Calculus: Help ASAP
Using n = 4 equal-width rectangles, approximate the integral from negative 2 to 2 of the quantity x cubed plus 8, dx. Use the mid-point of each sub-interval to determine the height of each rectangle.
Answers
Answer:
32
Step-by-step explanation:
To solve this, you need to start by finding the width of the rectangles and the midpoints. If n=4, b=2, a=-2, and the width of each triangle is delta x = b-a / n, then each width is equal to 1 and there will be four midpoints (you can also tell the amount of midpoints by n=4). These midpoints are -1.5, -0.5, 0.5, and 1.5. The height of each of the rectangles is going to be equal to f(x*k), where x*k is the specific mid point. This means that you need to find f(-1.5), f(-0.5), f(0.5), and f(1.5). When putting these into the function you will get 4.625, 7.875, 8.125, and 11.375. Seeing as the Riemann Sum formula says the summation of f(x*k) * delta x, multiply each of the heights by the width of 1 and then add all of the values together. When you do this you will get 4.625 + 7.875 + 8.125 +11.375 which all totals to 32. This means that the approximation of the given integral is 32.
Related Questions
Solve for x. x3 = 343 A) 6 B) 7 C) 8 D) 9
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__________________________________
Note: Given: " x³ = 343 " ; Solve for "x" ;
__________________________________
∛(343) = 7 .
__________________________________
7³ = 7 × 7 × 7 = 343 .
7³ = 7 × 7 × 7 =
→ 7³ = 7 × 7 × 7 = 49 * 7 = 343 .
__________________________________
The value of x is 7 .
Hence the correct option B .
Given: " x³ = 343
Solve for x,
Rewriting x³ = 343
∛(343) = 7
7³ = 7 × 7 × 7 = 343 .
7³ = 7 × 7 × 7
= 49 * 7
= 343
Therefore correct option is B .
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Which expressions are equivalent to ? Check all that apply.
Answers
To determine if expressions are equivalent, we simplify them or substitute variables with actual values to see if they yield the same result. We simplify by eliminating terms where possible, grouping like terms, and applying mathematical operations.
Explanation:Without the original mathematical expressions, it's difficult to provide direct answers to your question. Normally, we determine whether expressions are equivalent by simplifying them using algebraic rules or substituting variable with actual values to see if they produce the same results.
For example, the expressions 2(3 + 5) and 6 + 10 are equivalent because they both simplify to 16. We identify equivalent expressions by simplifying which includes eliminating terms where possible, grouping like terms, and applying mathematical operations.
Ultimately, the exact process may vary depending on the complexity and specific form of the expressions in question.
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The expressions equivalent to [tex]$\sqrt[3]{128}^x$[/tex] are (c) [tex]$(4 \sqrt[3]{2})^x$[/tex] and (d) [tex]$\left(4\left(2^{\frac{1}{3}}\right)\right)^x$[/tex] due to their compatible structures with the original expression.
To determine which expressions are equivalent to [tex]$\sqrt[3]{128}^x$[/tex], let's simplify the given expression first:
[tex]\[\sqrt[3]{128}^x = 2^x \times \sqrt[3]{2}^x\][/tex]
Now, let's compare this with the provided options:
a. [tex]$128^{\frac{x}{3}}$[/tex] - Not equivalent.
b. [tex]$128^{\frac{3}{x}}$[/tex] - Not equivalent.
c. [tex]$(4 \sqrt[3]{2})^x$[/tex] - Equivalent, as [tex]$4 = 2^{\frac{3}{2}}$[/tex].
d. [tex]$\left(4\left(2^{\frac{1}{3}}\right)\right)^x$[/tex] - Equivalent, as [tex]$2^{\frac{1}{3}} = \sqrt[3]{2}$[/tex].
e. [tex]$(2 \sqrt[3]{4})^x$[/tex] - Not equivalent.
Therefore, the expressions (c) [tex]$(4 \sqrt[3]{2})^x$[/tex] and (d) [tex]$\left(4\left(2^{\frac{1}{3}}\right)\right)^x$[/tex] are equivalent to [tex]$\sqrt[3]{128}^x$[/tex].
Geoff and Trevor each roll a fair six-sided die. What is the probability that the product of the numbers they roll is even?
Answers
odd*even=even
odd*odd=odd
even*even=even=2*2,4*2,6*2,2*4,2*6,2*2
odd*even=
odd*odd=3 odds in each
9 odds*odds
1-9/36=27/36=3/4
total=36
The probability that the product of the numbers they roll is even is, 2/3
We have to given that,
Geoff and Trevor each roll a fair six-sided die.
