The values of the other trigonometric functions for the given values of sin(Ф) and cos(Ф) are as follows, cos(Ф) = -5/4, sec(Ф) = -4/5, tan(Ф) = 16/25, cot(Ф) = 25/16.
To find the values of the other trigonometric functions of Ф, we can use the given information of sin(Ф) and cos(Ф).
We know that sin(Ф) = -4/5 and cos(Ф) = -5/4.
Recall that cos(Ф) is the reciprocal of sin(Ф), so we can determine cos(Ф) by finding the reciprocal of sin(Ф):
cos(Ф) = 1/sin(Ф) = 1/(-4/5) = -5/4
Similarly, we can find sec(Ф) by taking the reciprocal of cos(Ф):
sec(Ф) = 1/cos(Ф) = 1/(-5/4) = -4/5
To find tan(Ф), we can use the identities tan(Ф) = sin(Ф)/cos(Ф):
tan(Ф) = sin(Ф)/cos(Ф) = (-4/5)/(-5/4) = 16/25
Next, we can find cot(Ф) by taking the reciprocal of tan(Ф):
cot(Ф) = 1/tan(Ф) = 1/(16/25) = 25/16
Finally, we can find sec(Ф) by taking the reciprocal of csc(Ф):
cot(Ф) = 1/csc(Ф) = 1/(-5/4) = -4/5
Therefore, the values of the other trigonometric functions for the given values of sin(Ф) and cos(Ф) are as follows:
cos(Ф) = -5/4
sec(Ф) = -4/5
tan(Ф) = 16/25
cot(Ф) = 25/16
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Create a real word probe involving three lengths the form a right triangle , Give the measurement of the legs then solve for the missing hypotenuse.
The length of the missing hypotenuse is approximately 8.06 feet
Let's create a real-world scenario involving a right triangle. Imagine you are a construction worker tasked with building a roof for a house. The roof needs to have a triangular shape and one of the corners needs to form a right angle.
The two sides that meet at the right angle measure 4 feet and 7 feet respectively. Now, you need to figure out the length of the third side (the hypotenuse) so that you can properly cut the roofing material. To solve for the missing hypotenuse, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
where a and b are the lengths of the legs (in this case, 4 feet and 7 feet) and c is the length of the hypotenuse (which we are solving for).
Plugging in the values:
4^2 + 7^2 = c^2
16 + 49 = c^2
65 = c^2
Taking the square root of both sides:
c = √65 feet (approx. 8.06 feet)
. This will allow you to properly cut the roofing material to fit the triangular shape of the roof.
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What is the value of y in this linear system?
The value of y in this linear system as per the given data, the value of y in the linear system is 18.
To find the value of y inside the linear device, we are able to use the given equations:
Equation 1: x + y + z = 62
Equation 2: x - y = 12
Equation three: 2x + y + z = ninety two
To remedy this gadget, we can dispose of the variable x via subtracting Equation 2 from Equation 1:
(x + y + z) - (x - y) = 62 - 12
Simplifying, we get:
2y + z = 50
Next, we can subtract Equation 2 from Equation 3 to eliminate the variable x once more:
(2x + y + z) - (x - y) = 92 - 12
Simplifying, we get:
x + 2y + z = 80
(x + 2y + z) - (2y + z) = 80 - 50
Simplifying, we get:
x = 30
30 - y = 12
Solving for y, we get:
y = 18
Thus, the correct option is B.
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Rosie bought 5⁄9 pounds of bananas and 5⁄12 pounds of oranges. How much fruit did Rosie buy in all?
Answer:
35/36
Step-by-step explanation:
5/9 + 5/12 =
We need to get a common denominator of 9 and 12, which is 36.
5/9 * 4/4 = 20/36
5/12 * 3/3 = 15/36
20/36 + 15/36
35/36
Name:
Frequency
Period:
Chapter 8: Review
Use the data to answer questions 1-8.
8-iron, distance to hole (yards): 20 12 12 8 6 11 7 7 10 12 8 10 11 20
1) Organize the data from least to greatest.
6,7,7,8,8,10,10,11,11,12,12,12,20,20
2) Use the data to create a histogram.
Date:
0 5 10 15 20 25 30
Distance to Hole (yds)
5) What is the median of the data?
6) What is the First Quartile(Q1)?_
7) What is the Third Quartile(Q3)?
8) What is the interquartile range (IQR)?
