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2 years ago

−10x − 5y ≥ 15 x + y ≤ −1 what are the quadrants containing a solution to the above system of linear inequalities.

Mathematics

1 answer:

Paraphin [41]2 years ago

5 0

Let's convert these inequalities to Slope Intercept Form so that we can graph them easily.

−10x − 5y ≥ 15
Add 10x to both sides.
-5y ≥ 10x + 15
Divide both sides by -5 and flip the inequality sign.
y ≤ -2x - 3

x + y ≤ − 1
Subtract x from both sides.
y ≤ -x − 1

When graphed, the solutions lay in Quadrants II, III, and IV. You can see this in the picture I've included.

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If a,b,c and d are positive real numbers such that logab=8/9, logbc=-3/4, logcd=2, find the value of logd(abc)

Eva8 [605]

We can expand the logarithm of a product as a sum of logarithms:

$\log_dabc=\log_da+\log_db+\log_dc$

Then using the change of base formula, we can derive the relationship

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So we end up with

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###

Another way to do this:

$\log_ab=\dfrac89\implies a^{8/9}=b\implies a=b^{9/8}$

$\log_bc=-\dfrac34\implies b^{-3/4}=c\implies b=c^{-4/3}$

$\log_cd=2\implies c^2=d\implies\log_dc^2=1\implies\log_dc=\dfrac12$

Then

$abc=(c^{-4/3})^{9/8}c^{-4/3}c=c^{-11/6}$

So we have

$\log_dabc=\log_dc^{-11/6}=-\dfrac{11}6\log_dc=-\dfrac{11}6\cdot\dfrac12=-\dfrac{11}{12}$

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From the photo above i interpreted the question and drew a triangle to make it easier to solve

Tan is used to solve the question as we were given opposite (as height of the cliff) and to find Adjacent ( the distance between the foot of the cliff to the boat)

Tan θ =Opp/Adj

Tan 22°=15/a

Cross Multiply

aTanθ=15°

Divide both sides by Tan 22

aTan22/Tan22 = 15/Tan 22

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a = 37.13 m

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