Evaluate the definite integral from x=0 to x=1
the cubed root of (1 + 7x) dx
To evaluate the definite integral from x=0 to x=1 of the cubed root of (1 + 7x), we need to find the antiderivative, then calculate the difference in its values at x=1 and x=0 according to the fundamental theorem of calculus.
Explanation:The task is to evaluate the definite integral from x=0 to x=1 of the cubed root of (1 + 7x). To find the integral of this function, we need to apply the fundamental theorem of calculus. This theorem allows us to evaluate definite integrals as the net or accumulated area under the curve from one point to another.
Let's denote the function to integrate as f(x) = (1 + 7x)^(1/3). Our goal is to find the integral of f(x) with respect to x, within the bounds of 0 to 1.
To solve this integral, we would typically look for a suitable antiderivative of f(x), which, when evaluated at the upper and lower limits of integration, would provide us with the definite integral value.
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Which of the following is equivalent to 4.5 m?
Select one:
a. 450 km
b. 450 cm
c. 0.45 km
d. 45 cm
In his
garden Tim
plants the seed 4 and one fourth
in. below the ground. After one month the tomato plant has grown a total of 8 and one half
in. How many inches is the plant above the ground?
The sum of two numbers is 28 . The first number, x, is three times the second number,y. Which system of equations can be used to find the two numbers
Answer:
d
Step-by-step explanation:
edge 2020
Find the highest common factor of 20 and 28
Answer:
4
Step-by-step explanation:
The factors of 20 are: 1, 2, 4, 5, 10, 20
The factors of 28 are: 1, 2, 4, 7, 14, 28
Then the greatest common factor is 4.
When mrs. myles gave a test, the scores were normally distributed with a mean of 72 and a standard deviation of 8. this means that 95% of her students scored between which two scores?
A shop has one pound bags of peanuts for $2.00 and three pound bags of peanuts for $5.50. If you buy 5 bags and spend $17.00, how many of each size bag did you buy?
Answer:
3 one-pound bags; 2 three-pound bags
Step-by-step explanation:
h
round 0.7008 to the greatest nonzero place
The number 0.7008 rounded to the greatest non zero place is 1.
What is rounding of digit?Rounding is a process to estimate a particular number in a context.
To round a number look at the next digit in the right place, if the digit is less than 5, round down and if the digit is 5 or more than 5, roundup.
Now the given number is,
0.7008
To round the number to the greatest non zero place.
The greatest non zero digit in the number 0.7008 is 0.
The digit '0' in the given number is at ones place.
So, we will round the number 0.7008 to the nearest ones place.
Since, the digit to right the ones place that is tenths place is 7, which is greater than 5.
So, the digit will roundup to 1.
Thus, the number 0.7008 rounded to the greatest non zero place is 1.
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For several years, the state of New Hampshire Fish and Game Department earned several thousand dollars each year by auctioning wildlife killed along the Granite State’s roadways. The “road kill,” required to be in relatively good shape, was stored in a large freezer until the annual December auction. During the most recent auction three different collections of species made up the vast majority of frozen wildlife up for bid. Each of those collections made up one- third of the combined total. There was a set of bobcats, foxes and otters. There was a group of beavers and fishers (a weasel like animal). The final third was a large collection of black bears. Beavers made up 16.1% of the overall total. There were as many bobcats as beavers. There were four more foxes than otters. There were 16 fishers. What was the total number of road kill in these three collections, and how many were there of each species? (Hint: one-third equals 33.3%)
Final answer:
To find the total number of road kill in the three collections, we set up and solve an equation. Each species is assigned a variable, and using the information given, we can find the number of animals in each collection.
Explanation:
To find the total number of road kill in the three collections, we need to determine how many animals are in each collection. Let's assign variables to each species: bobcats = x, beavers = 16.1%x, foxes = x + 4, otters = x - 4, fishers = 16.1%. Given that each collection makes up one-third of the total, we can set up the equation: x + 16.1%x + x + x - 4 + 16.1%x = (1/3) * total. Simplifying the equation, we get 3.3x - 4 = (1/3) * total. Since beavers make up 16.1% of the total, we can substitute 16.1%x for beavers in the equation: 3.3x - 4 = (1/3) * total. Solving for x, we get x = (4 + (1/3) * total) / 3.3. Since bobcats and beavers have the same number, x = 16.1%x, which can be written as x = 0.161x. Equating the two, we get x = 0.161x. Finally, solving for x, we find that x = 0.161x, which simplifies to x = 0.161x. Therefore, each collection has the following numbers of animals: bobcats = 0.161x, beavers = 16.1%x, foxes = x + 4, otters = x - 4, and fishers = 16.1% total.
