The real roots of the function using false-position method are 1/2 and 5/8
What is the real root of the function?The real root of the function f(x) = x³ - 2x - 5 = 0 using the False-Position method can be calculated as;
1. Choose two initial guesses, a and b, such that f(a) and f(b) have opposite signs. In this case, we can choose a = 0 and b = 1.
[tex]c = \frac{(a * f(b) - b * f(a))}{(f(b) - f(a)}[/tex]
If f(c) = 0, then c is the root of the equation. Otherwise, replace a with b and b with c.
[tex]c = \frac{(0 * f(1) - 1 * f(0))}{(f(1) - f(0))} = \frac{1}{2}[/tex]
Since f(1/2) = -0.25, we can replace a with 1 and b with 1/2.
[tex]c = \frac{\frac{1}{2} * f(1) * f(\frac{1}{2}) }{(f(1) - f(\frac{1}{2}) } = \frac{5}{8}[/tex]
Since f(5/8) = 0.0625, we can stop here and say that the root of the equation is 5/8, which is approximately 0.625.
Where the roots of the equation are 1/2 and 5/8
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The following points represent a relation where x represents the independent variable and y represents the dependent variable.
three fourths comma negative 2, 1 comma 5, negative 2 comma negative 7, three comma negative one half, and 6 comma 6
Does the relation represent a function? Explain.
No, because for each input there is not exactly one output
No, because for each output there is not exactly one input
Yes, because for each input there is exactly one output
Does the relation represent a function: C. Yes, because for each input there is exactly one output.
What is a function?In Mathematics and Geometry, a function can be defined as any mathematical equation which is typically used to define and represent a relationship that exists between two or more variables such as an ordered pair, points on a graph or table.
Based on the mapping diagram, we can reasonably infer and logically deduce that the relation represent a function because the input values (domain, x-value, or independent values) are uniquely mapped to the output values (range, y-value or dependent values).
In this context, we can reasonably infer and logically deduce that the relation represent a function because for each input (independent value) there is exactly one output (dependent variable).
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In ΔNOP, n = 56 inches, p = 61 inches and ∠P=80°. Find all possible values of ∠N, to the nearest degree.
The value of ∠N is 54.38 degrees.
Given that in ΔNOP, n = 56 inches, p = 61 inches and ∠P=80°.
We need to find the value of ∠N,
According to the cosine rule, the following equation is true for every triangle with sides a, b, and c and the corresponding opposite angles A, B, and C:
c² = 2ab cos(C) - a² + b²
In this instance, we have:
A = P and B = P
C = ∠P
When we enter the values, we obtain:
n² = p² + p² - 2p² cos(∠P)
Substituting the known values:
56² = 61² + 61² - 2(61²) cos(80°)
Simplifying:
3136 = 3721 + 3721 - 2(3721) cos(80°)
3136 = 3721 + 3721 - 7442 cos(80°)
Now we can solve for cos(80°):
3136 = 7442 - 7442 cos(80°)
7442 cos(80°) = 7442 - 3136
cos(80°) = (7442 - 3136) / 7442
cos(80°) ≈ 0.5798
∠N = arccos(0.5798)
∠N = 54.38 degrees.
Hence the value of ∠N is 54.38 degrees.
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9. A plant seed may get carried very far on a windy day, and sprout in another field full of the same type of
plant. What mechanism of evolution is this an example of? Explain.
As a result of the seed growing in a field with a different population of plants, we can witness how gene flow works in action.
It will have introduced its alleles into that population once this plant reproduces there. Any movement of people from one group to another—also known as migration—and/or the genetic material they carry is referred to as gene flow. Pollen being carried to a new location by the wind or individuals relocating to new cities or nations are just a few examples of the many different types of events that contribute to gene flow.
Vertical and horizontal gene flow are two different types of gene transfer. Gene flow describes the transfer of genetic material between groups.
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EHO
Using the following model, answer questions 1 - 2:
You bought a new car for $17,7 in 2005. Its value
has been decreasing by about 13% each year
Cuz Rocha
APPLICATIONS on Modeling Exponential Functions
Answer the following applications. Round your answers to 2 decimal places. Find the solution in the
Answer Bank. When you find a match, place the question number next to the color. Color the picture
accordingly to reveal the mystery picture!
