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2 years ago

7

Fred works as a gardener. He charges at least $15 to drive to a residence and

1 answer:

Amanda [17]2 years ago

7 0

We are required to find an inequality which best represents the relationship between the number of hours gardening g and the total charge c

The inequality which best represents the relationship between the number of hours gardening g and the total charge c is c ≥ 15 + 12g

At least means greater than or equal to (≥)

fixed charge = $15

charges per hour = $12

Total charge = c

Number of hours = g

The inequality:

<em>Total charge ≥ fixed charge + (charges per hour × Number of hours</em>

c ≥ 15 + (12 × g)

c ≥ 15 + (12g)

c ≥ 15 + 12g

Therefore, the inequality which best represents the relationship between the number of hours gardening g and the total charge c is c ≥ 15 + 12g

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a) $\:\:=\sqrt{14}\cdot \frac{\:\:}{\sqrt{14} }$

b) $\:\:=\sqrt{29} \cdot \frac{\:\:}{\sqrt{29} }$

c) $\:\:=7\cdot \frac{\:\:}{7}$

Step-by-step explanation:

a) Let <u>a</u>=<2,1,-3>

The magnitude of <u>a</u> is $|a|=\sqrt{2^2+1^2+(-3)^2}$

$|a|=\sqrt{4+1+9}=\sqrt{14}$

The unit vector in the direction of a is

$\hat{a}=\frac{\:\:}{\sqrt{14} }$

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$\:\:=\sqrt{14}\cdot \frac{\:\:}{\sqrt{14} }$

b) Let a=2i - 3j + 4k

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$|a|=\sqrt{4+9+16}=\sqrt{29}$

$\hat{a}=\frac{\:\:}{\sqrt{29} }$

Using the relation $a=|a|\hat{a}$ , we have

$\:\:=\sqrt{29} \cdot \frac{\:\:}{\sqrt{29} }$

c) Let us first find the sum of <1, 2, -3> and <2, 4, 1> to get:

<1+2, 2+4, -3+1>=<3, 6, -2>

Let a=<3, 6, -2>

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$|a|=\sqrt{3^2+6^2+(-2)^2}$

$|a|=\sqrt{9+36+4}=\sqrt{49}=7$

The unit vector in the direction of <u>a</u> is

$\hat{a}=\frac{\:\:}{7}$

Using the relation $a=|a|\hat{a}$ , we have

$\:\:=7\cdot \frac{\:\:}{7}$

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