Ariel wants to write 8 entries for her blog. After 2 hours, she has 5 entries left. After 4 hours, she has 2 entries left. Which graph represents Ariel's remaining entries?
graph of line going through (0, 0) with a slope of 1.5
graph of line going through (0, 2) with a slope of 2
graph of line going through (0, 8) with a slope of 1.5
graph of line going through (0, 3) with a slope of 3
Let x be a time in hours and y be an amount of remaining entries. You have that:
At start Ariel wants to write 8 entries for her blog. This means that x=0 and y=8 (0 entries were written). The point with coordinates (0,8) belongs to needed graph.After 2 hours, she has 5 entries left. This gives you that at x=2, y=5 and graph passes through the point (2,5).After 4 hours, she has 2 entries left. This gives you that at x=4, y=2 and graph passes through the point (4,2).Find the slope of the line that is passing through the points [tex] (x_1,y_1)[/tex] and [tex] (x_2,y_2)[/tex] by formula
[tex] \dfrac{y_2-y_1}{x_2-x_1}.[/tex]
Thus, the slope is
[tex] \dfrac{5-2}{2-4}=-1.5.[/tex]
Answer: graph of line going through (0, 8) with a slope of -1.5
Iced tea, x, costs $4 per gallon and lemonade, y, costs $6 per gallon. You need to purchase at least 9 gallons of drinks for a neighborhood picnic, but have at most $55 to spend. Model the scenario with a system of inequalities. Which of the following options represents a possible solution to the system of inequalities?
Answer:
The system of inequalities is equal to
[tex]x+y\geq 9[/tex]
[tex]4x+6y\leq 55[/tex]
The graph in the attached figure
Step-by-step explanation:
Let
x------> the number of gallons of iced tea
y-----> the number of gallons of lemonade
we know that
[tex]x+y\geq 9[/tex] -----> inequality A
[tex]4x+6y\leq 55[/tex] -----> inequality B
using a graphing tool
the solution is the shaded area
see the graph in the attached figure
The answer is 10,1
The explanation is below. The graph is correct and the point 10,1 is in the shaded area that is covered by both equations.
Right isosceles triangles are similar.
Always
Sometimes
Never
Answer:
always
I just did it on my website
how do you simplify radicals?
What is the slope of the line passing through the points (1, −5)(1, −5) and (4, 1)(4, 1)?
−2
−4/5
2
5/4
Question Help
Factor the expression.
7y squared+10y+ 3
20 POINT QUESTION
Solve the system of equations using the elimination method.
8x + 7y = 89
2x + 5y = 45
Explain each step and show how to verify your results.
PLEASE HURRY!!! i promise brainliest answer to the first CORRECT answer
8x + 7y =89
2x + 5y=45
You want to be able to subtract one away from the other one so you are just left with either x or y. to do this we could multiply the bottom equation by 4
so you would get
8x+7y=89
8x + 20y= 180
Now we can subtract equation 1 from equation 2 so you get
13y=91
this gives you y=7 so to find x we can simply substitute y into an equation;
2x + 5x7=45
2x + 35= 45
2x = 10
x =5
so the final answer is y = 7/ x = 5
1. What is the slope of the line that passes through the points (-2, 5) and (1, 4)?
a. -3
b. -2
c. -1/3
d. 1/3
2. A line has a slope -5/3. Through which two points could this line pass?
a. (12,13) (17, 10)
b. (16, 15) (13, 10)
c. (0, 7) (3, 10)
d. (11, 13) (8, 18)
3. The pair of points (6,y) and (10, -1) lie on a line with slope 1/4. What is the value of y?
a. -5
b. -2
c. 2
d. 5
4. What is the slope of a vertical line?
a. -1
b. 0
c. 1
d. Undefined
5. The table below gives the best cost per person to rent a fishing charter boat. Find the rate of change given that it is a constant. Also explain what the rate of change means for this situation.
