Answer:
21.38
Step-by-step explanation:
Find the diagram attached
In order to get PS, we need to get the length of QS first
According to triangle QRS;
QS =opposite
QR = 39(adjacent)
Using SOH CAH TOA
Tan theta = opp/adj
Tan 28 = QS/39
QS = 39tan28
QS = 39(0.5317)
QS = 20.74
Get PS
sin theta = QS/PS
sin 76 = 20.74/PS
PS = 20.74/sin76
PS = 20.74/0.9703
PS = 21.38
Hence the length of PS is 21.38
Answer:
the width is 10 m
Step-by-step explanation:
if the relationship between area and width is
A = 80*w − w²
for an area A=700 m² , we have
700 m² = 80*w − w²
w² - 80*w + 700 m² = 0
aw² + b*w + c = 0
where a=1 , b=-80 and c=700
this quadratic equation has as solution the following formula
w = [-b ± √ ( b² - 4*a*c) ]/(2*a)
replacing values
w = [80 ± √ ( 80² - 4*1*700) ]/(2*1) = (80 ± 60)/2
then
w₁=(80 - 60)/2 = 10 m
w₂ =(80 + 60)/2 = 70 m
since the area has the form A= length * width = 80*w − w² = (80− w)*w
then the length of the rectangle is
length = 80− w
for w₁=10 m → length = 80− 10 = 70 m
for w₁=70 m → length = 80− 70 = 10 m
by definition the shorter side is the width ( and the longer one , the length) , therefore the only possible option is the first one .
Thus the width is 10 m
The applicable relation between force, mass, and acceleration is ...
... F = <em>m</em>a
Fill in the given values and solve for the mass.
... 0.75 N = <em>m</em>·3 m/s²
... (0.75 kg·m/s)/(3 m/s²) = <em>m</em> = 0.25 kg
The mass of the ball is 0.25 kg.
Answer:
x=47 feet
Step-by-step explanation:
Since angle VTY is congruent to angle VTK, segment TY bisects angle VTK. Since Y is on segment VK, between V and K, we can use the Angle Bisector Theorem, which states that:
Now, X=VY+YK
Substituting the values, we get
X=
X=
Answer:
2.814 * 10^14
Step-by-step explanation:
For exponential growth:
A = A0*e^kt
A = final amount ; A0 = initial amount ; t = time
Since bacterium doubles ever half hour ;
In 1 hour number of bacterium will be 2² = 4
Hence
Final amount after 1 hour
4 = 1*e^k*1
4 =e^k
Take In of both sides
In(4) = k
Number of bacterium in 24 hours
A = 1*e^In4 * 24
A = e^24In4
A = e^33.271064
A = 281474976710656
A = 2.814 * 10^14
