Answer:
bu ney ben anlamadım gerçek
NO LINKS!! URGENT HELP PLEASE!!
O is the center of the regular dodecagon below. Find its area. Round to the nearest tenth.
Answer:
80.4 square units.
Step-by-step explanation:
solution Given:
apothem(a)=5
no of side(n)= 12
Area(A)-?
The area of a regular polygon can be found using the following formula:
[tex]\boxed{\bold{Area =\frac{1}{2}* n * s * a}}[/tex]
where:
n is the number of sidess is the length of one sidea is the apothemIn this case, we have:
n = 12s = ?a = 5First, we need to find S.
We can find the length of one side using the following formula:
[tex]\boxed{\bold{s = 2 * a * tan(\frac{\pi}{n})}}[/tex]
substituting value:
[tex]\bold{s = 2 * 5 * tan(\frac{\pi}{12})=2.679}[/tex] here π is 180°
To find the area substituting value in the above area's formula:
[tex]\bold{Area = \frac{1}{2}* 12 * 2.679 * 5=80.37\: sqaure\: units}[/tex]
in nearest tenth 80.4 square units.
Therefore, the area of the regular polygon is 80.4 square units.
Answer:
80.4 square units (nearest tenth)
Step-by-step explanation:
The given diagram shows a regular dodecagon (12-sided polygon) with an apothem of 5 units.
The apothem of a regular polygon is the distance from the center of the polygon to the midpoint of one of its sides.
We can calculate the side length of a regular polygon given its apothem using the following formula:
[tex]\boxed{\begin{minipage}{5.5cm}\underline{Apothem of a regular polygon}\\\\$a=\dfrac{s}{2 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\where:\\\phantom{ww}$\bullet$ $s$ is the side length.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]
Substitute n = 12 and a = 5 into the equation to create an expression for s:
[tex]5=\dfrac{s}{2 \tan \left(\dfrac{180^{\circ}}{12}\right)}[/tex]
[tex]s=10\tan \left(15^{\circ}\right)[/tex]
Now we can use the standard formula for an area of a regular polygon:
[tex]\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\cdot s\cdot a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}[/tex]
Substitute the found expression for s, n = 12 and a = 5 into the formula and solve for A:
[tex]A=\dfrac{12 \cdot 10\tan \left(15^{\circ}\right) \cdot 5}{2}[/tex]
[tex]A=\dfrac{600\tan \left(15^{\circ}\right)}{2}[/tex]
[tex]A=300\tan \left(15^{\circ}\right)[/tex]
[tex]A=80.3847577...[/tex]
[tex]A=80.4\; \sf square\;units\;(nearest\;tenth)[/tex]
Therefore, the area of a regular dodecagon with an apothem of 5 units is 80.4 square units, rounded to the nearest tenth.
Write and solve an equation to find the value of x.
Using the image below, answer the following question: you are asked to pick 2
marbles out of the bag, what is the probability of picking a blue marble and then a
green marble, without replacing the blue one?
PLEASE URGENT
The probability of picking a blue marble and then a green marble without replacing the blue one is 4/45.
We have,
We see that there are 10 marbles.
Now,
Number of blue marbles = 2
Number of green marbles = 4
Now,
The probability of picking a blue marble first is 2/10, as there are 2 blue marbles out of 10 in total.
After picking a blue marble, there will be 9 marbles left in the bag.
The probability of picking a green marble second, without replacing the blue one, is 4/9, as there are 4 green marbles remaining out of the 9 marbles in total.
Now,
P(blue marble and green marble) = P(blue marble) x P(green marble)
= (2/10) x (4/9)
= 8/90
= 4/45.
Therefore,
The probability of picking a blue marble and then a green marble without replacing the blue one is 4/45.
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100 Points! Geometry question. Photo attached. Determine whether the pair of triangles is similar. If so, write a similarity statement. If not, what would be sufficient to prove the triangles similar? Explain your reasoning. Please show as much work as possible. Thank you!
