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3 years ago

Prove the divisibility of the following numbers:

Mathematics

1 answer:

fomenos3 years ago

5 0

Answer:

Step-by-step explanation:

prove : 25^9 + 5^7 ≡ 0 ( mod 30) or 5^18 + 5^7 ≡ 0 ( mod 30)

because : 25= 5²

calculate 5^p for 1 ; 2;3 ; 4....

5^1 ≡ 5 ( mod 30)

5^2 ≡ 25 ( mod 30)

5^3 ≡ 5 ( mod 30)

5^4 ≡ 25 ( mod 30)

p = 2k+1 5^p ≡ 5 ( mod 30)

p = 2k 5^p ≡ 25 ( mod 30)

so : 5^18 ≡ 25 ( mod 30) ......(*)

5^7 ≡ 5 ( mod 30)...........(**)

add (*) and (**) :5^18 + 5^7 ≡ 0 ( mod 30) because : 30≡0 (mod30)

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Step-by-step explanation:

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3 years ago

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Answer:

Step-by-step explanation:

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3 years ago

What is -1/3+w=5 3/8 express in simplest form

Elodia [21]

Let's solve your equation step-by-step.
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Step 1: Simplify both sides of the equation.
w+ $\frac{-1}{3}$ = $\frac{43}{8}$ 
Step 2: Add $\frac{1}{3}$ to both sides.
w+ $\frac{-1}{3}$ + $\frac{1}{3}$ = $\frac{43}{8}$ + $\frac{1}{3}$ 
w= $\frac{137}{24}$ 

Answer:w=5 $\frac{17}{24}$

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3 years ago

The cross section of a parabolic reflector has a vertical axis of symmetry with its vertex at (0,0) . The focus of the reflector

Paha777 [63]

Answer:

The depth of the reflector is 0.84 feet

Step-by-step explanation:

(See the figure below)

The equation of a parabola centered at the origin with an axis of symmetry on y-axis is:

$x^{2}=4py$ (1)

With p the distance from the origin to the focus using p=6, the equation (1) of the parabola becomes:

$x^{2}=4(6)y=24y$ (2)

Note that the point B is on the parabola, so this point should satisfy the parabola equation (2) that allow us to use the value x=4.5 to find the y value associated to it, that it is the depth (h) of the reflector:

$(4.5)^{2}=24y$ , solving for y