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3 years ago

Which expression has the greatest value? 3/4÷1/3 1 7/8÷1 1/2 3/4÷1 1/2 1 7/8÷1/3

Mathematics

1 answer:

sergiy2304 [10]3 years ago

3 0

Answer:

1 7/8÷1/3

Step-by-step explanation:

3/4÷1/3 = 3/4×3 = 9/4 = 2.25

1 7/8÷1/2 = 15/8×2 = 15/4 = 3.75

3/4÷1 1/2 = 3/4÷3/2 = 3/4×2/3 = 1/2 = .5

1 7/8÷1/3 = 15/8×3 = 45/8 = 5.625 (largest)

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Answer:

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3 years ago

5/100 as a decimal in Dollar form

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Step-by-step explanation:

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Find the angles between -pi and pi that satisfy:<br><br> (−√3) sin(v)+cos(v)=√3

MAXImum [283]

Observe that

$\sin\left(\dfrac\pi6-v\right)=\sin\dfrac\pi6\cos v-\cos\dfrac\pi6\sin v=\dfrac12\cos v-\dfrac{\sqrt3}2\sin v$

In the original equation, divide both sides by $\dfrac12$ :

$-\sqrt3\sin v+\cos v=\sqrt3\implies\dfrac12\cos v-\dfrac{\sqrt3}2\sin v=\dfrac{\sqrt3}2$

$\implies\sin\left(\dfrac\pi6-v\right)=\dfrac{\sqrt3}2$

Next,

$\sin x=\dfrac{\sqrt3}2\implies x=\dfrac\pi3+2n\pi,x=\dfrac{2\pi}3+2n\pi$

where $n$ is any integer. Then

$\sin\left(\dfrac\pi6-v\right)\implies v=-\dfrac\pi6-2n\pi,v=-\dfrac\pi2-2n\pi$

Fix $n=0$ to ensure $-\pi$ , so that

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4 years ago

Solve the following system of equations for a and for b:

viktelen [127]

Answer:

$a=3\\b=1$

Step-by-step explanation:

$9a+3b=30\\8a+4b=28$

Let's solve the second equation for a to later on replace it in the first equation.

$8a+4b=28\\8a=28-4b\\a=\frac{28-4b}{8}$

Now plug this into the first equation.

$9a+3b=30\\9(\frac{28-4b}{8})+3b=30$

Distribute the 9

$(\frac{252-36b}{8}) +3b=30$

Break down the fraction.

$\frac{252}{8}-\frac{36b}{8}+3b=30$

Simplify.

$\frac{63}{2}-\frac{9}{2}b+3b=30$

Subtract $\frac{63}{2}$

$-\frac{9}{2}b+3b=30-\frac{63}{2}$

Combine like terms.

$\frac{-9+2*3}{2}b=\frac{30*2-63}{2}$

$\frac{-9+6}{2}b=\frac{60-63}{2}$

$\frac{-3}{2}b=\frac{-3}{2}$

Muliply by the reciprocal or inverted fraction next to b.

$(-\frac{2}{3})(-\frac{3}{2}) b=-\frac{3}{2}(-\frac{2}{3})$

$b=1$

Now plug this value into any of the equations to find the value of a.

$8a+4b=28\\8a+4(1)=28\\8a+4=28\\8a=28-4\\8a=24\\a=\frac{24}{8}\\ a=3$

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4 years ago