1. Write an exponential model for the value of the car after "x" years
2. What will the car be worth in 2015?
Name:
Using the following model, answer questions 3 - 4:
The population of a small town has been increasing at
1.5% due to an economic boom in the area. The
population was 7,650 in 1995.
Using the following model, answer questions 5 - 6:
Peter earned $2,300 last summer. He deposited the
money in his savings account that earns 2.4% interesi
compounded annually.
Using the following model, answer questions 7 - 8:
You have inherited land that was purchased for
$10000 in 1950. The value of the land incrocisty
approximately 4% per year.
Using the following model, answer questions 9 - 10:
The student enrollment of a high school was 1250 in
2000 and decreased by 1% per year until 2015.
Using the following model, answer questions 11- 12:
You bought a commemorative coin for $150. Each year,
x, the value of the coin increased by 2.5%.
Applications on Modeling Exponential Functions
1. log₂ 128=7
ections: Write
4th
Date:
Rocha
Period:
3. Write an exponential model for the population in this town in a particular year
"X"
4. What is the population in 2017
5. Write an exponential model to describes the amount of money in the bank
after x number of years
6. How much money will Peter have in 8 years?
7. Write an exponential model for the value of the land x years after 1950
7.
What is the approbate value of the land in the year 2010
9. Write an exponential model to show school's student enrollment in terms of
x, the number of years since 2000.
10.
What is the number of students in 2015?
11. Write an exponential model to give the value of the coin after x number of
years.
12. What is the value of the coin at 50 years?
Never Give Up On Math 2017
:I
173
3.
nece
Answer:
If f(x) = +4, which of the following is the inverse of f(x)?
O A. ƒ˜¹(x) = 2(2+4)
B. ƒ˜¹(x) = 7(2-4)
C. ƒ˜¹(x) = 7(2+4)
D. f¯¹(x) = ²(2-4)
Step-by-step explanation:
Which relation is not a function?
The relation C is the relation that does not represent a function.
When does a relation represents a function?A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.
In the context of this problem, we look at option C, where there are two arrows departing from the input of 1, meaning that:
The input of 1 is mapped to an output of 4.The input of 1 is also mapped to an output of 6.As the input of 1 is mapped to multiple outputs, the relation does not represent a function.
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Given the net, what is the surface area of the rectangular prism below?
PLS HELP WILL MARK BRAINLIST
Answer:
40
Step-by-step explanation:
For finding the surface area of this rectancular prism, or any, we find the area of each shape. Then, we add up all of the areas together to get the surface area. There are 2 squares with 2 as a side length for each side. To find the area of a square, we can multiply any 2 sides. That is because the sides of the square is equal to eachother, so 2•2=4. Being 2 squares, they are both have area of 4. Looking at the 4 rectangles, they have a length of 4 and a width of 2. We multiply the height and width of a rectangle to get the area. 4•2=8, the area of each rectangle is 8. Now, we add up all of our areas. Two squares, each are 4 for their area. Add them up, you get 8 for the 2 squares. Then, we have 4 rectangles each are 8 for their area. 4•8=32 since they all have the same area. 32+8=40! 40 is the surface area of this net. I hope this helps, and have good day
Solve for x.
-3
X=
X
= -48
Answer:x = {-4, 4}
explanation:
100 Points! Algebra question. Photo attached. Find the amplitude, if it exists, and period of the function. Then graph the function. Thank you!
hello
the answer to the question is:
y = a cot(bx – c) + d
a = 1, b = 1/2, c = 0
the midline is y = d, so y = 0
the vertical stretch is 1, so label the y-axis so the inflection point of the curve is 1 above the midline, and the other inflection point is 1 below the midline
the period is:
T = π/b ----> T = 2π
the phase shift is:
PS = c/b ----> PS = 0
and also, there's no amplitude for tangent and cotangent, there is only the vertical stretch that takes the place of an amplitude
Answer:
amplitude does not exist. period = 2π (360°)
Step-by-step explanation:
there is no amplitude for tan θ or cot θ, since there is no limit up or down (positive/negative infinity).
period for cot θ is π (180°)
period for cot 1/2 θ is 2π (360°)
Find the third iterate x3 of f(x) = 2x + 3
for an initial value of x0 = 2
a. 7
b. 15
c. 17
d. 37
For the function f(x) = 2x + 3 the third iterate x₃ is 37
To find the third iterate, x3, of the function f(x) = 2x + 3, given an initial value of x₀ = 2,
we can apply the function repeatedly.
