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Tatiana [17]
3 years ago
15

A = √7 + √c and b = √63 + √d where c and d are positive integers.

Mathematics
1 answer:
mrs_skeptik [129]3 years ago
3 0

Answer:

\displaystyle a:b=\frac{1}{3}

Step-by-step explanation:

<u>Ratios </u>

We are given the following relations:

a=\sqrt{7}+\sqrt{c}\qquad \qquad[1]

b=\sqrt{63}+\sqrt{d}\qquad \qquad[2]

\displaystyle \frac{c}{d}=\frac{1}{9} \qquad \qquad [3]

From [3]:

9c=d

Replacing into [2]:

b=\sqrt{63}+\sqrt{9c}

We can express 63=9*7:

b=\sqrt{9*7}+\sqrt{9c}

Taking the square root of 9:

b=3\sqrt{7}+3\sqrt{c}

Factoring:

b=3(\sqrt{7}+\sqrt{c})

Find the ration a:b:

\displaystyle a:b=\frac{\sqrt{7}+\sqrt{c}}{3(\sqrt{7}+\sqrt{c})}

Simplifying:

\boxed{a:b=\frac{1}{3}}

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3 0
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7 0
3 years ago
What is the sign of f on the interval -2
TEA [102]

Answer:

f is sometimes positive and sometimes negative.

Step-by-step explanation:

f(x)=(x-3)(x+2)(x+4)(x+4)(x-1)(2x-9)

Take x=-1\in(-2,\frac{9}{2})\ as-2

f(-1)=(-1-3)(-1+2)(-1+4)(-1-1)(-2-9)\\\\=(-4)(1)(3)(-2)(-11)\\\\=-264\\\\f(-1)

Take x=2\in(-2,\frac{9}{2})\ as\ -2

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Hence f(x) for x=-1 and f(x)>0 for x=2

So f is sometimes positive and sometimes negative in the interval.

3 0
3 years ago
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Answer:

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Step-by-step explanation:

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