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Aloiza [94]
3 years ago
9

Who invented crayons

Mathematics
2 answers:
galben [10]3 years ago
8 0
Alice Binney invented them.
charle [14.2K]3 years ago
8 0
Binney and Smith in 1902.
Hope I helped.
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Simplify: cos2x-cos4 all over sin2x + sin 4x
GrogVix [38]

Answer:

\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}=\tan\left(x\right)

Step-by-step explanation:

\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}

Apply formula:

\cos\left(A\right)-\cos\left(B\right)=-2\cdot\sin\left(\frac{A+B}{2}\right)\cdot\sin\left(\frac{A-B}{2}\right) and

\sin\left(A\right)+\sin\left(B\right)=2\cdot\sin\left(\frac{A+B}{2}\right)\cdot\sin\left(\frac{A-B}{2}\right)

We get:

=\frac{-2\cdot\sin\left(\frac{2x+4x}{2}\right)\cdot\sin\left(\frac{2x-4x}{2}\right)}{2\cdot\sin\left(\frac{2x+4x}{2}\right)\cdot\cos\left(\frac{2x-4x}{2}\right)}

=\frac{-\sin\left(\frac{2x-4x}{2}\right)}{\cos\left(\frac{2x-4x}{2}\right)}

=\frac{-\sin\left(\frac{-2x}{2}\right)}{\cos\left(\frac{-2x}{2}\right)}

=\frac{-\sin\left(-x\right)}{\cos\left(-x\right)}

=\frac{-\cdot-\sin\left(x\right)}{\cos\left(x\right)}

=\frac{\sin\left(x\right)}{\cos\left(x\right)}

=\tan\left(x\right)

Hence final answer is

\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}=\tan\left(x\right)

6 0
3 years ago
80+90=8+9 add a 0 to the end of your answer
Len [333]

Answer:

The answer is 170

Step-by-step explanation:

Because 8 + 9 = 17, if we multiply all of these values by ten or add a zero to the end of each number, we should get

80 + 90 = 170

8 0
2 years ago
Out of every 1000 packages received by a merchant, three are damaged. In a day, the merchant received 600 damaged packages. How
lukranit [14]

Answer:

1.8 undamaged packages

Step-by-step explanation:

3/1000 x 600

Multiply

1.8

8 0
3 years ago
HELLPP MEE ! I NEED HELP FAST
Kipish [7]
Your answer is option C. Hope I answered it on time
4 0
3 years ago
Read 2 more answers
What is the approximate distance between the points (-3,-4)(-8,1) on a coordinate grid?
Alex

\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-8-(-3)]^2+[1-(-4)]^2}\implies d=\sqrt{(-8+3)^2+(1+4)^2} \\\\\\ d=\sqrt{25+25}\implies d=\sqrt{50}\implies d\approx 7.071

3 0
3 years ago
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