Answer:
∆TSU ~ ∆PJM by SAS since 10/14 = 5/7 and 15/21 = 5/7, and angle S is congruent to angle J.
Write 0.75 as a fraction in its simplest form
Answer:
0.75 can be written as :-
[tex] \frac{75}{100} [/tex]
and in simplest form it is:-
[tex] \frac{3}{4} [/tex]
so the answer is 3/4
Gauri Spends 0.75 of her salary every month if she earns rs 12000 per month in how many months will she save rupees 39000
Answer:
13 months--------------------
If Gauri spends 0.75 of her salary every month, that means she saves 0.25 of her salary:
0.25 * 12000 = 3000Divide the total 39000 by her monthly savings:
39000 / 3000 = 13So it will take Gauri 13 months to save rupees 39000.
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
SRTZ is not a parallelogram.
Slope of SZ:
[tex]m = \frac{ - 2 - 1}{1 - ( - 2)} = - 1[/tex]
Slope of RT:
[tex]m = \frac{0 - 3}{2 - 1} = - 3[/tex]
Since the slopes of SZ and RT are not equal, SRTZ is not a parallelogram.
Answer and why!!!!!!
The expression (yx + y + px + p) / (5x² + 10x +5) * (10x + 10) / (y² + yp) is simplified to obtain
2/y
How to simplify the expressionThe given expression is
(yx + y + px + p) / (5x² + 10x +5) * (10x + 10) / (y² + yp)
The expression is simplified individually, using different each equation in the expression
yx + y + px + p
= y(x + 1) + p(x + 1)
= (y + p)(x + 1)
5x² + 10x +5
= 5(x² + 2x + 1)
= 5(x² + 1)
(10x + 10)
= 10(x + 1)
(y² + yp)
= y(y + p)
bringing the equations together and simplifying further
(y + p)(x + 1) / 5(x² + 1) * 10(x + 1) / y(y + p)
= 10(x + 1)(x + 1) / 5y(x² + 1)
= 10(x² + 1) / 5y(x² + 1)
= 2/y
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Donna is thinking about buying a house that costs $125,000. If she puts down $25,000 and is able to get a 5 percent mortgage, she wants an estimate of her total monthly housing expenses. The average annual cost for owning a house, beyond the 5% cost of mortgage interest, is 4.09 percent of the value of the house. Not including the opportunity cost of the down payment, amortization on the loan, or any tax benefits from homeownership, what will be her monthly cost the first month?
A. $206.25
B. $279.60
C. $842.71
D. $746.43
Donna can expect her total monthly housing expenses to be approximately $842.71 for the first month after purchasing the house, assuming no tax benefits or amortization on the loan.
To calculate Donna's monthly housing expenses, we first need to determine the total amount of the mortgage. Since she puts down $25,000 on a $125,000 house, she will need to take out a mortgage for $100,000.
Next, we can calculate the annual cost of owning the house beyond the 5% cost of mortgage interest, which is given as 4.09% of the value of the house. So, 4.09% of $125,000 is:
0.0409 x $125,000 = $5,112.50
This means that Donna can expect to pay approximately $5,112.50 per year in additional expenses associated with owning the house.
To calculate the monthly cost, we simply divide this by 12:
$5,112.50 / 12 = $426.04
So, Donna can expect to pay approximately $426.04 per month in additional expenses associated with owning the house.
Adding the cost of the mortgage interest, we can calculate her total monthly housing expenses as follows:
Total monthly housing expenses = Mortgage interest + Additional annual costs / 12
Mortgage interest = 5% of $100,000 = $5,000 per year or $416.67 per month
Total monthly housing expenses = $416.67 + ($5,112.50 / 12) = $416.67 + $426.04 = $842.71
Hence, Donna can expect her total monthly housing expenses to be approximately $842.71
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What is the interquartile range for data set? 27,4,54,78,27,48,79,64,5,6,41,71
The Interquartile range for the given data set is 51.
