Step-by-step explanation:
Given that,
The diameter of the merry-go-round, d = 14 feet
Time taken, t = 6 seconds
Radius, r = 7 feet
The linear speed of the merry-go-round is given by :

Also,

Where
 is the angular speed
 is the angular speed
So,

Hence, his linear and angular speeds are 7.33 m/s and 1.04 rad/s.
 
        
             
        
        
        
The problem says that <span>Brandon sights a helicopter above a building that is 200 feet away at an angle of elevation of 30 degrees. So, you can calculate the height asked, by following this procedure:
</span>
 Tan(α)=Opposite leg/Adjacent leg
 α=30°
 Opposite leg=x
 Adjacent leg=200 feet
 When you substitute these values into the formula above (Tan(α)=Opposite leg/Adjacent leg), you have:
 Tan(α)=Opposite leg/Adjacent leg
 Tan(30°)=x/200
 
 You must clear "x":
 x=200xTan(30°)
 Therefore, the value of "x" is:
 x=115 feet
<span>
 How high above the ground the is the helicopter?
 The answer is: 115 feet</span>
        
             
        
        
        
Answer:
The amount that would be in the account after 30 years is $368,353 
Step-by-step explanation:
Here, we want to calculate the amount that will be present in the account after 30 years if the interest is compounded yearly
We proceed to use the formula below;
A = [P(1 + r)^t-1]/r
From the question;
P is the amount deposited yearly which is $4,500
r is the interest rate = 2.5% = 2.5/100 = 0.025
t is the number of years which is 30
Substituting these values into the equation, we have;
A = [4500(1 + 0.025)^30-1]/0.025
A = [4500(1.025)^29]/0.025
A = 368,353.3309607034
To the nearest whole dollars, this is;
$368,353
 
        
             
        
        
        
Answer:
i think it is 120
Step-by-step explanation:
 4 multiplied by 30 is 120
 
        
             
        
        
        
<span>a translation 2 units left and 2 units up</span>