Hence, in response to the provided question, we can say that As a result, derivatives the integral has a value of -i/2.
what is derivative?In mathematics, the derivative of a function with real variables measures how sensitively the function's value changes in reaction to changes in its parameters. Derivatives are the fundamental tools of calculus. Differentiation (the rate of change of a function with respect to a variable in mathematics) (in mathematics, the rate of change of a function with respect to a variable). The use of derivatives is essential in the solution of calculus and differential equation problems. The definition of "derivative" or "taking a derivative" in calculus is finding the "slope" of a certain function. einsteinerupload of. Derivatives are rate of change metrics that apply to almost any function.
To use the Cauchy Integral Theorem to evaluate the integral (3z+1)/(z(z-2)2), we must first determine whether the function has any singularities in the region we are integrating across.
We can write the function to find the residue at z=0 as:
A/z + B/(z-2) + C/(z-2)2 = (3z+1)/(z(z-2)2)
3z+1 = A(z-2)^2 + Bz(z-2) + Cz
When we set z=0, we get:
1 = 4A
So, A = 1/4.
Set z=2 in the following equation and its derivative to determine B and C:
9 = 4B + 2C
3 = 4A - 2B - C
B = -1/2 and C = 7/4.
So, A=1/4 is the remnant at z=0, while B=-1/2 is the residue at z=2.
Applying the residue theorem, the integral is as follows:
dz = 2i [Res(z=0) + Res(z=2)] = 3z+1/(z(z-2)2
= 2πi [1/4 - 1/2]
= -πi/2.
As a result, the integral has a value of -i/2.
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I will mark you brainiest!
One of the sides of a rectangle has the length of 7. Which of the following points, when paired with (6, 5), will make a side equal to this length?
A) (7, 5)
B) (6, 12)
C) (6, 7)
D) (12, 5)
Answer:its b 6,12
Step-by-step explanation:
Find all solutions of the following polynomial equation.
-7x + 4x²-28 + x³ = 0
Therefore , the solution of the given problem of quadratic equation comes out to be x = 2, -3 + √(5)i, -3 - √(5)i.
What is quadratic equation ?Regression modelling uses the polynomial answer x = ax2 + b + c=0 for one-variable equations. The First Proposition of Algebra claims that since this proposition has a second order, there can only be one solution. There are simple and complicated solutions available variable . Even as the name suggests, a "non-linear formula" has four factors. According to this, there might be just one squared term. In the formula ax2 + bx + c = 0
Here,
The provided polynomial equation can be rewritten as follows:
=> x³ + 4x² - 7x - 28 = 0
The constant term in this situation is -28, with components of 1, 2, 4, 7, 14, and 28, and a leading coefficient of 1. Therefore, 1, 2, 4, 7, 14, and 28 are among the polynomial's potential rational solutions.
It is possible to factor the polynomial by discovering that x = 2 is one of its roots.
=> (x - 2)(x² + 6x + 14) = 0
The quadratic formula can be used to calculate the quadratic factor:
=> x = (-6 ± √(6² - 4114)) / (2*1)
=> (-6 ± √(-20)) / 2
=> -3 ± √(5)i
Thus, the following are the answers to the algebraic equation:
=> x = 2, -3 + √(5)i, -3 - √(5)i.
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In a race, 24 out of the 25 bicyclists finished in less than 56 minutes. What percent of bicyclists finished the race in less than 56 minutes? Write an equivalent fraction to find the percent.
The percentage of bicyclists that finished the race in less than 56 minutes is 96 %
What is percentage?Percentage is a ratio out of hundred
If in a race, 24 out of the 25 bicyclists finished in less than 56 minutes. To find what percent of bicyclists finished the race in less than 56 minutes, we first write it in a fraction as number/total
Since
number = 24 and total = 25We have that
fraction = number/total
= 24/25
Now to write it as a percentage, we multiply by 100.
So, we have that percentage = fraction × 100 %
So, we have that in percentage = 24/25 × 100 %
= 24 × 4 %
= 96 %
So, the percentage is 96 %
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You have realised that instead of reducing your car's short-term insurance ium as its book value decreases, your insurer has actually increased the premium % per year "to keep up with inflation". If your premium started off at R450 per month. have you paid in total after 2 years?