The interquartile range for a given data set, the values of the first quartile (Q1) and the third quartile (Q3). The interquartile range is the difference between Q3 and Q1.
First, let's arrange the data set in ascending order:
4, 5, 6, 27, 27, 41, 48, 54, 64, 71, 78, 79
To find Q1, which represents the lower quartile, we need to locate the median of the lower half of the data set. Since the data set has 12 values, the lower half consists of the first 6 values:
4, 5, 6, 27, 27, 41
The median of this lower half is the average of the middle two values, which are 6 and 27:
Q1 = (6 + 27) / 2 = 33 / 2 = 16.5
To find Q3, the upper quartile, we need to locate the median of the upper half of the data set. Again, since the data set has 12 values, the upper half consists of the last 6 values:
48, 54, 64, 71, 78, 79
The median of this upper half is the average of the middle two values, which are 64 and 71:
Q3 = (64 + 71) / 2 = 135 / 2 = 67.5
Finally, we can calculate the interquartile range by subtracting Q1 from Q3:
Interquartile range = Q3 - Q1 = 67.5 - 16.5 = 51
Therefore, the interquartile range for the given data set is 51.
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please help. i’m struggling on part C
a) The area formula for the rectangle is equal to A = r² · sin 2θ.
b) By derivative tests, the maximum possible area of the rectangle is 16 square centimeters.
c) The dimensions of the rectangle are: Width: 5.66 cm, Height: 2.83 cm
How to find the maximum possible area of a rectangle inscribed in a semicircle
In this problem we must determine the maximum possible area of a rectangle inscribed in a semicircle by means of first and second derivative tests. First, derive the area formula of the rectangle:
A = w · h
A = (2 · r · cos θ) · (r · sin θ)
A = 2 · r² · sin θ · cos θ
A = r² · sin 2θ
Where:
w - Width, in centimeters.h - Height, in centimeters.A - Area, in square centimeters.r - Radius, in centiemters. θ - Angle, in degrees.Second, perform first derivative test: (r - Constant)
A = 2 · r² · cos 2θ
2 · r² · cos 2θ = 0
cos 2θ = 0
θ = 45°
Third, perform second derivative test: (θ = 45°)
A'' = - 4 · r² · sin 2θ
A'' = - 4 · r² (MAXIMUM)
Fourth, determine the maximum possible area of the rectangle:
A = 4² · sin 90°
A = 16 cm²
Fifth, determine the width and the height of the rectangle: (r = 4, θ = 45°)
w = 2 · r · cos θ
w = 2 · 4 · cos 45°
w = 8 · √2 / 2
w = 4√2 cm
w = 5.66 cm
h = r · sin θ
h = 4 · sin 45°
h = 4 · √2 / 2
h = 2√2 cm
h = 2.83 cm
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Select the values that are solutions to the inequality x2 + 3x – 4 > 0.
Answer: To solve the inequality x^2 + 3x - 4 > 0, we can use the method of factoring.
First, we can factor the quadratic expression:
x^2 + 3x - 4 = (x + 4)(x - 1)
Now we can find the values of x that make the expression greater than zero by looking at the sign of the expression for each factor and applying the sign rules of multiplication:
If both factors are positive, the expression is positive.If both factors are negative, the expression is positive.If one factor is positive and one factor is negative, the expression is negative.
Using this method, we can create a sign chart:
x x + 4 x - 1 x^2 + 3x - 4
-4 0 -5 +6
-1 + - -
1 + + +
0 + - -
2 + + +
From the sign chart, we can see that the expression is greater than zero for x < -4 or x > 1. Therefore, the solutions to the inequality are all real numbers x such that x < -4 or x > 1. We can write this as:
x < -4 or x > 1
Determine if the given side lengths could be used to form a unique triangle, many different triangles, or no triangles.
