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2 years ago

Write an equation of the line in slope-intercept form: y-intercept of 2, x-intercept of 4

Mathematics

1 answer:

zvonat [6]2 years ago

3 0

Answer:

$\sf y=-\dfrac12x+2$

Step-by-step explanation:

y-intercept is when x = 0, so (0, 2)

x-intercept is when y = 0, so (4, 0)

$\sf slope=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{0-2}{4-0}=-\dfrac12$

Slope-intercept form of linear equation: $\sf y=mx+b$

(where m is the slope and b is the y-intercept)

Given:

$\sf m=-\dfrac12$
b = 2

$\sf \implies y=-\dfrac12x+2$

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2 years ago

PLEASE HELP!

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Answer:

See below

Step-by-step explanation:

Use the formulae directly

For a cone, with base radius = r and height = h, here are the related formula

$\textrm{Slant height l} = \sqrt{r^2 + h^2}$ (1)

$\textrm{Lateral surface area} = \pi r l$

$\textrm {Base area} = \pi r^2$

$\textrm { Total Surface Area SA} = \textrm{Base Area + Lateral Area} = \pi r^2 + \pi rl = \pi r(r + l)$ (2)

$\textrm{Volume V = } (1/3) \pi r^2h$ (3)

Therefore directly plugging in the numbers in the above equations:

Note:

l = slant height in cm
SA = total surface area in sqcm
V = Volume in cubic cm

Figure(a)

r = 4, h = 8

$\textrm{l} = \sqrt{4^2 + 8^2} =\sqrt{80} = 8.944 \\\textrm{SA} = 4\pi(4 + 8.944) = 4\pi(12.944) = 162.66\\\textrm{V} = (1/3)\pi(4^2)(8) = 134.04$

Figure(b)

r = 7, h =15

$\textrm{l} = \sqrt{7^2 + 15^2} =\sqrt{274} = 16.55$

$\textrm{SA} = 7\pi(7 + 16.55) = 517.89$

Figure (c)

r = 5, l = 8

$h = \sqrt{l^2 - r^2} = \sqrt{8^2 - 5^2} = \sqrt{39} = 6.245\\SA = \textrm{SA} = 5\pi(5 + 8) = 204.2\\V = (1/3)\pi(5^2)(6.245) = 163.5$

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