People l Cost ($)
2 l 110
3 l 165
4 l 220
5 l 275
a. 1/55
b. 110/1
c. 1/275
d. 55/1
The slope between points (-2, 5) and (1, 4) is -1/3. The pair of points (16, 15) and (13, 10) could lie on a line with a slope of -5/3. For a line with slope 1/4 passing through (6, y) and (10, -1), the value of y is 2. The slope of a vertical line is undefined. The rate of change in the charter boat cost is $55 per additional person.
Explanation:The slope of a line passing through two points can be found using the formula slope = (y2 - y1) / (x2 - x1). For the points (-2, 5) and (1, 4), the slope is (4 - 5) / (1 - (-2)) = -1 / 3, which is choice c, -1/3. For a line with a slope of -5/3, we can pick two points and use the slope formula to verify that the slope between them is -5/3. For example, using points (16, 15) and (13, 10), the slope would be (10 - 15) / (13 - 16) = -5 / -3, which is indeed 5/3, making choice b, (16, 15) (13, 10), correct.
For a pair of points (6, y) and (10, -1) lying on a line with slope 1/4, we can set up the equation 1/4 = (-1 - y) / (10 - 6) and solve for y to find that y = 2, so the answer is choice c, 2. The slope of a vertical line is undefined because the change in x is zero, hence choice d, Undefined, is the correct answer.
For the fishing charter boat cost problem, the rate of change or the cost per additional person is the difference in cost divided by the difference in the number of people. For example, for 3 and 2 people, the rate is (165 - 110) / (3 - 2) = 55, so the rate of change is 55 dollars per additional person, which is choice d, 55/1. This rate of change represents the additional cost for each extra person joining the fishing charter.
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A regular pentagon and a square share a mutual vertex B. The sides AB and BC are sides of a third polygon with vertex B. How many sides does this polygon have?
In a regular pentagon with equal sides and angles, the sum of the inside angles is 540 degrees. The third polygon P has 6 sides.
What is the Pentagon?In a regular pentagon with equal sides and angles, the sum of the inside angles is 540 degrees, and each angle is 108 degrees. Some actual items, including stars, soccer balls, and even street signs, contain pentagons.
Since P has a vertex at B, we can assume that its other sides emanate from B. Let's call the length of one of these sides x. Since the angle formed by AB and BC is a right angle, we can use the Pythagorean theorem to find the length of AC, which is the hypotenuse of the right triangle ABC:
AC² = AB^²+ BC²= s² + s² = 2s²
AC = √(2s²) = s x √(2)
Now, we can use the fact that AB and BC are sides of a regular pentagon and a square, respectively, to find the value of x. Since a regular pentagon has five sides of equal length, we know that AB is also a side of the Pentagon. Therefore:
AB = s
Similarly, since a square has all sides of equal length, we know that BC is also a side of the square. Therefore:
BC = s
Now, we can use the fact that the sum of the interior angles of a polygon with n sides is (n-2) x 180 degrees to find the value of n for polygon P. Since P has one right angle at B and two angles of 108 degrees (since a regular pentagon has interior angles of 108 degrees),
Set up the following equation:
90 + 108 + 108 + (n-3)180 = 180n
Simplifying, we get:
n = (540-90-108-108)/(180-180) + 3
n = 6
Therefore, the third polygon P has 6 sides.
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A tangent-tangent angle intercepts two arcs that measure 135 degrees and 225 degrees. What is the measure of the tangent tangent angle?
Answer:
[tex]M=45 degrees[/tex]
Step-by-step explanation:
It is given that A tangent-tangent angle intercepts two arcs that measure 135 degrees and 225 degrees, thus in this the vertex lies outside, therefore
The measure of the tangent tangent angle is the half of the difference of the two given arc, that is
[tex]M=\frac{1}{2}(225-135)[/tex]
⇒[tex]M=\frac{90}{2}[/tex]
⇒[tex]M=45 degrees[/tex]
Therefore, The measure of the tangent tangent angle is 45 degrees.
The base angle of an isosceles triangle measures 54°. What is the measure of its vertex angle?
Answer:
72[tex]\degree[/tex]
Step-by-step explanation:
We know that the sum of all the angles of any triangle is 180[tex]\degree[/tex]
We have to use the above property in order to find the measurement of the vertex angle.
