Answer:
To approximate the positive zero of the given polynomial function f(x), we can use numerical methods such as the Newton-Raphson method or the bisection method. Here, we will use the latter method.
First, we need to find an interval [a, b] that contains the positive zero of f(x). We can do this by observing the behavior of the function near the origin and near large positive values of x. We can see that f(0) = -1 is negative and that f(x) becomes more and more negative as x approaches infinity. This suggests that the positive zero of f(x) is somewhere in the interval (0, infinity).
We can evaluate f(x) at x = 1 and x = 2 to determine which half of the interval contains the positive zero. We have:
f(1) = 2(1)² - 1 - 16(1)³ - 3(1)² - 8(1) - 2 = -24
f(2) = 2(2)² - 1 - 16(2)³ - 3(2)² - 8(2) - 2 = -207
Since f(1) is negative and f(2) is very negative, we can conclude that the positive zero of f(x) is in the interval (1, 2).
Next, we can use the bisection method to refine the interval and approximate the positive zero to two decimal places. We start by evaluating f(c), where c is the midpoint of the interval (1, 2):
c = (1 + 2)/2 = 1.5
f(c) = 2(1.5)² - 1 - 16(1.5)³ - 3(1.5)² - 8(1.5) - 2 ≈ -97.875
Since f(c) is negative, the positive zero of f(x) must be in the interval (c, 2). We can repeat the process by finding the midpoint of this interval:
c = (1.5 + 2)/2 = 1.75
f(c) = 2(1.75)² - 1 - 16(1.75)³ - 3(1.75)² - 8(1.75) - 2 ≈ -38.104
Again, f(c) is negative, so the positive zero of f(x) must be in the interval (c, 2). We can repeat the process until the interval is small enough to obtain the desired level of accuracy.
Using a calculator or a computer program, we can continue the bisection method and find that the positive zero of f(x) is approximately 1.49, rounded to two decimal places.
Step-by-step explanation:
A rope connects the top of a pole to the ground. The rope is 15 yd long and touches the ground 11 yd from the pole. How tall is the pole?
The height of the pole is approximately 10.2 yards tall.
Let's use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse (the longest side).
In this case, the pole is the vertical side of the right triangle, the ground is the horizontal side, and the rope is the hypotenuse. Let's call the height of the pole "h". Then we have:
h² + 11² = 15²
Simplifying:
h² + 121 = 225
Subtracting 121 from both sides:
h² = 104
Taking the square root of both sides:
h = √104
Simplifying:
h ≈ 10.2
Therefore, the pole is approximately 10.2 yards tall.
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A fence is 8 feet tall. A rope is attached to the top of the fence and fastened to the ground 6 feet from the base of the fence. What is the length of the rope?
Answer:
Using the Pythagorean theorem, the length of the rope can be found as follows:
c^2 = a^2 + b^2
where c is the length of the rope, a is the height of the fence (8 feet), and b is the distance from the fence to the point where the rope is attached to the ground (6 feet).
Plugging in the values, we get:
c^2 = 8^2 + 6^2
c^2 = 64 + 36
c^2 = 100
c = √100
c = 10
Therefore, the length of the rope is 10 feet.
Answer:
The length of the rope is 10 feet.
Step-by-step explanation:
To find the length of the rope attached to the top of an 8-foot-tall fence and fastened to the ground 6 feet away, we can use the Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In this case, the vertical leg is the height of the fence (8 feet) and the horizontal leg is the distance from the base of the fence to where the rope is fastened (6 feet). Therefore, the length of the rope (the hypotenuse) is given by:
hypotenuse^2 = vertical leg^2 + horizontal leg^2
Substituting the values, we get:
hypotenuse^2 = 8^2 + 6^2
hypotenuse^2 = 64 + 36
hypotenuse^2 = 100
Taking the square root of both sides, we get:
hypotenuse = 10
So the length of the rope is 10 feet.
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PLEASE HELP!!! MIDDLE SCHOOL MATH
Based on the scatter plot below, which is a better prediction for y when x = 74?
PLEASE LOOK AT THE PICTURE!!!!!!!!!!!!!!
The better prediction for y, when x = 74, based on the scatter plot, can be found to be 57.
How to find the better prediction ?Looking at the scatter plot, the better prediction of y when the value of x is 74 can be found by looking for the values of y that have a value of x that is around 74.
