x+23 = -1
Step 3 (x + 5)2 =-1
Step 1 x²+ 10x+24-2-0-2
Step 2 x²+ 10x+22=-2
Step 3 (x+5)2 = -2
O
Step 1 x²+ 10x+24+2=0+2
Step 2
x²+ 10x + 26 = 2
Step 3
(x + 5)2 = 2
Step 1 x²+ 10x + 24 + 1 = 0+1
Step 2 x²+ 10x + 25 = 1
Step 3 (x + 5)2 = 1
3
Answers
The correct steps to transform x² + 10x + 24 = 0 into the form (x − p)² = q is a.
Step 1 x² + 10x + 24 − 1 = 0 − 1
Step 2 x² + 10x + 23 = −1
Step 3 (x + 5)² = −1 and
d.
Step 1 x² + 10x + 24 + 1 = 0 + 1
Step 2 x² + 10x + 25 = 1
Step 3 (x + 5)² = 1
What is meant by factorization?Factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.
a² + b² + 2ab = (a + b)²
Given: x² + 10x + 24 = 0
= x² + 2x × 5 + 24
so b² has to equal 25 = 5²
Now, x² + 10x + 24 = 0
x² + 2x × 5 + 24 + 1 = 0 + 1
simplifying the above equation, we get
x² + 2x × 5 + 25 = 1
(x + 5)² = 1
Therefore, the correct answer is option
a.
Step 1 x² + 10x + 24 − 1 = 0 − 1
Step 2 x² + 10x + 23 = −1
Step 3 (x + 5)² = −1 and
d.
Step 1 x² + 10x + 24 + 1 = 0 + 1
Step 2 x² + 10x + 25 = 1
Step 3 (x + 5)² = 1
The complete question is:
Which of the following tables shows the correct steps to transform x² + 10x + 24 = 0 into the form (x − p)² = q?[p and q are integers] (5 points)
Select one:
a.
Step 1 x² + 10x + 24 − 1 = 0 − 1
Step 2 x² + 10x + 23 = −1
Step 3 (x + 5)² = −1
b.
Step 1 x² + 10x + 24 − 2 = 0 − 2
Step 2 x² + 10x + 22 = −2
Step 3 (x + 5)² = −2
c.
Step 1 x² + 10x + 24 + 2 = 0 + 2
Step 2 x² + 10x + 26 = 2
Step 3 (x + 5)² = 2
d.
Step 1 x² + 10x + 24 + 1 = 0 + 1
Step 2 x² + 10x + 25 = 1
Step 3 (x + 5)² = 1
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The tallest man living is Sultan Kosen from Turkey. He measures 2510 mm. How many meters tall is he?
Answers
Given:
The height of tallest man is 2510 mm.
Explanation:
The conversion unit for mm to meter is,
[tex]1\text{ mm=}\frac{1}{1000}\text{ meter}[/tex]Determine the height in meters.
[tex]\begin{gathered} 2510\text{ mm=2510 mm}\cdot\frac{1\text{ m}}{1000\text{ mm}} \\ =2.510\text{ m} \end{gathered}[/tex]So height of tallest man Sultan Kosen is 2.510 meters.
Answer: 2.510 meters
13 of 13 Want an extra challenge? This screen is **optional**: 30° If you want more practice to really level up your Right Triangle Trig skills, see if you can solve for the missing sides of the Right Triangle pictured to the left. a You can enter your results and check your work in the table below 7 HINT: The side that is 7 units long is OPPOSITE the 30° angle. Length of Hypotenuse (c) Length of Other Leg (a) Did I Get Them Right?! ( Nope. Keep trying Reset
Answers
Looking at the triangle, the reference angle is 30 degrees. The hypotenuse of the triangle is c. The opposite side of the triangle is 7 and the adjacent side is a.
We would determine the hypotenuse, c by applying the sine trigonometric ratio which is expressed as
Sin# = opposite side/hypotenuse
Sin 30 = 7/c
cSin30 = 7
c = 7/Sin 30 = 7/0.5
c = 14
We would determine the adjacent side, a by applying the tangent trigonometric ratio which is expressed as
Tan# = opposite side/adjacent side
Tan 30 = 7/a
aTan30 = 7
a = 7/Tan 30 = 7/0.5774
c = 12.12
help me please
thank you
Answers
Answer:
Domain: [1, 7]
Range: [-4, 2]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
A teacher gives pens and pencils to elementary students at an equal rate.
Pencils Pens
21 63
33 A
45 135
B 153
Determine the missing value for the letter B.
Answers
The missing value for the letter B is 51.
Given,
A teacher gives pens and pencils to elementary students at an equal rate.