3.4 cm, 3.1 cm, 6.6 cm
We can see here that the given side lengths cannot be used to form a unique triangle because the shorter sides do not add up to the longer side.
What is a triangle?The fundamental geometric shape of a triangle has three sides and three angles. It is a triangular polygon with three edges.
We can see here that in order to determine if the given side lengths:
3.4 cm, 3.1 cm, 6.6 cm
can form a unique triangle, many different triangles, or no triangle, we need to check if they satisfy the triangle inequality theorem.
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
Let's check the conditions:
3.4 cm + 3.1 cm = 6.5 cm
6.5 cm > 6.6 cm (Not satisfied)
3.4 cm + 6.6 cm = 10 cm
10 cm > 3.1 cm (Satisfied)
3.1 cm + 6.6 cm = 9.7 cm
9.7 cm > 3.4 cm (Satisfied)
he specified side lengths cannot be used to create a triangle because the total of the two shorter sides' lengths (3.4 cm and 3.1 cm) is not larger than the length of the longest side (6.6 cm).
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Please help due soon
Stmt of cash flows problem
Balance Sheet for Stand Corp Dec 31st:
Cash
Accounts Receivable
Inventory
Total Current Assets
2022
$177,000
$180,000
$100,000
$457,000
2021
$78.000
$185.000
$100.000
$363,000
Investments
Equipment
Accumulated Deprec
Total Non-Current Liabs
$52,000
$298,000
($106,000)
$244.000
$74,000
$240,000
($89.000)
$225,000
Total Assets
$701.000
$588.000
Current Liabilities
$134.000
$151.000
Common Stock
Retained Earnings
$260.000
$307,000
$260,000
$177,000
Total Liabs & Equity
$701.000
$588,000
OTHER INFORMATION:
-Investments were sold in 2022 at a loss of $10.000
-No equipment was sold in 2022
-Cash dividends were paid in 2022
-Net Income for 2022 was $160,000
REQUIRED:Prepare the Statement of Cash Flows:
1. Prepare the Statement of Cash Flows
2. Calculate Free Cash Flow
The Free Cash Flow based on the information given will be $115,000
How to explain the cash flowStatement of Cash Flows for Stand Corp for the year ended December 31, 2022
Cash flows from operating activities:
Net income $160,000
Adjustments to reconcile net income to net cash provided by operating activities:
Depreciation expense $17,000
Loss on sale of investments $10,000
Changes in current assets and liabilities:
Increase in accounts receivable ($5,000)
Increase in inventory ($20,000)
Increase in accounts payable $17,000
Increase in accrued expenses $11,000
Net cash provided by operating activities $190,000
Cash flows from investing activities:
Sale of investments $52,000
Purchase of equipment ($75,000)
Net cash used in investing activities ($23,000)
Cash flows from financing activities:
Payment of cash dividends ($25,000)
Net cash used in financing activities ($25,000)
Net increase in cash $142,000
Cash at beginning of year $78,000
Cash at end of year $220,000
Free Cash Flow = Net cash provided by operating activities - Purchase of equipment
Free Cash Flow = $190,000 - $75,000
Free Cash Flow = $115,000
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Cual es la distancia que recorrió luis en su bicicleta rodada 20p (2.54) después que las llantas dieran 50 vueltas completas
porfaaa
Luis traveled approximately 31,736.8 inches on his bicycle.
We have,
To find the distance that Luis traveled on his bicycle, we need to calculate the circumference of the tires and then multiply it by the number of complete turns.
Given:
Radius of the tires (r) = 20p (2.54) inches
Number of complete turns (n) = 50
The circumference of a circle can be calculated using the formula:
Circumference = 2πr
Substituting the given radius into the formula, we have:
Circumference = 2π * (20p) inches
Now we can calculate the distance traveled (d):
Distance = Circumference x Number of complete turns
Distance = 2π x (20p) x 50 inches
To simplify the calculation, we can approximate π as 3.14:
Distance ≈ 2 x 3.14 x (20 x 2.54) x 50 inches
Calculating this expression, we find:
Distance ≈ 31736.8 inches
Therefore,
Luis traveled approximately 31,736.8 inches on his bicycle.
