We can calculate the residual treatment effect for a time after the first 24 hours by adding up the integrals for each subsequent 24-hour period until the residual treatment effect falls to or below 20 ng/ml
How to solveTo determine the optimal dosage amount A for each Delay Type, we need to first define the surge function for each delay type as:
Extended: f(t) = [tex]At^2e^-^0^.^3^t[/tex]
Medium: f(t) = [tex]At^3e^-^0^.^5^t[/tex]
Rapid: f(t) = [tex]At^3e^-^0^.^7^t[/tex]
To find the optimal dosage amount A, we need to maximize the treatment effect while ensuring that the dose does not exceed 100ng/ml at any time and falls to be at or below 20ng/ml by 24 hours.
The treatment effect can be calculated by integrating the surge function over time from 0 to 24 hours and then adding up the integrals for each subsequent 24-hour period until the residual treatment effect falls to or below 20ng/ml
For the Delay Type and dosage level selected, we can calculate the treatment effect over the first 24 hours by integrating the surge function from 0 to 24 hours.
Then, we can calculate the residual treatment effect for a time after the first 24 hours by adding up the integrals for each subsequent 24-hour period until the residual treatment effect falls to or below 20 ng/ml..
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I really need help with this two please help to find x value and explain with reasons
In the first triangle, the angle x = 45°
In the second triangle, the angle y = 75°
In the second triangle, the angle x = 45°
How to find the angles in the triangles?To find the angles in the triangles, we proceed as folows.
a. In the first triangle, let the base angle to the left be p. We know that we have a parallelogram there.
Now, in the parallelogram,
102° + p = 180°sum of (interior angles of a parallelogram)
So, p = 180° - 102°
= 78°
Now, in the larger triangle,
x + p + 57° = 180° (sum of angles in a triangle)
Since p = 78°, we have that
x + 78° + 57° = 180°
x + 135° = 180°
x = 180° - 135°
= 45°
So, x = 45°
b. In figure 2, we have two isoceles triangles.
i. In the first triangle, both base angles are y.
So, y + y + 30° = 180° (sum of angles in atriangle)
2y + 30° = 180°
2y = 180° - 30°
2y = 150°
y = 150°/2
y = 75°
So, y = 75°
ii. In the second triangle also, both base angles are x and the other angle is a right angle which is 90°.
So, x + x + 90° = 180° (sum of angles in a triangle)
2x + 90° = 180°
2x = 180° - 90°
2x = 90°
x = 90°/2
x = 45°
So, x = 45°
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The area model shows 2 1/4. What is 2×2 1/4?
Step-by-step explanation:
2 1/4 = 9/4
2 × 2 1/4 = 2 × 9/4 = 9/2
Select the correct answer.
These lines are perpendicular. Is this statement true or false?
y = - 2/5x + 4
y =5/2x-3
A.true
B. false
The statement "These lines are perpendicular" is true.
These lines are perpendicular. Is this statement true or false?To determine if the two lines are perpendicular, we need to check if the product of their slopes is -1. That is, if:
m1 × m2 = -1
where m1 is the slope of the first line and m2 is the slope of the second line.
The slopes of the two lines are:
m1 = -2/5
m2 = 5/2
So, m1 × m2 = (-2/5) × (5/2) = -1
Since the product of the slopes is -1, the two lines are perpendicular. Therefore, the statement "These lines are perpendicular" is true.
The correct answer is A. true.
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Freshman
Sophomores
Total
Blology
0.15
0.2
0.35
Which statement is false?
Chemistry
0.1
0.25
0.35
Physical
science
0.2
0.1
0.3
OA. 15% of her students are in biology.
OB. 30% of her students are in physical science.
OC. 35% of her students are in chemistry.
OD. 45% of her students are freshmen.
Total
0.45
0.55
1.0
The statement that is false, given the table of Ms Stewart's class would be A. 15 % of her students are in biology.
