What is the length of BC?
Enter your answer in the box.
BC=
A football coach sits on a sled while two of his players build their strength by dragging the sled across the field with ropes. the friction force on the sled is 1140 n and the angle between the two ropes is 25.0 ∘. how hard must each player pull to drag the coach at a steady 2.30 m/s ? assume both players pull with the same force.
To drag the coach at a constant speed, each player needs to apply a force of approximately 583.89 N to counteract the friction force of 1140 N on the sled, calculated using trigonometry and Newton's Second Law of Motion.
Explanation:The key concept in this question involves Newton's Second Law of Motion and the dynamics of forces acting at angles. The friction force on the sled is given as 1140 N, and since the football coach is moving at a steady speed, we can infer that the net force is zero, implying that the pulling forces balance out the friction force.
To find the force each player must exert, we first determine the total force needed to overcome friction. Since the rope's angle is 25.0° (half the angle between the ropes), the total horizontal force exerted by the two players (F-total) needs to match the friction force. Using trigonometry, the force each player exerts (F-player) can be expressed as:
F-player = F-total / (2 × cos(25.0°/2)) = 1140 N / (2 × cos(12.5°))
So, we calculate the force:
F-player = 1140 N / (2 × cos(12.5°)) = 1140 N / (2 × 0.9763) = 1140 N / 1.9526 = 583.89 N
Therefore, each player needs to exert approximately 583.89 N to drag the coach at a steady speed of 2.30 m/s.
jack has a 8-ft long board. he cut off 1/6 of it how long is the remaining piece in feet and inches
Find three numbers with an LCM of 84
What is the value of the expression ?
The value of this expression is [tex] 3 x 10^{6} [/tex]
In order to find this, you divide each term separately. First we'll start with the numbers in the front.
[tex] \frac{4.8}{1.6} = 3 [/tex]
Now that we have the first number, we look to the 10s and the powers they are raised to. Since we are looking at powers of the same number, we can use the properties of exponents to simply subtract the numbers they are raised to.
[tex] \frac{10^{9}}{10^{3}} = 10^{6} [/tex]
Then we put the two back together for the final answer.
[tex] 3 x 10^{6} [/tex]
A bag has 4 red marbles, 5 white marbles, and 6 blue marbles. three marbles are drawn from the bag (without replacement). what is the probability that they are all the same color?
The probability that the three marbles drawn are all the same color is 64/3375.
Explanation:To find the probability that all three marbles drawn are the same color, we need to consider two cases:
1. The probability of drawing three red marbles
2. The probability of drawing three white marbles
For the first case, the probability of drawing one red marble from the bag is 4/15. After replacing the marble, the probability of drawing another red marble is still 4/15. So, the probability of drawing three red marbles is (4/15) * (4/15) * (4/15).
For the second case, the probability of drawing one white marble from the bag is 5/15. After replacing the marble, the probability of drawing another white marble is still 5/15. So, the probability of drawing three white marbles is (5/15) * (5/15) * (5/15).
Adding the probabilities of the two cases, we get (4/15) * (4/15) * (4/15) + (5/15) * (5/15) * (5/15), which simplifies to 64/3375.
An unfair die is twice as likely to roll an even number than an odd number. what is the probability of it rolling an odd number?
PLZ HELP ASAP!! I will give brainliest!!!
53*(3 1/5-4 1/2)/(2 3/4+1 2/3) Plz give ur answer as a mixed number!!
Thanks!!! Plz give the right answer!!
(5, 3) and (8, -2) Write the standard form of the equation of the line that passes through the given points.
PLZZZZ ANSWER ASAP TY
Aliza needs to run at a rate faster than 8.8 feet per second in order to exceed her fastest time in a race. After running for 15 minutes, her coach determines that she is running at an average rate of 5.8 miles per hour. He converts the average rate to feet per second as shown below:
He concludes that she is not running fast enough to exceed her fastest time.
Answer:
Check: He used an incorrect time ratio converting hours to minutes
Check: He incorrectly concluded that she is not running fast enough
Do not check: His units do not cancel
Do not check: He used an incorrect distance ratio converting miles to feet
Do not check: He cannot determine her average rate in miles per hour after only 15 minutes
Step-by-step explanation:
You're welcome bud :)
A = bh; A =96, b = 12 What does h equal?
Final answer:
To find the height h, divide the area A (96) by the base b (12) to get h = 8.
