For the point (7,8) in the coordinate plane which represents a ratio, Adela claims that you can find equivalent ratio by adding the same number to both coordinate of the point is incorrect.
Adela claim is not correct. To find an equivalent ratio, you should multiply (or divide) both coordinates by the same nonzero number instead of adding the same number.
1. The point (7,8) represents the ratio 7:8.
2. If we add the same number to both coordinates, let's say 2, we get the point (9,10), which represents the ratio 9:10.
3. We can check if 7:8 and 9:10 are equivalent ratios by cross-multiplying:
7 * 10 = 70 and 8 * 9 = 72. Since 70 ≠ 72, these ratios are not equivalent.
Therefore, Adela's claim is incorrect because adding the same number to both coordinates of the point does not result in an equivalent ratio. To find equivalent ratios, you should multiply (or divide) both coordinates by the same nonzero number.
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If nori made 2% in interest on $5,000 and her brother Sean made 1% in interest on $10,000, who made more money in interest?
Answer: Nori
Step-by-step explanation:
2% of 5000 = 100
1% of 1000 = 10
rotation 90 degrees clockwise about the origin, ignore the dots i kinda started it then i got lost
When the points are rotated 90 degrees clockwise about the origin, the result is:
I: (1, -3)J: (-1, -5)H: (-3, -3)How to rotate about the origin ?To rotate a point 90 degrees clockwise about the origin, you can use the following rule: (x, y) becomes (y, -x). Let's apply this rule to the given points:
I - (3, 1)
Rotated I: (1, -3)
J - (5, -1)
Rotated J: (-1, -5)
H - (3, -3)
Rotated H: (-3, -3)
So, after a 90-degree clockwise rotation about the origin, the new coordinates of the points are:
I: (1, -3)
J: (-1, -5)
H: (-3, -3)
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3) Find the maximum and minimum values of f(x,y) = xyon the region inside the triangle whose vertices are (6,2), (0,3), and (6.0).
Therefore, the maximum value of f(x,y) inside the triangle is 80/9, which occurs along the line y = (-1/2)x + 4 at the point (8/3, 10/3), and the minimum value is -32, which occurs at the critical point (-8,4).
To find the maximum and minimum values of f(x,y) = xy on the region inside the triangle whose vertices are (6,2), (0,3), and (6,0), we use the method of Lagrange multipliers.
First, we need to find the critical points of f(x,y) subject to the constraint that (x,y) lies inside the triangle. We can express this constraint using the equations of the lines that form the sides of the triangle:
y = (-1/2)x + 4
y = (3/2)x
y = 0
Next, we set up the Lagrange multiplier equation:
∇f = λ∇g
where g(x,y) is the equation of the constraint, i.e., the triangle.
We have:
f(x,y) = xy
∇f = <y, x>
g(x,y) = y - (-1/2)x - 4 = 0
∇g = <-1/2, 1>
Setting ∇f = λ∇g, we get:
y = (-1/2)λ
x = λ
Substituting these into the constraint equation, we get:
(-1/2)λ - 4 = 0
Solving for λ, we get:
λ = -8
Substituting this into y = (-1/2)λ and x = λ, we get:
x = -8 and y = 4
Therefore, the only critical point of f(x,y) inside the triangle is (-8,4).
Next, we need to check the values of f(x,y) at the vertices and along the sides of the triangle.
At the vertices:
f(6,2) = 12
f(0,3) = 0
f(6,0) = 0
Along the line y = (3/2)x:
f(x, (3/2)x) = (3/2)x^2
Using the vertex (6,2) and the x-intercept (4/3, 2), we can see that the maximum value of (3/2)x^2 on this line occurs at x = 4. Therefore, the maximum value of f(x,y) along this line is:
f(4,6) = 24
Along the line y = (-1/2)x + 4:
f(x, (-1/2)x + 4) = (-1/2)x^2 + 4x
Using the vertex (6,2) and the x-intercept (8,0), we can see that the maximum value of (-1/2)x^2 + 4x on this line occurs at x = 8/3. Therefore, the maximum value of f(x,y) along this line is:
f(8/3,10/3) = 80/9
Finally, we need to check the values of f(x,y) at the critical point (-8,4). We have:
f(-8,4) = -32
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An 8-sided solid is labeled with faces 1, 2, 3, skip ,4, 5, 6, skip. what is the sample space for the number solid, and what is the probability of rolling a 1?
