question involving a mural painted by Deagan, which features a triangle, for a conference room at LWHS. You'd like to know the measure of the base.
Unfortunately, it seems that some essential information is missing from your question, such as the dimensions or other properties of the triangle. In order to accurately answer your question and calculate the measure of the base, please provide more information about the triangle or any related information given in the problem.
Once you provide the necessary information, I'd be happy to help you find the measure of the base and explain the process step-by-step!
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Andi moved a game piece down 4 pieces
choose all of the expressions that could be used to indicate how many spaces the game piece was moved.
The expression 4 that could be used to find spaces in the game piece was moved.
Since Integers are the collection of negative, and positive numbers including zero. Then the positive integers lie on the right side of the zero on the number line and the negative lie on the left side of zero on the number line.
We are given that Andi moved a game piece down 4 pieces
The expression in option 1: |-4| which is equal to 4
The expression in option 2: |4| which is equal to 4
The expression in option 3: -|4| which is equal to -4
The expression in option 4: 4 which is equal to -4
∴The correct expression is option 4
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If the probability of an event is 88/83 what is the probability of the event not happening? 88' Write your answer as a simplified fraction.
The probability of the event not happening is 5/83.
Here, probability refers to the likelihood of a given event occurring and that the inequality f(x) > 3g(x) holds for all x > 0.
If the probability of an event happening is 88/83, then the probability of the event not happening is 1 minus the probability of the event happening. This can be expressed as:
1 - 88/83
To simplify this expression, we can first find a common denominator for 1 and 88/83, which is 83/83:
83/83 - 88/83
-5/83
Therefore, the probability of the event not happening is 5/83.
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Answer the questions below to determine what kind of function is depicted below
Answer:
This function is an exponential function because the base is a constant and the exponent is a variable.
the following table shows the number of miles a hiker walked on a trail each day for 6 days. day 1 2 3 4 5 6 number of miles 8 5 7 2 9 8 what was the mean number of miles the hiker walked for the 6 days? responses 3.5 3.5 4.5 4.5 6.5 6.5 7.5 7.5 8
The mean number of miles the hiker walked for the 6 days was 6.5 miles.
To calculate the mean or average of a set of numbers, we add up all the numbers and then divide the sum by the number of items in the set. In this case, we have the number of miles the hiker walked on each of the six days. To find the total number of miles the hiker walked, we simply add up all the numbers
8 + 5 + 7 + 2 + 9 + 8 = 39
Next, we divide the total number of miles by the number of days (which is 6) to get the average or mean number of miles the hiker walked per day:
Mean number of miles = Total number of miles / Number of days
= 39 / 6
= 6.5
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Your local high school is putting on a musical. They have sold 1000 tickets. Adult tickets
were sold for $8. 50, while child tickets were sold for $4. 50. A total of $7100 was
collected from ticket sells. How many tickets of each kind were sold?
650 adult tickets were sold.
Let's denote the number of adult tickets sold by A and the number of child tickets sold by C.
From the problem, we know that:
A + C = 1000 (the total number of tickets sold is 1000)
8.50A + 4.50C = 7100 (the total revenue from ticket sales is $7100)
We can use the first equation to solve for A in terms of C:
A = 1000 - C
Substituting this expression for A into the second equation, we get:
8.50(1000 - C) + 4.50C = 7100
Expanding and simplifying:
8500 - 8.50C + 4.50C = 7100
4C = 1400
C = 350
So 350 child tickets were sold. We can use the first equation to find the number of adult tickets sold:
A + 350 = 1000
A = 650
Therefore, 650 adult tickets were sold.
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La rueda de una bicicleta mide 62.2 cm de diámetro, ¿cuál es el perímetro de la rueda?
Answer:
"Querido hijo, estás despedido" es una novela juvenil escrita por Jordi Sierra i Fabra que se divide en 17 capítulos. A continuación, se presenta un breve resumen de cada uno de ellos:
Capítulo 1: El protagonista, Leo, es un adolescente que vive en un hogar en el que sus padres son muy estrictos y le exigen que saque buenas notas en la escuela.
Capítulo 2: Leo tiene una discusión con su padre, quien le dice que si no mejora sus notas, lo echará de casa.