5 10 15 20 25 30
Distance to Hole (yds)
3) What is the mean (average) of the data? Round your answer to the nearest tenth.
4) Make a box plot of the data.
Can somebody help with the whole thing besides number 1
From the given data mean is 11.86, median is 10.5 and inter quartile range is 5.
The given data is 6, 7, 7, 8, 8, 10, 10, 11, 11, 12, 12, 12, 20, 20.
2) Histogram (Plotted below)
3) Mean = (6+7+7+8+8+10+10+11+11+12+12+12+12+20+20)/14
= 166/14
= 11.86
4) Box plot (Plotted below)
5) Median = (10+11)/2
= 21/2
= 10.5
6) Q1 = 7
7) Q3 = 12
8) IQR=Q3-Q1
= 12-7
= 5
Therefore, from the given data mean is 11.86, median is 10.5 and inter quartile range is 5.
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Write what the variable n represents in each expression.
L. Lisa can run the 100-yard dash 5 seconds faster than Jerry. Lisa's time is n-5
seconds.
M. Pedro is 3 times younger than his father. Pedro is n + 3 years old.
N. Lucia has $10.00 less than her sister. Lucia has n-10 dollars.
O. Jack is 2 times taller than his younger brother. Jack is 2 x n inches tall.
For the given mathematical statements:
For L: n represents jerry's run time.
For M: n represents the age of his father.
For N: n represents amount her sister has.
For O: n represents age of his younger brother.
To write the variables n represents each expression,
Take the following steps:
→ Identify the variable in each expression.
→ Determine what the variable represents by looking at the context of the problem and the information provided in the expression.
→ Write down the meaning of the variable for each expression.
Therefore,
L. Lisa can run the 100-yard dash 5 seconds faster than Jerry. Lisa's time is n-5 seconds.
Here,
n represents jerry's run time.
M: Pedro is 3 times younger than his father. Pedro is n + 3 years old.
Here,
n represents the age of his father,
N: Lucia has $10.00 less than her sister. Lucia has n-10 dollars.
Here,
n represents amount her sister has.
O: Jack is 2 times taller than his younger brother. Jack is 2 x n inches tall.
Here,
n represents age of his younger brother.
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PLEASE HELP ASAP
Solve -4 - 1 3/5
Answer:
Step-by-step explanation:
That's 6th grade math but the answer is -5 3/5, this is because subtracting a positive number from a negative adding them together and adding a negative sign.
What do we use to make a prediction when there is not enough evidence to conclude that there is a significant linear relationship? Do we use the mean of the y values or the regression equation?
When there is not enough evidence to conclude a significant linear relationship between variables, it is not appropriate to use a regression equation to make predictions. In such cases, it is more reasonable to rely on the mean of the y values to make predictions.
The mean of the y values provides a simple and neutral estimate of the average response variable value, irrespective of any relationship with the predictor variable. This approach assumes that, on average, future observations will be similar to the past observations in terms of the response variable. While this may not account for potential variations or patterns, it represents a conservative estimate that is not influenced by an unsupported assumption of a linear relationship.
It is important to note that using the mean as a prediction in this context assumes that there are no other relevant predictors or factors influencing the response variable. If there are additional variables that might affect the relationship, you may need to consider alternative approaches, such as exploring other models or using additional information to make predictions.
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20 points
Use Pythagoras' theorem to work out the
height of the equilateral triangle below.
Give your answer in centimetres
(cm)
Answer:
9 × √3 cm or approximately 15.59 cm
Step-by-step explanation:
(look at the picture)
[1] Find the 4-point DFT of the signal [3, 2, -5, 4]
Answer:
Therefore, the 4-point DFT of the signal [3, 2, -5, 4] is [4, 5 - 9i, 0, -1 + i].
Step-by-step explanation:
To find the 4-point Discrete Fourier Transform (DFT) of the given signal [3, 2, -5, 4], we can use the formula for DFT:
X(k) = Σ[n=0 to N-1] x(n) * exp(-j * 2π * k * n / N)
where X(k) is the DFT coefficient at frequency index k, x(n) is the input signal, N is the length of the signal, and j is the imaginary unit.
