Answer:
Anita Bath's home was worth $ 593,195.62 in 2007.
Step-by-step explanation:
Given that from 1992 to 2007 the average home price increased by 8% per year, and in 1992 Anita Bath bought a house for $ 187,000, to determine what was it worth in 2007 the following calculation must be performed:
2007 - 1992 = 15
187000 x 1.08 ^ 15 = X
187000 x 3.172 = X
593,195.62 = X
Therefore, Anita Bath's home was worth $ 593,195.62 in 2007.
Answer:
The shadow is decreasing at the rate of 3.55 inch/min
Step-by-step explanation:
The height of the building = 60ft
The shadow of the building on the level ground is 25ft long
Ѳ is increasing at the rate of 0.24°/min
Using SOHCAHTOA,
Tan Ѳ = opposite/ adjacent
= height of the building / length of the shadow
Tan Ѳ = h/x
X= h/tan Ѳ
Recall that tan Ѳ = sin Ѳ/cos Ѳ
X= h/x (sin Ѳ/cos Ѳ)
Differentiate with respect to t
dx/dt = (-h/sin²Ѳ)dѲ/dt
When x= 25ft
tanѲ = h/x
= 60/25
Ѳ= tan^-1(60/25)
= 67.38°
dѲ/dt= 0.24°/min
Convert the height in ft to inches
1 ft = 12 inches
Therefore, 60ft = 60*12
= 720 inches
Convert degree/min to radian/min
1°= 0.0175radian
Therefore, 0.24° = 0.24 * 0.0175
= 0.0042 radian/min
Recall that
dx/dt = (-h/sin²Ѳ)dѲ/dt
= (-720/sin²(67.38))*0.0042
= (-720/0.8521)*0.0042
-3.55 inch/min
Therefore, the rate at which the length of the shadow of the building decreases is 3.55 inches/min
Answer:
A rhombus is both a rectangle and a rhombus. All the sides are equal and each angle measure 90 degrees. So yes it can be a rhombus.
Step-by-step explanation:
Solving for variables in equations is important for many reasons. Of course, it's important to be able to solve for them so you can pass math tests. But even more so, it's important for real-life applications. There are many uses for solving equations. They can provide answers for mathematicians, accountants, insurance companies- you name it! There are way too many to list! It may not seem important now, but just keep working at it! I personally think solving equations is a ton of fun!
