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3 years ago

9

Mr. Stevenson is ordering shirts and hats for his Boy Scout troop. There are 45 scouts in the troop. Hats come in packs of 3, an

d shirts come in packs of 5. What is the least number of packs of each he should order so that each scout will have 1 hat and 1 shirt, and none will be left over?

1 answer:

luda_lava [24]3 years ago

5 0

9 packs of shirts 15 packs of hats

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URGENT HELP PLEASE!

Vaselesa [24]

Answer:

(a) $x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}$

(b) $x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}$

Step-by-step explanation:

It is given that $0\leq x\leq 2\pi$ .

(a)

$\sqrt{2}\sin 2x=1$

$\sin 2x=\dfrac{1}{\sqrt{2}}$

$\sin 2x=\dfrac{\pi}{4}$

$2x=\dfrac{\pi}{4},\dfrac{3\pi}{4},\dfrac{9\pi}{4},\dfrac{11\pi}{4}$ $[\because \sin x=\sin y\Rightarrow x=n\pi+(-1)^ny]$

$x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}$

(b)

$\csc^2 x-\csc x-2=0$

$\csc^2 x-2\csc x+\csc x-2=0$

$\csc x(\csc x-2)+1(\csc x-2)=0$

$(\csc x+1)(\csc x-2)=0$

$\csc x=-1\text{ or }\csc x=2$

$\sin x=-1\text{ or }\sin x=\dfrac{1}{2}$ $[\because \sin x=\dfrac{1}{\csc x}]$

$x=\dfrac{3\pi}{2}\text{ or }x=\dfrac{\pi}{6},\dfrac{5\pi}{6}$

Therefore, $x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}$ .

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2 years ago

Rewrite the following equation in logarithmic form.

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Answer:

log2(0.25) = -2

512 = 8^3

Step-by-step explanation:

<em>Use of formula: </em><em>loga (b) = c ⇔ b = a^c</em>

Rewrite the following equation in logarithmic form. 0.25 = 2^-2

log2(0.25) = -2

Rewrite the following equation in exponential form. log8 (512) = 3

512 = 8^3

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3 years ago

Multiply by 4,subtract 5, find the input when the output is 29

Alborosie

Answer:

17/2

Step-by-step explanation:

4x-5=29

4x=34

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lys-0071 [83]

Answer: $-\frac{8}{77}$

Step-by-step explanation:

$\frac{\frac{4}{7} }{-\frac{11}{2} }$

Multiply by the reciprocal in order to get rid of the fraction in the denominator.

$\frac{\frac{4}{7} }{-\frac{11}{2} }*-\frac{2}{11}$

$\frac{4}{7}*-\frac{2}{11}$

$-\frac{8}{77}$

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It is the same as Cylinder A.

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