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Wize High School Grade 12 Pre-Calculus Textbook > Radical Functions

Applications of Radical Functions

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Example: Applications of Radical Functions

A rectangular field has a perimeter of 24 meters with a length of 4 meters and a width of x+2\sqrt{x+2} meters. Find the area of the rectangle.


The perimeter of a rectangle is:
P=2w+2lP=2w+2l
where w = width and l = length ad l,w≥0l,w\geq0. Thus,
P=2w+2l24=2(x+2)+2(4)16=2x+28=x+282=x+264−2=x∴  x=62\begin{array}{rcl} P&=&2w+2l\\\\ 24&=&2(\sqrt{x+2})+2(4)\\\\ 16&=&2\sqrt{x+2}\\\\ 8&=&\sqrt{x+2}\\\\ 8^2&=&x+2\\\\ 64-2&=&x\\\\ \therefore~~x&=&62 \end{array}

Verify:
24=2(62+2)+2(4)16=262+28=62+28=8✓\begin{array}{rclc} 24&=&2(\sqrt{62+2})+2(4)\\\\ 16&=&2\sqrt{62+2}\\\\ 8&=&\sqrt{62+2}\\\\ 8&=&8&\checkmark \end{array}

So, the width is x+2=62+2=8\sqrt{x+2}=\sqrt{62+2}=8.

Therefore, the area of the rectangular field is:
A=8⋅4=32m2A=8\cdot4=32m^2

Practice: Applications of Radical Functions

Solve for VV
r=3V34πr=\sqrt{\frac{3V^3}{4\pi}}

Practice: Applications of Radical Functions

A garden is in the shape of an isosceles right triangle. The hypotenuse is 10ft. long. The cost of fencing is $1.25/ft. How much will it cost to fence in the garden?
Extra Practice
Let (a,b)(a,b) be on the graph y=−2−4x+2−1y=-2\sqrt{-4x+2}-1.
What point must be on:
Applications of Radical Functions
Practice: Applications of Radical Functions
A 3-foot ladder is leaning against a wall creating a 45∘45^{\circ} with the ground. How far away is the foot of the ladder from the foot of the wall?
Applications of Radical Functions
Practice: Applications of Radical Functions
Sally leaves her house to go for a jog. She leaves point A and runs 8km to point B. She takes a 2-minute water break and then continues along to point C. She takes another 2-minute water break at point C and then runs home to point A.
If the distance from BC=AC\text{BC}=\text{AC} and she runs at an average of 11km/hr11\text{km/hr}, how long did Sally go for a run?
Applications of Radical Functions
Practice: Applications of Radical Functions
A small sandpit is in the shape of an isosceles right triangle. The hypotenuse is 25 inches. long. The cost of the materials for the sandpit is $2.46/in. How much will it cost to make that sandpit?
Applications of Radical Functions
Practice: Applications of Radical Functions
Solve for AA
B=35a7−623+4B=^3\sqrt{\dfrac{5a^7-6}{23}}+4
Applications of Radical Functions
Practice: Applications of Radical Functions
Solve for y.y.
x=25−25y236πx=\sqrt{\dfrac{25-25y^2}{36\pi}}
Applications of Radical Functions
Practice: Applications of Radical Functions
Solve for bb.
a=4−10b36πa=\sqrt{\frac{4-10b^3}{6\pi}}