Capítulo 3: Leo tiene un accidente de bicicleta y es atendido por la enfermera del colegio, la señorita Rovira.
Capítulo 4: Leo recibe la noticia de que su padre ha muerto en un accidente de tráfico.
Capítulo 5: En el funeral de su padre, Leo se siente alejado de su familia y amigos.
Capítulo 6: Leo recibe una carta de su padre en la que le explica que ha dejado un testamento y que su hermana mayor, Berta, será la administradora de la herencia.
Capítulo 7: Berta le comunica a Leo que su padre le ha dejado una empresa de limpieza y que él será el encargado de dirigirla.
Capítulo 8: Leo descubre que la empresa está en quiebra y que tendrá que tomar medidas drásticas para salvarla.
Capítulo 9: Leo empieza a tomar el control de la empresa y a hacer cambios en su funcionamiento.
Capítulo 10: Leo contrata a un joven llamado Iván, quien se convierte en su mano derecha en la empresa.
Capítulo 11: Leo se encuentra con la señorita Rovira, quien lo ayuda a tomar una importante decisión en la empresa.
Capítulo 12: Leo tiene una reunión con los trabajadores de la empresa y les comunica los cambios que va a hacer.
Capítulo 13: Leo se siente muy presionado por las exigencias de la empresa y se desahoga con su amigo Santi.
Capítulo 14: Leo tiene un encontronazo con su hermana Berta, quien intenta influir en la gestión de la empresa.
Capítulo 15: Leo descubre que Iván le ha estado robando dinero a la empresa y tiene que tomar medidas para solucionar el problema.
Capítulo 16: Leo consigue salvar la empresa y hace balance de lo que ha aprendido en el proceso.
Capítulo 17: La historia termina con Leo en paz consigo mismo y con su familia, habiendo aprendido importantes lecciones sobre la vida y el trabajo.
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Stacy's time in her 50-meter freestyle race as measured with a stopwatch was 32. 4 seconds. The more precise electronic touchpad measured her time as 32. 36 seconds. What is the percent error for the stopwatch's measurement?
To find the percent error for the stopwatch's measurement of Stacy's time in her 50-meter freestyle race, we'll use the following formula:
Percent Error = (|(Measured Value - Actual Value)| / Actual Value) * 100
Here, the Measured Value is the stopwatch's time (32.4 seconds), and the Actual Value is the electronic touchpad's time (32.36 seconds).
Step 1: Calculate the absolute difference between the measured and actual values:
|32.4 - 32.36| = 0.04
Step 2: Divide the absolute difference by the actual value:
0.04 / 32.36 = 0.001236
Step 3: Multiply the result by 100 to get the percentage:
0.001236 * 100 = 0.1236%
The percent error for the stopwatch's measurement of Stacy's time in her 50-meter freestyle race is approximately 0.124%.
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The radian measure -1.7 pi is equivalent to -306 degrees.
How does sleep affect memory retention?To find the percent error of the stopwatch's measurement, we need to compare it to the more precise electronic touchpad measurement. The formula for percent error is:
percent error = (|measured value - actual value| / actual value) x 100%
In this case, the measured value is 32.4 seconds, the actual value is 32.36 seconds, and the absolute difference between them is 0.04 seconds. Plugging these values into the formula, we get:
percent error = (|32.4 - 32.36| / 32.36) x 100% = 0.124%
Therefore, the percent error for the stopwatch's measurement is 0.124%. This means that the stopwatch's measurement was very close to the actual value, with an error of only 0.124% of the actual value.
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(From Unit 7, Lesson 3. )
The Colorado state flag consists of three horizontal stripes of equal height. The
side lengths of the flag are in the ratio 2 : 3. The diameter of the gold-colored disk is
equal to the height of the center stripe. What percentage of the flag is gold?
The total area of the flag is the sum of the areas of the three stripes and the percentage of the flag that is gold is approximately 0.459%
Let's call this height "h".
We also know that the side lengths of the flag are in the ratio 2:3. This means that if the shortest side is 2x, then the longest side is 3x. Since the three stripes are of equal height, each one must be h/3 in height.
