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2 years ago

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A circle has a radius of 3 units. What is the area of the circle? Round to the nearest hundredth. Use 3.14 for pi.

1 answer:

Troyanec [42]2 years ago

5 0

Answer:

Step-by-step explanation:

Ac=3.14*r^2

Ac=9*3.14=28.27

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Find the set of values of k for which the line y=kx-4 intersects the curve y=x²-2x at 2 distinct points?

Sonbull [250]

Answer:

$-6 < k < 2$

Step-by-step explanation:

Given

$y = x^2 - 2x$

$y =kx -4$

Required

Possible values of k

The general quadratic equation is:

$ax^2 + bx + c = 0$

Subtract $y = x^2 - 2x$ and $y =kx -4$

$y - y = x^2 - 2x - kx +4$

$0 = x^2 - 2x - kx +4$

Factorize:

$0 = x^2 +x(-2 - k) +4$

Rewrite as:

$x^2 +x(-2 - k) +4=0$

Compare the above equation to: $ax^2 + bx + c = 0$

$a = 1$

$b= -2-k$

$c =4$

For the equation to have two distinct solution, the following must be true:

$b^2 - 4ac > 0$

So, we have:

$(-2-k)^2 -4*1*4>0$

$(-2-k)^2 -16>0$

Expand

$4 +4k+k^2-16>0$

Rewrite as:

$k^2 + 4k - 16 + 4 >0$

$k^2 + 4k - 12 >0$

Expand

$k^2 + 6k-2k - 12 >0$

Factorize

$k(k + 6)-2(k + 6) >0$

Factor out k + 6

$(k -2)(k + 6) >0$

Split:

$k -2 > 0$ or $k + 6> 0$

So:

$k > 2$ or k $> -6$

To make the above inequality true, we set:

$k < 2$ or $k >-6$

So, the set of values of k is:

$-6 < k < 2$

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2 years ago

For all positive integers x ,what is the greatest common factor of the numbers 256x and 144x

gogolik [260]

First, let's factor both of these numbers.

256x:

$2^{8} * x$

144x:

$3^{2} * 2^{4} * x$

Both of these numbers contain $2^{4} * x$ , so that would be the greatest common factor. This could also be written as 16x.

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2 years ago

A classroom is 32 1/2 feet long, 30 feet wide, and 7 1/2 feet high what is the volume

kondor19780726 [428]

Answer:

6000

Step-by-step explanation:

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2 years ago

PLEASE HELP!!<br> Solve each inequality and graph its solution.

12345 [234]

Answer:

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in this line of circles, the ratio of the red circles to blue circles is 1:3. how many more red circles would need to be added t

Tems11 [23]

Answer:

Step-by-step explanation:

If we assume that initially

Number of red counter is 1

Number of blue counter is 3

Now to make ratio reverse you need to add 8 more red counters so that ratio becomes

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2 years ago