How is this statement false ?The table shows that out of all he students, Ms. Stewart has 35 % that are doing Biology and not 15 %. But, she does have 15 % of Freshmen doing Biology and not of all her students.
30 % of the students are indeed engaged in doing physical science, and 35 % of her students are in chemistry from the table. 45 % of the total cohort that Ms. Stewart teaches are freshmen.
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What is the opposite of 12 written in simplest terms?
Answer:
Step-by-step explanation:
It is -12.
The opposite of a positive number would be its negative.
What is the total payment required to pay off a promissory note issued for $500.00 at 8% ordinary interest and a 90-day term? A. $507.20 C. $508.00 B. $540.00 D. $510.00
The total payment required to pay off the promissory note debt of 90 days term is D. $510.00.
The promissory note issued is for $500.
The interest rate is 8%.
Furthermore, the time frame is 90 days.
So the total payment is
= $500 + ($500 × 8% × 90 days ÷ 360 days)
= $500 + ($500 × 8% × 1/4)
= $500 + 10
= $510
Promissory notes are sometimes known as an IOU, a loan arrangement, or simply a note. It is a legal lending contract in which the borrower pledges to return the lender a specific amount of money within a specific time frame.
This type of document is legally binding and imposes a legal duty to repay the loan. Mortgages, school loans, car loans, company loans, and personal loans between family and friends all use promissory notes.
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3 divide 2 5ths in a facrtion
When 3 is divided by 2/5 , the answer is 7.5
Let's compare our whole number and fraction so that we can see the issue we are attempting to tackle.
3 divided by 2/5
In this case, creating a new numerator just requires multiplying the numerator by the full number. After that, the original numerator becomes the new denominator.
3*5/2 = 15/2
Most people prefer to express results in decimals, and all you have to do to do so is divide the numerator by the denominator:
15/2 = 7.5
What is Numerator?The portion written above the horizontal line is referred to as the numerator. Example: 2/5 ,here 2 is numerator.
What is Decimal?A decimal number consists of both a whole number and a fractional number. The numerical value of complete and partially whole amounts is expressed using decimal numbers, which are in between integers.
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The complete question is
what happens when 3 divide by 2/5ths in a facrtion?
Need help don’t know how to do failed 3 times cause of it help
The expression that can be used to find out the amount of time it would take Sal to finish the remaining homework is C. 4 / 9 x 3 / 5 .
How to find the expression ?To find the expression that would show the time it would take for Sal to finish his homework, the formula would be:
= Proportion of questions remaining x Time taken to finish one question
Proportion of questions remaining:
= 1 - 5 / 9
= 4 / 9
Time taken to finish one question:
= 3 / 5 minutes
The expression is therefore:
4 / 9 x 3 / 5
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The trifecta at most racetracks consists of selecting the first-, second-, and third-place finishers in a particular race in
their proper order. If there are ten entries in the trifecta race, how many tickets must you purchase to guarantee a win?
You would need to purchase 720 different tickets to guarantee a win.
how many finishers must be selected?You must pick the first three finishers in the correct order to win a trifecta race with 10 entries.
Since there are ten participants in the race, there are ten ways to select the winner of the first place prize. In the wake of choosing the primary spot finisher, there are just 9 passages remaining, so the quantity of ways of choosing the second-place finisher is 9.
Finally, since there are only eight entries left after selecting the first two, there are 8 ways to select the third-place finisher.
Therefore, the total number of possible winning trifecta combinations is:
10 x 9 x 8 = 720
This indicates that in order to guarantee a win, you would need to purchase 720 distinct tickets. However, it is essential to keep in mind that betting on a race in this manner may not always be the most profitable or efficient option, and that purchasing each and every possible combination can be very costly. It's vital to painstakingly think about the chances, payouts, and your financial plan prior to putting down any wagers.
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Find the surface area
Round to the nearest tenth
The total surface area of the given cone is 628 in².
What is the area of the cone?
