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Mathematics

1 answer:

tankabanditka [31]2 years ago

3 0

Ce clasă ești sa văd daca te pot ajuta

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Given $a \equiv 1 \pmod{7}$, $b \equiv 2 \pmod{7}$, and $c \equiv 6 \pmod{7}$, what is the remainder when $a^{81} b^{91} c^{27}$

Blizzard [7]

$\begin{cases}a\equiv1\pmod7\\b\equiv2\pmod7\\c\equiv6\pmod7\end{cases}$

$a^{81}\equiv1^{81}\equiv1\pmod7$

$b^{91}\equiv2^{91}\pmod7$

$2^{91}\equiv(2^3)^{30}\times2^1\equiv8^{30}\times2\pmod7$
$8\equiv1\pmod7$
$2\equiv2\pmod7$
$\implies2^{91}\equiv1^{30}\times2\equiv2\pmod7$

$c^{27}\equiv6^{27}\pmod7$

$6^{27}\equiv(-1)^{27}\equiv-1\equiv6\pmod7$

$\implies a^{81}b^{91}c^{27}\equiv1\times2\times6\equiv12\equiv5\pmod7$

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2 years ago

HELP PLSS I HAVE 10 minutes

omeli [17]

Answer:

h≈1.43

Step-by-step explanation:

Simply ,Square the radius, and then divide the radius squared into the tripled volume. For this example, the radius is 2. The square of 2 is 4, and 300 divided by 4 is 75. Divide the amount calculated in Step 2 by pi, which is an unending math constant that begins 3.14, to calculate the cone's height.

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2 years ago

If (2,3) is reflected over the y axis what is the new coordinates

Andrei [34K]

Answer:

(-2,3)

Step-by-step explanation:

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (its sign is changed). Notice that B is 5 horizontal units to the right of the y-axis, and B' is 5 horizontal units to the left of the y-axis. the y-axis is the point (-x,y).

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2 years ago

½x + 1 ⅔ subtracted from 1 ½x - 1 ⅓<br> simplify IF NEEDED

Volgvan

Answer:

$( \frac{1}{2} x + 1 \frac{2}{3} ) - (1 \frac{1}{2} x - 1 \frac{1}{3} ) \\ = ( \frac{1}{2} - \frac{3}{2} )x + ( \frac{5}{3} + \frac{4}{3} ) \\ = \frac{ - 2}{2} x + \frac{9}{3} \\ = - x + 3 \\ = 3 - x$