Explanation:
The problem statement A = bh is a formula to calculate the area of a rectangle, where A is the area, b is the base or width, and h is the height. You're given that the area A is 96 and the base b is 12; you need to find the height h. You can rearrange the formula to solve for h by dividing both sides by b:
h = A / b.
Plug in the values that you know:
h = 96 / 12 = 8.
So, the height h equals 8.
An architect is designing an atrium for a hotel. the atrium is to be rectangular with a perimeter of 756756 ft of brass piping. what dimensions will maximize the area of the atrium?
To maximize the atrium area with a 756-ft perimeter, the dimensions should be 189 ft x 189 ft, with an area of 35,721 sq ft.
To find the dimensions that will maximize the area of the rectangular atrium, we need to set up an equation based on the given perimeter and then use calculus to find the dimensions that maximize the area.
Let's denote the length of the atrium as "L" and the width as "W."
The perimeter of a rectangle is given by the formula:
Perimeter = 2L + 2W
In this case, the perimeter is 756 ft, so we have:
2L + 2W = 756
Divide both sides of the equation by 2 to solve for L:
L + W = 378
Now, we can express L in terms of W:
L = 378 - W
The area of a rectangle is given by the formula:
Area = L * W
Substitute the expression for L in terms of W:
Area = (378 - W) * W
Area = 378W - W^2
To maximize the area, we need to find the critical points.
Take the derivative of the area formula with respect to W and set it equal to zero:
d(Area)/dW = 378 - 2W = 0
Solve for W:
2W = 378
W = 189
Now, we can find the corresponding value of L using L = 378 - W:
L = 378 - 189
L = 189
So, the dimensions that will maximize the area of the atrium are:
Length (L) = 189 ft
Width (W) = 189 ft
The maximum area of the atrium will be:
Area = L * W
Area = 189 ft * 189 ft
Area = 35,721 square feet.
For similar question on perimeter.
https://brainly.com/question/19819849
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which expression is equivalent to 60x^20y^24/30x^10y^12 brainly
Answer:
[tex]\frac{60x^{20}y^{24}}{30x^{10}y^{12}}[/tex] in simplest form would be [tex]2x^{10}y^{12}.[/tex]
Step-by-step explanation:
Given expression [tex]\frac{60x^{20}y^{24}}{30x^{10}y^{12}}[/tex].
Let us simplify given rational expression in smaller parts.
[tex]\frac{60}{30} = 2[/tex]
[tex]\frac{x^{20}}{x^{10}} = x^{20-10} = x^{10}[/tex]
[tex]\frac{y^{24}}{y^{12}} = y^{24-12} = y^{12}.[/tex]
Combining all terms together, we get
[tex]2x^{10}y^{12}.[/tex]
Therefore,
[tex]\frac{60x^{20}y^{24}}{30x^{10}y^{12}}[/tex] in simplest form would be [tex]2x^{10}y^{12}.[/tex]
If 3,661,740 cubic feet of dirt has to be removed for a roadway, how many cubic yards of gravel would be needed.
You order two drinks for 2.49 each and an entree for 12.95. if sales tax is 5% what is your total bill
Ninety one students signed up for the skating club. Coach Link wants to form teams with the same number of members on each team, but says that is impossible: the only teams he can make are 91 teams of 1 or 1 team of 91. Is coach Link correct. Explain why or why not.
Actually I believe that Coach Link is incorrect in saying that he can only make 91 teams of 1 or 1 team of 91.
To find the number of teams he can make, we have to find the whole number that can divide 91 and give also a whole number answer. In this case, I found it to be 7.
91 / 7 = 13
So this means that Coach Link can also make 7 teams of 13 or 13 teams of 7.
9 divided by 3/2?????????????
Volume is a three-dimensional measure.
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false
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A cell phone company orders 600 new phones from a manufacturer. If the probability of a phone being defective is 3.5%, predict how many of the phones are likely to be defective. Round to the nearest whole number.
18 phones
26 phones
210 phones
21 phones
The length of a certain rectangle is twice its width. if the lenth is decreased by 3 cm, the area of the resultign recatangle is 12 sq cm less than the area of the original rectangle. find the original dimensions
Sharina simplified the expression 3(2x – 6 – x + 1)2 – 2 + 4x. In Step 1 she simplified within the parentheses. In Step 2 she expanded the exponent. Which is a possible next step? Simplify the expression by adding and subtracting from left to right. Combine like terms within the parentheses. Combine all x-terms. Distribute the 3 to each term in the parentheses by multiplying.