The overall area a cone occupies in a three-dimensional space is referred to as its total surface area. It is equivalent to the total of the cone's curved surface and base. Total Surface Area (TSA) = CSA + Area of Circular Base is the formula for calculating a cone's total surface area.
Given :
Slant height of the cone = 17 inches
Diameter of the cone = 16 inches
Radius of the cone = Diameter/2
= 16/2
= 8 inches
Total Surface area of the cone = πr(l+r)
= π*8(17+8)
= 8π* 25
= 200π
= 628 in².
Hence, the total surface area of the given cone is 628 in².
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Help please !!!!!!!!!!!!!!!!!!!!!
The constant of proportionality is 2/3
The length of the missing sides of triangle NRF are:
RF = 4.5
NR = 6
Similar Triangles : Calculating the constant of proportionalityFrom the question, we are to calculate the constant of proportionality in the similar triangles
Constant of proportionality =
Corresponding side length on triangle GTY / Corresponding side length on triangle NRF
Constant of proportionality = GY / NF
Constant of proportionality = 6 / 9
Constant of proportionality = 2/3
We are to find the length of the missing sides of triangle NRF
By the similarity theorem, we can write that
3 / RF = 6 / 9
3 / RF = 2/3
Cross multiply
2 × RF = 3 × 3
2 × RF = 9
RF = 9/2
RF = 4.5
4 / NR= 6 / 9
4 / NR= 2/3
Cross multiply
2 × NR = 4 × 3
2 × NR = 12
NR = 12/2
NR = 6
Hence,
The length of the missing sides are
RF = 4.5
NR = 6
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Find the measure of angle A.
A
8x + 2
10x - 4
38°
Answer:
8x + 2 + 10x - 4 + 38 = 180
18x + 36 = 180
18x = 144, so x = 8
Angle A measures 8(8) + 2 = 64 + 2 = 66°.
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
The statements that are always true regarding the diagram are:
m∠1 + m∠5 = 180°
m∠2 + m∠3 = m∠6
m∠3 + m∠4 + m∠5 = 180°
Explain the term diagram
It refers to a value or position that is higher or greater than another value or position. It is often used in comparisons or to describe the relative positions of objects or points on a graph or coordinate plane. The opposite of "above" is "below," which refers to a value or position that is lower or lesser.
According to the given information
We know that the sum of the measures of the three interior angles of a triangle is always 180°. Therefore, we have:
m∠2 + m∠3 + m∠5 = 180°
From the given information, we know that:
m∠2 + m∠1 = 180° (linear pair of angles)
m∠3 + m∠4 = 180° (linear pair of angles)
m∠5 + m∠6 = 180° (exterior angle theorem)
Rearranging these equations, we get:
m∠1 = 180° - m∠2
m∠4 = 180° - m∠3
m∠6 = 180° - m∠5
Substituting these expressions into the above equation for the sum of the interior angles, we get:
m∠2 + m∠3 + m∠5 = m∠2 + (180° - m∠1) + m∠5
m∠3 + m∠4 + m∠5 = (180° - m∠3) + m∠4 + m∠5
Simplifying these equations, we get:
m∠1 + m∠5 = 180°
m∠2 + m∠3 = m∠6
Therefore, the statements that are always true regarding the diagram are:
m∠1 + m∠5 = 180°
m∠2 + m∠3 = m∠6
m∠3 + m∠4 + m∠5 = 180° (which is equivalent to option 2)
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Four cards labeled A, B, C, and D are randomly placed in four boxes labeled A, B, C, and D. Count the number of elements in the event that no box contains a card with the same letter as the box. elements
There are 24 possible arrangements for the elements in the occurrences where there are no cards in the box with the same letter.
What is Permutation?Arrangement of objects in a specific order.
From the information provided:
Using the permutation method, the four cards that are arbitrarily placed in the four boxes can be represented as follows:
No box has a card that begins with the same letter as the box, which suggests that:
There are four different ways to arrange Card A in a box, three different ways to arrange Card B in a box, two methods to arrange Card C in a box, and one way to arrange Card D in a box.
