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3 years ago

Write the equation of a line that is parallel to 3x+2y=10 and passes through the point (4,-5). Answer in slope-intercept form.

Mathematics

1 answer:

SCORPION-xisa [38]3 years ago

4 0

The equation of line is:

$y = \frac{-3}{2}x+1$

Further explanation:

The standard form of equation in point-slope form is:

$y = mx+b$

Given equation is:

3x+2y=10

We have to convert it into point slope form, for which we have to isolate y on one side of equation

$3x+2y = 10\\2y = -3x +10\\y = \frac{-3}{2}x + \frac{10}{2}\\y = \frac{-3}{2}x + 5$

Comparing with standard form:

m = -3/2

As the new line is parallel to given line, their slopes will be equal

So,

$y = \frac{-3}{2}x+b$

To find the value of b, putting the given point (4,-5) in equation

$-5 = \frac{-3}{2}(4)+b\\-5 = -6+b\\b = -5+6 \\b = 1\\So\ the\ equation\ is:\\y = \frac{-3}{2}x+1$

Keywords: Point-slope form, equation of line

Learn more about point-slope form of equation at:

#LearnwithBrainly

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3 years ago

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Answer:

a) $P[C]=p^n$

b) $P[M]=p^{8n}(9-8p^n)$

c) n=62

d) n=138

Step-by-step explanation:

Note: "Each chip contains n transistors"

a) A chip needs all n transistor working to function correctly. If p is the probability that a transistor is working ok, then:

$P[C]=p^n$

b) The memory module works with when even one of the chips is defective. It means it works either if 8 chips or 9 chips are ok. The probability of the chips failing is independent of each other.

We can calculate this as a binomial distribution problem, with n=9 and k≥8:

$P[M]=P[C_9]+P[C_8]\\\\P[M]=\binom{9}{9}P[C]^9(1-P[C])^0+\binom{9}{8}P[C]^8(1-P[C])^1\\\\P[M]=P[C]^9+9P[C]^8(1-P[C])\\\\P[M]=p^{9n}+9p^{8n}(1-p^n)\\\\P[M]=p^{8n}(p^{n}+9(1-p^n))\\\\P[M]=p^{8n}(9-8p^n)$

$P[M]=(0.999)^{8n}(9-8(0.999)^n)=0.9$

This equation was solved graphically and the result is that the maximum number of chips to have a reliability of the memory module equal or bigger than 0.9 is 62 transistors per chip. See picture attached.

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3 years ago

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3 years ago

A helicopter is flying above a town. the local high school is directly to the east of the helicopter at a 20° angle of depressio

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Explanation:

When you draw the situation you find two triangles.

1) Triangle to the east of the helicopter

a) elevation angle from the high school to the helicopter = depression angle from the helicopter to the high school = 20°

b) hypotensue = distance between the high school and the helicopter

c) opposite-leg to angle 20° = heigth of the helicopter

d) adyacent leg to the angle 20° = horizontal distance between the high school and the helicopter = x

2) triangle to the west of the helicopter

a) elevation angle from elementary school to the helicopter = depression angle from helicopter to the elementary school = 62°

b) distance between the helicopter and the elementary school = hypotenuse

c) opposite-leg to angle 62° = height of the helicopter

d) adyacent-leg to angle 62° = horizontal distance between the elementary school and the helicopter = 5 - x

3) tangent ratios

a) triangle with the helicpoter and the high school

tan 20° = Height / x ⇒ height = x tan 20°

b) triangle with the helicopter and the elementary school

tan 62° = Height / (5 - x) ⇒ height = (5 - x) tan 62°

c) equal the height from both triangles:

x tan 20° = (5 - x) tan 62°

x tan 20° = 5 tan 62° - x tan 62°

x tan 20° + x tan 62° = 5 tan 62°

x (tan 20° + tan 62°) = 5 tan 62°

⇒ x = 5 tant 62° / ( tan 20° + tan 62°)

⇒ x = 4,19 miles

=> height = x tan 20° = 4,19 tan 20° = 1,525 miles

4) Calculate the hypotenuse of this triangle:

hipotenuese ² = x² + height ² = (4.19)² + (1.525)² = 19.88 miles²

hipotenuse = 4.46 miles

Rounded to the nearest tenth = 4.5 miles

That is the distance between the helicopter and the high school.

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