PLEASE HELP!!
1. calculate the length of the track
2. how many laps do you need to travel 1609 meters (about 1 mile)?
3. how much of a rectangular area does the track take up
Note: turns 1, 2, 4, 5, 6, 8 and 9 all have a radius of 3 meters. Turns 3 and 7 each have a radius of 2.25 meters
#1) 163.81 m
#2) About 9.8 laps.
#3) 1314 square meters
Explanation
#1) We first add all of the horizontal and vertical sections:
30+8+6+6+12+30+20 = 112 m
Now we find the distance around each curve. The distance around a circle is the circumference; the formula for circumference is
C=πd.
We will use 3.14 for π for each curve:
Curve 5: The radius is 3, so the diameter is 2*3 = 6. This is 1/4 of a curve, so we multiply the circumference by 1/4:
1/4(3.14)(6) = 4.71
Curve 4: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.
Curve 3: This is 1/2 of a curve, so we will multiply the circumference by 1/2. The radius is 2.25, so the diameter is 2*2.25 = 4.5:
1/2(3.14)(4.5) = 7.065
Curve 2: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.
Curve 1: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.
Curve 9: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.
Curve 8: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.
Curve 7: This is another 1/2 curve with a radius of 2.25, so the distance around is 7.065, just as curve 3.
Curve 6: This is 1/2 of a curve with a radius of 3, so the distance around is 1/2(3.14)(2*3) = 9.42
The total distance around the curved parts is:
4.71+4.71+7.065+4.71+4.71+4.71+4.71+7.065+9.42 = 51.81
Together this gives us 112+51.81 = 163.81.
#2) To find the number of laps it takes to go 1609 meters, divide:
1609/163.81 = 9.8
#3) To find the rectangular area, we first need the total distance across and the total distance vertically.
Horizontally, we have a radius of 3, a horizontal distance of 30, and another radius of 3:
3+30+3 = 36
(looking at the right hand side)
Vertically, we have a radius of 3, vertical distance of 8, radius of 3, radius of 2.25, radius of 2.25, radius of 3, vertical distance of 12, and radius of 3:
3+8+3+2.25+2.25+3+12+3 = 36.5
The area is then 36(36.5) = 1314 m²
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the gas station is 44 kilometers away. how far is the station in miles if 1 mile is 1.6 kilometers
Will mark as Brainliest.
The number of wild flowers growing each year in a meadow is modeled by the function f(x).
f(x)= \frac{1000}{1+9e^{-0.4x} }
Which statements are true about the population of wild flowers?
Select each correct answer.
A. Initially there were 100 wild flowers growing in the meadow.
B. 42 more wildflowers will grow in the 11th year than in the 10th year.
C. After approximately 9 years, the rate for the number of wild flowers decreases.
D. In the 15th year, there will be 1050 wild flowers in the meadow.
Using the provided function, statement A is true as there were initially 100 wildflowers. Statements B, C, and D require calculations using the function and its derivative to determine their truth, which has not been provided in this format.
The function f(x) = \frac{1000}{1+9e^{-0.4x}} models the number of wild flowers growing each year in a meadow. Let's evaluate the truth of the given statements.
A. Initially there were 100 wild flowers: To verify, we calculate f(0). Since e^0 is 1, f(0) = \frac{1000}{1+9(1)} = \frac{1000}{10} = 100. This statement is true.B. 42 more wildflowers in the 11th year than in the 10th year: We need to calculate f(11) - f(10). If this difference is 42, then the statement is true. After calculations, if the result is not 42, then the statement is false.C. After approximately 9 years, the rate of growth decreases: We analyze the behavior of the function's derivative to determine the changing rates. If the derivative decreases after 9 years, this statement is true.D. In the 15th year, there will be 1050 wild flowers: We calculate f(15). If it equals 1050, then the statement is true. If not, it is false.To answer these, we would need to calculate values explicitly using the function provided, and for statement C, we would need to find the first derivative and analyze its behavior over time.
A decorative fish tank is in the shape of a right rectangular prism is shown in the diagram. What is the volume of the fish tank? A) 18 m³ B) 2212 m³ C)2614 m³ D)105 m³
How do you write 5/9 as a percentage
Answer:
55.5
Step-by-step explanation:
divide numerator by denominator
The height of a triangle is twice the length of its base. The area of the triangle is 50m^2. Find the height and base to the nearest tenth of a meter
What is the value of x (10x-20) (6x+8)
Answer:
7.
Step-by-step explanation:
Some penguins were playing on the ice. Ten of them dove in the water. A few seconds later, 6 of those penguins jumped back onto the ice. Now there are 12 penguins on the ice. How many penguins were on the ice to start? Use numbers, pictures,or words to show how you got the answer.
There were 16 penguins on the ice at the start.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount of penguins at start, hence:
x - 10 + 6 = 12
x - 4 = 12
Add 4 to both sides of the equation:
x - 4 + 4 = 12 + 4
x = 16
There were 16 penguins on the ice at the start.
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A 10-ft-long slide is attached to a deck that is 5 ft high. Find the distance from the bottom of the deck to the bottom of the slide to the nearest tenth.
Final answer:
The distance from the bottom of the deck to the bottom of the slide is approximately 8.7 feet when calculated using the Pythagorean theorem for a right-angled triangle formed by the slide, the deck, and the ground.
Explanation:
The student wants to find the horizontal distance from the base of the deck to the bottom of a 10-ft-long slide that makes a right angle with the deck which is 5 ft high. This scenario forms a right-angled triangle where the slide is the hypotenuse, the deck is one leg (height), and the distance from the base of the deck to the bottom of the slide is the other leg (base).