Thus, the Permutation of the four cards can be calculated as:
[tex]4^p_4 = 4! = (4 * 3 * 2 * 1) = 24[/tex]
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A quadratic function yields negative values between x = 2 and x = 6. Its minimum value is −2. What are the coordinates of the y-intercept? Enter your answer by filling in the boxes.
Answer:
Since the quadratic function has a minimum value at some point between x = 2 and x = 6, its graph is a downward-facing parabola.
Let's assume that the function is of form f(x) = ax^2 + bx + c, where a, b, and c are constants.
Since the minimum value of the function is −2, we know that the vertex of the parabola lies on the line y = -2. Also, we know that the x-coordinate of the vertex is the average of 2 and 6, which is 4.
Therefore, the equation of the parabola can be written as f(x) = a(x-4)^2 - 2.
Since the y-intercept is the value of y when x = 0, we can find it by plugging in x = 0 into the equation of the parabola:
f(0) = a(0-4)^2 - 2
f(0) = 16a - 2
We know that the function yields negative values between x = 2 and x = 6, so the parabola must intersect the y-axis below the x-axis. This means that the y-intercept is negative.
To find the y-intercept, we need to solve the equation 16a - 2 = 0, which gives us a = 1/8.
Therefore, the equation of the parabola is f(x) = (1/8)(x-4)^2 - 2.
Finally, we can find the y-intercept by plugging in x = 0:
f(0) = (1/8)(0-4)^2 - 2
f(0) = 8 - 2
f(0) = 6
So the coordinates of the y-intercept are (0, 6).
8 6 points Create an equation that represents the relationship between x and y in the table. HAAA #1 X y 488.8 -1 -2 10 y = 8 Answer -8 0 8 X + 2 6 Answe 4 4
The equation is given as y = -x + 8
What is the purpose of equation?The purpose of an equation is to find the value of the variable that makes the equation true. Equations are used in various fields of mathematics and science to represent relationships between different quantities and to solve problems.
To create an equation that represents the relationship between x and y in the table, we need to first determine the pattern or trend in the data.
From the given data, we can see that as x increases by 2, y decreases by 2. This suggests that there is a linear relationship between x and y.
Using the two points (-2,10) and (0,8), we can find the slope:
m = (y2 - y1) / (x2 - x1) = (8 - 10) / (0 - (-2)) = -1
Now that we have the slope, we can use any point on the line to find the y-intercept. Let's use the point (0,8):
8 = (-1)(0) + b
b = 8
Therefore, the equation that represents the relationship between x and y in the table is:
y = -x + 8
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Find the size of angle p. Give your answer
in degrees (°).
137⁰
60°
60°
112°
р
134
Not drawn accurately
PLEASE HELPPP
Answer:
76°
Step-by-step explanation:
The sum of the interior angles of any quadrilateral is 360°.
p = 360 - 60 - 134 - 90 = 76
2. Consider this scatter plot.
a)
Draw a line of best fit on the picture of the scatterplot above. (2 pts.)
b) Is there a positive or negative association between a car's price and age? Explain your answer using as
much detail as possible. (3 pts.)
Answer:
Answer: A
Step-by-step explanation: cuz of the
pie chart
Help please !!!!!!!!!!!!!!!!!!!!!!!!
Thus, the length of walk way around the filed is the perimeter of the right triangle which is found as: 206.023 m .
Explain about the perimeter of triangle:The quickest approach to determine a triangle's perimeter is to sum up all of its sides' lengths, but you must first determine each side's length if you don't already know it.
The walk way around the filed is the perimeter of the right triangle.
walk way = base + height + hypotenuse
walk way = B + P + H
base B = 80 - 10 = 70 m
Altitude P = 70 - 20 = 50 m
For the hypotenuse H , use the Pythagorean theorem:
H² = B² + P²
H² = 70² + 50²
H² = 4900 + 2500
H² = 7400
H = 86.023
So,
walk way = B + P + H
walk way = 70 + 50 + 86.023
walk way = 206.023 m
Thus, the walk way around the filed is the perimeter of the right triangle which is found as: 206.023 m .