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The complete question.
What is the distance that Luis traveled on his bicycle rolled 20p (2.54) after the tires gave 50 complete turns
Please solve this question
The solution to the given composite function is calculated as: 12
How to solve Composite functions?Composite functions are defined as when the output of one function is used as the input of another. If we have a function f and another function g, the function f of g of x is said to be the composition of the two functions.
We are given the functions:
f(x) = 2[tex]x^{\frac{1}{3} }[/tex]
g(x) = -[tex]x^{\frac{4}{3} }[/tex]
Thus:
(f - g)(-8) = 2[tex]x^{\frac{1}{3} }[/tex] + [tex]x^{\frac{4}{3} }[/tex]
= 2∛-8 + (∛-8)⁴
= (2 * -2) + (-2)⁴
= -4 + 16
= 12
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a quadratic function is defined by f(x) = x*2 - 8x - 4.
Which expression also defines f and best reveals the max and mini of the function?
a) (x-4)*2 - 20
B) (x-4)*2 + 12
c) x(x-8) -4
d) (x-4)*2 + 20
The expression that best reveals the maximum and minimum of the function[tex]f(x) = x^2 - 8x - 4 is (x - 4)^2 - 20.[/tex] Option A
How to find the expressionThe vertex form of a quadratic function is given by[tex]f(x) = a(x - h)^2 + k[/tex] where (h, k) represents the coordinates of the vertex.
In the given quadratic function [tex]f(x) = x^2 - 8x - 4[/tex], we can rewrite it in the vertex form by completing the square:
[tex]f(x) = (x - 4)^2 - 16 - 4\\f(x) = (x - 4)^2 - 20[/tex]
From this expression, we can see that the vertex of the quadratic function is at the point (4, -20).
The term[tex](x - 4)^2[/tex] tells us that the vertex is at x = 4, and the constant term -20 indicates the y-coordinate of the vertex.
The expression that best reveals the maximum and minimum of the function[tex]f(x) = x^2 - 8x - 4[/tex] is [tex](x - 4)^2 - 20.[/tex]
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Find the volume of the pyramid above
Find the surface are of the pyramid above pls help
The volume of the pyramid is 18069333.33 units³ and the surface area is 391600 units ²
What is a pyramid?A pyramid is a three-dimensional figure. It has a flat polygon base. All the other faces are triangles and are called lateral faces.
Surface area of a pyramid is expressed as;
area of 4 lateral face + area of base
area of base = 440²
= 193600 units²
area of a lateral = 1/2 bh
= 1/2 × 440 × 356
= 78320
For four surfaces = 4 × 78320 = 313280
Total surface area = 313280+78320
= 391600 units ²
Volume of a pyramid is expressed as;
V = 1/3base area × height
V = 1/3 × 440² × 280
V = 18069333.33 units³
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Please help me, first time I got it wrong
The conditional value probability is solved and P ( F | E ) = 6/17
Given data ,
P ( E ) = 0.85
P ( F ) = 0.4
P ( E ∩ F ) = 0.3
Now , the formula for conditional probability to calculate P(F|E):
P(F|E) = P(E ∩ F) / P(E)
We are given that P(E) = 0.85 and P(E ∩ F) = 0.3, so we can substitute those values in:
P(F|E) = 0.3 / 0.85
Simplifying this fraction, we get:
P(F|E) = 6/17
Hence , the probability of F given that E has occurred is 6/17 or approximately 0.35.
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Help I need the answer to this
The graph of the logarithmic function is attached below with a vertical asymptote at x = -8 and two integer coordinates at (2, -7) and (1, -10).
