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3 years ago

An airplane cruises 1 kilometer in 1/12 of a minute. what is its cruising speed?

Mathematics

1 answer:

rewona [7]3 years ago

5 0

Answer:

An airplane cruises 1 kilometer in 1/12 of a minute. What is its cruising speed?<u>200</u>

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Can anyone please help me graph this and tell me if the equation is correct thank you

photoshop1234 [79]

Answer:

yes it is

Step-by-step explanation:

5 0

3 years ago

Determine all prime numbers a, b and c for which the expression a ^ 2 + b ^ 2 + c ^ 2 - 1 is a perfect square .

kogti [31]

Answer:

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Step-by-step explanation:

From Algebra we know that a second order polynomial is a perfect square if and only if $(x+y)^{2} = x^{2} + 2\cdot x\cdot y + y^{2}$ . From statement, we must fulfill the following identity:

$a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}$

By Associative and Commutative properties, we can reorganize the expression as follows:

$a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2}$ (1)

Then, we have the following system of equations:

$x = a$ (2)

$(b^{2}-1) = 2\cdot x\cdot y$ (3)

$y = c$ (4)

By (2) and (4) in (3), we have the following expression:

$(b^{2} - 1) = 2\cdot a \cdot c$

$b^{2} = 1 + 2\cdot a \cdot c$

$b = \sqrt{1 + 2\cdot a\cdot c}$

From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, $a, b, c > 1$ . If $a$ , $b$ and $c$ are prime numbers, then $2\cdot a\cdot c$ must be an even composite number, which means that $a$ and $c$ can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.

In addition, $b$ must be a natural number, which means that:

$1 + 2\cdot a\cdot c \ge 4$

$2\cdot a \cdot c \ge 3$

$a\cdot c \ge \frac{3}{2}$

But the lowest possible product made by two prime numbers is $2^{2} = 4$ . Hence, $a\cdot c \ge 4$ .

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Example: $a = 2$ , $c = 2$

$b = \sqrt{1 + 2\cdot (2)\cdot (2)}$

$b = 3$

4 0

3 years ago

Help guysss im in 6th really need help

NNADVOKAT [17]

5 times as many. Since dog B has 2 and dog A has 10, A = 2 * X, since you’re solving for the multiplication comparison. 10/2 = 5, so you’ve got 5 times as many.

3 0

2 years ago

If one liter of paint covers 100 square feet, how many gallons of paint will cover 800 square meters?

mr_godi [17]

It takes 8 liters to cover 800 sqft of floor

there are 3.78541 liters in a gallon so it would take 2.11338 gallons to cover the floor

6 0

3 years ago

At a local fitness center, members pay a $10 membership fee and $5 for each aerobics class. Nonmembers pay $6 for each aerob

sveta [45]

One way to solve it is writing two equations based on the info so

y = 5x + 10 for members
y = 6x for nonmembers

(the + 10 isn't included in the second equation because nonmembers won't pay a membership fee)

and to find their intersection point (where the values will be the same), you just set them equal to each other:

5x + 10 = 6x

subtract 5x

x = 10 classes

7 0

3 years ago