Here, Number of possible outcomes for Geoff,
1, 2, 3, 4, 5, 6
And, Number of outcomes for Trevor,
1, 2, 3, 4, 5, 6
Hence, Possible outcomes for product of the numbers they roll is even are,
2 x 1 = 2
2 x 2 = 4
2 x 3 = 6
2 x 4 = 8
2 x 5 = 10
2 x 6 = 12
3 x 2 = 6
3 x 4 = 12
3 x 6 = 18
4 x 1 = 2
4 x 2 = 8
4 x 3 = 12
4 x 4 = 16
4 x 5 = 20
4 x 6 = 24
5 x 2 = 10
5 x 4 = 20
5 x 6 = 30
6 x 1 = 6
6 x 2 = 12
6 x 3 = 18
6 x 4 = 24
6 x 5 = 30
6 x 6 = 36
Hence, Total possible outcomes = 24
And., Total outcomes = 6x 6 = 36
So, the probability that the product of the numbers they roll is even is,
P = 24 / 36
P = 12/18
P = 2/3
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Point blank is the vertex of the angle marked in the figure
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we know that
The angle marked in the figure is the angle CEB
The vertex is the intersection point of the line CD and the line AB
The intersection point is the point E
therefore
The answer is
Point E is the vertex of the angle CEB
Let g(x)=2x and h(x)=x^2+4
(g o h)(0)
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Hope this helped. Have a great day!
Name the five categories food can be grouped into.
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Fruit
Grain
Protein
Dairy
Hope i helped :)
2: Vegetables
3: Grains
4: Protein Foods, (such as Meat, poultry, fish, seafood, eggs, nuts, seeds, soy products and beans)
5. Dairy
Quinn used compensation to find the product of 37x4. First, she found 40x4=160. Then she adjusted that product by adding 3 groups of 4 to get her final answer of 172. What did she do incorrectly?
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What is the value of the expression? (−51)0 −510 −1 0 1 Plz Helpppppp MEEEEEEEEEEE
Answers
Anything multiplied with 0 is going to be 0
Answer:
that answer is incorrect!! you can check by typing in your browser calculator and typing (-51)^0 im teling you its wrong the answers 1 again answer is 1 you can also check tiger mathh
Step-by-step explanation:
For sets a={1,2,3} and b={a,b,c,d}, find the number of functions from a to b,
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A 20.0 kg sled is being pulled across a horizontal surface at constant velocity. The pulling force has a magnitude of 80.0N and is directed at an angle of 30.0º above the horizontal. Determine the coefficient of kinetic friction.
Answers
The coefficient of kinetic friction is 0.58
To determine the coefficient of kinetic friction [tex](\(\mu_k\))[/tex], we can use the following approach:
1. Identify the horizontal component of the pulling force [tex](\(F_{\text{pull, horizontal}}\))[/tex] and set it equal to the force of kinetic friction [tex](\(f_k\))[/tex].
2. The equation for the horizontal component of the pulling force is:
[tex]\[ F_{\text{pull, horizontal}} = F_{\text{pull}} \cdot \cos(30^\circ) \][/tex]
3. The equation for the force of kinetic friction is:
[tex]\[ f_k = \mu_k \cdot N \][/tex]
4. Since the sled is on a horizontal surface, the normal force [tex](\(N\))[/tex] is equal to the weight of the sled [tex](\(m \cdot g\))[/tex], where m is the mass of the sled and g is the acceleration due to gravity.
Putting these equations together and setting them equal to each other because the sled is moving at constant velocity, we get:
[tex]\[ F_{\text{pull}} \cdot \cos(30^\circ) = \mu_k \cdot m \cdot g \][/tex]
Now, substitute the given values:
[tex]\[ 80 \cdot \cos(30^\circ) = \mu_k \cdot 20 \cdot 9.8 \][/tex]
Solve for [tex]\(\mu_k\)[/tex]:
[tex]\[ \mu_k = \frac{80 \cdot \cos(30^\circ)}{20 \cdot 9.8} \][/tex]
Calculating this expression yields:
[tex]\[ \mu_k \approx 0.58 \][/tex]
So, the calculated coefficient of kinetic friction is approximately 0.58, which matches the provided answer.