For the given signal [3, 2, -5, 4], with N = 4, the 4-point DFT coefficients can be calculated as follows:
For k = 0:
X(0) = (3 * exp(-j * 2π * 0 * 0 / 4)) + (2 * exp(-j * 2π * 0 * 1 / 4)) + (-5 * exp(-j * 2π * 0 * 2 / 4)) + (4 * exp(-j * 2π * 0 * 3 / 4))
= 3 + 2 - 5 + 4
= 4
For k = 1:
X(1) = (3 * exp(-j * 2π * 1 * 0 / 4)) + (2 * exp(-j * 2π * 1 * 1 / 4)) + (-5 * exp(-j * 2π * 1 * 2 / 4)) + (4 * exp(-j * 2π * 1 * 3 / 4))
= 3 + 2 - 5i - 4i
= 5 - 9i
For k = 2:
X(2) = (3 * exp(-j * 2π * 2 * 0 / 4)) + (2 * exp(-j * 2π * 2 * 1 / 4)) + (-5 * exp(-j * 2π * 2 * 2 / 4)) + (4 * exp(-j * 2π * 2 * 3 / 4))
= 3 - 2 - 5 + 4
= 0
For k = 3:
X(3) = (3 * exp(-j * 2π * 3 * 0 / 4)) + (2 * exp(-j * 2π * 3 * 1 / 4)) + (-5 * exp(-j * 2π * 3 * 2 / 4)) + (4 * exp(-j * 2π * 3 * 3 / 4))
= 3 - 2 + 5i - 4i
= -1 + i
Therefore, the 4-point DFT of the signal [3, 2, -5, 4] is [4, 5 - 9i, 0, -1 + i].
Select the correct answer.
Solve for x.
x²+x-6=0
A.
B.
-2,3
2,-3
OD. 2,3
-2, -3
C.
Answer:
2,-3
Step-by-step explanation:
The correct answer is 2 and -3 .
Given ,
Equation : x²+x-6=0
Now to find the value of x we need to find the roots/ solutions of the equation by either factor method or by quadratic formula.
So,
x² + x - 6 = 0
By factor method,
x² + 3x - 2x - 6 = 0
Take the common terms ,
x(x + 3) -2(x + 3) = 0
(x-2)(x + 3) = 0
Thus the roots of x are 2 and -3 .
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Which shapes are similar but not congruent to shape 1
There are countless possibilities for shapes that are similar but not congruent to shape 1, as long as they maintain the same proportions and shape.
There are many shapes that are similar but not congruent to shape 1. Similar shapes have the same shape, but their sizes may be different. In contrast, congruent shapes have the same shape and size.
One example of a similar shape to shape 1 is a rectangle that is twice as long and half as wide. Another example could be a square that is three times larger in area than shape 1.
A parallelogram that has the same base as shape 1 but is three times as tall is also similar but not congruent.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
B.) 3/4
Step-by-step explanation:
There are 13 diamond cards in a deck of 52. Divide 52 by 13 to get 4. 4 helps you get a simplified version of the equation. 4/4 subtracted by 1/4 is 3/4 that's what you have left.
Class:
The perimeter of an isosceles triangle ABC with base BC is 15.6 m. Find the length of its sides
if the base is 3 m shorter than a leg
Find AC
Find AB
Find BC
The lengths of the sides of the triangle are:
AC = 6.2 m
AB = 11.88 m
BC = 3.2 m
Let x be the length of each of the legs of the isosceles triangle.
And let y be the length of the base of the triangle.
From the given statement, we have,
The perimeter of the triangle is 15.6 m,
therefore,
⇒ x + x + y = 15.6
Simplifying:
⇒ 2x + y = 15.6
The base of the triangle is 3 m shorter than a leg,
so,
⇒ y = x - 3
Now we can substitute this expression for y into the previous equation:
⇒ 2x + (x - 3) = 15.6
Simplifying:
⇒ 3x - 3 = 15.6
Adding 3 to both sides:
⇒ 3x = 18.6
Dividing by 3:
⇒ x = 6.2
So each leg of the triangle has length 6.2 m.
Now use the expression for y that we found earlier:
⇒ y = x - 3
= 6.2 - 3
= 3.2
So the base of the triangle has length 3.2 m.
Use the Pythagorean theorem to find the lengths of AC and AB:
AC is one of the legs of the triangle, so its length is 6.2 m.
To find AB, we can draw the altitude from A to BC, splitting the triangle into two right triangles. Let h be the length of this altitude.
Then we have:
⇒ h + (y/2) = x
Substituting the values we found earlier:
⇒ h + 1.6 = 6.2
Simplifying:
⇒ h = 6.2 - 1.6
h = 5.94
So the length of AB is 2h, or:
AB = 2h
= 2(5.94)
= 11.88
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A cuboctahedron has 6 square faces and 8 equilateral triangle faces. It can be made by slicing off the corners of a cube, as shown. If each edge of a cuboctahedron has length 32 cm, find the volume of the cuboctahedron.