Now we can use this information to find the area of the gold-colored disk and the total area of the flag. The area of a circle is given by the formula A = πr^2, where r is the radius. Since the diameter is equal to the height of the center stripe (which is h/3), the radius of the disk is h/6. So the area of the disk is:
A_disk = π(h/6)^2 = πh^2/36
The total area of the flag is the sum of the areas of the three stripes. Since each stripe is h/3 in height and the shortest side is 2x, the area of each stripe is:
A_stripe = (2x)(h/3) = 2hx/3
So the total area of the flag is:
A_flag = 3(A_stripe) = 6hx
To find the percentage of the flag that is gold, we need to divide the area of the gold-colored disk by the total area of the flag and multiply by 100.
percentage = (A_disk / A_flag) x 100
Substituting our expressions for A_disk and A_flag, we get:
percentage = (πh^2/36) / (6hx) x 100
Simplifying, we can cancel out the factor of h and get:
percentage = (π/216)x100
So the percentage of the flag that is gold is approximately 0.459% (rounded to three decimal places).
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Which ones are solutions to
7x+4y=-23
(-1,-4)
(2,6)
(-5,3)
(6,-7)
Hello!
In this question, we are asked to find which set of points are solutions to our equation: 7x + 4y = -23
In order to find which points are solutions to our equation, we will plug the values into our equation and solve. If both sides of the equation are equal, the point will be a solution.
Note: Our coordinate point is in the format of (x,y), so we will plug in the values according to its variable.
Solve:
(-1,-4):
Plug in coordinate.
7(-1) + 4(-4) = -23
Simplify.
-7 - 16 = -23
-23 = -23
Since it is equal, (-1,-4) is a solution.
(2,6):
Plug in coordinate.
7(2) + 4(6) = -23
Simplify.
14 + 24 = -23
38 = -23
Since it is not equal, making it false, (2,6) is not a solution.
(-5,3):
Plug in coordinate.
7(-5) + 4(3) = -23
Simplify.
-35 + 12 = -23
-23 = -23
Since it is equal, (-5,3) is a solution.
(6,-7):
Plug in coordinate.
7(6) + 4(-7) = -23
Simplify.
42 - 28 = -23
14 = -23
Since it is not equal, making it false, (6,-7) is not a solution.
Answer:
The solutions to the equation are: (-1,-4) and (-5,3).
F(x) and g(x) are polynomial functions.
determine whether each expression is always, sometimes, or never a polynomial.
f(x)+g(x)
and
f(x) / g(x)
F(x) and G(x) are polynomial functions in which the expression f(x) + g(x) is always a polynomial and f(x)/g(x) is sometimes a polynomial.
Let F(x) be a polynomial = 2x + 4
g(x) be a polynomial = 6x² + 12x
putting the value in the expression
f(x) + g(x) = 2x + 4 + 6x² + 12x
f(x) + g(x) = 6x² + 14x + 4
6x² + 14x + 4 is a polynomial
Now, putting the value in the equation
f(x)/g(x) = 2x + 4/6x² + 12x
Taking 3x common from 6x² + 12
We get 3x(3x+4)
f(x)/g(x) = 2x+4/3x(2x+4)
f(x)/g(x) = 1/3x
1/3x is not a polynomial
Hence, it sometimes a polynomial.
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Find the radius of the circle with equation x² + y² = 19²
r=0
Submit Answer
The radius of the circle of the equation is 19 units
Finding the radius of the circle of the equationFrom the question, we have the following parameters that can be used in our computation:
x² + y² = 19²
The equation of a circle is represented as
(x - a)² + (y - b)² = r²
Where
Center = (a, b)
Radius = r
using the above as a guide, we have the following:
Center = (a, b) = (0, 0)
Radius = r = 19
Hence, the radius of the circle of the equation is 19 units
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in the figure below, AC and BD are diameters of the circle P what is the arc measure of minor BC
The arc measure of minor BC is 155°
How to determine the arc measure of minor BC?An arc is a segment of a circle is defined by two endpoints and the set of points on the curve between them.
The length of an arc is a fraction of the circumference of the circle, and can be calculated using the angle between the two endpoints and the radius of the circle.
