A bag of rice weighs 3.18 pounds. Find its mass in kilograms.

Find the area of the circle with the given radius or diameter. Use = 3.14. r = 2 A =? 6.28 sq. units

Marizza181 [45]

I believe it is 12.56 sq. Units

7 0

3 years ago

The sequence$$1,2,1,2,2,1,2,2,2,1,2,2,2,2,1,2,2,2,2,2,1,2,\dots$$consists of $1$'s separated by blocks of $2$'s with $n$ $2$'s i

kicyunya [14]

Consider the lengths of consecutive 1-2 blocks.

block 1 - 1, 2 - length 2

block 2 - 1, 2, 2 - length 3

block 3 - 1, 2, 2, 2 - length 4

block 4 - 1, 2, 2, 2, 2 - length 5

and so on.

Recall the formula for the sum of consecutive positive integers,

$\displaystyle \sum_{i=1}^j i = 1 + 2 + 3 + \cdots + j = \frac{j(j+1)}2 \implies \sum_{i=2}^j = \frac{j(j+1) - 2}2$

Now,

$1234 = \dfrac{j(j+1)-2}2 \implies 2470 = j(j+1) \implies j\approx49.2016$

which means that the 1234th term in the sequence occurs somewhere about 1/5 of the way through the 49th 1-2 block.

In the first 48 blocks, the sequence contains 48 copies of 1 and 1 + 2 + 3 + ... + 47 copies of 2, hence they make up a total of

$\displaystyle \sum_{i=1}^48 1 + \sum_{i=1}^{48} i = 48+\frac{48(48+1)}2 = 1224$

numbers, and their sum is

$\displaystyle \sum_{i=1}^{48} 1 + \sum_{i=1}^{48} 2i = 48 + 48(48+1) = 48\times50 = 2400$

This leaves us with the contribution of the first 10 terms in the 49th block, which consist of one 1 and nine 2s with a sum of $1+9\times2=19$ .

So, the sum of the first 1234 terms in the sequence is 2419.

8 0

2 years ago

PLEASE HELP! INVERSE QUESTION!

Katena32 [7]

Last one.

Hope this helps.

3 0

3 years ago

Find the values of the sine, cosine, and tangent for ZA.<br><br> (TOP OF TRIANGLE IS (A))

Sloan [31]

$\bigstar\:{\underline{\sf{In\:right\:angled\:triangle\:ABC\::}}}\\\\$

AC = 7 m
BC = 4 m

⠀⠀⠀

$\bf{\dag}\:{\underline{\frak{By\:using\:Pythagoras\: Theorem,}}}\\\\$

$\star\:{\underline{\boxed{\frak{\purple{(Hypotenus)^2 = (Perpendicular)^2 + (Base)^2}}}}}\\\\\\ :\implies\sf (AB)^2 = (AC)^2 + (BC)^2\\\\\\ :\implies\sf (AB)^2 = (AB)^2 = (7)^2 = (4)^2\\\\\\ :\implies\sf (AB)^2 = 49 + 16\\\\\\ :\implies\sf (AB)^2 = 65\\\\\\ :\implies{\underline{\boxed{\pmb{\frak{AB = \sqrt{65}}}}}}\:\bigstar\\\\$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

☆ Now Let's find value of sin A, cos A and tan A,

⠀⠀⠀

sin A = Perpendicular/Hypotenus = $\sf \dfrac{4}{\sqrt{65}} \times \dfrac{\sqrt{65}}{\sqrt{65}} = \pink{\dfrac{4 \sqrt{65}}{65}}$

⠀⠀⠀

cos A = Base/Hypotenus = $\sf \dfrac{7}{\sqrt{65}} \times \dfrac{\sqrt{65}}{\sqrt{65}} = \pink{\dfrac{7 \sqrt{65}}{65}}$

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tan A = Perpendicular/Base = ${\sf{\pink{\dfrac{4}{7}}}}$

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$\therefore\:{\underline{\sf{Hence,\: {\pmb{Option\:A)}}\:{\sf{is\:correct}}.}}}$

4 0

3 years ago

Please Hurry!!

r-ruslan [8.4K]

The answer is B. y = -1/5x +1/2.

EXPLANATION

First solve for the slope:
$m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{0 - \frac{3}{5} }{ \frac{1}{2} - \frac{1}{5} } \\ m = - \frac{1}{5}$
After finding the slope, look for the linear equation with the same value of m (parallel equation).

4 0

3 years ago