The sample space for the number solid is {1, 2, 3, 4, 5, 6} and the probability of rolling 1 is 1/6.
The sample space refers to the set of all possible outcomes of an experiment, while a sample value is a specific outcome in the sample space.
For the given 8-sided solid, the sample space would be {1, 2, 3, 4, 5, 6}, as the faces labeled "skip" are not counted as sample values.
Now, let's calculate the probability of rolling a 1. Probability is the likelihood of a particular outcome occurring, which can be calculated by dividing the number of successful outcomes (in this case, rolling a 1) by the total number of possible outcomes.
The total number of possible outcomes is 6 (1, 2, 3, 4, 5, and 6). There is only one successful outcome: rolling a 1.
So, the probability of rolling a 1 is:
P(1) = (Number of successful outcomes) / (Total number of possible outcomes)
P(1) = 1 / 6
Thus, the probability of rolling a 1 on this 8-sided solid is 1/6 or approximately 0.1667, or 16.67%.\
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Find the derivative of the vector function r(t) = ln(7-t^2)i + sqrt(13+tj – 4e^{9t} r’(t) =
The derivative of the vector function is: r'(t) = (-2t/(7-t^2)) i + (1/(2sqrt(13+t))) j - 36e^(9t) k
We are given a vector function r(t) = ln(7-t^2)i + sqrt(13+t)j – 4e^(9t)k, and we need to find its derivative r'(t).
The derivative of a vector function is obtained by differentiating each component of the vector function separately.
So, let's differentiate each component:
r(t) = ln(7-t^2)i + sqrt(13+t)j – 4e^(9t)k
r'(t) = (d/dt) ln(7-t^2) i + (d/dt) sqrt(13+t) j - (d/dt) 4e^(9t) k
Using the chain rule of differentiation, we have:
r'(t) = -2t/(7-t^2) i + 1/(2sqrt(13+t)) j - 36e^(9t) k
Therefore, the derivative of the vector function is:
r'(t) = (-2t/(7-t^2)) i + (1/(2sqrt(13+t))) j - 36e^(9t) k
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240:360=?:120 (Please quickly)
Answer:
? equals 80
Step-by-step explanation:
Which point on the number line has the least absolute value?
The point with the least absolute value on the number line is always the point zero.
The absolute value of a number is the distance that number is from zero on the number line. Therefore, the point on the number line with the least absolute value is the point closest to zero. This point is located at zero itself, as it is the point on the number line that is equidistant from both the positive and negative numbers.
To further explain, consider the following examples:
- The point 3 is 3 units away from zero, but the point -3 is also 3 units away from zero.
- The point 5 is 5 units away from zero, but the point -5 is also 5 units away from zero.
- The point 0 is 0 units away from zero, making it the point with the least absolute value on the number line.
In conclusion, the point with the least absolute value on the number line is always the point zero.
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The mainsail of a boat has the dimensions shown. If the mainsail is a right triangle, what is the exact height of the mainsail shown?
a.) 2√6 feet
b.) 24 feet
c.) 4√78 feet
d.) 2√410 feet
Step-by-step explanation:
use Pythagorean theorem to find the height
c = 38 ft
a = 14 ft
a² + b² = c²
(14)² + b² = (38)²
b² = 1444 - 196
b² = 1248
b = √1248
b = √16 × 78
b = 4√78 feet
#CMIIWplease do both will give brainliest and it's for 72 points
Step-by-step explanation:
Pick any of the two points...I'll use the first two
calculate slope: m = ( y1-y2) / (x1-x2) = (-14 - -5) / (-2 -1) = -9/-3 = 3
equation of a line in slope intercept form is y = mx+ b
so now you have y = 3x + b
sub in any of the x,y points given (8,16) to calculate 'b'
16 = 3 (8) + b
b = -8
so your first line is y = 3x - 8
In a similar fashion, for the second one m = - 5/8 and b = 2
y = -5/8 x + 2
Mrs. Austin has 10 students in her class. She asked them whether they like football (F) or basketball (B). Sarah, Allen, kara, Todd said football. Joseph, Lydia, Matt said basketball. Caleb and Britney said they like both. Ethan said he didn't like either. 1. Define the universal set. 2. Define the two subsets.
1.The universal set is defined as {Sarah, Allen, Kara, Todd, Joseph, Lydia, Matt, Caleb, Britney, Ethan}.