We can say that measure of arc BC is m∠ BPC. Also, arc AD is m∠ APD
By Vertical Angles Theorem. That is:
Provided AC and BD are diameters,
m∠ BPC = m∠ APD
m∠ BPC = 155°
Since m∠ BPC = 155°
Therefore, the arc measure of minor BC is 155°
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Complete Question
See attached image
The Yert family hires a landscaping company for 30 weeks. There are two companies to choose from. Green Lawns charges 2 for the first time they service your lawn, and the price will multiply by a factor of 0. 90 every week thereafter. Green Thumbs charges 400 for the first time they service your lawn, and then charges an additional 40 every week thereafter. At 30 weeks, if the Yert family chooses the company that is cheaper, how much money will they save?
Let's first calculate the total cost of using Green Lawns for 30 weeks. We can use the formula for the sum of a geometric series to do this:
Total cost of Green Lawns =[tex]2(1 - 0.9^30) / (1 - 0.9) + 0.9^30 * 2[/tex]
Total cost of Green Lawns = [tex]2(1.7379) / 0.1 + 0.0359[/tex]
Total cost of Green Lawns = 38.8179
Now let's calculate the total cost of using Green Thumbs for 30 weeks:
Total cost of Green Thumbs = [tex]400 + 40 * 29[/tex]
Total cost of Green Thumbs = 1160
Therefore, the Yert family would save:
$1160 - $38.8179 = $1121.18
So the Yert family would save $1,121.18 by choosing Green Lawns over Green Thumbs for 30 weeks.
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The probability that Trevor studies for at least 50 minutes and passes his Algebra test is 0.88. The probability that he studies for at least 50 minutes is 0.92.
Step-by-step explanation:
If we let A be the event that Trevor studies for at least 50 minutes, and let B be the event that he passes his Algebra test, then we know:
P(A and B) = 0.88
P(A) = 0.92
We want to find the probability that Trevor passes his Algebra test given that he studied for at least 50 minutes, or in other words, we want to find P(B|A).
We can use Bayes' theorem to find this probability:
P(B|A) = P(A and B) / P(A)
Substituting in our values, we get:
P(B|A) = 0.88 / 0.92
Simplifying this fraction, we get:
P(B|A) = 0.9565
Therefore, the probability that Trevor passes his Algebra test given that he studied for at least 50 minutes is approximately 0.9565.
please help with question 9
The value of the function g(x) = 4x⁴ - 4x³ - 10x - 51
What are functions?Functions are defined as those expressions or equations showing the relationship between two variables.
From the information given, we have the functions;
f(x) = 4x³ + 3x² - 12x - 32
h(x) = 4x⁴ - 3x² + 2x - 19
(f + g(x) = h(x)
To determine the function, let us follow the expression
f(x) + g(x) = h(x)
Make g(x), the subject of formula
g(x) = h(x) - f(x)
Substitute the expressions
g(x) = 4x⁴ - 3x² + 2x - 19 - 4x³ + 3x² - 12x - 32
Now, collect the like terms, we get;
g(x) = 4x⁴ - 4x³ - 3x² + 3x² + 2x - 12x - 19 - 32
Add or subtract the values
g(x) = 4x⁴ - 4x³ - 10x - 51
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Lines c and d are perpendicular. The equation of line c is y=−1/2x+1 . What is the equation of line d ?
Answer:
y=2x+3
Step-by-step explanation:
When a line is perpendicular to another line, it means that the slope is the opposite reciprocal of the other slope.
We can see that line C has a slope of -1/2, meaning that the opposite reciprocal is 2. This overall means that line D has a slope of 2.
We can also see that line d (from the graph) has a y-intercept of (0,3).
To write this equation:
y=2x+3
Hope this helps! :)
A food truck owner charges z dollars per burrito combo and $1. 50 for a side of guacamole. The expression 5 (x + 1. 50) represents the
total cost of 5 burrito combos and 5 sides of guacamole.
Which expression also represents the total cost of 5 burrito combos, which cost a dollars each, and 5 sides of guacamole, which cost $1. 50
each?
0
The expression that fits perfect for the given requirement is 5z + 7.50, under the condition that a food truck owner charges z dollars per burrito combo and $1.50 for a side of guacamole.
Here we have to apply the principles of solving algebraic equations, due to the expression provided.
From the given information, here the food truck owner charges z dollars per burrito combo along with $1.50 for a side of guacamole.
According to the information it is given that the expression is 5(z+1.50) which helps to state the total cost of 5 burrito combos and 5 sides of guacamole.