(Hint: Find the volume of the original cube, and subtract the volume of the corners that are removed.)
The volume of the cuboctahedron is approximately [tex]32768 cm^3 - 512 * sqrt(3) cm^3.[/tex]
To find the volume of the cuboctahedronBy using the clue provided, we may determine the volume of the original cube and then deduct the volume of the cut corners.
All of the edges of the original cube measure 32 cm. As a result, its volume can be determined as follows:
[tex]Volume of cube = (Edge length)^3 = (32 cm)^3 = 32^3 cm^3 = 32768 cm^3[/tex]
Let's now determine the volume of the corners that were eliminated. Each corner has a similar equilateral triangle with sides that are 16 cm long.
The volume of one equilateral triangle can be calculated using the formula:
Volume of equilateral triangle =[tex](sqrt(3) / 4) * (Side length)^2[/tex]
Plugging in the values, we have:
Volume of one corner [tex]= (sqrt(3) / 4) * (16 cm)^2[/tex]
Since there are 8 corners that are removed, we multiply the volume of one corner by 8 to get the total volume of the removed corners:
Total volume of corners = [tex]8 * [(sqrt(3) / 4) * (16 cm)^2][/tex]
Simplifying the expression:
Total volume of corners = [tex]8 * (sqrt(3) / 4) * (16 cm)^2[/tex]
=[tex]2 * sqrt(3) * (16 cm)^2[/tex]
Now, we can subtract the volume of the corners from the volume of the original cube to find the volume of the cuboctahedron:
Volume of cuboctahedron = Volume of cube - Total volume of corners
[tex]= 32768 cm^3 - 2 * sqrt(3) * (16 cm)^2[/tex]
Calculating the expression:
Volume of cuboctahedron ≈ [tex]32768 cm^3 - 2 * sqrt(3) * (16 cm)^2[/tex]
≈ [tex]32768 cm^3 - 2 * sqrt(3) * 256 cm^2[/tex]
≈ [tex]32768 cm^3 - 512 * sqrt(3) cm^3[/tex]
Therefore, the volume of the cuboctahedron is approximately[tex]32768 cm^3 - 512 * sqrt(3) cm^3.[/tex]
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Derivative/Derivada
1) In(2x²-x)
The derivative is f'(x) = (4x - 1) / (2x² - x).
To find the derivative of the function f(x) = ln(2x² - x), we can use the chain rule.
Begin by identifying the function to be differentiated, which is f(x) = ln(2x² - x).
Apply the chain rule, which states that if we have a composition of functions, f(g(x)), the derivative is given by (f'(g(x))) g'(x).
Let's consider the inner function g(x) = 2x² - x.
To differentiate g(x), we need to apply the power rule and the constant rule. The derivative of 2x² is 4x, and the derivative of -x is -1.
Now, we differentiate the outer function f'(g(x)). The derivative of ln(x) is 1/x.
Finally, we multiply the derivatives obtained in steps 3 and 4. Thus, the derivative of f(x) = ln(2x² - x) is:
f'(x) = (1 / (2x² - x)) * (4x - 1)
Simplifying further, we have:
f'(x) = (4x - 1) / (2x² - x)
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What is the modulus and argument of (1+i)^2 divided by (1-√3 i)^4
The modulus is √7 / 5 and the argument is π/6 for the given complex expression.
To find the modulus and argument of the complex expression ((1+i)^2) / ((1-√3i)^4), we can simplify the expression and then calculate the modulus and argument separately.
