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3 years ago

Choose one of the factors of x3 + 343

Mathematics

1 answer:

amm18123 years ago

3 0

If we observe closely the given, we can note that the terms given are perfect cubes. That is,

x^3 is cube of x and

343 is cube of 7

Hence, the expression is the sum of two cubes. For the sum of cubes, we follow the following rule for the factoring:

a^3 + b^3 = (a + b)(a^2 – ab + b^2)

Applying the rule to the given, the factors would be:

X^3 + 373 = (x + 7)(x^2 – 7x + 49)

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A rectangle is shown below.

Dahasolnce [82]

Answer:

a) 247.25 cm²

b) 62.0 cm

Step-by-step explanation:

All of these upper-bound/lower-bound problems are worked the same way. The bounds on the measurement are presumed to be half of one unit of the least-significant digit.

Here, the least significant digit of both numbers is in the "units" place, so the maximum error is presumed to be 1/2 unit, or ±0.5 cm.

If the measurement were 7.36 inches, the least significant digit is in the hundredths place, so the maximum error is presumed to be half a hundredth, or ±0.5 × 0.01 inches = ±0.005 inches.

To find the bounds on the measurement, you add or subtract this maximum error from the measurement. So, for the measurements in this problem, the maximum and minimum they can be are ...

21 cm: minimum of 21 - 0.5 = 20.5 cm; maximum of 21 + 0.5 = 21.5 cm

11 cm: minimum of 10.5 cm; maximum of 11.5 cm

If you wanted to express these as an inequality, you'd have to remember that half-units are rounded up, so the inequalities would be ...

20.5 cm ≤ long side < 21.5 cm

10.5 cm ≤ short side < 11.5 cm

a) The area is computed as the product of the rectangle's side length measurements. The area will be a maximum when both measurements are a maximum:

Amax = (21.5 cm)(11.5 cm)

Amax = 247.25 cm²

b) The perimeter is twice the sum of the lengths of two adjacent sides of the rectangle. The minimum perimeter will be the sum using the minimum side lengths, or ...

Pmin = 2(20.5 cm +10.5 cm) = 2(31.0 cm)

Pmin = 62.0 cm

_____

Comment on measurement bounds

You have to remember that these concepts are mathematical in nature, so only an approximation of the real world. If you have ever used a tape measure to measure a distance of any length, you will have discovered a couple of things:

different tape measures are different lengths
the measurement you make depends on how tight you stretch the tape (and often, on temperature and/or humidity)
it is amazingly hard to choose the "nearest" measurement when the value is halfway between marks on the tape. (That is, there is some fuzziness in the boundary between nearest units.)

So, mathematically, there will be very specific definitions and procedures to follow regarding measurement values. In the real world, you have to remember these are only an approximation to reality, hopefully a useful one.

7 0

3 years ago

A tangent from point P to a circle of radius 4 cm is 10 cm long. Find: a the distance of P from the centre of the circle <br

d1i1m1o1n [39]

Answer:

see explanation

Step-by-step explanation:

The tangent and the radius at the point of contact form a right angle

Using Pythagoras' identity on the right triangle formed.

Let x be the distance from the centre to P, then

x² = 4² + 10² = 16 + 100 = 116 ( take the square root of both sides )

x = $\sqrt{116}$ ≈ 10.77 cm (to 2 dec. places )

let the required angle be Θ, then

Using the sine or cosine ratio in the right triangle.

cosΘ = $\frac{adjacent}{hypotenuse}$ = $\frac{10}{\sqrt{116} }$

Θ = $cos^{-1}$ ( $\frac{10}{\sqrt{116} }$ ) ≈ 21.8°

7 0

3 years ago

How do I solve for -31 -8r = -3(5r -6)

Dennis_Churaev [7]

Our current equation is:
-8r -31 = -3(5r -6)
To solve for this, we need to get r on one side of the equation and then simplify if needed.
On the right side of the equation, we have a pending Distributive Property, which is when you multiply the number/variable outside of the parenthesis by all numbers/variables in the parenthesis.
Let's simplify this Distributive Property to help understand our equation better.
-3(5r -6)
Multiply -3 by each number/variable separately (unless they are already being multiplied, like 2x, 1/2x, etc).
-3(5r) + -3(-6).
-3(5r) = -15r
-3(-6) = 18 (both negatives need to be in parenthesis to keep a product as negative, and if you do not multiply them in that way, you will end up with a positive product).
Your equation now is:
-8r -31 = -15r + 18
Add 15r to both sides to get r on one side.
7r -31 = 18 is now our current equation.
Add 31 to both sides to get 7r by itself.
7r = 49 is now our equation.
r is still being multiplied by 7, so we need to do the opposite of multiplying by 7.
Divide both sides by 7.
r = 7.
I hope this helps!

8 0

3 years ago

Find the center-radius form of the equation of the circle described. Then graph the circle. Center (0,0), radius 8

Pani-rosa [81]

If the center is (0, 0), then there is no side to side or up or down motion. The center is at the origin. The standard form of a circle is (x-h)^2 + (y-k)^2 = r^2. Your h and your k are both 0's, so just fill in and square the radius:
x^2 + y^2 = 64

7 0

3 years ago

The Jackson High School gymnastics team sells calendars for their annual fundraiser. The function rule below describes the amoun

Virty [35]

A=178
b= 253
c=298
d= I cant make a table Dx

8 0

3 years ago