9514 1404 393
Answer:
13.3 m
Step-by-step explanation:
Let d represent the length of the diagonal. Then the length of the rectangle is (d-2) and the width is (d-6). The area is the product of length and width, so is ...
A = LW
83 = (d -2)(d -6) = d² -8d +12
71 = d² -8d . . . . . . . . subtract 12 to get the constant out of the way
d² -8d +16 = 87 . . . . add (-8/2)² = 16 to both sides to complete the square
(d -4)² = 87 . . . . . . . write as a square
d -4 = √87 . . . . . . . positive square root
d = 4 +√87 ≈ 13.3 . . . . add 4
The diagonal is about 13.3 meters long.
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<em>Additional comment</em>
If you check to see if the side lengths actually correspond to those of a rectangle, you find that they do not. <em>The geometry described here is impossible</em>. The rectangle with the proposed relations between sides and diagonal would have a diagonal of about 12.899 m and an area of about 75.19 m².
Answer:
(A.)A computer randomly generates 6 put of 100 numbers.
Step-by-step explanation:
This is an actual probability.
Given:
Radius of the circle = 4 meters
Measure of arc = 135 degrees
To find:
The area of the sector bounded by the given arc.
Solution:
Formula for area of a sector is:
Where, r is the radius and is the central angle or measure of intercepted arc.
Putting in the above formula, we get
Therefore, the exact area of the given sector is square meters.
Length- centimeter, kilometer, millimeter, meter
mass- gram, kilogram
capacity- liter, milliliter
have a nice day!hope you do well on the rest of your homework!!
Answer:
700 lei
Step-by-step explanation:
You have a geometric sequence for which you know the common ratio and the last term.
There are only three terms, so you can solve the problem in either of two ways.
1. The brute force method
(easiest for only a few terms)
Each term is half the one before it, so each term is double the one after it.
3rd term = 100 lei
2nd term = 200
1st term = 400
Total = 700 lei
Oana spent 700 lei
2. Using formulas (best for longer sequences)
The general formula for your sequence is
aₙ = a₁rⁿ⁻¹
For your sequence,
a₃ = 100; r = 0.5
(a) Calculate a₁
Set the last term equal to the general formula.
a₃ = a₁(0.5)ⁿ⁻¹
100 = a₁(0.5)² = 0.25a₁
a₁ = 100/0.25 = 400
(b) Calculate the sum
The general formula for the sum of a geometric sequence is
Oana spent 700 lei.