To calculate the total amount paid over two years, we first need to determine the annual premium increase percentage. Let's assume the insurer increases the premium by 5% per year to keep up with inflation.
After the first year, the new premium would be:
R450 + (5% of R450) = R472.50 per month
After the second year, the new premium would be:
R472.50 + (5% of R472.50) = R496.13 per month
To calculate the total amount paid over two years, we can use the following formula:
Total amount paid = (monthly premium x 12 months x number of years)
= (R450 x 12 x 2) + (R472.50 x 12 x 1) + (R496.13 x 12 x 1)
= R10,800 + R5,670 + R5,953.56
= R22,423.56
Therefore, you would have paid a total of R22,423.56 over two years.
Pleaseeeeeeeeeeeee help
Answer:
Step-by-step explanation:
i cant see good
Answer:
I think it would be commutative property
Step-by-step explanation:
the commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The commutative property only works with addition and multiplication.
Write in descending order in terms of y
In descending order in terms of y, the expression is -x³y⁵ - 2x²y³ + 4xy + x⁴.
What is descending order?When a pattern of numbers in mathematics has a decreasing value, the numbers are said to be in descending order. It indicates that the numbers are sorted from highest to lowest. Information is considered to be in descending order if it is arranged from highest to lowest. For example 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 are ordered in descending order. In other terms, it is considered to be in descending order if the numbers are listed from greatest to smallest.
The given expression is:
x⁴- x³y⁵+ 4xy - 2x²y³
To arrange in descending order, place the highest value first followed by the smaller value.
Therefore, in decreasing order in terms of y, the expression is -x³y⁵ - 2x²y³ + 4xy + x⁴.
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Find a formula for the linear function depicted in the following graph.
f(x)=
Step-by-step explanation:
f(X)=ax+q
domain: X element of real numbers
If 9% of a number equals 10, find 27% of that number.
Solve four-sixths minus three-twelfths equals blank.
one-sixth
five-twelfths
seven-twelfths
thirty-six seventy-seconds
Question 4(Multiple Choice Worth 2 points)
(05.04 LC)
Solve seven-eighths minus nine-sixteenths equals blank.
two-sixteenths
two-eighths
five-sixteenths
sixteen thirty-seconds
Question 5(Multiple Choice Worth 2 points)
(05.04 LC)
Solve two-fifths minus one-seventh equals blank.
one-fifth
one-seventh
nine thirty-fifths
three-twelfths
By answering the presented question, we may conclude that As a result, fraction the answer is nine thirty-fifths.
what is fraction?A whole can be represented by any number of equal sections or fractions. In standard English, fractions represent the number of units of a specific size. 8, 3/4. A whole contains fractions. In mathematics, numbers are stated as the ratio of the numerator to the denominator. Each of these is an integer in simple fractions. A fraction exists in the numerator or denominator of a complex fraction. True fractions have numerators that are smaller than their denominators. A fraction is a sum that represents a piece of a total. You may assess it by dividing it up into smaller chunks. Half of a whole number or object, for example, is represented as 12.
We can simplify both fractions to have a common denominator of 12 for the first problem:
Four-sixths = Eighteenths
Three-twelfths + three-twelfths = three-twelfths
As a result, the phrase becomes: 8/12 - 3/12 = 5/12
As a result, the answer is five-twelfths.
For the second case, we may reduce both fractions again such that they have a common denominator of 16:
Seventy-eighths = fourteenteenths
Nineteenths + nineteenths = nineteenths
As a result, the equation becomes: 14/16 - 9/16 = 5/16.
As a result, the answer is five-sixteenths.
We can simplify both fractions to obtain a common denominator of 35 for the third problem:
Two-fifths = 14-thirty-fifths
One-seventh Equals thirty-fifths
As a result, the phrase becomes: 14/35 - 5/35 = 9/35
As a result, the answer is nine thirty-fifths.
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calculati 14,7+21,8+0,9
Answer:
18.4
Step-by-step explanation:
ur welcome
3. The trick with ratios is to always multiply or divide the numbers by the same value. If a recipe uses 3 cups of flour and 2 cups of milk and 2 quantities of the recipe is needed, what would be the ratio for 2 quantities of flour and milk?