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i need help on problems 5-11
A scatter plot would be an appropriate data display to show the relationship between the speed of the vehicle and the number of accidents.
Why is a scatter plot appropriate for showing the relationship between speed and accidents?A scatter plot is a graphical representation of two continuous variables, where data points are plotted on a Cartesian coordinate system. The horizontal axis can represent the speed of the vehicle, while the vertical axis can represent the number of accidents. Each data point on the scatter plot would represent a specific observation of speed and the corresponding number of accidents.
By using a scatter plot, the EMT can visually display how changes in vehicle speed are related to the number of accidents. Scatter plots are effective for identifying trends, patterns, and outliers in data, making them suitable for illustrating the relationship between two continuous variables.
Answered question "An EMT wants to use a data display to show students the relationship between the speed of the vehicle and the number of accidents. Choose an appropriate data display for the situation. Explain your reasoning"
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For an investment of 26,245, a quarterly statement reports that the account is 26,292. The statement reports that for the same quarter, the rate of return of the investment was - 0.02%. Given the information regarding the investment quarterly activity, does the reported rate of return seem reasonable?
No. The reported return rate appears lower than expected.
Rate of returnsTo determine whether the reported rate of return is reasonable or not, we can calculate the expected rate of return based on the investment amount and the ending value of the account.
First, we need to calculate the total number of quarters that have elapsed between the initial investment and the current quarter. Let's assume that the investment has been held for n quarters.
Then, we can use the following formula to calculate the expected rate of return:
Expected rate of return = (Ending value / Initial investment) ^ (1/n) - 1
Plugging in the given values, we get:
n = 1 (since we are only given information for a single quarter)
Initial investment = 26,245
Ending value = 26,292
Expected rate of return = (26,292 / 26,245) ^ (1/1) - 1 = 0.18%
Comparing the expected rate of return of 0.18% with the reported rate of return of -0.02%, we can see that they are quite different. However, it's important to note that a single quarter's rate of return may not be indicative of the overall performance of the investment.
Therefore, while the reported rate of return seems lower than expected, we would need to consider the performance over a longer period of time to make a more informed assessment of the investment's performance.
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1. Supposed two coins are tossed, let P be the random variable representing the number of heads that occur. Find the values of the random variable P.
The possible values of the random variable P are 0, 1, or 2.
Describe Probability?A triangle is a polygon with three straight sides and three angles. It is one of the most fundamental shapes in geometry and is used extensively in mathematics, science, engineering, and art. The sum of the interior angles of a triangle is always 180 degrees, and the length of the sides and the size of the angles determine the shape of the triangle.
Triangles can be classified according to the length of their sides and the size of their angles. A scalene triangle has three unequal sides and three unequal angles. An isosceles triangle has two equal sides and two equal angles. A equilateral triangle has three equal sides and three equal angles, each measuring 60 degrees. Triangles can also be classified based on the size of their angles: an acute triangle has three acute angles (less than 90 degrees), a right triangle has one right angle (90 degrees), and an obtuse triangle has one obtuse angle (greater than 90 degrees).
Triangles have many important properties and applications in geometry. For example, the Pythagorean theorem is a fundamental relationship between the sides of a right triangle, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The area of a triangle can be calculated using the formula 1/2 x base x height, and this formula can be used to solve many practical problems involving triangles.
The random variable P can take on four possible values, depending on how many heads are obtained:
P = 0 if both coins show tails.
P = 1 if exactly one of the coins shows heads.
P = 2 if both coins show heads.
Therefore, the possible values of the random variable P are 0, 1, or 2.
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Solve for x
225 times 1/3=x
Answer:
75=x
Step-by-step explanation:
A particular sawdust pile has a base diameter of 35 feet when the height is 30 feet. Find the volume of this sawdust pile when it is 40 feet high.
