Answer:
The stone would take approximately 10.107 seconds to fall 500 meters.
Step-by-step explanation:
According to the statement of the problem, the following relationship of direct proportionality is built:
Where:
- Time spent by the stone, measured in seconds.
- Height change experimented by the stone, measured in meters.
- Proportionality constant, measured in 
.
First, the proportionality constant is determined by clearing the respective variable and replacing all known variables:
If 
and 
, then:
Then, the expression is 
. Finally, if 
, then the time is:
The stone would take approximately 10.107 seconds to fall 500 meters.
Find the area of the fabric
The fabric is circular, so we find the area using the area of circle formula
a = π × r²
input the numbers
a = π × r²
a = 3.14 × (1.2)²
a = 3.14 × 1.44
a = 4.5216 ft²
Calculate the total cost
Multiply the cost by the area
cost = 5.4 × 4.5216
cost = 24.417
The total cost is approximately $24.42
Answer:
Range: (2, 14)
General Formulas and Concepts:
<u>Algebra I</u>
- Range is the set of y-values that are outputted by function f(x)
Step-by-step explanation:
According to the graph, our line's y-values span from 2 to 14. Since both 2 and 14 are open dot, they are exclusive from the range:
Interval Notation: (2, 14)
Inequality Notation: 2 < y < 14
Answer:
For an inground pool, a patio area ranges between $3 and $40 per square foot. That wide range depends largely on the materials you use to build the space.
Para una piscina enterrada, el área de un patio varía entre $ 3 y $ 40 por pie cuadrado. Esa amplia gama depende en gran medida de los materiales que utilice para construir el espacio.
Step-by-step explanation:
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Answer: Angle x equals 19 degrees
Step-by-step explanation: We have two polygons, one with five sides and the other with eight sides. The question states that the pentagon has exactly one line of symmetry which means the line that runs down from point D to line AB divides the shape into exactly two equal sides. Hence angle A measures the same size as angle B (in the pentagon).
First step is to calculate the angles in the pentagon. The sum of angles in a polygon is given as
(n - 2) x 180 {where n is the number of sides}
= 3 x 180
= 540
This means the total angles in the pentagon can be expressed as
A + B + 84 + 112 + 112 = 540
A + B + 308 = 540
Subtract 308 from both sides of the equation
A + B = 232
Since we have earlier determined that angle A measures the same size as angle B, we simply divide 232 into two equal sides, so 232/2 = 116
Having determined angle A as 116 degrees, we can now compute the value of angle A in the octagon ABFGHIJK. Since the figure is a regular octagon, that means all the angles are of equal measurement. So, the sum of interior angles is given as
(n - 2) x 180 {where n is the number of sides}
= 6 x 180
= 1080
If the total sum of the interior angles equals 1080, then each angle becomes
1080/8
= 135 degrees.
That means angle A in the octagon measures 135, while in the pentagon it measures 116. The size of angle x is simply the difference between both values which is
x = 135 - 116
x = 19 degrees