Now our triangle is isosceles , that is the two equal sides will be containing equal angle. One of them is given as 54[tex]\degree[/tex]
And hence the other will also be 54[tex]\degree[/tex].
Let the vertex angle be x
180=54+54+×
180=108+×
x=180-108
x=72
Hence the vertex angle is 72[tex]\degree[/tex]
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
7, -11, and 2 + 6i
f(x) = x4 - 53x2 + 468x - 3080
f(x) = x4 - 9x3 - 42x2 + 234x - 3080
f(x) = x4 - 117x2 + 468x - 3080
f(x) = x4 - 9x3 + 42x2 - 234x + 3080
The polynomial function of minimum degree with real coefficients that has the zeros 7, -11, and 2 + 6i is obtained by also including the conjugate zero 2 - 6i and multiplying the corresponding factors. The proper polynomial is found after multiplying these factors and simplifying, but the given options do not match the correct polynomial. There may be an error in the given options.
Explanation:To write a polynomial function of minimum degree with real coefficients given the zeros 7, -11, and 2 + 6i, we must remember that complex zeros in polynomials with real coefficients always come in conjugate pairs. Therefore, the conjugate of 2 + 6i, which is 2 - 6i, must also be a zero of the polynomial.
First, we write a factor for each zero: (x - 7), (x + 11), (x - (2 + 6i)), and (x - (2 - 6i)). Multiplying these factors together will give us the required polynomial:
(x - 7)(x + 11)((x - 2) - 6i)((x - 2) + 6i)After multiplying and simplifying these factors, and combining like terms, the polynomial function in standard form with these zeros and with real coefficients is:
f(x) = x´ - 9x³ + 42x² - 154x + 3080
However, none of the given options match the correct polynomial derived from the provided zeros. It's possible there was a mistake in the multiplication or combining like terms, or there is an error in the options provided.
Which term is used to describe two quantities that may or may not be equivalent?
factor
solution
product
equality
Find parametric equations for the sphere centered at the origin and with radius 3. Use the parameters s and t in your answer.
Final answer:
Parametric equations for a sphere centered at the origin with radius 3 are x = 3 sin(t) cos(s), y = 3 sin(t) sin(s), and z = 3 cos(t), where t is the angle from the vertical and s is the angle from the x-axis on the xy-plane.
Explanation:
To find parametric equations for a sphere centered at the origin with radius 3 using parameters s and t, we make use of spherical coordinates. In spherical coordinates, a point on the sphere can be expressed as:
x = r sin(t) cos(s)
y = r sin(t) sin(s)
z = r cos(t)
Where r is the radius of the sphere, t is the angle with the vertical (ranging from 0 to π), and s is the angle on the xy-plane from the x-axis (ranging from 0 to 2π). Given that the radius r is 3, the parametric equations become:
x( s, t) = 3 sin(t) cos(s)
y( s, t) = 3 sin(t) sin(s)
z( s, t) = 3 cos(t)
Final answer:
To find the parametric equations for a sphere with radius 3 centered at the origin, we use spherical coordinates with parameters s and t to define the x, y, and z components in terms of trigonometric functions. The resulting parametric equations are x(s, t) = 3sin(t)cos(s), y(s, t) = 3sin(t)sin(s), and z(s, t) = 3cos(t).
Explanation:
Finding Parametric Equations for a Sphere
To find the parametric equations for a sphere centered at the origin with radius 3 using the parameters s and t, we use spherical coordinates. In spherical coordinates, you can represent any point on the surface of a sphere using two angles, commonly named θ (theta) and φ (phi), and the radius r. Since we're given a radius of 3, we can set r to be 3.
The standard spherical coordinates in terms of s and t can be expressed as:
x(s, t) = 3sin(t)cos(s)y(s, t) = 3sin(t)sin(s)z(s, t) = 3cos(t)Here, t represents the polar angle, measured from the positive z-axis, and s is the azimuthal angle in the xy-plane from the positive x-axis. The range of these parameters is usually 0 ≤ t ≤ π and 0 ≤ s < 2π to cover the entire surface of the sphere.
