The total energy of the beam just as it hits the ground would be equivalent to the initial potential energy when it was held at a height of 40 m, assuming no air resistance.
Explanation:The question is about understanding the concept of conservation of energy, specifically the transformation of potential energy to kinetic energy. When the beam was held at a height of 40 m, it had potential energy given by the formula:
PE = mgh
where m is the mass of the beam, g is the acceleration due to gravity, and h is the height. Assuming no air resistance, when the beam falls, all of its potential energy will be converted to kinetic energy, which can be determined by the formula:
KE = 1/2 mv^2
However, as we don't know the exact speed of the beam just as it's hitting the ground, we don't need it because the total energy remains constant. So, just as the beam hits the ground the total energy will be the same as the initial potential energy when it was still.
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A spinner is divided into many sections of equal size. Some sections are red, some are blue, and the remaining are green. The probability of the arrow landing on a section colored red is 11 over 20. The probability of the arrow landing on a section colored blue is 6 over 20. What is the probability of the arrow landing on a green-colored section?
A triangular lake-front lot has a perimeter of 1300 feet. One side is 300 feet longer than the shortest side, while the third side is 400 feet longer than the shortest side. Find the lengths of all three sides.
A) 200 ft, 500 ft, 600 ft
B) 300 ft, 300 ft, 300 ft
C) 100 ft, 200 ft, 300 ft
D) 300 ft, 600 ft, 700 ft
On September 30, picture perfect physicians invested$100,000 in new medical equipment. What is the new assets, liabilities and equity
Find the volume v of the described solid s. the base of s is an elliptical region with boundary curve 4x2 + 9y2 = 36. cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.
The volume [tex]\( V \)[/tex] of the solid [tex]\( S \)[/tex] is 32 cubic units.
To find the volume [tex]\( V \)[/tex] of the solid [tex]\( S \),[/tex] where the base is an elliptical region defined by the equation [tex]\( 4x^2 + 9y^2 = 36 \),[/tex] and the cross-sections perpendicular to the [tex]\( x \)[/tex]-axis are isosceles right triangles with their hypotenuse lying on the base, we proceed as follows:
The equation [tex]\( 4x^2 + 9y^2 = 36 \)[/tex] represents an ellipse centered at the origin with semi-major axis [tex]\( \sqrt{9} = 3 \)[/tex] along the [tex]\( y \)[/tex]-axis and semi-minor axis [tex]\( \sqrt{4} = 2 \)[/tex] along the [tex]\( x \)[/tex]-axis.
Each cross-section perpendicular to the [tex]\( x \)[/tex]-axis is an isosceles right triangle with its hypotenuse on the elliptical base. The height [tex]\( h(x) \)[/tex] of each triangle at a given [tex]\( x \)[/tex] is determined by the elliptical equation.
For a fixed [tex]\( x \),[/tex] the corresponding [tex]\( y \)[/tex] values on the ellipse satisfy [tex]\( 4x^2 + 9y^2 = 36 \).[/tex] Solving for [tex]\( y \)[/tex], we get:
[tex]\[ y = \frac{2}{3} \sqrt{36 - 4x^2} \][/tex]
The height of the triangle is [tex]\( \frac{2}{3} \sqrt{36 - 4x^2} \).[/tex]
To find the volume [tex]\( V \)[/tex] of the solid [tex]\( S \),[/tex] integrate the area of each triangular cross-section along the [tex]\( x \)[/tex]-axis from [tex]\( x = -3 \) to \( x = 3 \):[/tex]
[tex]\[ V = \int_{-3}^{3} \text{Area of triangle at } x \, dx \][/tex]
The area of each triangle is [tex]\( \frac{1}{2} \cdot \text{base} \cdot \text{height} = \frac{1}{2} \cdot 2h(x) \cdot h(x) = h(x)^2 \).[/tex]
Thus,
[tex]\[ V = \int_{-3}^{3} h(x)^2 \, dx = \int_{-3}^{3} \left( \frac{2}{3} \sqrt{36 - 4x^2} \right)^2 \, dx \][/tex]
[tex]\[ V = \int_{-3}^{3} \frac{4}{9} (36 - 4x^2) \, dx \][/tex]
[tex]\[ V = \frac{4}{9} \int_{-3}^{3} (36 - 4x^2) \, dx \][/tex]
[tex]\[ V = \frac{4}{9} \left[ 36x - \frac{4x^3}{3} \right]_{-3}^{3} \][/tex]
Solving further,
[tex]\[ V = \frac{4}{9} \left[ \left( 36 \cdot 3 - \frac{4 \cdot 27}{3} \right) - \left( 36 \cdot (-3) - \frac{4 \cdot (-27)}{3} \right) \right] \][/tex]
[tex]\[ V = \frac{4}{9} \left[ (108 - 36) - (-108 + 36) \right] \][/tex]
[tex]\[ V = \frac{4}{9} \left[ 72 \right] \][/tex]
[tex]\[ V = \frac{4 \cdot 72}{9} \][/tex]
[tex]\[ V = 32 \][/tex]
Therefore, the volume [tex]\( V \)[/tex] of the solid [tex]\( S \)[/tex] is 32 cubic units.
