Write 0.326 in two other ways.
2 answers:
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Answer:
Step-by-step explanation:
GIVEN: A box with no top is to be constructed from a piece of cardboard whose length measures more than its width. The box is to be formed by cutting squares that measure
on each side from the four corners and then folding up the sides.
TO FIND: If the volume of the box will be , what are the dimensions of the piece of cardboard.
SOLUTION:
Let the width of cardboard be
length of cardboard
As box is formed by cutting squares from corners of cardboard
length of cardboard
width of cardboard
height of cardboard
volume of cardboard
solving we get
width of cardboard
length of cardboard
height of cardboard
Answer:
f(x) = 2x³ - 5x² + 7x - 7
Step-by-step explanation:
In the division statement: m ÷ n = q +
- m is the dividend
- n is the divisor
- q is the quotient
- r is the remainder
- m = q × n + r
Let us use the fact above to solve the question
∵ f(x) is divided by (2x - 3), the quotient is x² - x + 2 and the remainder is -1
∴ f(x) is the dividend ⇒ m
∴ (2x - 3) is the divisor ⇒ n
∴ (x² - x + 2) is the quotient ⇒ q
∴ -1 is the remainder ⇒ r
→ Use the rule above to find f(x)
∵ f(x) = (x² - x + 2) × (2x - 3) + -1
∴ f(x) = (x² - x + 2)(2x - 3) - 1
→ Multiply the 2 brackets at first
∵ (x² - x + 2)(2x - 3) = x²(2x) + x²(-3) + -x(2x) + -x(-3) + 2(2x) + 2(-3)
∴ (x² - x + 2)(2x - 3) = 2x³ - 3x² - 2x² + 3x + 4x - 6
→ Add the like terms
∴ (x² - x + 2)(2x - 3) = 2x³ + (-3x² - 2x²) + (3x + 4x) - 6
∴ (x² - x + 2)(2x - 3) = 2x³ + (-5x²) + 7x - 6
∴ (x² - x + 2)(2x - 3) = 2x³ - 5x² + 7x - 6
→ Substitute it in f(x)
∴ f(x) = 2x³ - 5x² + 7x - 6 - 1
→ Add the like term
∵ f(x) = 2x³ - 5x² + 7x + (- 6 - 1)
∴ f(x) = 2x³ - 5x² + 7x + (-7)
∴ f(x) = 2x³ - 5x² + 7x - 7