What is graph of a logarithmic function?The basic logarithmic function is of the form f(x) = logax (r) y = logax, where a > 0. It is the inverse of the exponential function ay = x. Log functions include natural logarithm (ln) or common logarithm (log).
To plot the graph of the given function, we simply need to use a graphing calculator.
The given function is;
f(x) = -3log₃(x + 8) - 4
To find the asymptotes of the graph;
x + 8 > 0
x > -8
The vertical asymptotes is at x = -8
The two points with integer coordinates are (2, -7) and (1, -10)
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Find the value for the side marked below. Round your answer to the nearest tenth 210 37 degrees
Using the cosine ratio, the value of the marked side in the image given below is approximately: y = 167.7.
How to Find the Value of the Marked Side Using the Cosine Ratio?The cosine ratio is defined as the ratio of the length of the hypotenuse of the right triangle over the length of the side that is adjacent to the reference angle. It is given as:
cos ∅ = length of hypotenuse/length of adjacent side.
From the image attached below, we have the following:
Reference angle (∅) = 37°
length of hypotenuse = 210
length of adjacent side = y
Plug in the values:
cos 37 = y/210
210 * cos 37 = y
y = 167.7
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Math
Language arts
Seventh grade> Y.7 Circles: word problems P56
Submit
Recommendations
millimeters
Y
The button on Jasmine's pants has a radius of 5 millimeters. What is the button's
diameter?
9
Answer:
10 millimeters
Step-by-step explanation:
The diameter of the button is twice the radius. Therefore, the diameter of Jasmine's pants button is 10 millimeters.
Can someone please answer and provide an explanation for these problems?
The center and radius for each equation are as follows:
40. Center: (3, 2), Radius: 8
41. Center: (-8, 4), Radius: 6
42. Center: (-4, 12), Radius: 2
43. Center: (4, -15), Radius: 3
What is the center and radius of the equations?The standard equations of a circle is given as (x - h)² + (y - k)² = r²
Where the center are (h, k) and the radius of the circle is r.
40. (x - 3)² + (y - 2)² = 64
Center: (3, 2)
Radius: √64 = 8
41. (x + 8)² + (y - 4)² = 36
Center: (-8, 4)
Radius: √36 = 6
42. (x + 4)² + (y - 12)² = 4
Center: (-4, 12)
Radius: √4 = 2
43. (x - 4)² + (y + 15)² = 9
Center: (4, -15)
Radius: √9 = 3
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En el laboratorio de análisis de minerales unas pequeñas gotas de ácido Nítrico (HNO3); cae sobre la piel de un analista y le produce una quemadura. ¿Cuántas moléculas de HNO3 provocaron la quemadura si las gotas presentan una masa de 0,49 g?
Entonces n is 0,00779 moles,
Los casi 5 sextillones (5 con 21 ceros) de moléculas de HNO3 provocaron la quemadura en la piel del analista.
Para responder a esta pregunta, necesitamos saber la masa molar de HNO3, que es 63,01 g/mol. Usando esta información, podemos calcular el número de moles de HNO3 en los 0,49 g de gotas usando la fórmula: n = m/M, donde n es el número de moles, m es la masa y M es la masa molar.
Como un mol contiene el número de moléculas de Avogadro (6,022 x 10^23), podemos calcular el número de moléculas de HNO3 en las gotas que causaron la quemadura: 0,00779 moles x 6,022 x 10^23 moléculas/mol = 4,69 x 10^21 moléculas .
Es importante recordar que los ácidos concentrados como el HNO3 pueden ser extremadamente peligrosos y pueden causar quemaduras graves, por lo que siempre se deben tomar las precauciones de seguridad adecuadas en un entorno de laboratorio.
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What is the value of x? Show all your work.
Please help. 100 points.