Complete question:
A 20 kg sled is being pulled across a horizontal force at a constant velocity the pulling force has a magnitude of 80 N and it's directed at an angle of 30° above the horizontal determine the coefficient of kinetic friction.
please show work along with answer:
[tex] \frac{1 + \tan(x) }{1 + \cot(x) } [/tex]
Answers
[tex] \dfrac{1+tan(x)}{1+cotg(x)} = \dfrac{1+ \frac{sin(x)}{cos(x)} }{1+ \frac{cos(x)}{sin(x)}} \\\\ = \dfrac{cos(x)+sin(x)}{cos(x)*( \frac{sin(x)+cos(x)}{sin(x)} } )\\\\ = \dfrac{sin(x)}{cos(x)} \\\\ \boxed{=tan(x)}\\\\ [/tex]
which is an equivalent form of the expresion 1800(1.2)?
1800=(1/2)
1800=(5/6)
1800=(6/5)
1800=(2/1)
Answers
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
1800(1.2).
We need to find the equivalent form:
we can rewrite 1.2 as [tex]\dfrac{12}{10}[/tex]
After find the lowest term which is [tex]\dfrac{6}{5}[/tex]
[tex]1800(1.2)\\\\=18000(\dfrac{12}{10})\\\\=18000(\dfrac{6}{5})[/tex]
Hence, it is equivalent to [tex]18000(\dfrac{6}{5})[/tex]
Thus, Third option is correct.
Which statement best explains whether △PQR is congruent to △XYZ?
△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a rotation of 180° about the origin.
△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a translation 5 units down followed by a reflection across the y-axis.
△PQR is not congruent to △XYZ because there is no sequence of rigid motions that maps △PQR to △XYZ.
△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a reflection across the y-axis followed by a reflection across the x-axis.
Answers
Answer:
△PQR is not congruent to △XYZ because there is no sequence of rigid motions that maps △PQR to △XYZ.
Step-by-step explanation:
We can see from the diagram that XYZ is not the same size as PQR. This means there is no series of rigid motions, which preserve segment length, that maps PQR to XYZ.
Answer:
△PQR is not congruent to △XYZ because there is no sequence of rigid motions that maps △PQR to △XYZ.
Step-by-step explanation:
what is the equation of the graphed line in point-slope form?
a. y – 1 = (x + 3)
b. y – 1 = (x – 3)
c. y + 1 = (x – 3)
d. y + 1 = (x + 3)
Answers
slope = (-3 - 1) / (-3 - 3) = -4/-6 = 2/3
y - y1 = m(x - x1)
slope(m) = 2/3
(3,1)...x1 = 3 and y1 = 1
now we sub
y - 1 = 2/3(x - 3) <==
Answer:
[tex]y-1 = \frac{2}{3}(x-3)[/tex]
Step-by-step explanation:
To find the equation of graphed line we pick two points from the line
(3,1) and (-3,-3)
Equation of a line is y=mx+b
where 'm' is the slope and b is the y intercept
slope [tex]m= \frac{y2-y1}{x2-x1} =\frac{1+3}{3+3} = \frac{2}{3}[/tex]
we use point slope formula
y-y1= m(x-x1)
here point(x1,y1) is (3,1) and slope m = 2/3
Plug in all the value
[tex]y-1 = \frac{2}{3} (x-3)[/tex]
Strike out bowling balls produces 800 bowling balls per day using 2 workers who each work 8 hours per day. what is strike out's productivity?
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Hope this helps!
Why might algebra tiles not be a good tool to use to factor x2 + 18x + 80? Explain.
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Algebra tiles would not be a good tool to use to factor the trinomial because you would need to drag an x-squared tile, 18 x-tiles, and 80 plus tiles. That is a total of 99 tiles. It would take a lot of time to drag that many tiles on the board and there might not be enough space to hold all of them. You would also need to determine how to arrange all those tiles to make a rectangle. Since 80 is a multiple of 10, you might recognize that 10 and 8 are the factors that add to 18, which would give you the values to use in the X method.
Alex sells cars at Keith Palmer Ford. He earn$400 a week plus $150 per car he sells. if he earn $1450 last week, how many cars did he sell? brainly
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1050/150=7
7 cars
what is the solution to 7ln(x+2.8)=11.2
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Which formula gives the coordinates of the midpoint of the segment connecting points (a,
b.and (c, d)?