If the base diameter of the sawdust pile is 35 feet when the height is 30 feet, then when it is 40 feet high, the diameter will be 46.7 feet, while the volume will be 68,545.37 feet³.
What is the volumeThe volume refers to the capacity of a three-dimensional object.
The formula for volume with diameter and height is V = πd²h/4.
Base diameter of the sawdust pile = 35 feet
Height = 30 feet
Base diameter of the sawdust pile when the height is 40 feet = 46.7 feet
(35/30 x 40)
Given height = 40 feet
Computed base diameter = 46.7 feet
Volume = πd²h/4
= 22/7 x 46.7² x 40/4
= 3.143 x 2,180.89 x 10
= 68,545.37 feet³
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A dance instructor ears $75 for teaching 3 classes. The instructor receives a 10% raise. Enter how much the instructor earns, in dollars, per class after the raise.
Which of the following sets of numbers could represent the three sides of a triangle O (6,8,14} O {11, 14, 22} O {13, 20, 34) O {13, 20, 35}
The set of numbers that can represent the sides of a triangle are:
{11, 14, 22} and {13, 20, 35}.
How to Determine the Set of Numbers that Can Represent the Sides of a Triangle?We can determine which set of numbers would represent the sides of a triangle by applying the triangle inequality theorem.
This theorem states that the sum of any two sides of a triangle must be greater than the length of the third side to make it a triangle.
Applying the theorem, we have:
A. (6,8,14)
6 + 8 > 14 (not true, since 6 + 8 = 14 and not greater than 14)
6 + 14 > 8 (true)
8 + 14 > 6 (true)
Therefore, (6,8,14) cannot represent the sides of a triangle.
B. {11, 14, 22}
11 + 14 > 22 (not true, since 11 + 14 = 25 and not less than 22)
11 + 22 > 14 (true)
14 + 22 > 11 (true)
Therefore, {11, 14, 22} does not represent the sides of a triangle.
C. {13, 20, 34}
13 + 20 > 34 (not true, since 13 + 20 = 33 and not greater than 34)
13 + 34 > 20 (true)
20 + 34 > 13 (true)
Thus, {13, 20, 34} cannot represent the sides of a triangle.
D. {13, 20, 35}
13 + 20 > 35 (not true, since 13 + 20 = 33 and not less than 35)
13 + 35 > 20 (true)
20 + 35 > 13 (true)
This means, {13, 20, 35} can represent the sides of a triangle.
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4. Which of the following angles is vertical to angle /DEB?
A
C
109°
E
D
B
The angle that is vertical to angle DEB is A.
What is a vertical angle?A vertical angle is an angle formed by two intersecting lines or planes that are perpendicular to each other. Specifically, it is the angle between two straight lines or planes that intersect each other and are perpendicular to the horizontal plane.
The measure of a vertical angle is always the same as the measure of the other vertical angle formed by the same two intersecting lines or planes. This is because vertical angles are always congruent, meaning they have the same size and shape. Vertical angles are commonly used in geometry and trigonometry to solve problems involving angles, lines, and plane.
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Help me solve and show my work please
The above prompts are related to the concepts of Degrees, Radians, Sines and Cosines. See the solutions below.
What are the solutions to the above prompts?
1)
(a) Cos 150 degrees
To convert 150 degrees to radians, we multiply by π/180:
150 degrees = (150π/180) radians = (5π/6) radians
We can use the unit circle and reference angle of π/6 to find the cosine of 5π/6:
cos(5π/6) = -cos(π/6) = -(√3/2) = -√3/2
Therefore, cos 150 degrees = -√3/2.
(b) Sin 240 degrees
To convert 240 degrees to radians, we multiply by π/180:
240 degrees = (240π/180) radians = (4π/3) radians
We can use the unit circle and reference angle of π/3 to find the sine of 4π/3:
sin(4π/3) = -sin(π/3) = -(√3/2) = -√3/2
Therefore, sin 240 degrees = -√3/2.