From the scatter plot, we see that the value of x of 74, would correspond with the value of y of 57. We can therefore infer that y = 57 is the better prediction for x = 74.
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(7 × 6) ÷ 2 [{45 + 3(7 x 2-15 + 6)} +4
Step-by-step explanation:
you remember the priorities of mathematical operations :
1. brackets
2. exponents
3. multiplications and divisions
4. additions and subtractions
it is irrelevant how close or how far apart the operands are written.
I think, missing operators are multiplications.
so, by writing really everything
(7 × 6) ÷ 2 × [{45 + 3 × (7 × 2 - 15 + 6)} + 4]
we get in a first step :
(42) ÷ 2 × [{45 + 3 × (14 - 15 + 6)} + 4]
second step
21 × [{45 + 3 × (5)} + 4]
third step
21 × [{45 + 15} + 4]
fourth step
21 × [60 + 4]
fifth step
21 × 64
sixth step
1,344
Karla invests $10,000 into an account with a 2.2% interest that is compounded annually.
How much money will she have in this account if she keeps it for 5 years? Round your answer to the nearest dollar. Do not round at any other point in the solving process; only round your answer.
Karla will have approximately $11,149 in the account after 5 years, rounded to the nearest dollar.
How much money will Karia have in this account if she keeps it for 5 years?The formula accrued amount in a compounded interest is expressed as;
A = P( 1 + r/n )^( n × t )
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given that:
Principal P = $10,000Compounded annually n = 1Time t = 5 yearsInterest rate r = 2.2%Accrued amount A = ?First, convert R as a percent to r as a decimal
r = R/100
r = 2.2/100
r = 0.022
Plug the given values into the above formula and solve for A.
A = P( 1 + r/n )^( n × t )
A = 10,000( 1 + 0.022/1 )^( 1 × 5 )
A = 10,000( 1 + 0.022 )^( 5 )
A = 10,000( 1.022 )^( 5 )
A = $11,149
Therefore, the accrued amount after 5 years is $11,149.
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Use the power-reducing formulas to rewrite the expression in terms of first powers of the cosines of multiple angles.
5 cos4(x)
Using the power reducing formulas the expression [tex]5cos^4(x) = 5(1 + cos(2x))^{2/4}[/tex].
What are power-reducing formula?We can define higher powers of a trigonometric function in terms of lower powers of the same function using the power-reducing formulas, which are trigonometric identities. Higher powers of cosine can be expressed using this formula in terms of sine and cosine's initial powers. For the other trigonometric functions, such as sine and tangent, there are equivalent formulas. These formulas can be used to solve trigonometric equations and to simplify trigonometric expressions.
The given function is 5cos^4(x).
Now, the power reducing formulas are given by:
[tex]cos(2x) = cos^2(x) - sin^2(x) = 2cos^2(x) - 1\\cos^2(x) = (1 + cos(2x))/2[/tex]
Substituting the value of second equation in 1 we have:
cos(2x) = 2(1 + cos(2x))/4 - 1
[tex]cos(2x) = (2cos^2(x) - 1) = cos^2(x) - sin^2(x)[/tex]
Now we have:
[tex]cos^2(x) = (1 + cos(2x))/2[/tex]
Thus,
[tex]cos^4(x) = (1 + cos(2x))/2)^2[/tex]
Now multiplying by 5:
[tex]5cos^4(x) = 5(1 + cos(2x))^{2/4}[/tex]
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Marcus receives an inheritance of $9,000. He decides to invest this money in a 19-year certificate of deposit (CD) that pays 7.5% interest compounded monthly. How much money will Marcus receive when he redeems the CD at the end of the 19 years?
The amount that Marcus will receive when he redeems the CD at the end of the 19 years, which is described as the compounded future value, is $37,255.14.
What is the future value?The future value is the present investment or value compounded at an interest rate.
The future value can be determined using the FV formula or an online finance calculator as follows:
N (# of periods) = 228 months (19 years x 12)
I/Y (Interest per year) = 7.5%
PV (Present Value) = $9,000
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $37,255.14
Total Interest: $28,255.14
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I am struggling if you have done this assignment before don't hesitate to send the whole thing
The values of x, y and z are given as follows:
x = 10.7.y = 12.3.z = 21.8.What is the geometric mean theorem?The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.