A rectangular floor is 21 ft long and 12ft wide. Reuben wants to carpet the floor with carpet tiles sold by the square yard. Use the facts to find the area in square yards.
Conversion facts for length:
1 foot (ft) = 12 inches
1 yard (yd) =3 feet
1 yard (yd) = 36 inches
1 yard = 3 feet:
21 feet / 3 ft = 7 yards
12 feet / 3 feet = 4 yards
7 x 4 = 28 square yards
he will need 28 tiles
The area of the rectangular floor will be 28 square yards.
What is the area of the rectangle?Let L be the length and W be the width of the rectangle.
Then the area of the rectangle will be
Area of the rectangle = L × W square units
A rectangular floor is 21 ft long and 12 ft wide.
We know that 1 foot = 1/3 yards.
Then the dimension of the rectangle in yards will be
L = 21 x 1/3 = 7 yards
W = 12 x 1/3 = 4 yards
Then the area of the rectangle will be
A = 7 x 4
A = 28 square yards
The area of the rectangular floor will be 28 square yards.
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The sum of three consecutive integers is −261−261. Find the three integers.
-261 / 3 =-87
-87 + -86 + -88 = -261
Find x. Round your answer to the nearest tenth of a degree.
Answer: [tex]x=49.6^{\circ}[/tex]
Step-by-step explanation:
In the given figure , we have right triangle with hypotenuse 21 units and the side opposite to angle x is 16 units.
According to the trigonometry,
[tex]\sin \theta = \dfrac{\text{side opposite of }\theta}{\text{Hypotenuse}}[/tex]
So for , the given figure , we have
[tex]\sin x = \dfrac{16}{21}\\\\\Rightarrow\ \sin x\approx0.7619\\\\\Rightarrow\ x=\sin^{-1}(0.7619)=0.8662\text{ radian}[/tex] (using sine calculation)
Convert radian into degrees , we have
[tex]x=0.8662\times\dfrac{180^{\circ}}{\pi}\\\\=0.8662\times\dfrac{180^{\circ}}{3.14159}=49.6319852107\approx49.6^{\circ}[/tex] [Round to the nearest tenth.]
Hence, [tex]x=49.6^{\circ}[/tex]
In the given right triangle, x = 49.6°
Missing angles of right trianglesThe triangle shown is a right triangle
The angle, θ = x
The opposite = 16
The hypotenuse = 21
Using the formula:
[tex]sin \theta = \frac{opposite}{hypotenuse}[/tex]
Substitute opposite = 16, hypotenuse = 21, and θ = x into the formula above to solve for x
[tex]sin x = \frac{16}{21} \\\\sin x = 0.7619\\\\x = sin^{-1}0.7619\\\\x=49.6^0[/tex]
Therefore, in the given right triangle, x = 49.6°
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Find the area of the helicoid (or spiral ramp) with vector equation r(u, v) = ucos(v) i + usin(v) j + v k, 0 ≤ u ≤ 1, 0 ≤ v ≤ 9π.