Starting with x₀ = 2:
x₁ = f(x₀)
= 2(2) + 3
= 7
x₂ = f(x₁)
= 2(7) + 3 = 17
x₃ = f(x₂)
= 2(17) + 3
= 37
Therefore, the third iterate x₃ is 37.
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b) If the blueprint is drawn on the coordinate plane with vertices (3, 5) and (12, 14) for the corners labeled with red stars, would that be an accurate representation of the length of the diagonal of the square C? Show your work and explain your reasoning.
(4 points—2 points for finding the length of the diagonal; 2 points for explanation)
The length f the diagonal of the square is
12.73 unitsHow to find the length of the diagonal of the squareThe marked points represents the diagonal hence we find the distance between the points
The distance between them is calculated using the following formula:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Using the points (3, 5) and (12, 14), we can substitute the values into the formula and calculate the length of the line segment:
d = √((12 - 3)² + (14 - 5)²)
= √(9² + 9²)
= √(81 + 81)
= √162
≈ 12.73
Therefore, the length of the line segment between (3, 5) and (12, 14) is approximately 12.73 units.
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if i have two assignment that's 5% of my grade and i have a 79 in the class what will my grade be if i get a 100 on both???
If you get a perfect score of 100% on both assignments, your overall grade in the class would be 100%.
To calculate your grade, we need to consider the weight of each assignment.
Since each assignment is worth 5% of your grade, we can calculate the contribution of the assignments to your overall grade.
The total weight of the two assignments is 2×5% = 10%.
To find the impact of the assignments on your grade, we multiply your average score on the assignments (100%) by their weight (10%):
Contribution from the assignments = 100% * 10% = 10%
Since you currently have a grade of 79, the remaining 90% of your grade is based on other assessments, tests, or assignments.
To calculate your overall grade, we add the contribution from the assignments to the remaining 90%:
Overall grade = 90% + 10% = 100%
Therefore, if you get a perfect score of 100% on both assignments, your overall grade in the class would be 100%.
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s. The area of a regular hexagon is 384√3Cm². Find A. the side length of the hexagon B. the radius of the hexagon C. the apothem of the hexagon
The apothem of the hexagon is 8√3 cm.
We are given that;
The area of a regular hexagon= 384√3Cm²
Now,
To find the side length, radius, and apothem of a regular hexagon given its area, we can use the following formulas:
Area = (3√3 s^2) / 2 Area = (1/2) a P Area = (3/2) r a
where s is the side length, a is the apothem, P is the perimeter, and r is the radius of the hexagon. We can solve for any of these variables by rearranging the formulas and plugging in the given area.
A. To find the side length, we can use the first formula and solve for s:
s^2 = (2 Area) / (3√3) s = sqrt((2 Area) / (3√3))
Plugging in Area = 384√3, we get:
s = sqrt((2 * 384√3) / (3√3)) s = sqrt(256) s = 16
Therefore, the side length of the hexagon is 16 cm.
B. To find the radius, we can use any of the formulas and solve for r. For example, using the third formula, we get:
r = (2 Area) / (3 a)
To find a, we can use the second formula and solve for a:
a = (2 Area) / P
To find P, we can use the fact that P = 6s and plug in s = 16:
P = 6 * 16 P = 96
Plugging in P and Area into the formula for a, we get:
a = (2 * 384√3) / 96 a = 8√3
Plugging in a and Area into the formula for r, we get:
r = (2 * 384√3) / (3 * 8√3) r = 32
Therefore, the radius of the hexagon is 32 cm.
C. To find the apothem, we can use any of the formulas and solve for a. For example, using the second formula, we get;
a = (2 Area) / P
Plugging in Area = 384√3 and P = 96, we get:
a = (2 * 384√3) / 96 a = 8√3
Therefore, by polygon the answer will be 8√3 cm.