Answer:
Distribute the 3 to each term in the parentheses by multiplying.
Step-by-step explanation:
3(2x – 6 – x + 1)^2 – 2 + 4x
In Step 1 she simplified within the parentheses.
The expression becomes [tex]3(x-5)^2 - 2 + 4x[/tex]
In Step 2 she expanded the exponent.
After expanding the exponent (x-5)^2 it becomes (x^2-10+25)
[tex]3(x^2-10+25) - 2 + 4x[/tex]
In the next step we distribute 3 inside the parenthesis in order to remove the parenthesis .
Answer: Distribute the 3 to each term in the parentheses by multiplying.
Can you wear slip on shoes without socks
To measure the height of the cloud cover at an airport, a worker shines a spotlight upward at an angle 75° from the horizontal. an observer at a distance d = 590 m away measures the angle of elevation to the spot of light to be 45°. find the height h of the cloud cover,
To find the height of the cloud cover, we use the tangent of the 45° elevation angle, which equals 1. Since the distance is 590 m, the height of the cloud cover is also 590 m.
To calculate the height of the cloud cover, we can use trigonometry. The problem describes two angles and a distance between the spotlight and the observer, which forms a right-angled triangle on the ground and a triangle from the observer to the light on the cloud. The two angles in use are 75° (the angle of the spotlight from the horizontal) and 45° (the angle of elevation from the observer to the light). Using the tangent function, which is the ratio of the opposite side over the adjacent side in a right-angled triangle, we can find the height of the cloud cover (h).
Since the angle of elevation from the observer to the light on the cloud is 45°, the tangent of this angle is 1. This means that for every unit distance from the observer to the point directly underneath the cloud cover, there is one unit of rise. As we are given that the distance (d) is 590 m ,, using the tangent relationship (tan(45°) = h/d), we find that the height of the cloud cover (h) is equal to the distance to the observer (d).
The calculations are as follows:
Therefore, the height of the cloud cover is 590 meters.
2.
The range of the following relation: R: {(3, -2), (1, 2), (-1, -4), (-1, 2)} is (1 point)
a) {-1, 1, 3}
b) {-1, -1, 1, 3}
c) {-4, -2, 2, 2}
d) {-4, -2, 2}
Answer:
D.
Step-by-step explanation:
The range is the (y) value. And you never repeat a number when finding the relation or domain (x). Therefor the best answer would be D.
Its not A because the numbers are for the domain (X value; First column)
Not B because its also for the Domain and it repeats -1 twice
Not C because it repeats 2 twice
Making D the reasonable answer
I hope this helps :))
Convert 45 miles per hour to feet per hour. Round your answer to the nearest hundredth, if necessary.
1 mile = 5280 feet
45 x 5280 = 237,600 feet per hour
I have lots of math questions and I need help!
Doug is going to the store to stock up on food for his dog. While in the store, Doug decides to buy a single bag of dog treats as well. If a large bag of dog food costs $57 and a bag of dog treats costs $9, how many large bags of dog food, x, did Doug buy if he spent $180 and all prices already include sales tax?
Final answer:
To find the number of large bags of dog food Doug bought, use the given prices and total spent in the store.
Explanation:
Doug bought 3 large bags of dog food.
To solve this problem, we can set up the equation: $57x + $9 = $180. From here, we can find x by rearranging the equation to solve for x.
Therefore, Doug bought 3 large bags of dog food, as each large bag costs $57 and he spent $180 in total.
The equation y = 1.55x + 110,419 approximates the total amount, in dollars, spent by a household to raise a child in the United States from birth to 17 years, given the household’s annual income, x. Assume the household’s total cost of raising a child is $197,219. What is the household’s annual income?
Answer: $56,000
Step-by-step explanation:
Given: The equation [tex]y=1.55x+110,419[/tex] approximates the total amount, in dollars, spent by a household to raise a child in the United States from birth to 17 years, given the household’s annual income, x.
The household’s total cost of raising a child = $197,219
Put the above value in the equation, we get
[tex]197,219=1.55x+110,419\\\Rightarrow\ 1.55x=197219-110419\\\Rightarrow\ x=\frac{86800}{1.55}\\\Rightarrow\ x=56,000[/tex]
Hence, the household’s annual income is $56,000.