2.Caleb and Britney are included in both subsets since they like both football and basketball.
1. The universal set (U) consists of all the students in Mrs. Austin's class. In this case, U = {Sarah, Allen, Kara, Todd, Joseph, Lydia, Matt, Caleb, Britney, Ethan}.
2. The two subsets are:
a) The set of students who like football (F) = {Sarah, Allen, Kara, Todd, Caleb, Britney}
b) The set of students who like basketball (B) = {Joseph, Lydia, Matt, Caleb, Britney}
Caleb and Britney are included in both subsets since they like both football and basketball.
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4 Il y f(x, y) da = Sot Shot Sot Staf (x, y) dxdy x D
Characteristics of the drawing of D, you can choose several answers:
1. It is the region in the first quadrant that is bounded from the right by the line x = 2
2. It is the region in the first quadrant that is bounded above by y = x
3. It is the region in the first quadrant that is bounded from the left by the line x = 0
4. It is the region in the first quadrant that is bounded above by y = x2
5. It is the region in the first quadrant that is bounded below by y = 0
6. It is the region in the first quadrant that is bounded below by y = 2
which of these 6 options is correct?
The correct option is option 3.
How to determine the boundaries of the region?Based on the given integral, region D is in the first quadrant, and its boundaries are not explicitly given. However, we can deduce the boundaries of D by looking at the integrand. Since the integrand is f(x,y), we can see that we are integrating over the entire region D, which means that D must be the rectangle that contains all the other regions mentioned in the options.
Therefore, option 1 is not correct, as D is not bounded from the right by x=2, but rather extends indefinitely to the right. Option 2 is also not correct, as D extends beyond the line y=x. Option 4 is not correct either, as D is not bounded above by y=x^2, but rather extends beyond it. Options 5 and 6 are also not correct, as D extends beyond the lines y=0 and y=2.
Therefore, the correct option is option 3, which states that D is the region in the first quadrant that is bounded from the left by the line x=0. This is correct, as D extends indefinitely to the right, and is bounded from the left by x=0.
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Find y such that
∫x^5 dx = ∫ x^y dx
The value of y that satisfies the equation [tex]\int x^5 dx = \int x^y dx[/tex] is y = -1.
We know that the indefinite integral of x^5 dx is (1/6) x^6 + C, where C is
the constant of integration. Therefore:
[tex]\int x^5 dx = (1/6) x^6 + C[/tex]
We want to find y such that [tex]\int x^5 dx = \int x^y dx[/tex]. Using the power rule of integration, the indefinite integral of [tex]x^y[/tex] dx is [tex](1/(y+1)) x^{(y+1)} + C[/tex], where C is the constant of integration. Therefore:
[tex]\int x^y dx = (1/(y+1)) x^{(y+1)} + C[/tex]
For these two integrals to be equal, we need:
[tex](1/6) x^6 + C = (1/(y+1)) x^{(y+1) } + C[/tex]
Subtracting C from both sides, we get:
[tex](1/6) x^6 = (1/(y+1)) x^{(y+1)}[/tex]
Multiplying both sides by (y+1), we get:
[tex](1/6) x^6 (y+1) = x^{(y+1)}[/tex]
Now, we can equate the powers of x on both sides:
[tex]x^6 (y+1) = x^{(y+1)}[/tex]
Using the fact that[tex]x^a \times x^b = x^{(a+b)}[/tex], we can simplify the left-hand side:
[tex]x^(6(y+1)) = x^{(y+1)}[/tex]
Now, we can equate the exponents on both sides:
6(y+1) = y+1
Simplifying, we get:
6y + 6 = y + 1
5y = -5
y = -1
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x-3 5. The function f(x)=- has X? - 8x+15 Math 1P97 Final Exam April 2010 page 3 of 19 a. a discontinuity at x = 3 only b. discontinuities at = 3 and x = 5 c. no discontinuities d. a discontinuity at x = 5 only e, none of the above
The correct option is: (d) a discontinuity at x = 5 only.
How to find which function f(x)=- has X?The function f(x) is defined as:
[tex]f(x) = (x-3)/(x^2 - 8x + 15)[/tex]
The denominator of this function can be factored as:
[tex]x^2 - 8x + 15 = (x - 3)(x - 5)[/tex]
So the function can be rewritten as:
f(x) = (x - 3)/[(x - 3)(x - 5)]
Simplifying this expression, we get:
f(x) = 1/(x - 5)
Now it is clear that the function has a discontinuity at x = 5, since the denominator of the simplified expression becomes zero at that point.