The bases for the triangle in this problem are given as follows:
6 and 19.
Hence the segment x is obtained as follows:
x² = 6 x 19
x = sqrt(6 x 19)
x = 10.68.
Applying the Pythagorean Theorem, the value of y is given as follows:
y² = 6² + 10.68²
y = sqrt(6² + 10.68²)
y = 12.25.
The value of z is given as follows:
z² = 10.68² + 19²
z = sqrt(10.68² + 19²)
z = 21.8.
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Abby is filling a 100 quart dog bath using a 2 gallon bucket. how many buckets will it take to fill the dog bath?
57% chance child is born with disease, a woman has 3 kids what is the probability all 3 get the disease?
The probability that all 3 children will be born with the disease is approximately 0.195 or 19.5%.
We have,
Assuming that the probability of a child being born with the disease is independent of whether or not their siblings are born with the disease, we can use the multiplication rule of probability:
P(all 3 children have the disease)
= P(first child has the disease) x P(second child has the disease) x P(third child has the disease)
Since each child has a 57% chance of being born with the disease:
P(all 3 children have the disease)
= 0.57 x 0.57 x 0.57
Now,
P(all 3 children have the disease)
= 0.195
Therefore,
The probability that all 3 children will be born with the disease is approximately 0.195 or 19.5%.
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50 Points! Multiple choice algebra graphing question. The related graph of a quadratic equation is shown at the right. Use the graph to determine the solutions of the equation. Photo attached. Thank you!
Answer:
(C) {-3, 2} is the correct answer.
2x^2-5x-3=0 what values of x make the equation true?
x=
x=
A triangle has two angles with measures of 118 and 18 degrees. The side across from the 18 degree angle has a length of 8 millimeters.
Which figure represents this triangle?
The figure that represent the triangle described in the question is option (C).
Understanding TriangleTriangle is a basic geometric shape that consists of three straight sides and three angles.
We can say triangle is a polygon with three sides and three vertices, and is one of the simplest and most fundamental shapes in geometry.
Class of Triangle based on sides
Equilateral: triangle with all sides of equal lengthIsosceles: triangle with two sides of equal lengthScalene: triangle with no sides of equal lengthClass of Triangle based on their angles
Acute triangles: all angles are less than 90 degreesRight triangles: one angle is exactly 90 degreesObtuse triangles: one angle is greater than 90 degreesLearn more about triangle here:
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Find three ordered pair of x-y=7
Answer:
The equation x - y = 7 represents a linear equation with two variables, x and y. To find three ordered pairs (x, y) that satisfy this equation, we can arbitrarily choose values for one variable and solve for the other.
Ordered Pair 1:
Let's choose x = 0:
x - y = 7
0 - y = 7 (Substituting x = 0)
y = -7
So, the first ordered pair is (0, -7).
Ordered Pair 2:
Let's choose y = 0:
x - y = 7
x - 0 = 7 (Substituting y = 0)
x = 7
So, the second ordered pair is (7, 0).
Ordered Pair 3:
Let's choose x = 5:
x - y = 7
5 - y = 7 (Substituting x = 5)
y = -2
So, the third ordered pair is (5, -2).
Therefore, three ordered pairs (x, y) that satisfy the equation x - y = 7 are: (0, -7), (7, 0), and (5, -2).
Find the sum of 401-137 then use estimation to see if your answer is reasonable
Since 260 is close to 264, our answer of 264 is reasonable.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.
The sum of 401-137 can be found by subtracting 137 from 401:
401 - 137 = 264
Therefore, the sum of 401-137 is 264.
To estimate whether this answer is reasonable, we can use rounding. We can round 401 to 400 and 137 to 140, which makes the subtraction easier to estimate mentally:
400 - 140 ≈ 260
Since 260 is close to 264, our answer of 264 is reasonable.
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What is 25% of 32?
Hint: We can think of 25% as a common
fraction.
Answer:8%
Step-by-step explanation:
you divide 25 by 32 and round to nearest tenth
hope this helps :)
If you have a piece of round cake that has an area of 100 square inches, and you know the piece sweeps out an angle of 50, find the radius of the cake.
If piece of cake has area of 100 in² and sweeps angle of 50°, then the radius of the cake is 15.13 inches.
