The definition of the tangent function tells you
tan(angle) = (300 ft) / (distance to mountain)
This equation can be rearranged to
(distance to mountain) = (300 ft) / tan(angle)

For the far end of the river,
distance to far end = (300 ft) / tan(24°) ≈ 673.8 ft

For the near end of the river
distance to near end = (300 ft) / tan(40°) ≈ 357.5 ft

Then the width of the river can be calculated by finding the difference of these distances:
width of river = distance to far end - distance to near end
width of river = 673.8 ft - 357.5 ft
width of river = 316.3 ft

The appropriate answer choice is
316 ft.

8 0

3 years ago

What is f(5) if f(1)= 3.2 and f(x+1)=5/2(f(x))

Yanka [14]

F(2) = (5/2)f(1) = 8.0
f(3) = (5/2)f(2) = 20
f(4) = (5/2)f(3) = 50
f(5) = (5/2)*50 = 125

7 0

3 years ago

Read 2 more answers

Six times a number increased by 20 is four less than eight times the number. Find the number

DaniilM [7]

Greetings!

"<span>Six times a number increased by 20 is four less than eight times the number. Find the number."...

This would be, as an equation:
</span> $6x+20=8x-4$

Solve:
Add 4 and -6x to both sides.
$(6x+20)+4+(-6x)=(8x-4)+4+(-6x)$
Simplify.
$24=2x$
Divide both sides by 2.
$(24)/2=(2x)/2$
Simplify.
$12=x$
$x=12$
<span>
x=12

Hope this helps.
-Benjamin

</span>

4 0

3 years ago

Two dice are rolled. Use the complement rule to find that the probability that the sum of the dice is less than 10.

Katarina [22]

Answer:

$\dfrac{5}{6}$

Step-by-step explanation:

When two dice are rolled, the sample space is

$\begin{array}{cccccc}(1,1)&(1,2)&(1,3)&(1,4)&(1,5)&(1,6)\\(2,1)&(2,2)&(2,3)&(2,4)&(2,5)&(2,6)\\(3,1)&(3,2)&(3,3)&(3,4)&(3,5)&(3,6)\\(4,1)&(4,2)&(4,3)&(4,4)&(4,5)&(4,6)\\(5,1)&(5,2)&(5,3)&(5,4)&(5,5)&(5,6)\\(6,1)&(6,2)&(6,3)&(6,4)&(6,5)&(6,6)\end{array}$