Let's simplify the expression first:
((1+i)²) / ((1-√3i)[tex]4[/tex])
Expanding the numerator:
(1+i)^2 = (1+i)(1+i) = 1 + 2i + i^2 = 1 + 2i - 1 = 2i
Expanding the denominator:
(1-√3i)^4 = (1-√3i)(1-√3i)(1-√3i)(1-√3i)
= (1 - 2√3i + 3i^2)(1 - 2√3i + 3i^2)
= (1 - 2√3i - 3)(1 - 2√3i - 3)
= (-2 - 2√3i)(-2 - 2√3i)
= 4 + 8√3i - 12i - 12√3
= -8 - 12√3 - 4i(3 + 2√3)
= -8 - 12√3 - 12i - 8√3i
= -20 - 20√3i
Now, let's calculate the modulus:
Modulus = |(2i) / (-20 - 20√3i)|
= |2i| / |-20 - 20√3i|
= 2 / |20 + 20√3i|
= 2 / √[tex](20^2[/tex] + (20√3)^2)
= 2 / √(400 + 2400)
= 2 / √2800
= 2 / (10√28)
= √28 / 10
= √7 / 5
Next, let's calculate the argument:
Argument = arg((2i) / (-20 - 20√3i))
= arg(2i) - arg(-20 - 20√3i)
= π/2 - arg(-20 - 20√3i)
To find the argument of -20 - 20√3i, we can use the arctan function:
arg(-20 - 20√3i) = arctan((-20√3) / -20)
= arctan(√3)
= π/3
Therefore, the argument of[tex]((1+i)^2) / ((1-\sqrt{3} i)^4)[/tex]is:
Argument = π/2 - π/3
= π/6
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i need help solving for the ? i want to know the steps and how to do it
The angle of intersecting arc theorem indicates that the angle marked ? in the drawing is 190°
What is the angle of intersecting chords theorem?The angle of intersecting chords theorem states that the angle formed by two chords when they intersect in a circle is equivalent to half the sum of the arcs they intercept on the circumference of the circle.
The angle of intersecting chords theorem states that we get;
The angle QPR formed = (1/2) × ((Arc QR) + (Arc NS))
Therefore, we get;
m∠QPR = 125° = (1/2) × ((Arc QR) + 60°)
2 × 125° = ((Arc QR) + 60°)
250° = (Arc QR) + 60°
(Arc QR) = 250° - 60° = 190°
The measure of the arc QR = 190°
m[tex]\widehat{QR}[/tex] = 190°
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You only need to do part B
Answer: 4/5
Step-by-step explanation:
Area of the rectangle is 15*8 or 120
There is a certain triangle, where 3^2+4^2=5^2
This is that exact triangle. How? Well, 5*2=10 and 3*2=6
In other words, the base is 4*2 or 8
8*6/2=24
24/120=1/5
So the chance of it NOT being inside the triangle is 4/5
PLEASE HELP ME I'M BEGGING YOU. I NEED THIS ANSWER IN ORDER TO GRADUATE. IF ANYONE CAN HELP PLEASE DO IT.
The solution of the system of linear equations is
(3, -1)
What is graphical solution of linear equations
The graphical solution of linear equations involves representing the equations as lines on a coordinate plane and finding the point of intersection, if any, which corresponds to the solution of the system of equations.
To graphically solve a system of two linear equations, you would typically plot the lines represented by each equation on the same coordinate plane.
The point(s) where the lines intersect would then represent the solution(s) to the system.
Examining the graph, the point of intersection is at
(3, -1)
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An artist's canvas has sides measuring 3x + 5 and 2x + 1 inches.
What is the area of the canvas? Show all work.
The artist laid the canvas flat on the floor and poured some paint in the center. The paint flows at a rate of r(t) = 2t where t represents time in minutes and r represents how far the paint is spreading on the canvas. The area of the paint can be expressed as A[r(t)]= rur?. What is the area of the circle created by the paint?
If the artist wants the circle to be at least 300 in?, will it be that large in 5 minutes? Support your answer with your work
The area of the circle created by the paint is given by the expression [tex]4πt^2[/tex] square units.
To find the area of the canvas, we need to multiply the lengths of its sides.
Given that the sides of the canvas measure 3x + 5 and 2x + 1 inches, the area can be calculated as follows:
Area = (3x + 5) * (2x + 1)
Using the distributive property, we can expand the expression:
Area = 6[tex]x^2[/tex]+ 3x + 10x + 5
Simplifying further, we have:
Area = 6[tex]x^2[/tex] + 13x + 5
Therefore, the area of the canvas is given by the expression 6x^2 + 13x + 5 square inches.
Now let's calculate the area of the circle created by the paint. The area of a circle can be calculated using the formula A = πr^2, where r represents the radius of the circle.
In this case, the paint is spreading at a rate of r(t) = 2t, where t represents time in minutes. So, after time t minutes, the radius of the circle will be 2t.
Substituting the radius into the area formula, we get:
A[r(t)] = π(2t)^2
= 4[tex]πt^2[/tex]
Therefore, the area of the circle created by the paint is given by the expression 4πt^2 square units.