Lets now formulate the expression for the given required equation
= 5(z + 1.50)
= 5z + 7.50.
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A food truck owner charges z dollars per burrito combo and $1.50 for a side of guacamole. The expression 5(z+1.50) represents the total cost of 5 burrito combos and 5 sides of guacamole. What expression also represent the cost of 5 burrito combos and 5 sides if guacamole that cost 1.50 each.
please answer and explain. show work 100 POINTS
In 2029, there will be an estimated A, 8.66 billion people in the world.
C, t = (ln(N/N₀))/k is the equation rewritten to solve for t.
How to determine exponential growth model?Part A:
Using the given exponential growth model, find the population in 2029 as follows:
N = N₀e^kt
N₀ = 7.95 billion (present population)
k = 1.08% = 0.0108 (rate of increase)
t = 2029 - 2022 = 7 (number of years)
N = 7.95 billion × e^(0.0108×7)
N ≈ 8.66 billion
Therefore, the world's population is expected to be 8.66 billion in 2029. Answer choice A is correct.
Part B:
To solve for t, isolate it on one side of the exponential growth model equation. Taking the natural logarithm of both sides:
ln(N/N₀) = kt
Divide both sides by k:
t = ln(N/N₀)/k
Therefore, the equation rewritten to solve for t is t = (ln(N/N₀))/k. Answer choice C is correct.
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How to get 51 by using all four numbers 8 5 6 7 once.
To get 51 using the numbers 8, 5, 6, and 7 exactly once each, you can use the following mathematical expression:
(8 x 6) - 7 + 5 = 51
How it works:
1. Multiply 8 by 6 to get 48: (8 x 6) = 48
2. Subtract 7 from 48 to get 41: 48 - 7 = 41
3. Add 5 to 41 to get 51: 41 + 5 = 51
Therefore, (8 x 6) - 7 + 5 = 51.
Answer:
Step-by-step explanation:
8 x (7 - 5) + 6 = 51
In a circle with radius 6 and angle intercepts an arc of length 3pi find the angle in radians in simplest form
In a circle with radius 6 and angle intercepts an arc of length 3π , the angle in radians in simplest form is π/2.
In a circle, the length of an arc is proportional to the angle that it intercepts. The ratio of the arc length to the circumference of the circle is equal to the ratio of the angle in radians to 2π. Thus, we can write:
(arc length) / (circumference) = (angle) / (2π)
In this problem, we are given that the circle has a radius of 6 and that the arc length is 3π. We can use the formula for the circumference of a circle, which is C = 2πr, to find the circumference of this circle:
C = 2πr = 2π(6) = 12π
Now we can use the formula above to find the angle in radians:
(3π) / (12π) = (angle) / (2π)
Simplifying this equation, we get:
angle = (3π * 2π) / 12π = 1/2 * π
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The math team wants to visit the Museum of Mathematics
to celebrate Pi Day. They have $210 to spend. They need to
buy 14 student tickets and 1 adult ticket. A student ticket
costs $12, and an adult ticket costs $17. The team also
wants to buy sugar-free fruit pies. Each pie costs $6. How
many whole pies can the team buy? Show your work.
Answer:
4
Step-by-step explanation:
14 student tickets times $12 = 168
168 + $17 = 185
210-185=25
6*4=$24
so they can buy 4 pies with 1 dollar left over
sorry if I am wrong
2a=−2+4(a+3)
a =
−4b=−5(3−b)+6
b =
Answer:
a = - 5 , b = 1
Step-by-step explanation:
2a = - 2 + 4(a + 3) ← distribute parenthesis
2a = - 2 + 4a + 12 ( subtract 4a from both sides )
- 2a = 10 ( divide both sides by - 2 )
a = - 5
-------------------------------------------
- 4b = - 5(3 - b) + 6 ← distribute parenthesis
- 4b = - 15 + 5b + 6 ( subtract 5b from both sides )
- 9b = - 9 ( divide both sides by - 9 )
b = 1
Step-by-step explanation:
2a=6(a+3)
2a=6a+18
2a-6a=18
-4a=18
-4a/-4=18/-4
a=-4.5
All the dimensions of a cube increase by a factor 3/2 how many times greater is the surface area? explain
If all the dimensions of a cube increase by a factor of 3/2, the surface area will increase by a factor of 9/2.