Answer:
12 cm
Step-by-step explanation:
By hypotenuse theorem,
x² + 35² = 37²
x² + 35*35 = 37*37
x² + 1225 = 1369
x² = 1369 - 1225
x² = 144
x² = 12*12
x² = 12²
x = 12 cm
what is 27% in a equivalent form using the two other forms of notian: fraction,decimal,or percent
You can write 27% as a fraction like this: [tex]\frac{27}{100}[/tex] . (27/100).
Or as a decimal 0.27.
Find the area of the stained glass window shown if the diameter of the semi-circle is 61 inches. Use 3.14 for , round your answer to the nearest square inch, and enter the number only.
Answer:
1460 square inches
Step-by-step explanation:
You want the area of a semicircle with diameter 61 inches.
AreaThe area of a circle is given by ...
A = (π/4)d²
The area of a semicircle is half that, so is ...
A = (π/8)d²
A = (3.14/8)(61 in)² ≈ 1460 in²
The area of the semicircular window is about 1460 square inches.
<95141404393>
NO LINKS!! URGENT HELP PLEASE!!!
Solve ΔABC using the Law of Cosines
1. B= 36°, c = 19, a = 11
2. a = 21, b = 26, c = 17
Answer:
1) A = 32.6°, C = 111.4°, b = 12.0
2) A = 53.6°, B = 85.7°, C = 40.7°
Step-by-step explanation:
Question 1
Given values of triangle ABC:
B= 36°c = 19a = 11First, find the measure of side b using the Law of Cosines for finding sides.
[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines (for finding sides)} \\\\$c^2=a^2+b^2-2ab \cos (C)$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]
As the given angle is B, change C for B in the formula and swap b and c:
[tex]b^2=a^2+c^2-2ac\cos(B)[/tex]
Substitute the given values and solve for b:
[tex]\implies b^2=11^2+19^2-2(11)(19)\cos(36^{\circ})[/tex]
[tex]\implies b^2=482-418\cos(36^{\circ})[/tex]
[tex]\implies b=\sqrt{482-418\cos(36^{\circ})}[/tex]
[tex]\implies b=11.9929519...[/tex]
Now we have the measures of all three sides of the triangle, we can use the Law of Cosines for finding angles to find the measures of angles A and C.
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Cosines (for finding angles)} \\\\$\cos(C)=\dfrac{a^2+b^2-c^2}{2ab}$\\\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides adjacent the angle. \\ \phantom{ww}$\bullet$ $c$ is the side opposite the angle.\\\end{minipage}}[/tex]
To find the measure of angle A, swap a and c in the formula, and change C for A:
[tex]\implies \cos(A)=\dfrac{c^2+b^2-a^2}{2cb}[/tex]
[tex]\implies \cos(A)=\dfrac{19^2+(11.9929519...)^2-11^2}{2(19)(11.9929519...)}[/tex]
[tex]\implies \cos(A)=0.842229094...[/tex]
[tex]\implies A=\cos^{-1}(0.842229094...)[/tex]
[tex]\implies A=32.6237394...^{\circ}[/tex]
To find the measure of angle C, substitute the values of a, b and c into the formula:
[tex]\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]
[tex]\implies \cos(C)=\dfrac{11^2+(11.9929519...)^2-19^2}{2(11)(11.9929519...)}[/tex]
[tex]\implies \cos(C)=-0.364490987...[/tex]
[tex]\implies C=\cos^{-1}(-0.364490987...)[/tex]
[tex]\implies C=111.376260...^{\circ}[/tex]
Therefore, the remaining side and angles for triangle ABC are:
b = 12.0A = 32.6°C = 111.4°[tex]\hrulefill[/tex]
Question 2To solve for the remaining angles of the triangle ABC given its side lengths, use the Law of Cosines for finding angles.
