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Heather and Joel bought a house for $157,200 and know that the house appreciates

Heather and Joel bought a house for $157,200 and know that the house appreciates every year. They keep track of their house value for 5 years and model their data with the exponential equation y = 150000(1.004)12t How much will their house be worth in 8 years?

2 months ago

Solution 1

Guest

Guest #3222

2 months ago

Heather and Joel bought a house for $157,200 and know that the house appreciates every year. They keep track of their house value for 5 years and model their data with the exponential equation y = 150000(1.004)12t How much will their house be worth in 8 years?

Solution:

Equation of the appreciation of the value of house is given by:-

$y=150000(1.004)^{12t}$

We need to find the worth of the house after 8 years

So, that means time, t=8

Let us plug t=8 in the equation $y=150000(1.004)^{12t}$

So, we get,

$y=150000(1.004)^{12*(8)}$

$y=150000(1.004)^{96}$

$y=150000(1.467021)$

y=150000*1.467021

y=220053.20

In 8 years the value appreciates to $220053.20, that s, worth of house after 8 years=$22005320

Solution 2

Guest

Guest #3223

2 months ago

We have to find value of the house in 8 years so we will plug t=8 years in given equation.

$y=150000(1.004)^{\left(12t\right)}$

$y=150000(1.004)^{\left(12*8\right)}$

$y=150000(1.004)^{96}$

$y=150000(1.46702133432)$

$y=220053.200148$

Hence house will worth approx $220053.20 in 8 years.

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A right triangle has one side, s, and a hypotenuse of 12 meters. Find the area of the triangle as a function of s. A) A(s) = 2s 144 - s2 B) A(s) = s 144 - s2 C) A(s) = 2s 12 - s2 D) A(s) = 12s 144 - s2 10) The base of a ladder is placed 5 feet away from a 13 foot tall wall. What is the minimum length ladder needed to reach the top of the wall (rounded to the nearest foot)? A) 12 ft B) 13 ft C) 14 ft D) 15 ft

Solution 1

Part a)
we know that
area of triangle=b*h/2
b=s
applying the Pythagoras theorem
h²=12²-s²--------> h=√(144-s²)
so
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Part b)
applying the Pythagoras theorem
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Question

A right triangle has one side, s, and a hypotenuse of 12 meters. Find the area of the triangle as a function of s. A) A(s) = 2s 144 - s2 B) A(s) = s 144 - s2 C) A(s) = 2s 12 - s2 D) A(s) = 12s 144 - s2 10) The base of a ladder is placed 5 feet away from a 13 foot tall wall. What is the minimum length ladder needed to reach the top of the wall (rounded to the nearest foot)? A) 12 ft B) 13 ft C) 14 ft D) 15 ft

Solution 1

Answer: A(s) = $\frac{s\sqrt{144-s^{2} } }{2}$ ; 10) c) 14ft

Step-by-step explanation: Area of a triangle is: A = $\frac{b.h}{2}$

where:

b is base of a triangle

h is height of a triangle

For this right triangle, it is known one side, s, and hypotenuse, 12. To determine the other side, we use Pythagoras Theorem:

hypotenuse² = side² + side²

$12^{2} = s^{2} + x^{2}$

$x^{2} = 12^{2} - s^{2}$

$x^{2} = 144 - s^{2}$

x = $\sqrt{144 - s^{2} }$

To determine the Area of the right triangle as function of s:

A = $\frac{b.h}{2}$

A = $\frac{1}{2}$ (s.x)

A = $\frac{1}{2}$ . (s. $\sqrt{144 - s^{2} }$ )

Therefore, the area of the right triangle is:

A = $\frac{1}{2}$ . (s. $\sqrt{144 - s^{2} }$ )

The ladder and the wall form a right triangle. The height of it is 13 ft, the base is 5ft and the hypotenuse is the length of the ladder. So, to find the minimum length, use Pythagoras Theorem:

hypotenuse² = side² + side²

h² = 13² + 5²

h² = 169 + 25

h = $\sqrt{194}$

h = 14

The minimum length the ladder has to have to reach the top is 14 ft.

Solution 2

A(s) equals 1/2 s square root of 144 minus s squared.. As s and r are the sides and the area of the triangle are 1/2(s)(r)

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