2)
To use the law of cosines, we need either a side and the two angles opposite that side, or two sides and the angle between them. In this case, we have two angles and the side opposite one of them, so we can use the law of sines to find the other side and then use the law of cosines to find the remaining side or angle.
Using the law of sines, we have:
sin A / AB = sin B / AC
where AC is the side opposite angle B. Substituting the given values, we get:
sin 52 / 26.7 = sin 70 / AC
Solving for AC, we get:
AC = sin 70 / sin 52 * 26.7 = 30.4
Now we can use the law of cosines to find the remaining side, x:
x^2 = AB^2 + AC^2 - 2ABACcos A
Substituting the given values, we get:
x^2 = 26.7^2 + 30.4^2 - 226.730.4*cos 52
Solving for x, we get:
x ≈ 22.1
Therefore, the missing side is approximately 22.1.
To find the area of the triangle, we can use the formula:
Area = (1/2) * a * b * sin C
where a and b are the lengths of the two sides, and C is the included angle. Substituting the given values, we get:
Area = (1/2) * 7 * 9 * sin 30
Using the fact that sin 30 = 1/2, we can simplify this to:
Area = (1/2) * 7 * 9 * (1/2) = 15.75
Therefore, the area of the triangle is 15.75 square units.
From the law of sines, we have:
sin A / a = sin B / b
Substituting the given values, we get:
sin 45° / (7√2) = sin B / 7
Solving for sin B, we get:
sin B = (7/7√2) * sin 45° = √2/2
Therefore, B = 45° or 135°. We can use the fact that the angles of a triangle sum to 180° to find C:
C = 180° - A - B = 90° or 0°
If C = 0°, then the triangle is degenerate and the sides a and b lie on top of each other. Therefore, we must have C = 90°.
Now we can use the Pythagorean theorem to find the remaining side:
c^2 = a^2 + b^2 - 2ab*cos C
Substituting the given values, we get:
c^2 = (7√2)^2 + 7^2 - 2(7√2)(7)*cos 90°
Solving for c, we get:
c = √(98 + 49) = √147 = 7√3
Therefore, the sides of the triangle are:
a = 7√2
b = 7
c = 7√3
Using the law of cosines to find x:
In triangle ABC with side lengths AB = 18, AC = 15, and angle A = 108 degrees, we want to find the length of side BC (denoted by x). Using the law of cosines:
x^2 = 18^2 + 15^2 - 2(18)(15)cos(108 degrees)
We can evaluate the cosine of 108 degrees using the identity cos(180 - 108) = -cos(108):
cos(108 degrees) = -cos(180 - 108 degrees) = -cos(72 degrees)
Substituting this into the equation above, we get:
x^2 = 18^2 + 15^2 - 2(18)(15)(-cos(72 degrees))
Simplifying:
x^2 = 729
Taking the square root of both sides:
x = ±27
Since x represents a length, we take the positive root:
x = 27
Therefore, the length of BC is 27 units.
Using the law of cosines to find theta:
In triangle ABC with side lengths AB = 20, BC = 12, and AC = 10, we want to find the measure of angle B (denoted by theta). Using the law of cosines:
cos(B) = (12^2 + 10^2 - 20^2) / (2(12)(10)) = -1/2
Since -1/2 is the cosine of an angle in the second quadrant, we have:
B = 180 degrees - arccos(-1/2)
Using a calculator, we find:
B ≈ 150.5 degrees
Therefore, the measure of angle B is approximately 150.5 degrees (or theta = 150.5 degrees).
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determine the area of the shaded region of a wooden patch in a circular park if the radius of the circle is: a. 8m b. 12
Answer:
22.88
Step-by-step explanation:
O/360 * π r squared
90/360 * 8 squared
1/4 * π (64)
4 π
Next:
b*h/2
8*12/2 = 48
8π - 48
8π = 25.12
48-25.12 = 22.88
in the figure below lines m and n are parallel m2= 62 and m3=73
Answer: 135
Step-by-step explanation: