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murzikaleks [220]
3 years ago
8

identify the graph and describe the solution set of this system of inequalities y<-3/2x-10, y>-3/2x-2

Mathematics
1 answer:
givi [52]3 years ago
6 0

Answer:

The system has no solution

Step-by-step explanation:

we have

y < -\frac{3}{2}x-10 ----> inequality A

The solution of the inequality A is the shaded area below the dashed line y=-\frac{3}{2}x-10

The slope of the dashed line is negative

The y-intercept of the dashed line is -10

The x-intercept of the dashed line is -20/3

y > -\frac{3}{2}x-2 ----> inequality B

The solution of the inequality B is the shaded area above the dashed line y=-\frac{3}{2}x-2

The slope of the dashed line is negative

The y-intercept of the dashed line is -2

The x-intercept of the dashed line is -4/3

Using a graphing tool

The dashed lines are parallel

therefore

The system has no solution

see the attached figure

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gavmur [86]

(a) Assuming that Q satisfies the differential equation Q' = -rQ, determine the decay constant r for carbon-14. (b) Find an expression for Q(t) at any time t, if Q(0) = Qo. (c) Suppose that certain remains are discovered in which the current residual amount of carbon-14 is 20% of the original amount. Determine the age of these remains.

Answer:

a) r = (In 2)/(t1/2) = (In 2)/5730 = 0.000121/year

b) Q(t) = Q₀ (e^-rt)

c) Are of the 20% remnant of Carbon-14 = 13301.14 years.

Step-by-step explanation:

Q' = -rQ

Q' = dQ/dt

dQ/dt = -rQ

dQ/Q = -rdt

Integrating the left hand side from Q₀ to Q₀/2 and the right hand side from 0 to t1/2 (half life, t1/2 = 5730 years)

In ((Q₀/2)/Q₀) = -r(t1/2)

In (1/2) = -r(t1/2)

In 2 = r(t1/2)

r = (In 2)/(t1/2) = (In 2)/5730 = 0.000121 /year

b) Q' = -rQ

Q' = dQ/dt

dQ/dt = -rQ

dQ/Q = -rdt

Integrating the left hand side from Q₀ to Q(t) and the right hand side from 0 to t.

In (Q(t)/Q₀) = -rt

Q(t)/Q₀ = e^(-rt)

Q(t) = Q₀ (e^-rt)

c) Q(t) = Q₀ (e^-rt)

Q(t) = 0.2Q₀, t = ? and r = 0.000121/year

0.2Q₀ = Q₀ (e^-rt)

0.2 = e^-rt

In 0.2 = -rt

-1.6094 = - 0.000121 × t

t = 1.6094/0.000121 = 13301.14 years.

Hope this Helps!

5 0
3 years ago
If y varies directly as x,and y is 6 when x is 72,what is the valueof y when x is 8
densk [106]

Answer:

Step-by-step explanation:

y & x

y = kx

When y = 6 , x = 72

6 = 72k

k = 6/72

k = 1/12

:- y = x/12

When x = 8

y = 8/12

y = 2/3

5 0
3 years ago
I REALLY NEED HELP!!!!
NISA [10]

Answer:

1  2/8 inches

Step-by-step explanation:

smallest = 2/8

largest = 1 4/8

difference = 1 2/8

4 0
3 years ago
Please help! This is 6th grade math on surface area.
KatRina [158]

Answer:

<u>144</u>

Step-by-step explanation:

Ok. I love problems like this.

You just have to find the surface are of each part and add it up!

To find the surface area of a rectangle, you multiple the base and the height. To find the surface area of a triangle, you multiple the base and height, and divide by 2 (because its half of a rectangle).

<u>Left rectangle:</u> 3*ll=33

<u>Middle rectangle:</u> 4*ll=44

<u>Right rectangle:</u> 5*ll=55

<u>Top triangle:</u> 3*4=12

                      12/2=6

<u>Bottom triangle:</u> 3*4=12

                           12/2=6

<u>ADD THEM ALL!!!</u> 33+44+55+6+6=<u>144</u>

<u></u>

<u></u>

(Also can I please please please have brainliest? I need it to level up!)

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3 years ago
The temperature is 6 degrees below zero
Butoxors [25]

Answer:

That's must be really cold!

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