To determine if the area of the circle will be at least 300 square inches in 5 minutes, we need to substitute t = 5 into the area formula and compare it with 300.
A[r(5)] = 4π[tex](5)^2[/tex]
= 4π(25)
= 100π
Since π is a constant value approximately equal to 3.14159, we can calculate:
A[r(5)] ≈ 100(3.14159)
≈ 314.159
The area of the circle after 5 minutes is approximately 314.159 square inches, which is larger than 300 square inches. Therefore, the circle will be larger than 300 square inches in 5 minutes.
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Jesse bought some excercise equipment on a payment plan. The total cost was $375 and his payments were $15 each. What percent of the total cost are the payments?
DUE: MAY 25, 2023 BY 9:15PM
1. (Types of Unemployment) Determine whether each of the following
would be considered frictional, structural, seasonal, or cyclical
unemployment: (1 Mark Each)
Just put the option next to the statement. Eg Frictional
a. Workers are laid off because the season for harvesting mangoes
came to a close.
b. A company operating in Antigua and Barbuda relocates overseas
because taxes are lower in the other country.
c. An employer wishes to hire an accountant. However he does not
hire the first person who applied for the job because he wishes to
see what other talent and experience is available.
d. Workers in a country are laid off due to a severe economic
recession.
2. (Inflation) Here are some recent data on the consumer price index:
Year CPI
Year CPI
2007 127.8
2017 140.3
2008 126.9
2009 128.7
2010 129.5
2011 133.4
Year CPI
2002 136.2
2013 135.4
2014 133.5
2015 135.8
2016 137.9
2018 142.6
2019 145.5
2020 144.5
2021 148.8
Compute the inflation rate for each year 2008 to 2021 and determine
which years were years of inflation? In which years did disinflation
occur? In which years did deflation occur? (10 Marks)
Unemployment can be defined as members of the labour force that do not have a job but are actively seeking employment.
Structural unemployment is an unemployment that occurs as a result of changes in the economy. These changes can be as a result of changes in technology, polices or competition. Structural unemployment tends to be permanent. Ned is structurally unemployed due to changes in his industry
The period of time a person is unemployed from the period he leaves his current job and the time he gets another job. Eg. The period from when graduates till when he gets a job, he is frictionally unemployed
Cyclical unemployment: it occurs as a result of fluctuations in the economy. Unemployment would be high in a downturn and low in a boom .Jane is not unemployed because she is not seeking employment.
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Question
New Orleans has 283 hotels with a population of 391, 006. If Atlanta was proportional to New Orleans in hotels to
population and Atlanta has a population of 498, 000, how many hotels will Atlanta have? Round to the nearest whole
number.
4. What is the range for the function f(x) = 7?
Answer:
7
Step-by-step explanation:
domain-only real numbers
range-only one number 7
What is the median of the following numbers?
9, 10, 6, 5, 6
Answer:
6
Step-by-step explanation:
Put the numbers from least to greatest. The cross out the numbers starting from the left to the right.
3 2/5 divided by 1 1/5 pleaseeee help its due on may 24
Answer:
2.83333333333
Step-by-step explanation:
(3 2/5) / (1 1/5) = 2.83333333333
Answer:
85/30 or 2.833333333
Step-by-step explanation:
When dividing fractions, you must find the reciprocal of the second number and multiply it as usual.
It is also much easier to solve after you convert these numbers to improper fractions.
In this case,
3 2/5 = 17/5
1 1/5 = 6/5
17/5 ÷ 6/5
17/5 x 5/6
85/30 (17/6 reduced)
or
2.83333333333333333333
Which angle is an exterior angle?
k, a, f, and c are the exterior angles of the given figure.
In a figure, an exterior angle refers to an angle formed by one side of the trapezium and the extension of an adjacent side.
In other words, an exterior angle is formed when you extend one of the sides of the trapezium and look at the angle it creates with the adjacent side.
The angle b degrees, g , d and 70 degrees are interior angles.
k, a, f, and c are the exterior angles of the given figure.
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NO LINKS!! URGENT HELP PLEASE!!
Please help me with #11, 12, and 13
Answer:
[tex]\textsf{11.} \quad x^2 + y^2 = 2304[/tex]
[tex]\textsf{12.} \quad \textsf{Yes, the house is within the broadcast range of the radio station.}[/tex]
[tex]\textsf{13.} \quad \textsf{Yes, the plant is within the range of the sprinkler.}[/tex]
Step-by-step explanation:
Question 11Since the base of the Capitol Dome is circular, we can use the equation of a circle to write the equation in standard form for the outside boundary of the dome.