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Cosines (for finding angles)} \\\\$\cos(C)=\dfrac{a^2+b^2-c^2}{2ab}$\\\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides adjacent the angle. \\ \phantom{ww}$\bullet$ $c$ is the side opposite the angle.\\\end{minipage}}[/tex]
Given sides of triangle ABC:
a = 21b = 26c = 17Substitute the values of a, b and c into the Law of Cosines formula and solve for angle C:
[tex]\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]
[tex]\implies \cos(C)=\dfrac{21^2+26^2-17^2}{2(21)(26)}[/tex]
[tex]\implies \cos(C)=\dfrac{828}{1092}[/tex]
[tex]\implies C=\cos^{-1}\left(\dfrac{828}{1092}\right)[/tex]
[tex]\implies C=40.690560...^{\circ}[/tex]
To find the measure of angle B, swap b and c in the formula, and change C for B:
[tex]\implies \cos(B)=\dfrac{a^2+c^2-b^2}{2ac}[/tex]
[tex]\implies \cos(B)=\dfrac{21^2+17^2-26^2}{2(21)(17)}[/tex]
[tex]\implies \cos(B)=\dfrac{54}{714}[/tex]
[tex]\implies B=\cos^{-1}\left(\dfrac{54}{714}\right)[/tex]
[tex]\implies B=85.6625640...^{\circ}[/tex]
To find the measure of angle A, swap a and c in the formula, and change C for A:
[tex]\implies \cos(A)=\dfrac{c^2+b^2-a^2}{2cb}[/tex]
[tex]\implies \cos(A)=\dfrac{17^2+26^2-21^2}{2(17)(26)}[/tex]
[tex]\implies \cos(A)=\dfrac{524}{884}[/tex]
[tex]\implies A=\cos^{-1}\left(\dfrac{524}{884}\right)[/tex]
[tex]\implies A=53.6468753...^{\circ}[/tex]
Therefore, the measures of the angles of triangle ABC with sides a = 21, b = 26 and c = 17 are:
A = 53.6°B = 85.7°C = 40.7°evaluate 5x - 2y + 4z when x=3 , y=2 and z=4 (a)5 (b) 16 (c) 27 (d) 20
When x = 3, y = 2, and z = 4, the value of the expression 5x - 2y + 4z is 27.
The correct answer is (c) 27.
To evaluate the expression 5x - 2y + 4z when x = 3, y = 2, and z = 4, we substitute the given values into the expression and perform the arithmetic calculations. Here's the step-by-step process:
Step 1: Replace x with 3, y with 2, and z with 4 in the expression:
5(3) - 2(2) + 4(4)Step 2:
Perform the multiplications first:
15 - 4 + 16
Step 3: Perform the additions and subtractions from left to right:
15 - 4 + 16 = 11 + 16 = 27.
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Sobre una embarcación de 160 kg que está en reposo con su proa apuntando a la orilla, comienza a caminar una persona de 70 kg desde la proa hacia la popa, a 0.80 m/s respecto a la embarcación. ¿Cuáles son las velocidades de la embarcación y de la persona respecto a la orilla? Desprecia la resistencia del agua al movimiento.
The velocities of the boat and the person relative to the shore are 1.337 m/s and 2.896 m/s, respectively.
How to calculate the velocityWe can use the conservation of momentum equation:
(mboat + mperson) * vboat = mperson * vperson
(160 kg + 70 kg) * vboat = 70 kg * (0.80 m/s + vperson)
230 kg * vboat = 56 kg * (0.80 m/s + vperson)
vboat = (56/230) * (0.80 m/s + vperson)
vperson = 0.80 m/s + vboat
vperson = 0.80 m/s + (56/230) * (0.80 m/s + vperson)
(174/115) * vperson = (504/115) * m/s
Dividing both sides by (174/115), we get:
vperson = 2.896 m/s
vboat = (56/230) * (0.80 m/s + vperson)
Substituting the value of vperson, we get:
vboat = 1.337 m/s
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On a 160-kg boat that is at rest with its bow pointed to the shore, a 70-kg person begins to walk from the bow to the stern at 0.80 m/s relative to the boat. What are the velocities of the boat and the person relative to the shore? Neglect the resistance of water to motion.