The area of the piece of cake is given as 100 square inches and
The piece of cake sweeps out an angle of 50 degrees, we have to find the radius of the cake;
We know that "Area" of a sector of a circle is given as : A = (θ/360)πr²,
where A = area of the sector, θ is = angle swept by sector, and r is radius of circle,
We know that area of "piece-of-cake" is = 100 square inches and
The "angle-swept' by the piece is = 50 degrees.
Substituting the values in area of sector formula,
We get,
⇒ 100 = (50/360)πr²,
⇒ r² = (100 × 360)/(50π)
⇒ r ≈ 15.13,
Therefore, the radius of the cake is approximately 15.13 inches.
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To the nearest millimeter, a cell phone is 135 mm long and 69 mm wide. What is the ratio of the width to the length?
The ratio of the width to the length is (Type the ratio as a simplified fraction.)
The ratio of the width to the length of the cell phone is 23/65.
What is ratio?
Ratio is the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
To find the ratio of the width to the length of the cell phone, we use the formula below.
Formula:
n = W/L............................. Equation 1Where:
n = Ratio of width to length of the cell phoneW = Width of the cell phoneL = Length of the cell phoneFrom the question,
Given:
W = 69 mmL = 135 mmSubstitute these values into equation 1
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Given f’(x)=-4x - 5 compute. F(3)- f(-1)
Answer:
-36
Step-by-step explanation:
To solve this problem, we need to integrate f'(x) to find f(x), and then evaluate f(3) and f(-1) to compute the expression f(3) - f(-1).
Integrating f'(x)=-4x - 5 with respect to x, we get:
f(x) = -2x^2 - 5x + C
Where C is the constant of integration.
To find the value of C, we can use the initial condition f(0) = 1. Substituting x = 0 and f(x) = 1 into the equation above, we get:
1 = -2(0)^2 - 5(0) + C
1 = C
So, we have:
f(x) = -2x^2 - 5x + 1
Now, we can evaluate f(3) and f(-1) and compute f(3) - f(-1):
f(3) = -2(3)^2 - 5(3) + 1 = -32
f(-1) = -2(-1)^2 - 5(-1) + 1 = 4
f(3) - f(-1) = (-32) - 4 = -36
Therefore, f(3) - f(-1) = -36.
Answer:
-36
Step-by-step explanation:
You want F(3) -F(1) given f'(x) = -4x -5.
IntegralThe desired difference is the definite integral ...
[tex]\displaystyle \int_{-1}^3{(-4x-5)}\,dx=\left[-2x^2-5x\right]_{-1}^3=-2(9-1)-5(3+1)\\\\=\boxed{-36}[/tex]
<95141404393>
poppy seed muffins 1
cinnamon rolls 3
bran muffins 2
apple fritters 2
croissants 2
Considering this data, how many of the next 20 pastries served should you expect to be bran muffins?
Answer:3/10
Step-by-step explanation:
I REALLY NEED THIS DONE PLS ITS VERY IMPORTANT!!!
Answer: The answer is D
Let (-3, 4) be a point on the terminal side of 0. Find the exact values of sin 0, csc 0, and cot 0.
Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4 using trigonometric ratio.
Trigonometric ratio calculation.
We know that the point (-3, 4) is on the terminal side of the angle θ, and we can use the Pythagorean theorem to find the value of the hypotenuse:
r² = x² + y²
r² = (-3)² + 4²
r² = 9 + 16
r² = 25
r = 5
Now we can find the values of sin θ, csc θ, and cot θ:
sin θ = y/r = 4/5
csc θ = r/y = 5/4
cot θ = x/y = -3/4
Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4.
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The table below gives the probability density of trees in a particular park. If a tree is selected at random, what is the probability that it is an elm or oak?
The probability of selecting an elm or oak tree is 0.38.
The probability of selecting an elm or oak tree is the sum of the probabilities of selecting an elm and selecting an oak:
P(elm or oak) = P(elm) + P(oak)
P(elm) = 0.04
P(Oak) =0.34
Plug in these values
= 0.04 + 0.34
= 0.38
Therefore, the probability of selecting an elm or oak tree is 0.38.
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A rectangle is bounded by the x- and y-axes and the graph of y= (6 - x)/2 (see figure). What length (x) and width (y) should the rectangle have so that its area is a maximum?
The rectangle with largest area has length 3 and width 3/2, with an area of 9/2.