Therefore, the correct option is:
d. a discontinuity at x = 5 only
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Let f: R+R be a function that satisfies O 0. (a) Show that the series cosh(f(n)) ne1 diverges regardless of the rule for f. (b) Show that the series ( f(n) 2n3 - 1 converges regardless"
As we have proved that the series cosh(f(n)) ne1 diverges regardless of the rule for f, and that the series f(n) 2n³ - 1 converges regardless of the rule for f.
The comparison test states that if the terms of a series can be bounded below by a divergent series, then the given series also diverges.
In this case, we can bound the terms of cosh(f(n)) below by the series eⁿ. To see why, note that cosh(x) >= 1 for all x > 0. Thus, we have cosh(f(n)) >= 1 for all n. On the other hand, we know that e^x > 1 for all x > 0. Therefore, we have eⁿ > 1 for all n.
Since eⁿ diverges by the assumption that f satisfies O<f(), the comparison test tells us that cosh(f(n)) ne1 also diverges. Thus, the series cosh(f(n)) ne1 diverges regardless of the rule for f.
Moving on to the second part of the question, we are asked to show that the series ( f(n) 2n3 - 1 converges regardless of the rule for f. Again, we can use the comparison test to show convergence.
We can bound the terms of the given series by the series 1/n². To see why, note that for all n > 1, we have f(n) > 0 since the domain of f is restricted to R+. Thus, we have f(n)² < f(n) 2n³ - 1. Dividing both sides by n⁶, we get f(n)²/n⁶ < ( f(n) 2n³ - 1)/n⁶.
Now, note that the series 1/n² converges by the p-test (which states that the series 1/nᵃ converges if p > 1).
Therefore, by the comparison test, the series ( f(n) 2n³ - 1 also converges regardless of the rule for f.
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Complete Question:
Let f: R+R be a function that satisfies O<f() So for all x > 0. (a) Show that the series cosh(f(n)) ne1 diverges regardless of the rule for f. (b) Show that the series ( f(n) 2n3 - 1 converges regardless of the rule for f.
Line x is parallel to line y. Line z intersect lines x and y. Determine whether each statement is Always True.
Line x is perpendicular to line y. Line z crosses lines x and y. Only statements 3 and 4 are true.
∠6 = ∠8 is not true because they both lie on the same plane and makes an angle of 180° and can never be true. ∠6 = ∠1 is also not true because ∠1 is clearly obtuse angle and ∠6 is clearly acute angle so they cannot be equal. Hence, statement a and b are false.
∠7 = ∠3 is always true because they are corresponding angles and corresponding angles are always equal. m∠2 + m∠4 = 180° is also true because they lie on same plane and have common vertex and hence, they are supplementary angles and make a sum of 180°. Hence, statement 3 and 4 is always true.
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i need help fast!!!!
Answer:
1st choice: 1/4(y - 10) = 2/3
Step-by-step explanation:
the "variable" is y
"is" means "=" (equals sign)
one fourth = 1/4
"difference of" means subtract
Answer: 1/4(y - 10) = 2/3
Out of all the people who like chocolate, what is the relative frequency for selecting a teen?
The relative frequency for selecting a teen out of all the people who like chocolate is calculated by dividing the number of teens who like chocolate (N) by the total number of people who like chocolate (T).
To find the relative frequency for selecting a teen out of all the people who like chocolate, you need to follow these steps:
Step 1: Determine the total number of people who like chocolate (let's call this T).
Step 2: Determine the number of teens who like chocolate (let's call this N).
Step 3: Calculate the relative frequency by dividing the number of teens who like chocolate (N) by the total number of people who like chocolate (T).
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What is a good percentage (in decimal form) to multiply your earning to estimate your paycheck?
To estimate your paycheck, a good percentage to multiply your earning by would be 0.75 or 75%. When calculating your paycheck, it's important to account for taxes, deductions, and other withholdings that may be taken out of your gross pay.
This accounts for taxes, deductions, and other withholdings that are typically taken out of your paycheck before you receive your net pay. For example, if you earn $1,000 per pay period, multiplying by 0.75 would give you an estimated net pay of $750. However, keep in mind that this is just an estimate and your actual net pay may vary depending on your specific tax situation and other factors.