[tex]\boxed{\begin{minipage}{4.5 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
In this case, since the origin is at the center of the dome, the center coordinates are (0, 0):
h = 0k = 0The diameter of the dome is given as 96 feet. Since the diameter of a circle is twice its radius, the radius of the circular base of the dome is:
r = 96 ÷ 2 = 48 ftSubstitute the values of h, k and r into the circle equation formula:
[tex](x - 0)^2 + (y - 0)^2 = 48^2[/tex]
Simplify:
[tex]x^2 + y^2 = 2304[/tex]
Therefore, the equation in standard form for the outside boundary of the dome is:
[tex]\boxed{x^2 + y^2 = 2304}[/tex]
[tex]\hrulefill[/tex]
Question 12To determine if your house is within the broadcast range of the radio station, we can calculate the distance between your house and the radio station using the distance formula. If the distance is less than or equal to the broadcast radius of 40 miles, then your house is within the broadcast range.
Given that your house is located 32 miles west and 21 miles north of the radio station, we can use these coordinates to calculate the distance.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where:\\ \phantom{ww}$\bullet$ $d$ is the distance between two points. \\\phantom{ww}$\bullet$ $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
Define the two points:
Let (x₁, y₁) represent the coordinates of the radio station, which is the origin (0, 0).Let (x₂, y₂) represent the coordinates of your house, which are (-32, 21).Substitute these values into the distance formula and solve for d:
[tex]\begin{aligned}d&=\sqrt{(-32-0)^2+(21-0)^2}\\&=\sqrt{(-32)^2+(21)^2}\\&=\sqrt{1024+441}\\&=\sqrt{1465}\\&=38.27\; \sf miles\;(2\;d.p.)\end{aligned}[/tex]
Therefore, the calculated distance between your house and the radio station is approximately 38.27 miles.
Since the distance is less than the broadcast radius of 40 miles, we can conclude that your house is within the broadcast range of the radio station.
[tex]\hrulefill[/tex]
Question 13To determine if the plant is within the range of the sprinkler, we can calculate the distance between the plant and the sprinkler using the distance formula. If the distance is less than or equal to the sprinkler's radius, then the plant is within the sprinkler's range.
Given that the sprinkler has a radius of 8 feet, we can use these coordinates to calculate the distance.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where:\\ \phantom{ww}$\bullet$ $d$ is the distance between two points. \\\phantom{ww}$\bullet$ $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
Define the two points:
Let (x₁, y₁) the coordinates of the sprinkler, which is the origin (0, 0).Let (x₂, y₂) represent the coordinates of the plant, which are (4, 6).Substitute these values into the distance formula and solve for d:
[tex]\begin{aligned}d&=\sqrt{(4-0)^2+(6-0)^2}\\&=\sqrt{(4)^2+(6)^2}\\&=\sqrt{16+36}\\&=\sqrt{52}\\&=7.21\; \sf feet\;(2\;d.p.)\end{aligned}[/tex]
The calculated distance between the plant and the sprinkler is approximately 7.21 feet.
Since the distance is less than the sprinkler's radius of 8 feet, we can conclude that the plant is within the range of the sprinkler.
The equation for the outside of the dome in standard form is x² + y² = 2304 and your house is within the broadcast range.
The center of the dome is at the origin of the coordinate plane, and the diameter of the dome is 96 feet, which means the radius is half of the diameter, so it is 48 feet.
The center of the dome is at the origin (0, 0), and the radius is 48 feet.
Therefore, the equation for the outside of the dome in standard form is:
x² + y² = 48²
x² + y² = 2304
Now let us determine if your house is within the broadcast range of the radio station, we need to check if it is within the radius of the broadcast.
The radio station has a broadcast radius of 40 miles. Your house is located 32 miles west and 21 miles north of the radio station.
Using the Pythagorean theorem, we can calculate the distance between your house and the radio station:
Distance = √((32)² + (21)²)
Distance = √(1024 + 441)
Distance = √1465
Distance = 38.27 miles
Since the distance between your house and the radio station is less than the broadcast radius of 40 miles, your house is within the broadcast range.
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Please answer the questions on the image
Answer:
Step-by-step explanation:
Help me fast, please
Answer:
A, B, and E. Hope this helps!