Answers
(a,b)...x1 = a and y1 = b
(c,d)...x2 = c and y2 = d
so ur formula would be :
m = (a + c)/2 , (b + d)/2 <==
Answer:
Formula that gives coordinates of the mid point of the segment connecting is [tex](\frac{a+c}{2},\frac{b+d}{2})[/tex]
Step-by-step explanation:
Given point are ( a , b ) and ( c , d )
To find : Coordinates of the mid point of the segment connecting given points.
We know that if point are [tex](x_1,y_1)\:\:and\:\:(x_2,y_2)[/tex]
then coordinate of the midpoints given by [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
So, Coordinates of the given points = [tex](\frac{a+c}{2},\frac{b+d}{2})[/tex]
Therefore, Formula that gives coordinates of the mid point of the segment connecting is [tex](\frac{a+c}{2},\frac{b+d}{2})[/tex]
Two benefits of following the 4 step method of problem solving
Answers
Following the 4-step method of problem-solving offers the benefits of structured decision-making and enhanced clarity in identifying and addressing core issues. These advantages significantly contribute to effective decision-making and successful implementation of solutions.
Explanation:The 4-step method, involving identification, planning, execution, and evaluation, provides a structured framework for tackling problems. In the identification phase, _Step 1_, issues are precisely pinpointed, aiding in accurate problem definition, crucial for effective decision-making. For instance, in a business scenario, if sales decline is the issue, this step helps clarify if it's due to product quality, marketing, or market changes, enabling focused decision-making.
Moving to the planning phase, _Step 2_, where strategies and solutions are devised, this structured approach ensures that all potential solutions are thoroughly explored, enhancing the quality of decisions made. This step involves a rigorous evaluation of each potential solution, ensuring a comprehensive understanding of their viability and implications.
During the execution phase, _Step 3_, the structured plan is put into action, benefiting from the earlier clarity and well-thought-out decisions. For example, if a marketing strategy was identified as a solution, this phase would involve implementing the chosen strategy with a clear roadmap, minimizing errors and optimizing resources.
Lastly, the evaluation phase, _Step 4_, allows for the assessment of the implemented solution's effectiveness. By systematically analyzing the outcomes against predefined metrics, this step ensures continuous improvement and learning from the process, contributing to more informed decision-making in the future. This structured approach, therefore, not only facilitates effective decision-making but also ensures successful implementation and ongoing refinement of solutions.
Here is complete question;
"What are two benefits of following the 4-step method of problem-solving, and how do they contribute to effective decision-making and solution implementation?"
y=x+2;x=-3 solve each system by graphing step by step
Answers
y=x+2
go to the positive number 2 on the y-axis and plot a point
now, since its postive, your line is gonna go like this:
p
p
p
p
p
p
so go up one, and to the right one from the 2 on the y-axis
and then go down one, to the left one from the 2 on the y-axis
connect the dots and this is your first line
now for the second line, go to the -3 on the x-axis and draw a vertical line up and down
this is your second line
now find where the two lines interesect and that is your answer
it'll be a point and look something like this if you write it out (x,y)
take the two points out nd write your answer in this form: x=a, y=b
tah dah!
The length of a rectangle is 5 cm more than twice its width. find the largest possible if the perimeter is at most 64 cm
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On anne's bicycle, the ratio of pedal turns to rear-wheel turns in second gear is 4 to 7. if her rear wheel turns 875 times per mile,how many times does she turn the pedal in one mile?hint:set up and solve as a propportion to find x.
Answers
Given that her rear miles turns 875 times in one mile and the ratio of pedal turns to rear wheel turns is 4 to 7, then
[tex] \frac{4}{7} = \frac{x}{875} \\ \\ \Rightarrow 7x=4(875)=3,500 \\ \\ \Rightarrow x= \frac{3,500}{7} =\bold{500}[/tex]
Therefore, she turns the pedal 500 times in one mile.
How do you solve rearranging equations
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The sum of two numbers is 18 less than twice the first number. their difference is 32 less than twice the second number. find each of the numbers
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(x+y)-18=2x
x+y-18=2x
x+y-2x=18
-x+y=18_______(1)
(x-y) -32=2y
x-y-32=2y
x-y-2y=32
x-3y=32_______(2)
from eqn (1) y=18+x____(3)
substitute eqn (3) into eqn(2)
x-3{18+x} = 32
x-54-3x=32
-2x=32+54
-2x = 86
x= -43
sub x=-43 into eqn (3)
y=18+(-43) = 18-43 = -25
The problem asks to solve a system of two equations by representing each condition as an equation. By simplifying and substituting, we can find the values of the two unknowns.