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Under which
transformation would AA'B'C', the wen 2.
image of AABC, not be congruent to AABC?
a. reflection over the y-axis
b.
rotation of 90° clockwise about the origin
c. translation of 3 units right and 2 units down
d. dilation with a scale factor of 2 centered at
the origin
Francium is a radioactive element discovered by Marguerite Perey in 1939 and named after her country. Francium has a half-life of 22 minutes.
a) Write an exponential function that models the mass how many grams remain from a 480-gram sample after t minutes.
b) How many grams remain after 2 hours?
After 2 hours, approximately 4.38 grams of Francium remain from the 480-gram sample.
What is Algebraic expression ?
An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It may contain one or more terms, with each term separated by a plus or minus sign. Algebraic expressions are used in algebra to represent mathematical relationships and formulas.
a) To write an exponential function that models the mass of Francium remaining after t minutes, we can use the formula:
N = N0 * [tex](1/2)^{(t / t1/2)}[/tex]
where N is the amount remaining after time t, N0 is the initial amount, t1/2 is the half-life, and (t/t1/2) means raised to the power of t/t1/2.
In this case, the initial amount is 480 grams, the half-life is 22 minutes, and we want to find the amount remaining after t minutes. Therefore, the exponential function that models the mass of Francium remaining after t minutes is:
N = 480 * [tex](1/2)^{t/22}[/tex]
b) 2 hours is equal to 120 minutes. To find how many grams of Francium remain after 2 hours, we can substitute t = 120 into the exponential function we found in part a):
N = 480 *[tex](1/2)^{ (120 / 22) }[/tex] ≈ 4.38 grams
Therefore, after 2 hours, approximately 4.38 grams of Francium remain from the 480-gram sample.
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I don't understand how to get the answer can someone help me?
Answer:
C. R+S+T = 201°
Step-by-step explanation:
You want to know which of the offered angle relations is true regarding quadrilateral RSTU.
AnglesThe sum of angles in a quadrilateral is 360°. You use this fact to find angle T. Then you can compute the various differences to see which one matches the answer choices.
T = 360° -R -S -U = 55°
In the attached calculator display, we have done exactly that. We find ...
T -R = 38° . . . . A is false
S -T = 74° . . . . B is false
R +S +T = 201° . . . . C is TRUE
R +T +U = 231° . . . . D is false
Answer:
To answer your question, we need to use some properties of rectangles and triangles.
A rectangle has four right angles, so angle R = angle S = angle T = angle U = 90 degrees.
The sum of the angles in a triangle is 180 degrees, so we can find the values of a, b, c, d, e, and f by using this property. For example, a + b + angle S = 180, so a + b = 90. Similarly, c + d = 90, e + f = 90, and f + g + angle U = 180, so f + g = 30.
Now we can evaluate each statement and see which one is true.
A) The difference between the measures of LT and LR is 4°. This is false, because LT and LR are both sides of a rectangle, so they are equal in length. The difference between them is zero, not four.
B) The difference between the measures of 2S and LT is 95°. This is false, because 2S is an angle and LT is a length. They have different units and cannot be compared or subtracted.
C) The sum of the measures of LR, 2S, and LT is 201°. This is false, because LR and LT are lengths and 2S is an angle. They have different units and cannot be added together.
D) The sum of the measures of LR, LT, and ZU is 193°. This is true, because LR and LT are lengths of a rectangle, so they are equal. ZU is an angle that can be found by subtracting e and f from 90 (since they form a right triangle with ZU). So ZU = 90 - e - f = 90 - (90 - c - d) - (90 - a - b) = a + b + c + d - 90. We know that a + b = c + d = 90, so ZU = 90 - 90 = 0.
Therefore, the sum of LR, LT, and ZU is LR + LT + 0 = 2LR = 2(17) = 34 degrees.
The correct answer is D.
Step-by-step explanation:
I hope that would help!!
Can I have Brainliest please?
