Answer:
Gymnasts always perform on padded mats because
- The padded floor increase the time. The time changes because the padded floor extends the time of the collision. The force is reduced by this time change.
Step-by-step explanation:
- The Impulse Momentum Theorem states that the change in momentum of an object is equal to the impulse applied on it.
J = Δ P ---- (1)
Where J is impulse and Δ P is change in momentum
We also know that impulse is the net force applied on a object which is represented by the following equation:
J = F ΔT
Putting this equation in equation (1), we get:
F ΔT = Δ P
So, this shows when the time is increases then the impulse decreases due to which the gymnasts always perform on padded mats.
To get the solution, we are looking for, we need to point out what we know.
1. We assume, that the number 54 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 54 is 100%, so we can write it down as 54=100%.
4. We know, that x is 2.9% of the output value, so we can write it down as x=2.9%.
5. Now we have two simple equations:
1) 54=100%
2) x=2.9%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
54/x=100%/2.9%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for what is 2.9% of 54
54/x=100/2.9
(54/x)*x=(100/2.9)*x - we multiply both sides of the equation by x
54=34.48275862069*x - we divide both sides of the equation by (34.48275862069) to get x
54/34.48275862069=x
1.566=x
x=1.566
now we have:
2.9% of 54=1.566
The size ot the "larger square" is 5cm
Answer:
a) 301.6 cm³
b) 188.5 cm²
Step-by-step explanation:
The volume and lateral surface area of the cone can be found using the given dimensions with the given formulas. All that is needed is to substitute the appropriate values and do the arithmetic.
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<h3>a) volume</h3>
The volume is given by the formula ...
V = 1/3πr²h
The dimensions are given on the diagram: r = 6 cm, h = 8 cm. Using these values in the formula, we find the volume to be ...
V = 1/3π(6 cm)²(8 cm) = 96π cm³ ≈ 301.6 cm³
The volume of the cone is about 301.6 cm³.
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<h3>b) area</h3>
The lateral area of the cone is given by the formula ...
A = πrl
The dimensions are given on the diagram: r = 6 cm, l = 10 cm (the slant height). Using these values in the formula, we find the area to be ...
A = π(6 cm)(10 cm) = 60π cm² ≈ 188.5 cm²
The area of the curved surface is about 188.5 cm².
Answer: 14.6
<u>Step-by-step explanation:</u>
Draw a right triangle such that the building is perpendicular to the ground (which is where the shadow is cast).
Use Pythagorean Theorem to find the length of the shadow (x):
x² + 34² = 37²
x² = 37² - 34²
x² = 213
√x² = √213
x = 14.59