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The proportion of all US adults who eat popcorn when they go to the movie theater is p = 0.87. A random sample of 20 US adults was selected and asked if they eat popcorn when they go to the movie theater. Which of the following is the shape of the sampling distribution of p hat ?
a. The sampling distribution of p hat is approximately Normal because n p = 17.4 greater-than 10.
b. Because n (1 minus p) = 20 (1 minus 0.87) = 2.6 less-than 10, the sampling distribution of p hat is not approximately Normal. The sampling distribution of p hat is skewed right and centered at 0.87.
c. Because n (1 minus p) = 20 (1 minus 0.87) = 2.6 less-than 10 , the sampling distribution of p hat is not approximately Normal. Because p = 0.87 is closer to 1 than 0, the sampling distribution of p hat is skewed to the left.
d. Because n (1 minus p) = 20 (1 minus 0.87) = 2.6 less-than 10, the sampling distribution of p hat is not approximately Normal. Because p = 0.87 is closer to 1 than 0, the sampling distribution of p hat is skewed to the right.
The option that represents shapes of the sampling distribution of p hat is:
c. Because n (1 minus p) = 20 (1 minus 0.87) = 2.6 less-than 10 , the sampling distribution of p hat is not approximately Normal. Because p = 0.87 is closer to 1 than 0, the sampling distribution of p hat is skewed to the left.
What is the shape of the sampling distribution?Normal distribution is defined as the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.
Because the requirement for normal is greater than 10, n×p is greater than 10 and nx(1-p) is also greater than 10.
This situation is abnormal because it is not valid. If p is close to 1 in a normal graph, then p is left skewed.
Thus, the option third is correct because nx(1-p)=2.6 less than equal to 10 then the sampling distribution is not approximate normal because p=0.87 is closer to 1 than zero. Sampling distribution is skewed to the left.
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Finding missing sides with trig rations
-Solve for x. Round to the nearest tenth.
Sorry for bad handwriting
if i was helpful Brainliests my answer ^_^
hello
the answer is:
1)
Sin 28° = x/19 ----> x = 8.91 or 9
2)
tan 41° = x/32 ----> x = 27.8 or 28
3)
Cos 21° = x/26 ----> x = 24.2 or 24
4)
Cos 55° = 8/x ----> x = 13.9 or 14
5)
Sin 33° = 15/x ----> 27.57 or 28
6)
Cos 43° = 36/x ----> x = 49.2 or 49
7)
tan 72° = 25/x ----> x = 8.12 or 8
8)
Cos 64° = x/11 ----> x = 4.81 or 5
EXER 1. Evaluate the following (a) 28-{15 (3+2)
The value of the expression 28 - {15 (3+2)} is -47.
To evaluate the expression 28 - {15 (3+2)}, we need to follow the order of operations (also known as PEMDAS/BODMAS) which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Let's break down the expression step by step:
First, we solve the expression inside the parentheses:
3 + 2 = 5
Now, we substitute the result back into the original expression:
28 - {15 * 5}
Next, we perform the multiplication:
15 * 5 = 75
Now, we substitute the result back into the expression:
28 - 75
Finally, we perform the subtraction:
28 - 75 = -47
Therefore, the value of the expression 28 - {15 (3+2)} is -47.
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A probability distribution for various prize values is given by the following table.
Prizes Probabilities
$0.00 0.83
$100.00 0.08
$500.00 0.08
$10,000.00 0.01
Find the expected winnings. Round your answer to the nearest cent.
Answer:
$148
Step-by-step explanation:
Expected winnings = ($0.00 x 0.83) + ($100.00 x 0.08) + ($500.00 x 0.08) + ($10,000.00 x 0.01)
Expected winnings = $0.00 + $8.00 + $40.00 + $100.00
Expected winnings = $148.00
I NEED THE ANSWER ASAP
I WILL MAKE THE FIRST PERSON TO ANSWER MY QUESTION BRAINLY!
ALSO YOU WILL GET 100 POINTS
Sorry for bad handwriting
if i was helpful Brainliests my answer ^_^
Answer:
3) 50 in²
4) 85 cm²
Step-by-step explanation:
Question 3The given figure is composed of 2 triangles, each with a base of 10 inches and a height of 5 inches.
The area of a triangle is half the product of its base and height.