Answer: ____
a) 1 : 3 b) 12 : 8 c) 4 : 8 d) 6 : 4
The ratio for 2 quantities of flour and milk is given as follows:
d. 6:4.
How to obtain the ratio?The ratio 2 quantities of flour and milk is obtained applying the proportions in the context of the problem.
A proportion is applied as to obtain the ratio between two amounts, you simply divide one amount by the other. The ratio is expressed as a fraction, and can also be expressed as a decimal or a percentage.
The amounts for a single recipe are given as follows:
3 cups of flour.2 cups of milk.Hence for two quantities, the amounts are multiplied by two as follows:
6 cups of flour.4 cups of milk.Meaning that the ratio is given as follows:
6:4.
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SKETCHPAD
Question 9
An online store sells plain rings for $3 each and rings decorated with initials for $4 each.
Tyler makes a table to compare the costs of the rings. Complete the pattern in the first two
columns of the table. Then, write the ordered pairs for the corresponding terms in the
third column.
a
D
✓
+
PENCIL
THIN V
BLACK V
Cost of plain rings (x) Cost of initial rings (y)
(in dollars)
(in dollars)
0
0
(
(
(
Ordered Pairs
(x, y)
(0, 0)
)
)
)
) I’m
The ordered pair (2,6) means that 2 plain rings and 6 initial rings were purchased, and the total cost would be 23 + 64 = 24 dollars.
Describe Ordered Pair?In mathematics, an ordered pair is a collection of two objects, which are arranged in a specific order. The order of the objects in the pair is important, as the ordered pair (a, b) is different from the ordered pair (b, a) if a and b are not equal.
The two objects in an ordered pair can be anything, such as numbers, variables, or other mathematical entities. The ordered pair (x, y), for example, can represent a point on a two-dimensional coordinate plane, where x represents the horizontal coordinate and y represents the vertical coordinate.
The ordered pair notation is commonly used in set theory and other branches of mathematics to represent relationships between two objects. Ordered pairs can also be used to define functions, where the first object in the pair represents an input to the function, and the second object represents the output.
Here's the completed table and ordered pairs:
Cost of plain rings (x) Cost of initial rings (y) (Ordered Pairs (x,y))
0 4 (0,4)
1 5 (1,5)
2 6 (2,6)
3 7 (3,7)
4 8 (4,8)
In each ordered pair, the first number represents the number of plain rings purchased (x) and the second number represents the number of initial rings purchased (y). For example, the ordered pair (2,6) means that 2 plain rings and 6 initial rings were purchased, and the total cost would be 23 + 64 = 24 dollars.
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PLEASE HELP !! I WILL GIVE BRAINLIEST ANDDD 100 POINTS ! :)
Step-by-step explanation:
Interchange just means to switch really. The first 3 will stay the same be cause they are the same numbers.
The last one will be (2,8) because that's (8,2) but with the numbers switched
factoring polynomial x(6x-1)-3(6x-1)
The factored version of the provided polynomial is (6x-1) according to the given assertion.(x-3).
What in mathematics is a polynomial?An expression that consists of variables, factors, and exponents and is mixed using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial. (No division operation by a variable).
To factor the polynomial x(6x-1)-3(6x-1), we can first simplify the expression by factoring out the common factor of (6x-1):
x(6x-1)-3(6x-1) = (6x-1)(x-3)
Therefore, the factored form of the given polynomial is (6x-1)(x-3).
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please answer quickly. I am begging you
Answer:
ok, what do you want me to answer?
multiply (d + 4) (d - 4)
Answer:
[tex]d^{2}[/tex] - 16.
Step-by-step explanation:
To solve for the product of (d + 4) and (d - 4), we can use the FOIL method.
What does 'FOIL' Stand for?First Outer Inner LastThis means we multiply the first terms, then the outer, then the inner, and finally the last terms, then we add all the products together.
So, (d + 4) (d - 4) can be expanded like this:
First: d × d = [tex]d^{2}[/tex] Outer: d × -4 = -4d Inner: 4 × d = 4d Last: 4 × -4 = -16Adding all of them together, we get: [tex]d^{2}[/tex] - 4d + 4d - 16, which simplifies to [tex]d^{2}[/tex] - 16.
