Answer: Radius = 8.575 cm Step-by-step explanation: Formula for volume of a pyramid is; V_p = ½Ah Where A is area of base and h is height Also, formula for volume of cone is given as; V_c = ⅓πr²h Now, we are told that V_p = V_c and that h is the same for both shapes. Thus ; ½Ah = ⅓πr²h h will cancel out to give; ½A = ⅓πr² Cross multiply to give; 3A/2π = r² Base area of pyramid is given as 154 cm². Thus; (3 × 154)/2π = r² r = √((3 × 154)/2π r = 8.575 cm
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Answer:
1. (10, -⁸/₃)
2. (2, ⁸/₃)
3. (12, -4)
Step-by-step explanation:
I will do the first 3 as examples.
1. Y is ⅔ of the distance from X to Z.
Y − X = ⅔ (Z − X)
The x-coordinate of Y is:
x − -6 = ⅔ (18 − -6)
x + 6 = ⅔ (24)
x + 6 = 16
x = 10
The y-coordinate of Y is:
y − 8 = ⅔ (-8 − 8)
y − 8 = ⅔ (-16)
y − 8 = -³²/₃
y = -⁸/₃
Y is at (10, -⁸/₃).
2. The ratio of XY to YZ is 1:2.
(Y − X) / (Z − Y) = 1 / 2
Cross multiply.
2 (Y − X) = Z − Y
The x-coordinate of Y is:
2 (x − -6) = 18 − x
2x + 12 = 18 − x
3x = 6
x = 2
The y-coordinate of Y is:
2 (y − 8) = -8 − y
2y − 16 = -8 − y
3y = 8
y = ⁸/₃
Y is at (2, ⁸/₃).
3. Y is ¼ of the distance from Z to X.
Y − Z = ¼ (X − Z)
The x-coordinate of Y is:
x − 18 = ¼ (-6 − 18)
x − 18 = ¼ (-24)
x − 18 = -6
x = 12
The y-coordinate of Y is:
y − -8 = ¼ (8 − -8)
y + 8 = ¼ (16)
y + 8 = 4
y = -4
Y is at (12, -4).
Answer:
Step-by-step explanation:
To find the equation, use the slope-intercept formula:
m is the slope and b is the y-intercept. Now, it'll really help to draw a line through the points, connecting them. If you look at point (0,2), we can see that this is the y-intercept (where a point sits on the y-axis when x=0). You can insert this into the equation by taking the y value:
Now, take any two points to find the slope. To make it easier, I'll use (1,5) and (0,2). Use the slope formula for when you know two points:
Rise over run is the change in the y-axis over the change in the x-axis. Insert values:
Solve:
Since both are negative, the result is a positive:
Insert this into the equation as m, the slope:
Done.
You would have open circles at 3 and 6.
x < 3 so the line will go from 3 to the left.
x > 6 so the line will go from 6 to the right.
<span>A solid that has faces which consist of two squares and four congruent rectangles is called a rectangular prism. It </span><span>has six faces that are rectangles. It has the same cross-section along a length, which makes it a </span>prism<span>. It is also a "cuboid". Hope this answers the question.</span>