Pencil ; 21 33 45 B
Pen ; 63 A 135 153
We have to determine the missing value of B.
Here,
Ratio of pencil to pen for each student.
Student 1; Pencil/pen = 21/63Each student get pencil and pen in the same ratio as 1/3
Then,
Student 2 gets;33/A = 1/3
33 × 3 = A
A = 99
Ratio = 33/99 = 1/3
Student 3 gets;45/135 = 1/3
Student 4 gets;B/153 = 1/3
3B = 153
B = 153/3 = 51
Ratio = 51/153
That is,
The missing value for the letter B is 51.
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If they had 15 oranges,9 peaches and 18 pears to distribute into the baskets.How many baskets can they make with the SAME number of pieces of fruit in each one?? How many pieces of each type of fruit will be in each basket?
Answers
Jill Has twenty carrots she sets some on display now she has two how many did she put on display?
Answers
Answer:
the answer is 18 because if Jill put 18 on display she would have 2 left
A sequence starts Give a rule that the sequence could follow.
Answers
Let's say "n" is the last denominator
A rule that the sequence could follow is
[tex]\frac{1}{2n}[/tex]With 2 as the first value of n, this means that the next term will be 1/2(2)=1/4 and so on.
The next 3 terms in the sequence will be
1/2(8)=1/16
1/2(16)=1/32
1/2(32)=1/64
Considering the function
H(x) = -x + 6
which statement is true?
A. The output value of the function is 4 when the input value is -2
B. The output value of the function is 7 when the input value is 1
C. The output value of the function is 6 when the input value is x
D. The output value of the function is 8 when the input value is -2
Answers
The statement which is true is Option(D) The output value of the function is 8 when the input value is -2.
What do mathematical functions mean?An expression, rule, or regulation that establishes a relationship between one variable (the independent variable) and another variable (the dependent variable) is referred to as a function in mathematics.
Given function:
H(x) = -x + 6
In Option A, the input value is -2 so the output of the function will be,
H(x) = -x + 6 = -(-2) +6 = 2+ 6 = 8 ,which is not equal to the given output value 4.
Hence, the statement is false.
Similarly in Option B and C, the input values are 1 and x.
H(x) = -x + 6 = -1 +6 = 5 ≠ 7
H(x) = -x + 6 ≠ 6
The given output values are not equal to the output values calculated.
So both statements are false.
In Option D the input value is -2 and the output value is 8 which is a correct statement as calculated in Option A.
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An employer pays $450 towards health insurance, while the employer pays $475. what is the ratio of employers contributions to the employees contributions?
Answers
Given :
An employee pays $450 towards health insurance
The second employer pays $475.
So, the ratio of employers contributions to the employees contributions=
[tex]475\colon450=\frac{475}{450}=19\colon18[/tex]
I would really appreciate if you helped me on all of these
Answers
33. For this problem you have to sole the following system of equations.
x+y=531
5.75x+1.25y=2013.75
After you solve the system of equations you get that
x=300, y=231
Therefore 300 full-price tickets were sold.
34. Since water is not acid, you have to solve the following equation
0*Water + 0.40*50 = 0.30*(Water+50)
After you solve the equation you get
Water = 16.67
So, you have to add 16.67 ML of water.
and that's the solution for 34.
35.
The next problem is very easy, notice that 12/6 = 2 and 4/6 = 0.666666=0.67 , therefore the scale factor would be 6. And that would be it.
All changes saved 5. Harry is purchasing bananas at the grocery store. The table below shows how many he can purchase and the cost. What is Harry's total cost if he wishes to purchase 7 bananas? Note: The table represents a proportional relationship of bananas per dollar. Number of Bananas
Answers
Let's determine the cost of each banana based on the given data.
Number of Bananas Total Cost Price per Banana
4 $2.48 $0.62
8 $4.96 $0.62
12 $7.44 $0.62
lt appears that each banana cost $0.62.
Thus, buying 7 bananas, it'll cost:
7 x 0.62 = $4.34
The answer is letter C.
please help me I am confused
Answers
The mass of a human cell In scientific notation is 1X 10^10 kg.
What is Scientific notation?
Scientific notation is a means to express values that are either too big or too little to be conveniently stated in decimal form (typically would lead to a long string of digits). It is also known as the standard form in the UK and scientific form, standard index form, and standard form. Scientists, mathematicians, and especially engineers frequently utilize this base ten notation because it can make some mathematical operations simpler.In many professions, huge numbers are typically expressed using the normalized scientific form, unless an alternative normalization method, such as engineering notation, is preferred.Given that mass of a human cell= is 0.000000000001 kg
In scientific notation = 1X 10^10 kg
The mass of a human cell In scientific notation is 1X 10^10 kg.