Have a nice day
Find the critical points for the function f(x, y) = x³ + y³ – 9x² – 3y - 6 = and classify each as a local maximum, local minimum, saddle point, or none of these. critical points: (give your points as a comma separated list of (x,y) coordinates.) classifications: (give your answers in a comma separated list, specifying maximum, minimum, saddle point, or none for each, in the same order as you entered your critical points)
The critical points and their classifications are:
(0, 1) - saddle point
(0, -1) - saddle point
(6, 1) - local minimum
(6, -1) - local minimum
To find the critical points of the function f(x, y) = x³ + y³ – 9x² – 3y - 6, we need to find the points where the partial derivatives of f with respect to x and y are zero.
∂f/∂x = 3x² - 18x = 3x(x - 6)
∂f/∂y = 3y² - 3 = 3(y² - 1)
Setting these partial derivatives equal to zero and solving for x and y, we get:
x = 0 or x = 6
y = ±1
So the critical points are (0, 1), (0, -1), (6, 1), and (6, -1).
To classify each critical point, we need to compute the second partial derivatives of f:
∂²f/∂x² = 6x - 18
∂²f/∂y² = 6y
∂²f/∂x∂y = 0
At (0, 1):
∂²f/∂x² = -18 < 0 (concave down)
∂²f/∂y² = 6 > 0 (concave up)
So (0, 1) is a saddle point.
At (0, -1):
∂²f/∂x² = -18 < 0 (concave down)
∂²f/∂y² = 6 > 0 (concave up)
So (0, -1) is a saddle point.
At (6, 1):
∂²f/∂x² = 18 > 0 (concave up)
∂²f/∂y² = 6 > 0 (concave up)
So (6, 1) is a local minimum.
At (6, -1):
∂²f/∂x² = 18 > 0 (concave up)
∂²f/∂y² = 6 > 0 (concave up)
So (6, -1) is a local minimum.
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consider light falling on a single slit, of width 1.2 μm, that produces its first minimum at an angle of 32.3°. randomized variables θ = 32.3° w = 1.2 μm
The wavelength of the light is approximately 0.687 μm.
Using the single slit diffraction formula, we have:
sin θ = (mλ) / w
where m is the order of the minimum, λ is the wavelength of the light, and w is the width of the slit.
We can rearrange the formula to solve for the wavelength of the light:
λ = (w sin θ) / m
Plugging in the given values, we get:
λ = (1.2 μm)(sin 32.3°) / 1 = 0.687 μm
Therefore, the wavelength of the light is approximately 0.687 μm.
The wavelength is the distance between two consecutive peaks or troughs in a wave. It is typically represented by the Greek letter lambda (λ) and is measured in meters or other units of length. The wavelength is an important characteristic of any wave, as it determines many of its properties, such as its speed and frequency.
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A function is a rule that assingns each value of independent variable to exactly value of the dependent variable
A function is a rule that assingns each value of independent variable to exactly one value of the dependent variable.
A function is a mathematical concept that relates two sets of values, known as the domain and the range. The domain is the set of independent variables, while the range is the set of dependent variables. A function is a rule that assigns to each value in the domain exactly one value in the range.
For example, if we have a function f(x) = 2x + 3, the domain would be any possible value of x, and the range would be any possible value of 2x + 3. So if we put x = 2, then f(x) = 2(2) + 3 = 7. Therefore, the function assigns the value of 7 to the value of 2 in the domain.
Functions are used in various branches of mathematics, science, and engineering to model and analyze relationships between two or more variables. They are an important concept in calculus, where they are used to study rates of change and optimization problems.
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the top of the farm silo is a hemisphere with a radius of 9ft. the bottom of the silo is a cylinder with a height of 35ft. how many cubic feet of grain can the solo hold? use 3.14 for pi and round your answer to the nearest cubic foot.
To find the total volume of the silo, we need to add the volume of the hemisphere on top to the volume of the cylinder at the bottom.
The volume of a hemisphere is given by:
V_hemi = (2/3)πr^3
where r is the radius of the hemisphere.
Substituting r = 9ft, we get:
V_hemi = (2/3)π(9ft)^3
= 1521π ft^3
The volume of a cylinder is given by:
V_cyl = πr^2h
where r is the radius of the cylinder and h is its height.
Substituting r = 9ft and h = 35ft, we get:
V_cyl = π(9ft)^2(35ft)
= 2673π ft^3
Therefore, the total volume of the silo is:
V_silo = V_hemi + V_cyl
= 1521π + 2673π
= 4194π ft^3
≈ 13160 ft^3
Rounding to the nearest cubic foot, the silo can hold approximately 13160 cubic feet of grain.