What is a rectangle?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. As a result, it is sometimes referred to as an equiangular quadrilateral. Because the opposing sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.
The equation for the area of a rectangle is length * width. For us here, it would be x * y. We can substitute the equation of the line for y and get
A = x * (6-x)/2
A = 3x - x2/2
To find the maximum of this equation, we first need to find a critical point. So we take the derivative and find the zeros:
A' = 3 - x = 0
x = 3
So we have a critical point at 3, which happens to be the maximum of the area equation. We plug this back into the line equation to get y:
y = (6 - 3)/2 = 3/2
So the rectangle with largest area has length 3 and width 3/2, with an area of 9/2.
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(12, 6), (28, 8) slope
Step-by-step explanation:
slope, m = ( y1-y2) / (x1-x2) = ( 6-8) / (12-28) = -2 / -16 = 1/8
A student is graduating in 12 months and receives and unsubsidized Stafford loan with a 6 month grace period from graduation. The loan is a total of $8,465 at 5.9% compounded monthly.
Please explain how you solved this, thanks. :)
If the loan is a total of $8,465 at 5.9% compounded monthly. at the end of the 12-month repayment period, the student will owe a total of $9246.35 on the loan.
How to find the future value?First, calculate the monthly interest rate by dividing the annual interest rate by 12:
Monthly interest rate = 5.9% / 12 = 0.004917
Next, calculate the number of months in the repayment period, including the grace period:
Total repayment period = 12 + 6 = 18 months
Use the formula for calculating the future value of a loan to find the total amount owed at the end of the repayment period:
FV = PV x (1 + r)^n
where:
PV = the present value of the loan (i.e. the amount borrowed)
r = the monthly interest rate
n = the number of months in the repayment period
Plugging in the numbers, we get:
FV = $8,465 x (1 + 0.004917)^18
FV = $9246.35
Therefore, the student will owe a total of $9246.35 on the loan.
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Keilantra's math teacher plots student grades on their weekly quizzes against the
number of hours they say they study on the pair of coordinate axes and then draws
the line of best fit. What does the slope of the line represent?
The slope of the line of best fit provides valuable information about the relationship between the two variables being plotted and can be used to make predictions about future data points or to identify patterns and trends in the data.
What is the slope?
The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).
The slope of the line of best fit on a scatter plot represents the rate of change between the two variables being plotted.
In the case of Keilantra's math teacher, the slope of the line of best fit between student grades on weekly quizzes and the number of hours they say they study represents the change in grades for every additional hour of studying.
For example, if the slope is positive (i.e., the line slopes upward from left to right), it indicates that as the number of hours studied increases, the average grade on the quiz tends to increase as well.
On the other hand, if the slope is negative (i.e., the line slopes downward from left to right), it indicates that as the number of hours studied increases, the average grade on the quiz tends to decrease.
Therefore, the slope of the line of best fit provides valuable information about the relationship between the two variables being plotted and can be used to make predictions about future data points or to identify patterns and trends in the data.
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7. Explain how the Bird would look, and what the ratio of each
type would be.
The ratios of each type are:
1/4 has big beak (BB)
2/4 has big short beak (Bb)
1/4 has short beak (bb)
How to calculate the Punnett square?A Punnett square is a diagram used to predict the possible outcomes of a genetic cross between two individuals.
B b
B BB Bb
b Bb bb
We have 1 BB, this implies that we have one bird with big beak.
We have 2 Bb, this implies that we have two bird with big short beak.
We have 1 bb, this implies that we have one bird with short beak.
The ratios of each type are:
1/4 (i.e. 25%) has big beak (BB)
2/4 (i.e. 50%) has big short beak (Bb)
1/4 (i.e. 25%) has short beak (bb)
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PLEASE HELP ASAP
The table shows values for functions f(x) and g(x).
x f(x) g(x)
1 7 7
3 10 3
5 0 5
7 5 0
9 5 5
11 7 11
Which answers are solutions to the equation f(x)=g(x)?
Select each correct answer.
Responses
1
3
5
9
10
Answer:
955 11 7 11
3101 thats my answer
Step-by-step explanation:
10 and 3 thank you
anyone know this answer cus I don’t
Answer: 13 units
Step-by-step explanation:
If you look at the corresponding side on the other triangle, it is also 13, and in the question it say the side on the other triangle has the same length as the one you are finding.