Therefore, (d + 4)(d - 4) = [tex]d^{2}[/tex] - 16.
Company XYZ closed at $53.21 per share with a P/E ratio of 13.26 . Answer the following questions. a. How much were earnings per share? b. Does the stock seem overpriced, How much were earnings per share? b. Does the stock seem overpriced, underpriced, or about right given that the historical P/E ratio is 12-14?ced, or about right given that the historical P/E ratio is 12-14?
Answer: a. To find the earnings per share (EPS), we can use the formula:
P/E ratio = Price per share / Earnings per share
Rearranging this formula to solve for EPS, we get:
Earnings per share = Price per share / P/E ratio
Substituting the given values, we have:
Earnings per share = $53.21/13.26 ≈ $4.01
Therefore, the earnings per share were approximately $4.01.
b. To determine if the stock is overpriced, underpriced, or about right given the historical P/E ratio of 12-14, we can compare the current P/E ratio to this range. Since the current P/E ratio is 13.26, which falls within the historical range, the stock seems to be about right in terms of valuation. However, it's important to note that other factors should also be considered before making any investment decisions.
Step-by-step explanation:
The histogram below gives the length of service of members of the Department of Mathematics and Statistics at a particular university. The
classes, in years of service, are 0-4.9, 5-9.9, etc., and the vertical axis represents the number of faculty.
What percent of the department faculty have 20 or more years of service?
Answer:
%
14
13-
12-
V
11
OF
18
9
8
7
6
5
10
4
3
24
1
8
Mathematics and Statistics Faculty
10
15
20
25
38
35
4
Answer:
approx 20% of the department faculty have 20 or more years of service
Step-by-step explanation:
To find the percentage of the department faculty with 20 or more years of service, we need to add up the number of faculty members in the "20-24.9" and "25 or more" year categories, since anyone with 20 or more years of service would fall into one of these categories.
Looking at the histogram, we see that there are 24 faculty members in the "20-24.9" year category, and an additional 4 in the "25 or more" year category. Therefore, the total number of faculty members with 20 or more years of service is 24 + 4 = 28.
To calculate the percentage of faculty members with 20 or more years of service, we need to divide this number by the total number of faculty members in the department, which we can find by adding up the heights of all the bars in the histogram. Based on the heights of the bars in the histogram, we can estimate that the total number of faculty members is approximately 140.
Therefore, the percentage of faculty members with 20 or more years of service is:
(28/140) x 100% = 20%
So, approximately 20% of the department faculty have 20 or more years of service.
The table below shows data for a class's midterm and final exam. Use the table to answer the following questions.
What is the 5 number summary for the class's Midterm Exam?
Minimum
Lower Quartile
Median
Upper Quartile
Maximum
The five-number summary of the class, determined by the results of the final test, is:
Minimum = 60
Lower quartile = 71.5.
Median = 85.
Upper Quartile = 94.
Maximum = 98
What is median?The median, a measure of the center of gravity, reflects the center of value in the collection when values are sorted in either ascending or descending order. The value that distinguishes the lower 50% of the information from the upper 50% of the data is, in other words, the value.
The lowest score is 60, which is the minimum. The highest score, 98, will serve as the maximum.
The formula: can be used to determine the lower quartile.
= (Second score + Third score) / 2
= (65 + 78) / 2
= 71.5.
The upper quartile is:
= (Third to last score + Second to last score) / 2
= (93 + 95) / 2
= 94
The median is:
= (5th score + 6th score) / 2
= (82 + 88) / 2
= 85
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5.A committee of 6 members is to be selected from 8 men and 7 women. In how many ways can this be done so as to include
a. 3 women
b. at least 4 men
c. at most 3 women
There are 252 different ways to assemble the committee.
What is permutation and combination?Permutation:
A simple definition of permutation is the various ways to arrange some or all of the members in a particular order.
It is the process of orderly disorganisation.
A permutation is what is meant by this.
Combination: Combination is the process of choosing one or more objects from a group of objects so that, unlike permutations, the order in which the objects are chosen is irrelevant.
It describes the combination of N items drawn randomly from a collection of K items at a time.