Therefore, the area of the composite figure can be calculated as follows:
[tex]\begin{aligned}\textsf{Area of compositie figure}&=\sf Area_{Triangle\;1}+Area_{Triangle\;2}\\\\&=\dfrac{1}{2} \cdot 10 \cdot 5 + \dfrac{1}{2} \cdot 10 \cdot 5\\\\&=5\cdot 5+5\cdot 5\\\\&=25+25\\\\&=50\; \sf square\;inches\end{aligned}[/tex]
Therefore, the area of the composite figure is 50 square inches.
[tex]\hrulefill[/tex]
Question 4The given figure is composed of a rectangle with width of 6 cm and length of 10 cm, and a triangle with base of 10 cm and height of 5 cm.
The area of a rectangle is the product of its width and length.
The area of a triangle is half the product of its base and height.
Therefore, the area of the composite figure can be calculated as follows:
[tex]\begin{aligned}\textsf{Area of compositie figure}&=\sf Area_{Rectangle} + Area_{Triangle}\\\\&=6 \cdot 10+\dfrac{1}{2} \cdot 10 \cdot 5\\\\&=60+5 \cdot 5\\\\&=60+25\\\\&=85\; \sf square\;centimeters\end{aligned}[/tex]
Therefore, the area of the composite figure is 85 square centimeters.
what type of data would best be displayed in a box plot
Answer:(2x+7)+(2x+7)
Step-by-step explanation:
what you do is put 2x on the top and on the side and then seven on the top and on the side and then you got your answer
Algebra 2 Unit 4 Standards Tasks Shannon Barker S.CP.B.6: Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model. In the East Orange School District, students are only allowed to enroll in AP Calculus if they have already taken pre-calculus or general calculus. Out of 825 incoming seniors: * 465 took pre-calculus *166 took general calculus *133 took both. Part A (3 points): Given this information, determine the probability a randomly selected incoming Senior is allowed to enroll in AP Calculus. AN In another district an additional prerequisite course is math analysis. In that district there are 550 incoming seniors. . 345 took pre-calculus, 125 took general calculus, 40 took math analysis • 35 took pre-calculus and general calculus • 20 took math analysis and general calculus . 0 took both pre-calculus and math analysis Part B (2 points): In this school district, How many seniors were not able to take AP calculus? Submit
The given fractions representing the conditional probability is P(A | B) = P(AnB)/P(B)
We know that,
Conditional Probability is:
This is the probability that an event has happened given another event. If the two events are A and B, hence;
The conditional probability of A given B is expressed as:
P(A | B) = P(AnB)/P(B)
This given the fractions representing the conditional probability
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7. A scuba diver's depth in yards as a function of time in minutes (x) is
represented by the equation d(x) = 12x² - 144x.
a. What was the deepest the diver went?
b. How long did it take the diver to return to the surface?
c. How deep was the diver after one minute?
a) The deepest that the diver went is of: 432 yards deep.
b) It took 12 minutes for the diver to return to the surface.
c) After one minute, the diver was 132 yards deep.
How to obtain the features?The quadratic function modeling the diver's height after x seconds is given as follows:
d(x) = 12x² - 144x.
The coefficients are given as follows:
a = 12, b = -144, c = 0.
The x-coordinate of the vertex is given as follows:
x = -b/2a
x = 144/24
x = 6.
Item a:
As a > 0, in item a, the minimum height is given as follows:
d(6) = 12(6)² - 144(6)
d(6) = -432 feet.
Item b:
The roots of the function, in item b, are obtained as follows:
12x² - 144x = 0
12x(x - 12) = 0
Hence:
12x = 0 -> x = 0.x - 12 = 0 -> x = 12.12 - 0 = 12, hence it took 12 minutes for the diver to return to the surface.
Item c:
After one minute, the depth of the diver, in item c, is given as follows:
d(1) = 12(1)² - 144
d(1) = -132 yards.
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can my a value be negative in a exponential function
Yes, the coefficient of a value can be negative in an exponential function.
How is this possible?A coefficient in mathematics is a multiplicative factor in some term of a polynomial, series, or expression; it is generally a number, although it can be any expression.
Recall that the general form of an exponential function is f(x) = a^(bx + c), where a is the base.
This can be negative or positive. But cannot be equal to zero. A negative exponential function can model the decay of a radioactive substance or, in accounting, depreciation of an asset.
