Mathematics, 25.02.2020 20:24, elizaa94

(1 point) A rectangle is inscribed with its base on the xx-axis and its upper corners on the parabola y=11−x2y=11−x2. What are the dimensions of such a rectangle with the greatest possible area?

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answered: AskaWaya

the rectangle has dimensions of length= 2√(11/3) and height=22/3

Step-by-step explanation:

since the parabola

y= 11-x²

is symmetric with respect to the y-axis ( meaning that y(x)=y(-x) );

area of rectangle with base from -x to x and height y = 2 *area of rectangle with base from 0 to x and height y

A=2*x*y

replacing y

A=2*x*( 11-x²) = 22*x - 2*x³

the maximum value can be found when the derivative of the area with respect to x is 0 , thus

dA/dx= 22 - 6*x² = 0

22 - 6*x² = 0

x max = √(22/6)

y max = 11-xmax² = 11-[√(22/6)]²= 11 - 22/6 = 44/6

then the rectangle with maximum area has dimensions of

length = 2*x max= 2√(22/6) and height=y max=44/6

answered: Guest

The household makes $424.45

answered: Guest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

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(1 point) A rectangle is inscribed with its base on the xx-axis and its upper corners on the parabol...