Un terreno de forma rectangular tiene un perímetro de 105 metros. Si el ancho es la mitad del largo, ¿Cuáles son las medidas del terreno? *
Sea "l" la medida del largo del terreno y "a" la medida del ancho del terreno.
De acuerdo con el problema, el ancho es la mitad del largo, es decir, a = l/2.
El perímetro de un rectángulo se calcula sumando las longitudes de sus cuatro lados, por lo que en este caso:
Perímetro = 2l + 2a = 2l + 2(l/2) = 3l
Sabemos que el perímetro es de 105 metros, entonces:
3l = 105
l = 105/3 = 35
Por lo tanto, el largo del terreno es 35 metros. Y, como el ancho es la mitad del largo, entonces:
a = l/2 = 35/2 = 17.5
Por lo tanto, el ancho del terreno es de 17.5 metros.
En resumen, las medidas del terreno son 35 metros de largo y 17.5 metros de ancho.
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) Nadia buys 4 1/5 pounds of plums. Nadia used a 55 cent coupon off her entire purchase. Her total after the coupon was $3. 23. If c represents the cost per pound for the plums, create and solve an equation to determine the cost per pound for the plums
If c represents the cost per pound for the plums, the cost per pound for the plums is $0.90.
First, we need to determine the total cost of the plums before the coupon was applied.
4 1/5 pounds can be written as a mixed number:
4 1/5 = 21/5
So, the total cost of the plums without the coupon can be found by multiplying the cost per pound (c) by 21/5:
Total cost = c * 21/5
Now we can create an equation to represent the total cost after the coupon was applied:
Total cost - coupon = $3.23
Substituting the expression for total cost:
c * 21/5 - 0.55 = 3.23
To solve for c, we can start by adding 0.55 to both sides:
c * 21/5 = 3.78
Then, we can isolate c by multiplying both sides by the reciprocal of 21/5:
c = 3.78 / (21/5)
c = 0.90
Therefore, the cost per pound for the plums is $0.90.
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It is kinda hard but just try it
Answer:
we 1st can get the weight of rat by
1 rat and 1 cat + 1 dog and rat = 30
2 rat + 1 cat + 1 dog = 30
Then 1 rat and cat measure 24 so
2 rat + 24 =30
2 rat + 24 =30 1 rat = 3 kg
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 10
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 10
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and 1 dog + 1 rat = 20 kg
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and 1 dog + 1 rat = 20 kg 1 dog + 3kg = 20 kg
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and 1 dog + 1 rat = 20 kg 1 dog + 3kg = 20 kg 1 dog = 17kg
so we get the weight of each now we r going to sum them 1 rat + 1 cat + 1 dog = x
1 rat + 1 cat + 1 dog = x 3 kg + 7 kg + 17 kg = x
1 rat + 1 cat + 1 dog = x 3 kg + 7 kg + 17 kg = x 27 kg = x ..... is the mass of 3 of them
Tanya made this graph that represents the total cost for each of the three locations. Depending on the number of students that attend. Which function represents the cost of the restaurant 
The functions that represents the cost are
(a) y = 8800, (b) y = 1900 + 4/7x and (c) y = 4800, x ≤ 150; y = 1200 + 24x x > 150
Identifying the function that represents the costFrom the question, we have the following parameters that can be used in our computation:
The graph
The function (a) is a horizontal line that passes through y = 8800
So, the function is
y = 8800
The function (b) is a linear function that passes through
(0, 1900) and (175, 2000)
So, the function is
y = 1900 + 4/7x
The function c is a piecewise function with the following properties
Horizontal line of y = 4800 uptill x = 150Linear function of (150, 4800) and (200, 6000)So, the function is
y = 4800, x ≤ 150
y = 1200 + 24x x > 150
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determine if each of the numbers below is a solution to the inequality 3x-2<2-2x
The solution set of the inequality 3x-2 < 2-2x is:
(4/5, ∞)
Which numbers are solutions for the inequality?To find this we need to isolate the variable in the inequality.
Here we have:
3x - 2 < 2 - 2x
add 2x in both sides and add 2 in both sides, then we will get:
3x + 2x < 2 + 2
5x < 4
Now we can divide both sides by 5 to get:
x < 4/5
That is the inequality solved.
Then the solution set of the inequality is:
(4/5, ∞)
The set of all real numbers larger than 4/5.
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