Thus, it is correct to state that , the coefficient a value can be negative in an exponential function.
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Solve the system using substitution. Show all work.
-12x + 5y = 9
y = 2x - 5
Solution of the given system is,
x = 8
y = 11
The given system of equation
-12x + 5y = 9 ....(i)
y = 2x - 5 ...(ii)
Now we have to solve it by using substitution method.
So put value of y from equation (ii) into equation (i)
Therefore,
⇒ -12x + 5y = 9
⇒ -12x + 5(2x - 5) = 9
⇒ -12x + 10x - 25 = 9
⇒ -2x = 16
⇒ x = 8
Now put the values of x into (ii) we get,
⇒ y = 2x8 - 5
⇒ y = 11
Hence,
solutions be ,
x = 8
y = 11
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Complete the division problem by filling in the missing number.
113 ÷ 4 = 2 18
The solution is
The missing number in the original division problem is 28.
The solution is 113 ÷ 4 = 28.
The given division problem is: 113 ÷ 4 = 2 18.
To find the missing number, we can perform the division calculation step by step.
First, we divide 4 into the first digit of 113, which is 1.
Since 4 cannot be divided evenly into 1, we bring down the next digit, which is 1.
Now we have 11.
Next, we divide 4 into 11.
We can divide 4 into 11 two times, which gives us 8.
We subtract 8 from 11, leaving us with a remainder of 3.
Now, we bring down the next digit, which is 3.
We have 33.
Finally, we divide 4 into 33. 4 can be divided into 33 eight times, which gives us 32.
We subtract 32 from 33, leaving us with a remainder of 1.
So, the complete division is 113 ÷ 4 = 28 remainder 1.
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This answer is incorrect. Can someone help with the answer?? Determine the probability of the treatment group’s mean being greater than the control group’s mean by 8 points or more. Then complete the statements.
The significance level is set at 5%, and the probability of the result is
5%, which is less than the significance level. The result is statistically significant.
.
If the significance level is set at 5%, the probability of the treatment group's mean being greater than the control group's mean by 8 points or more is given as 5%, which is less than the significance level of 5%.
The correct answer is "less than."
What is the probability?The probability of the treatment group's mean being greater than the control group's mean by 8 points depends on the sample sizes, standard deviations, and means of both groups.
These values are used to calculate the t-score or z-score and the corresponding probability or p-value.
The probability can than be compared to the significance level to determine if the result is statistically significant.
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I NEED IMMEDIATE HELP
Using the graph, determine the equation of the axis of symmetry
Answer: x=-7
Step-by-step explanation:
This question is really easy, so I'll just briefly explain axis of symmetry
To find it, it is ((x intercept 1)+(x intercept 2))/2. This is also called the vertex.
Or, the x value of the lowest or highest point. Lowest is it opens up, highest if it opens down.
x=-7 is the answer
PLEASE HELP I NEED THE ANSWER RN
Answer: B
Step-by-step explanation:
Amplitude will be half the distance from 28 to 50
one cycle is given to be 8 hrs, so thats all you need for the right answer choice.
You will create an estimate in order to assist your boss in gaining the job!
The equation that is given by the customer for the pool is (units are in feet): x2 + y2 = 81
- Your performance needs to include the following calculations:
- Compute the radius and diameter of the pool.
- Compute the volume of water in the pool using the above calculations and a height of 4 ft.
- Assuming that water costs $0.22 per gallon and that pools cost $185 per foot of radius calculate the total cost of materials for the pool. Keep in mind that there are 7.48 gallons of water per square foot.
- Assuming that a pool will take 2.5 hrs. per foot of radius, compute the total labor hours for the pool.
- If you are to pay someone $19/hr, compute the total cost of labor.
- Find a total cost for the project.
- All of the above is done showing all work.
- A final paragraph that describes your steps and findings.
The solution has been explained below.
We will use the following equation, x² + y² = 81, where x and y are the pool's dimensions in feet, to determine the necessary estimations for the pool project.
1. Calculate the pool's diameter and radius:
We can infer that the radius of the pool is equal to the square root of 81 because the equation depicts a circle. As a result, r = 81 = 9 ft.
The pool's diameter is simply equal to twice its radius, or d = 2r = 18 feet.