In our scenario, t and s would correspond to the angles θ and φ in spherical coordinates, respectively. However, we should specify the domain of the parameters to avoid ambiguity. This solution shows how to set up parametric equations for a sphere by using trigonometric functions to relate the spherical coordinates to Cartesian coordinates.
Given the function f(x) = 4 - 2x: If the domain is {-4, 0, 5}, find the range.
A) {-4, 4, -6}
B) {-4, 4, 14}
C) {12, 4, -6}
D) {12, 4, 14)
Justify each step of the solution by stating the property that was used to get to each step.
Given:
Step 1:
Step 2:
Step 3: 17x = 40
Step 4:
Step 1: Distributive Property. Step 2: Combine like terms. Step 3: Add 34x to both sides. Step 4: Divide by 17. x = 60/17.
Here's a step-by-step solution to the equation 2(10 - 13x) + 9x = -34x + 60, along with the properties used at each step:
Given equation: 2(10 - 13x) + 9x = -34x + 60
Step 1: Distribute the 2 on the left side of the equation.
Property used: Distributive Property
2 * 10 - 2 * 13x + 9x = -34x + 60
20 - 26x + 9x = -34x + 60
Step 2: Combine like terms on both sides of the equation.
Property used: Combining like terms
-26x + 9x = -34x + 60
(-26x + 9x) = (-34x + 60)
-17x = -34x + 60
Step 3: Add 34x to both sides of the equation to isolate the variable x on the right side.
Property used: Adding the same value to both sides of an equation to maintain equality.
-17x + 34x = -34x + 60 + 34x
17x = 60
Step 4: Finally, divide both sides by 17 to solve for x.
Property used: Dividing both sides of the equation by the same nonzero value to maintain equality.
(17x) / 17 = 60 / 17
x = 60 / 17
So, the solution to the equation is:
x = 60 / 17
Each step in this solution is justified by the properties of equality and arithmetic operations.
The complete question is here:
Justify each step of the solution by stating the property that was used to get to each step. Given: 2 (10-13x) + 9x = -34x + 60 Step 1: 20 - 26x + 9x = -34x + 60 Step 2: -17x = -34x + 10 Step 3: 17x = 40 Step 4: x =( 40)/(17) 40 on top of 17 as a fraction.
If you were solving a system of equations and you came to a statement like 1 = 3, what do you know about the solution to the system? (1 point)
The solution is (1, 3)
The solution is x = 1 and y = 3
There is no solution
There are infinitely many solutions
we know that
the statement
[tex]1=3[/tex] -----> is not true
so
The system has no solutions
For example
two parallel lines
[tex]y=5x+1[/tex] -----> equation A
[tex]y=5x+3[/tex] -----> equation B
The system has no solution. because the lines are parallel
If you equate equation A and equation B
[tex]5x+1=5x+3[/tex]
[tex]1=3[/tex] ------> is not true
therefore
the answer is the option
There is no solution
Answer:
There is no solution
Step-by-step explanation:
1 doesn't equal 3 so it can't have a solution
Cobalt-60 has a half-life of about 5 years.
How many grams of a 300 g sample will remain after 20 years?
A. 0.0625 g
B. 9.375 g
C. 18.75 g
D. 37.5 g
The answer to this question is C, i took the test.
Hope you have a great day!
pleas help this problem
Answer: she needs to complete 8 more paintings
Step-by-step explanation:every month she completes 5 paintings
it has beeen 6 months
6*5=30 paintings
needs 38
38-30=8 paintings more
Which of these sentences includes an infinitive phrase??
How are the two functions f(x) = 0.7(6)x and g(x) = 0.7(6)–x related to each other?
The functions f(x) = 0.7(6)x and g(x) = 0.7(6)–x are related to each other. f(x) represents exponential growth, while g(x) represents exponential decay. As f(x) increases, g(x) decreases, and vice versa.
Explanation:These two functions, f(x) = 0.7(6)x and g(x) = 0.7(6)–x, are related to each other in the following ways:
The function f(x) represents exponential growth, where the base is 0.7(6) and the exponent is x. As the value of x increases, f(x) will increase exponentially.The function g(x) represents exponential decay, where the base is 0.7(6) and the exponent is -x. As the value of x increases, g(x) will decrease exponentially.Therefore, f(x) and g(x) are related inversely to each other. As f(x) increases, g(x) decreases, and vice versa.