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3 years ago

Please help my exam is on this tomorrow

Mathematics

2 answers:

sesenic [268]3 years ago

8 0

Do you see the right triangle in the picture ?

The TANGENT of angle-x is 10m/17.3m. Do the division, find that number, then use your calculator or search online to find the angle that has that number for its tangent.

I get roughly 30 degrees, but you should check me.

Ivan3 years ago

6 0

We know that :

$Tan\theta = \frac{Opposite\;Side}{Adjacent\;Side}$

From the Figure :

$Tanx = \frac{Height\;of\;the\;Tree}{Shadow\;of\;the\;Tree}$

Given : Height of the Tree = 10 m

Length of its Shadow = 17.3 m

⇒ $Tanx = \frac{10}{17.3} = 0.578$

⇒ $x = Tan^-^1(0.578)$

⇒ x° = 30°

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Problem 9

lapo4ka [179]

Answer:

3:36PM

Step-by-step explanation:

Leon starts at 12PM with 12 gallons of gas, and after 2 hours he has used 5 gallons of gas. This means that every 2 hours he uses 5 gallons of gas.

Next we will find at what point Leon will stop to get gas. Since he will stop when the tank is at $\frac{1}{4}$ capacity, we can use the equation:

$\frac{1}{4} * 12 = \boxed{3}$

This shows $\frac{1}{4}$ of his tank's capacity ( $12$ ) is equal to $3$ gallons. This means he will stop for gas when $3$ gallons are remaining.

Now we need to find how many gallons of gas he uses, but as a unit rate. (This will allow us to find what time Leon will stop to get gas.) To find the unit rate, we will need to find how many gallons of gas he uses per hour.

$\frac{\mbox{5 gallons}}{\mbox{2 hours}} = \frac{\mbox{2.5 gallons}}{\mbox{1 hours}}$

This is a simple proportion, and now we know he uses $2.5$ gallons of gas per hour.

Now we can how many hours of gas Leon has left.

He has $7$ gallons of gas left at 2PM, so we can divide to find how many hours left of gas he has.

$\frac{7-3}{2.5} = 1.6$

The $7-3$ is because Leon doesn't stop when his tank is empty, he stops $3$ gallons earlier. We are dividing by $2.5$ because that is how much gas he uses per hour, meaning the result of this division ( $1.6$ ) is how many hours he has left.