Hence, There are 252 different ways to assemble the committee.
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solve this proof. help pls
Answer:
Step-by-step explanation:
Use SAS congruency; AD=DC, and they both share side BD. Also, BD is the perpendicular bisector to AC, so it also forms 2 right angles. Proof using SAS.
Or, if you don’t know SAS congruency, you may use SSS congruency;
Use the Pythagorean theorem. Side length AB^2 = AD^2 + BD^2
BC^2 = DC^2 + BD^2.
AD=DC, so therefore AB = BC. Use SSS congruency, and there you go.
Given the two lines l and m are parallel in the figure, name the following:
Answer:
Option B
3&5, 4&6
Step-by-step explanation:
An interior angle is an angle inside a shape
Please solve these 2 problems for me
The value of the perimeter:
1. 97. 3 units
2. 27. 8 units
How to determine the perimeter of the shapesThe formula for the perimeter of a triangle is expressed as;
P = a + b + c
Given that;
P is the perimeter of the trianglea, b and c are the length of the sidesFrom the diagram shown, we have that;
Using the tangent identity;
tan 44 = BC/29
find the value and cross multiply
BC = 28. 00
Also, AC ²= 29² + 28²
AC = √1625 = 40. 3
Then, the perimeter = 29 + 28. 00 + 40. 3 = 97. 3 units
For the second diagram;
Note that the perimeter of a rectangle is expressed as 2(length + width)
Substitute the values
Perimeter =2 ( 4 + 3) = 14 units
For triangle;
sin 45 = 4/t
cross multiply
t = 5. 7 units
To determine the adjacent side;
5.7² - 4² = x²
32. 5 - 16 = a²
a = √16. 49
a = 4. 1
Then, the perimeter = perimeter of rectangle + perimeter of triangle
= 14 + 13. 8
= 27. 8 units
Note that no specific unit was given as thus, we used 'units' as the measuring scale.
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Eli has a trophy case that is 4 3/5 feet by 2 feet by 3 1/2feet. What is the volume of Eli’s trophy case?
The volume of Eli's trophy case is 64.4 cubic feet.
Eli's trophy case's length, breadth, and height must be multiplied to determine its volume. The case has the following measurements:
Length = 4 3/5 feet
Width = 2 feet
Height = 3 1/2 feet
We can sum the improper fractions after converting the mixed integers to fractions to arrive at:
Length = 4 3/5 feet = (5*4 + 3)/5 = 23/5 feet
Height = 3 1/2 feet = (2*3 + 1)/2 = 7/2 feet
Now that we have the volume, we can multiply the length, width, and height:
Volume equals length, width, and height
= (23/5) feet x 2 feet x (7/2) feet
= (23 x 2 x 7)/(5 x 2) cubic feet
= (644/10) cubic feet
= 64.4 cubic feet
Eli's trophy case therefore has a 64.4 cubic foot volume.
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ABCD is a kite, so
�
�
‾
AC
⊥
⊥
�
�
‾
DB
and
�
�
=
�
�
DE=EB. Calculate the length of
�
�
‾
AC
, to the nearest tenth of a centimeter
The length of AC to the nearest tenth of a cm, in the given kite, is: 8.7 cm.
How to solveApplying the Pythagorean Theorem, the length of AC to the nearest tenth of a cm, in the given kite, is: 8.7 cm.
From the information given, we know the following:
DE = EB = 4cmAD = 5 cmCD = 7 cmTriangles AED and CED are right-angled triangles
Thus:
AC = AE + CE
Find AE and CE using the Pythagorean Theorem , where c if the hypotenuse of the right triangle.
Length of AE:
AE = [tex]\sqrt{5^2 -4^2}[/tex]
AE= [tex]\sqrt{9}[/tex]
AE= 3
Length of CE:
CE = [tex]\sqrt{7^2 -4^2}[/tex]
CE= [tex]\sqrt{33}[/tex]
CE= 5.7
Length of AC:
AC = AE + CE
Put the values together:
AC = 3 + 5.7
= 8.7cm
Therefore, the length of AC to the nearest tenth of a cm, in the given kite, is: 8.7 cm.