To solve for the distance (d), which is the base of the triangle, we can use the Pythagorean theorem:
a² + b² = c²
where
a is the height of the deck (5 ft)b is the distance from the bottom of the deck to the end of the slide (d)c is the length of the slide (10 ft)Plugging the known values into the equation, we get:
5² + d² = 10²
25 + d² = 100
d² = 100 - 25
d² = 75
d = √75
d ≈ 8.7 ft (to the nearest tenth)
There are 14 children in Erica's preschool class. During free time yesterday, 2 of them chose to do puzzles. What is the probability that a randomly selected child chose to do puzzles yesterday?
1/7 or 2/14... it is the same thing... :-)
Plz Help Meee!!!!! >.<
Ellie and heather drew floor models of their living rooms.ellis model reperessented 20 feet by 15 feet.hethers model represents the greater area?How much greater
The right rectangular prism will be sliced perpendicular to its base along the dashed line.
Select from the drop-down menus to correctly describe the cross section formed by the slice.
The cross section is a__________
with an area of_38_48_72_96____cm².( i only need help with the second one!!!!)
Answer:
The cross section is a Rectangle with an area of [tex]48cm^{2}[/tex]
Step-by-step explanation:
The cross section is a rectangle because it is a quadrilateral with four right angles (90° angles).
The area of a rectangle is the product of the length and width. In this case is [tex]8cm[/tex] and [tex]6cm[/tex] because the cross section is perpendicular to to is base therefore parallel to the side with this measures. We calculate it:
[tex]Area_{Rectangle}=length*width=8cm*6cm\\Area_{Rectangle}=48cm^{2}[/tex]
I’m confused on this question.
Please help.
The answer is $30,000.00
The way you find this is by using the formula, Percent x Part=Whole
.15 or 15% x $45,000.00= $30,000.00
hopes this helps,
Xeno
And a three week vacation to Paris Martha's expenses on food gifts and accommodations was $80 less than three times for airfare if the total expenses for the trip was $2660 how much was your airfare?
Which number is not a perfect square?
A) 4
B) 9
C) 144
D) 84
The post office is now calculating the volume of packages to determine the shipping cost. If a box measure 8 1/2 inches long, 5 1/4 inches wide, and 7 inches high, what is its volume?
Jamie’s dad put 12 gallons of gasoline in his car the gasoline costs 3.25$ a gallon how much did Jamie’s dad pay for the gasoline
To find out how much Jamie's dad paid for the gasoline, we need to multiply the amount of gasoline he bought by the cost per gallon.
We know that Jamie's dad bought 12 gallons of gasoline, and the cost per gallon is $3.25.
So, let's multiply these two numbers together.
First, take the 12 gallons of gasoline.
Then, multiply that number by the cost per gallon, which is $3.25.
So, 12 × $3.25 equals $39.00.
Therefore, Jamie's dad paid for the gasoline.
answer: $39.00
A line passes through the points (–5, 2) and (10, –1). Which is the equation of the line?
Answer:
Y=-1/5x + 1
Step-by-step explanation:
how do you convert degrees to radians?
One degree is equal 0.01745329252 radians:
1° = π/180° = 0.005555556π = 0.01745329252 rad
The angle α in radians is equal to the angle α in degrees times pi constant divided by 180 degrees:
α(radians) = α(degrees) × π / 180°
or
radians = degrees × π / 180°
ExampleConvert 30 degrees angle to radians:
α(radians) = α(degrees) × π / 180° = 30° × 3.1459 / 180° = 0.5236 rad
Degrees to radians in terms of piThe angle α in radians is equal to the angle α in degrees times pi constant divided by 180 degrees:
α(radians) = (α(degrees) / 180°) × π
ExampleConvert 30 degrees angle to radians in terms of pi:
α(radians) = (α(degrees) / 180°) × π = (30° / 180°) × π
= (1/6) × π = π/6 rad = 0.166667π rad
Final answer:
To convert degrees to radians, multiply the number of degrees by π and then divide by 180, or simply multiply by π/180. For instance, 45 degrees can be converted to radians as 45 degrees * (π/180) = π/4 radians.
Explanation:
To convert degrees to radians, you can use the basic formula that π radians equal 180 degrees. This means that to convert a degree measure to radians, you multiply the number of degrees by π and then divide by 180. This can be simplified to multiplying the number of degrees by π/180.
For example, if you wanted to convert 45 degrees to radians, you would perform the following calculation:
45 degrees * (π/180) = 45π/180 = π/4 radians.That means 45 degrees is equivalent to π/4 radians. Remember, the π symbol represents the mathematical constant pi, which is approximately 3.14159.
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2 1/4 simplified with 1/4
2 1/4 +1/4
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1 3/2
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Which choice best describes the association?
Positive linear association
Negative linear association
Non-linear association
No association
Whats the distance from point y to qx in the figure
If sin (13y-5) = cos (2y+5), then what is the value of y?
Given sin (13y-5) = cos (2y+5)
We have a formula regarding complementary angles that is given as follows :-
If sin(A) = cos(B), then A + B = 90 degrees.
where A and B are complementary angles.
Comparing it with given information, we get A = (13y-5) and B = (2y+5).
So the sum of two angles A = (13y-5) and B = (2y+5) would be 90 degrees.
(13y-5)° + (2y+5)° = 90°
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y = 6°
Hence, final answer is y = 6 degrees.
Please help me
i gotta turn this in in 10 minutes