The area f the helicoid ramp is:
∫∫A) | r(u) *r( v) | dudv
The solution is:
A = 10.35×π square units
r ( u , v ) = u×cosv i + u×sinv j +v k
To get
r (u ) = δ(r ( u , v ) ) / δu = [ cosv , sinv , 0 ]
r ( v ) = δ(r ( u , v ) ) / δv = [ -u×sinv , u×cosv , 1 ]
The vectorial product is:
i j k
r (u ) * r ( v ) cosv sinv 0
-u×sinv u×cosv 1
r (u ) * r ( v ) = i × ( sinv - 0 ) - j × ( cosv - 0 ) + k ( u×cos²v + u× sin²v )
r (u ) * r ( v ) = sinv i - cosv j + u k
Now
| r (u ) * r ( v ) | = √sin²v + cos²v + u² = √ 1 + u²
Then
A = ∫₀ (9π) dv ∫₀¹ √ 1 + u² du
∫₀¹ √ 1 + u² du = 1.15
A = 1.15 × v |( 0 , 9π )
A = 10.35×π square units
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What is the volume of the prism? 192 cubic units 200 cubic units 384 cubic units 400 cubic units
please help! really appreciate it
rugby 7 has 3 out of 5 sold out = 3/5 = 0.6
Junior Athletics has 3 out of 5 sold out = 3/5 = 0.6
Volley ball has 2 out of 5 sold out = 2/5 = 0.4
Volleyball is the answer for the first part
Part 2 = 3/5 x 3/5 =9/25
If a number A is a 2 digit number and its digits are transposed to form number B, then the difference between the larger of the two numbers and the smaller of the two numbers must be divisible by:
The difference is a multiple of 9, so it is always divisible by 9.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example: so
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The difference between the larger of the two numbers and the smaller of the two numbers.
A - B or B - A (whichever is greater)
If we transpose the digits of a two-digit number A to form B, then:
A = 10a + b, where a is the tens digit and b is the one's digit
B = 10b + a, where b is the tens digit and a is the one's digit
The difference between the two numbers.
= A - B
= (10a + b) - (10b + a)
= 9a - 9b
= 9(a - b)
or
B - A
= (10b + a) - (10a + b)
= 9b - 9a
= 9(b - a)
Either way, the difference is a multiple of 9, so it is always divisible by 9.
Therefore,
The difference is a multiple of 9, so it is always divisible by 9.
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7/2x-2=28-4x solve for x
What is 345,876 in short word form?
on a city map 2.5 inches represents 5 miles the library and the bank are 3 inches apart on the map what is the actual distance between the library and the bank
Answer:
6 miles.
Step-by-step explanation:
We have been given that on a city map 2.5 inches represents 5 miles the library and the bank are 3 inches apart on the map. We are asked to find the actual distance between the library and the bank.
[tex]\frac{\text{Actual distance}}{\text{Map distance}}=\frac{\text{5 miles}}{\text{2.5 inches}}[/tex]
[tex]\frac{\text{Actual distance}}{\text{3 inches}}=\frac{\text{5 miles}}{\text{2.5 inches}}[/tex]
[tex]\frac{\text{Actual distance}}{\text{3 inches}}*\text{3 inches}=\frac{\text{5 miles}}{\text{2.5 inches}}*\text{3 inches}[/tex]
[tex]\text{Actual distance}=\frac{\text{5 miles}}{2.5}*3[/tex]
[tex]\text{Actual distance}=\text{2 miles}*3[/tex]
[tex]\text{Actual distance}=\text{6 miles}[/tex]
Therefore, the actual distance between the library and the bank is 6 miles.
If it takes 0.20 dollars to buy a mexican peso and 0.60 dollars to buy a brazilian real, then it takes _____ pesos to buy one brazilian real.
It will takes 3 mexican pesos to buy one brazilian real .
According to the given condition
It takes 0.20 dollars to buy a mexican peso and 0.60 dollars to buy a brazilian real,
We have to determine that it takes how many mexican pesos to buy one brazilian real.
This question can be solved by applying the principles of unitary method
One peso will be bought in $ 0.20
One real will be bought in $ 0.60
1 dollar is equivalent to
[tex]\rm 1 \; dollar = \dfrac{1}{0.2} peso \\\\\rm 1 \; dollar = \dfrac{1}{0.6 } \; real[/tex]
[tex]\rm 1/0.2\; peso = 1/0.6 \; real \\1 \; real = 0.6/0.2 = 3 \; peso[/tex]
So it will take 3 pesos to buy one real
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Which pairs of triangles are similar? Check all that apply.