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Here is the problem.
a) The speed at which the car gets maximum gas mileage is given as follows: 48 miles per hour.
b) The max gas mileage is given as follows: 29.5 miles per gallon.
How to obtain the maximum gas mileage?The gas mileage is modeled as a function of the velocity x according to the quadratic function presented as follows:
m(x) = -0.028x² + 2.688x - 35.012.
The coefficients are given as follows:
a = -0.028, b = 2.688, c = -35.012.
The leading coefficient a is negative, hence the vertex represents the point at which the maximum mileage is obtained.
The velocity is given as follows:
x = -b/2a
x = -2.688/[2(-0.028)]
x = 48 miles per hour.
The max gas mileage is obtained as follows:
m(48) = -0.028(48)² + 2.688(48) - 35.012.
m(48) = 29.5 miles per gallon.
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A jet airplane begins a steady climb of 15° and flies for two miles (measured horizontally). What is the change in altitude in feet? Round your answer to the nearest hundredth of a foot.
Answer:
Rounding to the nearest hundredth of a foot, the change in altitude is approximately 514.77 feet.
Step-by-step explanation:
To solve this problem, we can use trigonometry. The angle of climb is 15 degrees, which means that the ratio of the change in altitude to the horizontal distance traveled is the tangent of 15 degrees:
tan(15°) = change in altitude / horizontal distance
We can rearrange this equation to solve for the change in altitude:
change in altitude = horizontal distance x tan(15°)
Substituting the given values, we get:
change in altitude = 2 miles x tan(15°)
We can convert the distance to feet by multiplying by 5280:
change in altitude = 2 miles x 5280 feet/mile x tan(15°)
Using a calculator, we get:
change in altitude ≈ 514.77 feet
Rounding to the nearest hundredth of a foot, the change in altitude is approximately 514.77 feet.
Heather invests $1,050 in an account with a 3.5% interest rate, making no other deposits or withdrawals. What will Heather’s account balance be after 7 years if the interest is compounded 6 times each year?
Heather's account balance will be approximately $1,340.55 after 7 years if the interest is compounded 6 times each year.
What is the accrued amount after 7 years?To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the account balance after a certain amount of time
P is the principal or initial amount invested
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the time period in years
Given tha data in the question;
P = $1,050R = 3.5%n (the interest is compounded 6 times each year) = 6t = 7 yearsFirst, convert R as a percent to r as a decimal
r = R/100
r = 3.5/100
r = 0.035 rate per year.
Substituting these values into the formula solve for accrued amount, we get:
A = P(1 + r/n)^(nt)
A = 1,050(1 + 0.035/6)^(6 × 7)
A = 1,050(1 + 0.005833333333333)⁴²
A = 1,050(1.005833333333333333)⁴²
A = $1,340.55
Therefore, the accrued amount is $1,340.55.
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i’m confused can someone pls help me
In the given diagram, using the tangent theorem, the value of x to the nearest tenth is 16.6
Tangent theorem: Calculating the value of xFrom the question we are to determine the value of x.
From one of the tangent theorems, we have that
The tangent to the circle is perpendicular to the radius of the circle at the point of contact.
Thus, the triangle is a right triangle
From the Pythagorean theorem which states that, in a right triangle, the square of the hypotenuse equals sum of squares of the other two sides.
Then, we can write that
x² = 9² + 14²
x² = 81 + 196
x² = 277
x = √277
x = 16.6433
x ≈ 16.6 (to the nearest tenth)
Hence, the value of x is 16.6
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Use the drawing tool to sketch the graph and label its parts.
The standard equation of a conic section with its center or vertex at the origin is x² = 4ay.
The graph of this conic section is a parabola that opens upward with with its vertex at the origin (0, 0).
What is a conic section?In Euclidean geometry, a conic section can be defined as a curve that is generated as the intersection of the surface of a right circular cone with a plane.
In Mathematics, the standard equation of a conic section is represented or modeled by the following mathematical equation:
(x - h)²/a² - (y - k)²/b² = 1
Where:
y and x represent the point.a, h, b, k represent a constant term.Based on the information provided about the vertex at (0, 0), the foci would be at (0, a) and the directrix would be represented by a horizontal line at y = -a. Therefore, the required equation of a conic section in standard form is given by:
x² = 4ay.
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