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2 years ago

Use the factor theorem to determine wheatger the first polynomial is a factor of the second polynomial x-3;2x^2-4x+30

Mathematics

1 answer:

ahrayia [7]2 years ago

5 0

Use the factor theorem to determine whether the first polynomial is a factor of the second polynomial x-3;2x^2-4x+30

x−3,2x^2−4x+30

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 23 in. by 13 in. by

faltersainse [42]

Answer:

The dimension of the box is 17.66 in by 7.66 in by 2.67 in.

Therefore the volume of the box is 361.19 $in^3$ .

Step-by-step explanation:

Given that the dimensions of a cardboard is 23 in by 13 in.

Let the side of the square be x in.

Then the length of the box= (23-2x) in

and the width of the box =(13-2x) in

and height = x in.

The volume of the box is = length ×width × height

=[(23-2x)(13-2x)x] $in^3$

=(299x-72x² +4 $x^3$ ) $in^3$

∴V=299x-72x² +4x³

Differentiating with respect x

V'= 299-144x+12x²

Again differentiating with respect x

V''= -144+24x

To find the dimensions, we set V'=0

∴299-144x+12x²=0

Applying Sridharacharya formula that is the solution of a quadratic equation ax²+bx+c is $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here a=12, b=-144 , c=299

$\therefore x=\frac{-(-144)\pm\sqrt{(-144)^2-4.12.299}}{2.12}$

$\Rightarrow x= 9.33, 2.67$

If we take x=9.33 in, then the width of the box [13-(2×9.33)] will negative.

∴x = 2.67 in

If at x = 2.67, V''<0 , then the volume of the box will be maximum or V''>0 then volume of the box will be minimum.

$V''|_{x=2.67}=-144+(24\times 2.67)=-79.92$

Therefore at x = 2.67, the volume of the box maximum.

The length of the box =[23-(2×2.67)] in

=17.66 in

The width of the box =[13-(2×2.67)] in

=7.66 in

The height of the box= 2.67 in

The dimension of the box is 17.66 in by 7.66 in by 2.67 in.

Therefore the volume of the box is =(17.66×7.66×2.67) $in^3$

=361.19 $in^3$

8 0

2 years ago

Two circles of radius 8 are tangent to the graph of

KengaRu [80]

Two circles of radius 4 are tangent to the graph of y^2 = 4x at the point (1, 2). ... I know how to find the tangent line from a circle and a given point, but ... 2a2=42. a2=8. a=±2√2. Then1−xc=±2√2 and 2−yc=±2√2. ... 4 from (1,2), so you could find these centers, and from there theequations of the circle

5 0

2 years ago

BEST ANSWER GETS BRAINLIEST!!!!!!!!

Ad libitum [116K]

Answer:

(x + 6, y + 0), 180° rotation, reflection over the x‐axis

Step-by-step explanation:

The answer can be found out simply , a trapezoid has its horizontal sides usually parallel meanwhile the vertical sides are not parallel.

The horizontal parallel sides are on the x-axis.

Reflection over y- axis would leave the trapezoid in a vertical position such that the trapezoid ABCD won't be carried on the transformed trapezoid as shown in figure.

So option 1 and 2 are removed.

Now, a 90 degree rotation would leave the trapezoid in a vertical position again so its not suitable again.

In,The final option (x + 6, y + 0), 180° rotation, reflection over the x‐axis, x+6 would allow the parallel sides to increase in value hence the trapezoid would increase in size,

180 degree rotation would leave the trapezoid in an opposite position and reflection over x-axis would bring it below the Original trapezoid. Hence, transformed trapezoid A`B`C`D` would carry original trapezoid ABCD onto itself