In AIJK, i = 1.3 cm, j = 6.8 cm and ZK=45°. Find the length of k, to the nearest 10th
1 answer:
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The answer is ![f^{-1}(x) = \sqrt[3]{ \frac{x-3}{6}}](https://tex.z-dn.net/?f=%20f%5E%7B-1%7D%28x%29%20%3D%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7Bx-3%7D%7B6%7D%7D)
Our function is f(x) = 6x³ + 3. We need to find f⁻¹(x)
Step 1: Substitute y for f(x):
y = 6x³ + 3
Step 2: Switch x and y because every (x, y) has its partner (y, x):
x = 6y³ + 3
Step 3: Solve for y:
![6y^{3} =x-3 \\ y^{3}= \frac{x-3}{6} \\ y = \sqrt[3]{ \frac{x-3}{6}}](https://tex.z-dn.net/?f=6y%5E%7B3%7D%20%3Dx-3%20%5C%5C%20%0Ay%5E%7B3%7D%3D%20%5Cfrac%7Bx-3%7D%7B6%7D%20%5C%5C%20%0Ay%20%3D%20%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7Bx-3%7D%7B6%7D%7D%20%20)
![f^{-1}(x) = \sqrt[3]{ \frac{x-3}{6}}](https://tex.z-dn.net/?f=%20f%5E%7B-1%7D%28x%29%20%3D%20%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7Bx-3%7D%7B6%7D%7D)
Our function is f(x) = 6x³ + 3. We need to find f⁻¹(x)
Step 1: Substitute y for f(x):
y = 6x³ + 3
Step 2: Switch x and y because every (x, y) has its partner (y, x):
x = 6y³ + 3
Step 3: Solve for y:
Complete Question
An open rectangular box with length of 6 feet, width of 4 feet and height of 2.5 feet is to be painted on all exterior sides, including the bottom, with a special waterproof coating. Each gallon of this special coating covers 12 square feet of surface area and costs $36.00. The box is then to be filled with water that weighs approximately 62 pounds per cubic foot.
A. Find the cost of painting this open box.
B. Find the weight of the water in the filled box
Answer:
A
B
Step-by-step explanation:
From the question we are told that
The length is
The width is
The height is
Generally the total surface area of the open, rectangular box is mathematically represented as
=>
=>
From the question we are told that
$36.00 worth of paint covers
So $x worth of paint covers
=>
=>
Generally the volume of the open, rectangular box is mathematically represented as
=>
=>
From the question we are told that
weigh 62 pounds
weigh z pounds
=>
=>