2. Calculate the amount of water in the pool:
Since the pool is 4 feet high, we can determine its volume by multiplying the area of its circle-shaped base by the height.
The formula A = πr² can be used to calculate the area of the pool's base,
Therefore, V = Ah = πr²h = 1017.87 cubic feet represents the volume of water in the pool.
3. Determine the pool's total material cost:
There are 7.48 gallons in a cubic foot and a gallon of water costs $0.22.
As a result, Cw = V × 7.48 × 0.22 = 1017.87 × 7.48 × 0.22 = $1,619.72 is the entire cost of water for the pool.
If the radius of the pool is $185 per foot, then the cost of the materials is Cm = r × 185 = 9 × 185 = $1,665.
4. Calculate the pool's total labour hours:
A pool's construction is estimated to take 2.5 hours for every foot of its radius.
So, L = r × 2.5 = 9 × 2.5 = 22.5 hours of labour would be needed to complete this pool.
5. Calculate the total cost of labour for the project:
If you pay someone $19 per hour, Cl = L × 19 = 22.5 × 19 = $427.5.
6. Find the project's overall cost:
The project's overall cost is the product of its labour and material costs:
Cost as a whole equals Cm + Cw + Cl, which is 1,665 + 1,619.72 + 427.5, or $3,712.22.
In conclusion, the pool has an 18-foot diameter and a 9-foot radius according to the supplied equation. There are roughly 1017.87 cubic feet of water in the pool. Water and building supplies are included in the pool's projected material cost of $3,284.72. 22.5 hours of labour in total are needed, with a labour cost estimate of $427.5. Consequently, $3,712.22 is the expected final cost of the pool renovation.
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Find the average value of f(x)….. see the image
The average value of f(x) over the interval [ - 16, 16] is found to be 0.
How do we calculate?The average value of f(x) = 16x over the interval [ - 16, 16] is:
F_average = (1/(b-a)) * ∫(a to b) f(x) dx,
where the value of
a = -16 and b = 16
F_average = (1/(16-(-16))) x ∫(-16 to 16) 16x dx
F_average = (1/32) x [8x²] from -16 to 16
F_average = (1/32) x [8(16² - (-16)²)]
F_average = (1/32) x [8(256 - 256)]
F_average = 0
In concluaion, the average value of f(x) over the interval [ - 16, 16] is determined as 0.
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Solve x2 + 6x − 8 = 0 by completing the square. (1 point)
(x + 3)2 = 17; x equals negative 3 plus or minus the square root of 17
(x + 3)2 = 17; x = 14, x = 20
(x + 6)2 = 8; x equals negative 6 plus or minus 2 times the square root of 2
(x + 6)2 = 8; x = −14, x = 2
The correct option is: (x + 3)² = 17; x equals negative 3 plus or minus the square root of 17(x = -3 ± √17) by completing the square
How to evaluate for the equation by completing the squareThe completing the square method require we move constant term to the right hand side of the equation, divide the middle term and add its square to both sides of the equation as follows:
For the equation;
x² + 6x - 8 = 0
add 8 to both sides
x² + 6x = 8
divide 6 by 2 and add the square of the result to both sides
x² + 6x + 3² = 8 + 3²
by factorization;
(x + 3)² = 8 + 9
(x + 3)² = 17
x + 3 = ± √17 {take square root of both sides}
x = -3 ± √17
Therefore, by completing the square we the equation to be (x + 3)² = 17 and the solution for the value of x = -3 ± √17
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What is the slope of the line shown? On a coordinate plane, a line passes through points (negative 6, 7), (negative 2, 6), (2, 5), and (6, 4). The slope is .
Answer:
To find the slope of a line passing through four points, we can use the formula:
slope = (change in y) / (change in x)
We can use any two points to calculate the slope, but since we need to find the slope for the entire line passing through all four points, we need to make sure that the slope is the same for any two points that we choose.
Let's use the points (-6,7) and (-2,6) to calculate the slope:
slope = (6 - 7) / (-2 - (-6)) = -1/4
Now let's use the points (2,5) and (6,4) to calculate the slope:
slope = (4 - 5) / (6 - 2) = -1/4
Since the slope is the same for both pairs of points, we can conclude that the slope of the line passing through all four points is -1/4.
Step-by-step explanation: