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4 years ago

Choose the correct simplification of the expression a^2*a^3

Mathematics

1 answer:

rusak2 [61]4 years ago

6 0

$a^2\cdot a^3=a^{2+3}=a^5$

Why?

$a^2=a\cdot a\\\\a^3=a\cdot a\cdot a\\\\a^2\cdot a^3=\underbrace{(a\cdot a)}_{2}\cdot\underbrace{(a\cdot a\cdot a)}_{3}=\underbrace{a\cdot a\cdot a\cdot a\cdot a}_{2+3=5}$

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Answer:

The Point in the first quadrant is $(\sqrt[2]{2.0268} ,6.559)$ .

Step-by-step explanation:

Since

we know the general equation of the circle whose center is at (h,k) and radius is r that is

$(x-h)^2+(y-k)^2 =r^2$

we have given center is (0,3) and radius is r= 4

substituting in the general equation of the circle we get

$x^2 +(y-3)^2 = 16$

Now substituting the y= 2.5x + 3 in the above equation we get

$x^2 +(2.5x + 3-3)^2 = 4^2$

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here subtracting 16 from both sides and also perform addition

we get

$7.25x^2 = 16$

dividing both sides by 7.25 we get

$x^2 =2.2068$

taking square root both sides we get

$x= \frac{+}{-}\sqrt[2]{2.0268}$

but we need positive value of x because both x and y are positive in the first quadrant

that is

$x= \sqrt[2]{2.0268}$

substituting this into the given equation of the line we get

y = 2.5( $\sqrt[2]{2.0268}$ )+3

y = 6.559

so the point in the first quadrant is ( $\sqrt[2]{2.0268}$ ,6.559)

that is required

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Step-by-step explanation:

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