Remember the rules of Sohcahtoa (Sine, cosine, tangent). For this problem we take the cosine of 38 because the labeled sides are the adjacent leg and the hypotenuse.
Cos(38)=79/x
Cosine of 38 is about 0.7880
0.7880=79/x
Next we multiply both sides by the denominator
(x) 0.7880=79 (x)
Then divide.
<u>0.7880x</u>= <u>79</u>
0.7880 0.7880
X=100.25
Hope this helped :)
Answer:

Step-by-step explanation:
-5/2 × (3x + 4) < 6x - 3x
-15/2x - 10 < 3x
-15x - 20 < 6x
-15x - 6x < 20
-21x < 20
<u>x</u><u> </u><u>></u><u> </u><u>-</u><u>2</u><u>0</u><u>/</u><u>2</u><u>1</u>
Answer:
average speed of hiker is 2.4 mph
Step-by-step explanation:
here is the solution : -
=》

=》

=》

average speed of hiker is 2.4 miles per hour
Answer:
V = πr²h
S=2πrh
h= 2/3 millimeters
new height= 8/3 millimeters
S= 8π millimeters square
New surface area = 32π millimeters square
Step-by-step explanation:
The volume of the cylinder is given by V = πr²h where r is the radius and h is the height.
The surface area of the cylinder is given by S= 2πrh + 2πr²
Where πr² gives the area of the base and 2πr² gives the area of the top and bottom surfaces. The surface area S of a cylinder, not including the top and bottom of the cylinder, is therefore S=2πrh.
V = πr²h
96π= π (6*6) (h+2)
96 = 36 (h+2)
96/36= h+2
h= 96/36-2
h= 96-72/36
h= 24/36
h= 4/6
h= 2/3 millimeters
New height
h + 2= 2/3 + 2
= 2+6/3= 8/3 millimeters
Now S =2πrh
S = 2π(6) (2/3)
S= 8π millimeters square
New Surface area
S = 2π(6) (8/3)
S= 32π millimeters square
Answer:

The doubling time is of 27.65 minutes.
Step-by-step explanation:
Exponential equation of growth:
The exponential equation for population growth is given by:

In which P(0) is the initial value and k is the growth rate.
A freshly inoculated bacterial culture of Streptococcus contains 100 cells.
This means that
. So

When the culture is checked 60 minutes later, it is determined that there are 450 cells present.
This means that
, and we use this to find k. So






So

Doubling time:
This is t for which P(t) = 2P(0) = 200. So






The doubling time is of 27.65 minutes.