6. Suppose that y varies inversely with x. Write an equation for the inverse variation,

Mathematics

1 answer:

Nostrana [21]3 years ago

6 0

Answer:

If y varies inversely as x, then we write it as:

y = k/x

where k is some constant.

If we multiply both sides of this equation by x we get an equation for k:

k = x*y

We are given that y=4 when x=7, therefore:

k = 7*4 = 28

Put this back into our original equation to get:

y = 28/x

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Find the volume of the square pyramid showing. round to the nearest 10th if necessary

solong [7]

The volume of a square pyramid is (1/3)(area of base)(height of pyramid).

Here the area of the base is (10 ft)^2 = 100 ft^2.

13 ft is the height of one of the triangular sides, but not the height of the pyramid. To find the latter, draw another triangle whose upper vertex is connected to the middle of one of the four equal sides of the base by a diagonal of length 13 ft. That "middle" is 5 units straight down from the upper vertex. Thus, you have a triangle with known hypotenuse (13 ft) and known opposite side 5 feet (half of 10 ft). What is the height of the pyramid?
To find this, use the Pyth. Thm.: (5 ft)^2 + y^2 = (13 ft)^2. y = 12 ft.

Then the vol. of the pyramid is (1/3)(area of base)(height of pyramid) =
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4 years ago

Prove that if a and b are positive integers whose sum is a prime p, their greatest common divisor is 1.

Tasya [4]

Proof by contadiction.

Let assume there exist such positive integers $a$ and $b$ whose sum is a prime number $p$ , that their greatest common divisor is greater than 1.

$a,b\in\mathbb{Z^+}\\d=\text{gcd}(a,b)>1\\\\a=de\\b=df\\e,f\in\mathbb{Z^+}\\\\a+b=p\\de+df=p\\d(e+f)=p\\$

Since $p$ is a prime number and $d>1$ , then $d=p \wedge e+f=1$ , but we assumed earlier that $e,f\in\mathbb{Z^+}$ , and there are no two positive integers that sum up to 1.