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A square has a side of length 1.6 yards. What is the area of the square inches? Round to the nearest tenth
Answers
Given that the side of the square is 1.6 yards.
The area of the square is
[tex]A=a^2[/tex]Substitute a=1.6, we get
[tex]A=1.6^2=2.56yards^2[/tex]We need to convert yards to inches.
We know that
[tex]1\text{ yard =36 inches}[/tex]Taking square on both sides, we get
[tex]1^2yard^2=36^2inches^2[/tex][tex]1yard^2=1296inches^2[/tex]Multiplying by 2.56 on both sides, we get
[tex]1\times2.56yard^2=1296\times2.56inches^2[/tex][tex]2.56yards^2=3317.76inches^2[/tex]Rounding to the nearest tenth, we get
[tex]2.56yards^2=3317.8inches^2[/tex]Hence the area of the given square is 3317.8 square inches.
A demand function for a certain product is given by the equation q = 1200 - 5p, where p is the price in
dollars, and q is the quantity demanded. Find a function to represent the revenue generated by producing
and selling q items. Use this function to determine the quantity that maximizes revenue. What price
should be charged in order to maximize revenue?
Answers
A function to represent the relation is f = q × p, the quantity that maximizes value could only be when q = p, therefore p = 200 so, q = 200 too according to demand function q = 1200 - 5p.
What is demand function?In mathematics, the relationship between demand and its factors is represented by a demand function. The function demonstrates how elements like a product's own price, buyer income, and the cost of related products affect demand for a given good (substitutes and complements).
We can deduce from the equation how they influence a product's demand, whether positively or negatively, and how much.
A function for generated revenue is simply f = q × p
where f is the generated revenue and
q is the quantity and
p is the price.
The quantity that maximizes value could only be when q = p
Lets substitute the value of q in q = 1200 - 5p,
q + 5p = 1200
But q = p so
p + 5p = 1200
6p = 1200
p = 1200/6
p = 200
So when price is 200 the revenue will be maximized as the quantity is equal to as price.
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Dina pours 16-ounce containers juice into a dispenser with a capacity of 960 ounces. The function y = 16x modeled this situation. What is the range of the function ?
Answers
The range of the function, y = 16x, is 60, where y is 960.
What is the range of a function?The range of the function, y = 16x, are the possible values that x can assume to meet the value of y.
Usually, the range of a function is the output value.
Since the value of y = 960, the range of the function will be 60 (960/16).
The capacity of the dispenser = 960 ounces
The capacity of the juice containers = 16 ounces
The function that models the situation is y = 16x
Where y = 960
x = 60 (960/16)
Thus, the implication is that the range of the function or the number of 16-ounce containers that can fill the dispenser with a capacity of 960 ounces is 60.
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three numbers have a sum of 180. the second number is 4 times the smallest number. the third number is 7 times the smallest number. what is the largest number?
Answers
12x=180
X=15
4x=60
7x=105
15+60+105=180
Answer:
105
Step-by-step explanation:
Let x, y and z be the 3 numbers in the order first, second and third
x + y + z = 180
Second number y is 3 times the smallest number and third number z is 7 times the smallest number. So smallest number has to be x
so y = 4x
z = 7x
x + y + z = x + 4x + 7x = 180
12x = 180
x = 15
Largest number = 7 x 15 = 105
A bag of marbles contains 6 blue glass marbles, 5 yellow glass marbles, 12 blue stone marbles, and 3 yellow stone marbles. What is the probability of selecting a marble and having that marble be either a blue marble or a stone marble? Express your answer as a decimal rounded to four decimal places. Probability
Answers
The probability of selecting or having a marble to be either a blue marble or a stone marble is 0.8076.
Given, a bag contains 6 blue glass marbles, 5 yellow glass marbles,
12 blue stone marbles and 3 yellow stone marbles.
Probability of selecting a marble and having that marble to be either blue marble or a stone marble = ?
we know that,
Glass marbles:
n(B) = 6 and n(Y)= 5
Stone marbles:
n(B) = 12 and n(Y) = 3
Probability = Number of favorable outcomes/Total number of outcomes.
Probability of selecting a marble and having that marble to be either blue marble or a stone marble:
total number of blue marbles = 18
total number of stone marbles = 15
total number of marbles in the bag = 26
⇒ 18+15-12/26
⇒ 33-12/26
⇒ 21/26
= 0.8076
Hence the probability of selecting a marble and having that marble be either a blue marble or a stone marble is 0.8076.
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