Answer:
option (2) and (5) are correct.
ΔABC ≅ ΔJLK
ΔDEF ≅ ΔGHI
Step-by-step explanation:
Given four right angled triangle with measure of sides.
We have to check for the pairs of triangle to be similar.
Two triangles are said to be similar if their corresponding angles are equal or their corresponding sides are same ratio.
Consider, ΔABC and ΔJLK.
∠C = ∠L = 90° (given)
Also ratio of corresponding sides are same ratio, that is
[tex]\frac{AC}{LJ}=\frac{14}{7}=\frac{2}{1}[/tex]
Also, [tex]\frac{CB}{KL}=\frac{20}{10}=\frac{2}{1}[/tex]
Thus, ΔABC ≅ ΔJLK.
Option (5) is correct.
Consider, ΔDEF and ΔGHI.
∠I = ∠F = 90° (given)
Also ratio of corresponding sides are same, that is
[tex]\frac{DF}{GI}=\frac{8}{12}=\frac{2}{3}[/tex]
Also, [tex]\frac{EF}{HI}=\frac{10}{15}=\frac{2}{3}[/tex]
Thus, ΔDEF ≅ ΔGHI.
Option (2) is correct.
Thus, option (2) and (5) are correct.
A sealed rectangle or box measuring 8 x 6 x 18 contains 864 Sugar cubes each measuring one by one by one how many sugar cubes are touching the box
The arrangement of the 864 cubes would be 18 6 by 8 layers.
All 48 would be touching the bottom of the box on the bottom layer and all 48 would be touching the top of the box on the top layer.
The cubes along both lengths would be touching the sides of the box for the remaining 16 layers. That would be16 cubes per layer or 256 cubes after counting both sides.
The cubes along the width would be touching the ends of the box for those 16 layers. Those need to be eliminated from the count since the corner cubes were already counted as part of the ones touching the sides. 4 cubes have not been previously counted for each width of 6 cubes. Both ends of the 16 layers has 8 cubes per layer or 128 cubes.
Therefore, that is 256 (sides) + 128 (ends) + 48 (top) + 48 (bottom) and that totals to 480 cubes touching the box.
The CEO of a corporation has $10,000 to give as bonuses. The amount of each employee receives depends on how many employees receive a bonus. This can be modeled as
y = 10000/x
What example is this variation?
The given model of the equation y = 10000/x represents inversely proportional variation.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Arithmetic operations can also be specified by the addition, subtract, divide, and multiply built-in functions.
The model of the equation is given in the question, as follows:
y = 10000/x
A corporation's CEO has $10,000 available for bonuses. The amount each employee earns is determined by the number of employees that receive a bonus.
We can see that the given equation characterizes inversely proportional variation.
Hence, this variation is an example of inversely proportional.
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A pair of dice are rolled. What is the probability of getting a sum greater then 7?
The probability of rolling a sum greater than 7 with a pair of dice is [tex]\( \frac{5}{12} \).[/tex]
To find the probability of getting a sum greater than 7 when rolling a pair of dice, let's first list all the possible outcomes when rolling two dice:
1. (1,1)
2. (1,2)
3. (1,3)
4. (1,4)
5. (1,5)
6. (1,6)
7. (2,1)
8. (2,2)
9. (2,3)
10. (2,4)
11. (2,5)
12. (2,6)
13. (3,1)
14. (3,2)
15. (3,3)
16. (3,4)
17. (3,5)
18. (3,6)
19. (4,1)
20. (4,2)
21. (4,3)
22. (4,4)
23. (4,5)
24. (4,6)
25. (5,1)
26. (5,2)
27. (5,3)
28. (5,4)
29. (5,5)
30. (5,6)
31. (6,1)
32. (6,2)
33. (6,3)
34. (6,4)
35. (6,5)
36. (6,6)
Out of these 36 possible outcomes, the sums greater than 7 are:
12, 17, 18, 22, 23, 24, 27, 28, 29, 30, 32, 33, 34, 35 and 36.
There are 15 favorable outcomes. So, the probability of getting a sum greater than 7 is:
[tex]\[ \frac{15}{36} = \frac{5}{12} \][/tex]
A baseball is hit with an initial upward velocity of 70 feet per second from a height of 4 feet above the ground. The equation h= −16t^2 +70t + 4 models the height in feet t seconds after it is hit. After the ball gets to its maximum height, it comes down and is caught by another player at a height of 6 feet above the ground. About how long after it was hit does it get caught?