Explanation:The question involves solving a system of two equations. Let's denote the first number as x and the second number as y. The given conditions can be represented as follows:
x + y = 2x - 18x - y = 2y - 32To simplify, we can rewrite the equations as:
y = x - 18x = 2y + 32We can substitute equation (1) into equation (2) to get:
x = 2(x - 18) + 32
Solving the equation will give us the value of x and substituting x into equation (1), we will get the value of y.
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He box plot shows the total amount of time, in minutes, the students of a class spend reading each day: a box plot is titled daily reading time and labeled time (min). the left most point on the number line is 15 and the right most point is 55. the box is labeled 21 on the left edge and 48 on the right edge. a vertical line is drawn inside the rectangle at the point 37. the whiskers are labeled as 16 and 53 what information is provided by the box plot? the mean for the data the median for the data the number of students who provided information the number of students who read for more than 21.5 minutes
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Evaluate BC for A = 5, B = -4, and C = 2.
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Answer: -8
Step-by-step explanation: Substitute the value of the variable into the expression and then simplify you should get the answer -8
BC= (-4)(2)=-8
A zoo has 3 mammals for every 5 reptiles. If the zoo has 72 mammals, how many reptiles does it have? [Type your answer as a number.]
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What is the perimeter of a polygon with vertices at
(−1, 3) , (−1, 6) , (2, 10) , (5, 6) , and (5, 3) ?
Enter your answer in the box. Do not round any side lengths.
Answers
we know that
the perimeter of a polygon is the sum of the length sides
in this problem we have five vertices
so
the polygon has five sides
Let
[tex]A(-1,3)\\B(-1,6)\\C(2,10)\\D(5,6)\\E(5,3)[/tex]
the perimeter is equal to
[tex]P=AB+BC+CD+DE+AE[/tex]
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Step 1
Find the distance AB
[tex]A(-1,3)\\B(-1,6)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(6-3)^{2}+(-1+1)^{2}}[/tex]
[tex]d=\sqrt{(3)^{2}+(0)^{2}}[/tex]
[tex]dAB=3\ units[/tex]
Step 2
Find the distance BC
[tex]B(-1,6)\\C(2,10)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(10-6)^{2}+(2+1)^{2}}[/tex]
[tex]d=\sqrt{(4)^{2}+(3)^{2}}[/tex]
[tex]dBC=5\ units[/tex]
Step 3
Find the distance CD
[tex]C(2,10)\\D(5,6)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(6-10)^{2}+(5-2)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(3)^{2}}[/tex]
[tex]dCD=5\ units[/tex]
Step 4
Find the distance DE
[tex]D(5,6)\\E(5,3)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(3-6)^{2}+(5-5)^{2}}[/tex]
[tex]d=\sqrt{(-3)^{2}+(0)^{2}}[/tex]
[tex]dDE=3\ units[/tex]
Step 5
Find the distance AE
[tex]A(-1,3)\\E(5,3)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(3-3)^{2}+(5+1)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(6)^{2}}[/tex]
[tex]dAE=6\ units[/tex]
Step 6
Find the perimeter
the perimeter is equal to
[tex]P=AB+BC+CD+DE+AE[/tex]
substitute the values
[tex]P=3+5+5+3+6=22\ units[/tex]
therefore
the answer is
the perimeter of the polygon is [tex]22\ units[/tex]
A graphic designer charges an hourly rate. In July, the only expense is for advertising. The function graphed models the designer's net income, y, for July for x hours of work.
Select True or False to describe each statement.
The x-intercept represents the amount the designer charges for 1 h of work.
The difference between 0 and the y-intercept represents the amount the designer spent on advertising.
The slope represents the designer's hourly rate.
Answers
The x-intercept is the value of x when y is zero, thus from the graph, the x-intercept represents the number of hours he has to work to cover for his expenses.
Therefore, the statement "The x-intercept represents the amount the designer charges for 1 h of work." is false.
The y-intercept is the value of y when x is 0, from the graph the y intercept represent the net income when he has not done any work, i.e. the y-intercept represent his expenses.
Therefore, the statement "The difference between 0 and the y-intercept represents the amount the designer spent on advertising." is true.
The slope of a straight line is given by the change in y divided by the corresponding change in x. From the graph, given that the y-axis represent the net income in dollars and the x-axis represent the time worked in hours. Change in y divided by change in x is given by dollars per hour which represent his hourly charge.
Therefore, the statement "The slope represents the designer's hourly rate." is true.