The weights of four puppies are shown in pounds. 9.5 ; 9 3 8 ; 9.125 ; 9 3 4 Which list shows these weights in order from greate
2 answers:
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Answer:
The equation of the line is y = x + 2
Step-by-step explanation:
The form of the equation that passes through two points (x1, y1) and (x2, y2) is y = m x + b, where
- m is the slope of the line whose rule is
- b is the y-intercept, you can find it by substituting x, y in the equation by (x1, y1) OR (x2, y2)
Let us solve the question:
∵ The line passes through the points (-3, -2) and (3, 6)
∴ x1 = -3 and x2 = 3
∴ y1 = -2 and y2 = 6
→ Use the rule of m to find it
∵
→ Simplify it by dividing up and down by 2
∴ m =
→ Substitute its value in the form of the equation above
∴ y = x + b
→ To find b substitute x and y by x1 and y1
∴ -2 = (-3) + b
∴ -2 = -4 + b
→ Add 4 to both sides
∴ -2 + 4 = -4 + 4 + b
∴ 2 = b
→ Substitute it in the form of the equation
∴ y = x + 2
∴ The equation of the line is y = x + 2
Answer: third option 268.8
Explanation:
For this kind of proble it is very important that you attach the figure because it contains important information to understand the question.
I have attached the figure for better understanding.
1) The top portion (and the bottom is congruent but rotated 180°) of the hourglass is a figure equivalent to a cylinder on top and a cone on bottom.
So the total volume contained in the top portion is the volume of a cylinder + the volume of a cone.
This is how you calculate the volume of the top portion:
1) The height of the cylinder is 54 mm - 18 mm = 36 mm
2) The formula for the volume of a cylinder is V = π (radius)^2 * height
radius = 8 mm
height = 36 mm
=> V = π(8mm)^2 * 36 mm = 2304π (mm)^3
3) The formula for the volume of a cone is V = (1/3)π(radius)^2 * height
radius = 8 mm
height = 18 mm
V = (1/3)π(8mm)^2 * 18 mm = 384π (mm)^3
4) The total volume of the top portion is volumen of the cylindrical part + voume of the cone:
Total voluem = 2304π (mm)^3 + 384π (mm)^3 = 2688π (mm)^3
5) To find the number of seconds <span>it take until all of the sand has dripped to the bottom of the hourglass you have to divide the total volumen of sand by the rate:
time in seconds = total volume of sand / rate of dripping
time in seconds = [2688 π (mm)^3 ] / [10π (mm)^3 / s] = 268.8 s
That is the answer: 268.8 s
</span>
Explanation:
For this kind of proble it is very important that you attach the figure because it contains important information to understand the question.
I have attached the figure for better understanding.
1) The top portion (and the bottom is congruent but rotated 180°) of the hourglass is a figure equivalent to a cylinder on top and a cone on bottom.
So the total volume contained in the top portion is the volume of a cylinder + the volume of a cone.
This is how you calculate the volume of the top portion:
1) The height of the cylinder is 54 mm - 18 mm = 36 mm
2) The formula for the volume of a cylinder is V = π (radius)^2 * height
radius = 8 mm
height = 36 mm
=> V = π(8mm)^2 * 36 mm = 2304π (mm)^3
3) The formula for the volume of a cone is V = (1/3)π(radius)^2 * height
radius = 8 mm
height = 18 mm
V = (1/3)π(8mm)^2 * 18 mm = 384π (mm)^3
4) The total volume of the top portion is volumen of the cylindrical part + voume of the cone:
Total voluem = 2304π (mm)^3 + 384π (mm)^3 = 2688π (mm)^3
5) To find the number of seconds <span>it take until all of the sand has dripped to the bottom of the hourglass you have to divide the total volumen of sand by the rate:
time in seconds = total volume of sand / rate of dripping
time in seconds = [2688 π (mm)^3 ] / [10π (mm)^3 / s] = 268.8 s
That is the answer: 268.8 s
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