If all the dimensions of a cube increase by a factor of 3/2, then the new dimensions of the cube will be 3/2 times the original dimensions.
Let's say the original side length of the cube was "s". Then the new side length would be (3/2)*s.
The surface area of a cube is given by the formula 6s^2, where s is the side length.
So the original surface area of the cube would be:
6s^2
And the new surface area of the cube would be:
6(3/2s)^2
= 6(9/4)s^2
= 27/2 s^2
To find how many times greater the new surface area is compared to the original surface area, we can divide the new surface area by the original surface area:
(27/2 s^2) / (6s^2)
= (9/2)
So the new surface area is 9/2 times greater than the original surface area.
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Does anyone have the answer
Answer:does anyone have the image
Step-by-step explanation:
Which equations have the same value of x as 3/5 (30 x minus 15) = 72? Select three options.
A. 18 x - 15 = 72
B. 50 x -25 = 72
C. 18 x - 9 = 72
D. 3 (6 x - 3) = 72
E. x = 4.5
The equations that have the same value of x as 3/5 (30 x - 15) = 72 are C, D, and E.
Choosing the equations that are equivalentTo solve for x in 3/5 (30 x - 15) = 72, we can first simplify the left side by distributing the 3/5:
3/5 (30 x - 15) = 18 x - 9
Now we can solve for x by setting the right side equal to 72:
18 x - 9 = 72
Adding 9 to both sides:
18 x = 81
Dividing by 18:
x = 4.5
So we know that option E is one of the correct answers.
To check which of the other options have the same value of x, we can substitute x = 4.5 into each equation and see if it simplifies to 72:
A. 18 x - 15 = 72
18(4.5) - 15 = 72
81 - 15 = 72 (not equivalent)
B. 50 x - 25 = 72
50(4.5) - 25 = 200 - 25 = 175 (not equivalent)
C. 18 x - 9 = 72
18(4.5) - 9 = 72 (equivalent)
D. 3 (6 x - 3) = 72
3(6(4.5) - 3) = 3(24) = 72 (equivalent)
Therefore, the equations that have the same value of x as 3/5 (30 x - 15) = 72 are C, D, and E.
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A helicopter takes off from the roof of a building and travels at 100 mph on a bearing of 558°e. the flight takes 3. 8 hr. to the nearest mile, how far south and
how far east has the helicopter traveled?
can someone pls help me
The helicopter traveled approximately 175.5 miles east and 299.1 miles south.
How to find the helicopter traveled?Let's say the building is located at point A and the helicopter travels to point B. We know that the bearing of B from A is 558°e, which means the angle formed by the line AB and the east direction is 558°.
Next, we can use trigonometry to find the horizontal and vertical components of the distance traveled. Let x be the horizontal distance (in miles) traveled by the helicopter and y be the vertical distance (in miles) traveled. We can then use the following equations:
cos(558°) = x / d
sin(558°) = y / d
where d is the total distance traveled (in miles). We can also use the formula:
d = r * t
where r is the speed of the helicopter (100 mph) and t is the time taken for the flight (3.8 hours). Substituting this into the first two equations, we get:
x = d * cos(558°)
y = d * sin(558°)
d = r * t = 100 * 3.8 = 380 miles (rounded to the nearest mile)
Substituting the values of d and the angle into the equations for x and y, we get:
x = 380 * cos(558°) ≈ -175.5 miles
y = 380 * sin(558°) ≈ 299.1 miles
Note that the negative sign for x indicates that the helicopter traveled west, not east. We can take the absolute value of x to get the distance traveled east:
|x| ≈ 175.5 miles
Therefore, the helicopter traveled approximately 175.5 miles east and 299.1 miles south.
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Find the linearization L(x) of the function at a. T f(x) = 7cos(x), a = - (Consider a=3.14159265359 ) 9 L(x)"
To find the linearization L(x) of the function f(x) = 7cos(x) at a = 3.14159265359, we'll use the formula:
L(x) = f(a) + f'(a)(x - a)
where f'(x) is the derivative of f(x) with respect to x.