By setting the given height (6 feet) in the height equation and using the quadratic formula to solve for time 't', we get two solutions. Since the ball reaches 6 feet twice in its ascension and decension, the latter value of t = 3.79 seconds would be the time it is caught.
Explanation:The question is regarding the time at which a baseball, hit with an initial upward velocity and caught at 6 feet above the ground, is caught. Firstly, input the given height of 6 feet into the height equation h= -16t^2 + 70t + 4 and solve for
t
. Based on the quadratic formula, we receive two solutions: t = 3.79 s and t = 0.54 s. Since the ball has two points at which it reaches the height of 6 feet during its trajectory - once while going up and once while coming down - the time when it is caught would be the larger value,
t = 3.79 s
. Therefore, approximately 3.79 seconds after being hit, the ball is caught.
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How to write two different pairs of decimals whose sums are 14.1. One pair should involve regrouping
which line would best fit the data shown in a scatterplot
g(x) = x2 + 2, find g(3).
Answer:
Plug in 3 for x on the right side
3^2+2,
3 squared equals 9 plus 2 equals 11
Final answer: 11
Step-by-step explanation:
.
Which of the following expressions is equal the expression of 4x - 2(3x - 9)
The following expressions 4x - 2(3x - 9) is equal the expression of
-2x + 18.
What is an expression?An expression is a set of terms combined using the operations +, -, x or ÷.
Given that:
4x - 2 (3x-9)
= 4x - 6x +18
= -2x +18
Hence, the expression 4x - 2 (3x-9) is equal to -2x+18.
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I really, really need help with my Accounting II class! I need 1-4 answered along with the bullet points at the bottom. Thank you in advance if anyone can help, this determines if I graduate!
Your manufacturing company incurs several costs to make the finished product, which are cans of eco-friendly paint. You purchase 100 empty cans at $2.00 each and 200 labels for the cans of paint at $1.00 each. You have two employees who bottle the paint into the cans and one additional employee who places a label on each can. You take a printout from your clock where the employees have entered their time and find that the wages due to these three employees is $2,000.00. You must also pay payroll taxes in the amount of $140.00 total for these three employees. A number of other costs incurred must be taken into consideration as well: depreciation on the factory machine of $150.00, utilities of $200.00, prepaid insurance of $600.00, and property taxes on your building of $2,000.00.
1) Prepare the journal entries to record the purchase of the raw materials, the labor incurred, and the overhead incurred.
2) Assume that $100.00 of the raw materials and $1,000.00 of the indirect materials were used. Prepare the journal entries to assign these materials to the jobs and overhead.
3) Of the $2,140.00 in factory labor, $500.00 was attributed to indirect labor costs. Prepare the journal entry to assign the labor to jobs and overhead.
4) You determine that direct labor cost is the activity base for determining the predetermined overhead rate. The following information is known about the estimated annual costs:
overhead costs: $18,000.00
direct labor costs: $25,000.00
-What is the predetermined overhead rate?
-What is the journal entry to assign overhead to jobs?
-Prepare the journal entry to transfer costs to Finished Goods.
-A sale of the goods takes place. The goods are sold for $5,000.00. Prepare the journal entry to record this sale.
If a quadratic function has two zeros, 112 and 122, then what is its axis of symmetry?
A right triangle has side lengths AC = 7 inches, BC = 24 inches, and AB = 25 inches.
What are the measures of the angles in triangle ABC?
Answer:
90, 74, 16 degrees
Step-by-step explanation:
Given that a right triangle has side lengths AC = 7 inches, BC = 24 inches, and AB = 25 inches.
We find that
AC square + BC square = AC square
[tex]7^2 +24^2 =625 = 25^2[/tex]
So angle C = 90 degrees.
sin A = 24/25
So A = 74 degrees and B = 16 degrees
The total interest paid on a 3-year loan at 9% interest compounded monthly is $1505.82 determine the monthly payment for the loan.
2w+2l=24 what is the value of l
h=7 + 29t-16t^2 find all values of t for which the balls height is 19ft