The area of the circle formed when the plane passes through the center of the given sphere is: 15π cm².
<h3>What is the Area of a Circle?</h3>
Area of a circle = πr² (radius of the circle = r).
Given the following:
- Radius of sphere = 8 cm
- Distance of the plane from the center of the sphere = 7 cm
Radius of the circle = √((radius of sphere)² - (distance of the plane from the center of sphere²)) = √(8² - 7²)
Radius of the circle = 3.87 cm
Area of the circle = π(3.87²) ≈ 15π cm².
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Answer:
then 2x = 0 and x - 3 = 0
Step-by-step explanation:
A negative sign under a square root means that the root is a not a real number.
A negative sign outside a square root means we can "cover it" and evaluate the square root.
When the sign is outside, you can do the root first, then apply the sign. Not so if the sign is inside.
Thus, √-49 is not real and -√64 = -8.
Answer:
The possible error made by Beth is directly multiplying scale of 5 to area of original triangle and getting area of enlarged triangle, which is wrong.
Step-by-step explanation:
Originally Triangle has height =3.5cm and width=4cm
Beth enlarged the same triangle by scale of 5 and calculate area of triangle
The area of triangle as given as A= $$\frac{1}{2} \texrm{ (base) (height)}$$
Area of original triangle is A =$$\frac{1}{2}(3.5 \times 4)$$
Since, The triangle is enlarged by scale of 5
New height =3.5x5 = cm and new width=4x5cm
Area of new triangle is
A' = $$\frac{1}{2} (\textrm{new width} ) ( \textrm{new height})$$
A' = $$\frac{1}{2}(3.5 \times 5)(4\times 5)$$
A' = $$\frac{1}{2}(3.5 \times 4)(5^{2})$$
A' = $$A (5^{2})$$
Now, Looking what error beth made is:
Beth found Area of new triangle is A' = $$\frac{1}{2}(3.5)(4)(5)$$
The possible error made by Beth is directly multiplying scale of 5 to area of original triangle and getting area of enlarged triangle, which is wrong.
I think the question for this problem is to formulate an equation that could describe the behavior of the trend. To do this, let's see the trend first. In the first hour, the number of transactions is 10. In the 2nd hour, the transactions is 2(10) = 20. In the third hour, the transactions is 20(2) = 40. So, we can see that the trend is 10, 20, 40, 80, ....and so on. You notice that this is a geometric progression, where r=2. Thus, the equation for this will be:
Number of transactions = 10(r)ⁿ⁻¹ = <em>10(2ⁿ⁻¹), where n is the number of hours</em>