First, let's find the value of f(a) at a = 3.14159265359:
f(a) = 7cos(a)
f(3.14159265359) = 7cos(3.14159265359) ≈ -7
Next, let's find the value of f'(a) at a = 3.14159265359:
f'(x) = -7sin(x)
f'(a) = -7sin(a)
f'(3.14159265359) = -7sin(3.14159265359) ≈ 0
Now we have all the pieces we need to plug into the formula for L(x):
L(x) = f(a) + f'(a)(x - a)
L(x) = -7 + 0(x - 3.14159265359)
L(x) = -7
So the linearization of the function f(x) = 7cos(x) at a = 3.14159265359 is:
L(x) = -7
To find the linearization L(x) of the function f(x) = 7cos(x) at a specific point a, we'll use the formula:
L(x) = f(a) + f'(a)(x - a)
Given that a = 3.14159265359 (approximating π), first we need to find f(a) and f'(a).
1. f(a) = 7cos(a) = 7cos(3.14159265359) ≈ -7
2. To find f'(x), we take the derivative of f(x):
f'(x) = -7sin(x)
Now, we can find f'(a):
f'(a) = -7sin(3.14159265359) ≈ 0
Finally, we can plug these values into the linearization formula:
L(x) = -7 + 0(x - 3.14159265359)
Simplifying, we get:
L(x) = -7
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If ad and bd are tangent to circle c, and ad= 13 and bd= 4x-3 find the value of x.
If ad and bd are tangent to circle c, and ad= 13 and bd= 4x-3, then the value of x is 4 or 4.5
To solve this problem, we'll need to use some geometry and algebra.
Using the Pythagorean theorem, we can set up two equations:
OA² + AD² = OD² (for right triangle OAD)
OB² + BD² = OD² (for right triangle OBD)
In these equations, "OD" is the radius of the circle. We don't know this value yet, but we can express it in terms of "x" using the fact that "BD" = 4x-3.
Now, we can simplify these equations by substituting in the values we know. We get:
OA² + 13² = OD²
OB² + (4x-3)² = OD²
This means we can set up the equation:
OA = OB
Now we can substitute in the expressions we found for "OA" and "OB" earlier:
√(OD² - 13²) = √(OD² - (4x-3)²)
We can then square both sides to eliminate the square roots:
OD² - 13² = OD² - (4x-3)²
Simplifying this equation, we get:
169 = (4x-3)²
Taking the square root of both sides (and remembering to include the positive and negative solutions), we get:
4x-3 = ±13
Solving for "x," we get two possible values:
x = 4
x = 4.5
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A scientist uses a submarine to study ocean life.
She begins at sea level, which is an elevation of 0 feet.
She travels straight down for 112 seconds at a speed of 0.8 feet per second.
She then travels directly up for 120 seconds at a speed of 0.6 feet per second.
After this 232-second period, how much time, in seconds, will it take for the scientist to travel back to sea level at 3.5 feet per second? If necessary, round your answer to the nearest tenth of a second.
The length of time, in seconds, that it will take for the scientist to travel back to sea level at 3.5 feet per second will be 5.0 seconds.
How to calculate the amount of timeTo calculate the amount of time, we will begin by calculating the distance traveled from sea level in all of the instances.
1. 112 seconds × 0.8 feet per second = 89.6 feet
2. 120 seconds × 0.6 feet per second = 72 feet
The distance from sea level is now: 89.6 feet - 72 feet
= 17.6 feet
The time, in seconds, that it will take for the scientist to travel back to sea level at 3.5 feet per second will be:
17.6 feet ÷ 3.5 feet per second
5.0 seconds to the nearest tenth.
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A cereal company packages their granola in cylindrical containers that have a diameter of 20 cm and a height of 17. 4 cm. Approximately how much granola will a container hold?
The volume of granola a cylindrical container can hold 5451.6 cubic centimeters if containers have a diameter of 20 cm and a height of 17. 4 cm.
The number of unit cubes (cubes of unit length) that can fit inside a cylinder determines its volume.
Identifying the radius (r) and height (h)
r = 10 cm
h = 17.4 cm
Calculating the volume (V) using the formula V = πr²h
V = π × (10 cm)² × 17.4 cm
V ≈ 3.14 × 100 cm² × 17.4 cm
V ≈ 5451.6 cm³
Approximately, a container will hold 5451.6 cubic centimeters of granola.
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