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Mathematics

2 answers:

FrozenT [24]2 years ago

7 0

Answer: (A)
Explanation: For there to be a solution at any one point, both inequalities must share a common point. This point will then satisfy both inequations, becoming a solution to both inequality.

Let's pick (A).
For there to be at least one solution, the first inequality must have a solution of $x \geq 3$ . Since the left side has clearly no points common to both graphs. Hence, no solution can exist that will satisfy both.

All of the other graphs have at least one point in common.
(B) has $x \leq -1$
(C) has $x = 1$
(D) has $x \leq -2$

riadik2000 [5.3K]2 years ago

4 0

A.the one you chosen <span />

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Answer: OPTION C.

Step-by-step explanation:

<h3> The complete exercise is: "Air pressure may be represented as a function of height (in meters) above the surface of the Earth, as shown below:</h3><h3> $P(h) =P_0e^{-0.00012h}$ </h3><h3> In this function $P_o$ is the air pressure at the surface of the earth, and $h$ is the height above the surface of the Earth, measured in meters. At what height will the air pressure equal 50% of the air pressure at the surface of the Earth"</h3><h3></h3>

Given the following function:

$P(h) =P_0e^{-0.00012h}$

In order to calculate at what height the air pressure will be equal 50% of the air pressure at the surface of the Earth, you can follow these steps:

1. You need to substitute $P(h)=0.5P_o$ into the function:

$0.5P_o=P_0e^{-0.00012h}$

2. Finally, you must solve for $h$ .

Remember the following property of logarithms:

$ln(b)^a=a*ln(b)\\\\ln(e)=1$

Then, you get this result:

$0.5P_o=\frac{P_o}{e^{0.00012h}}\\\\(0.5P_o)(e^{0.00012h})=P_o\\\\e^{0.00012h}=\frac{P_o}{0.5P_o}\\\\ln(e)^{0.00012h}=ln(2)\\\\0.00012h*1=ln(2)\\\\h=\frac{ln(2)}{0.00012}\\\\h=5576.2$