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Vinil7 [7]
3 years ago
15

A rectangle is constructed with its base on theâ x-axis and two of its vertices on the parabola yequals=2525minusâxsquared2. wha

t are the dimensions of the rectangle with the maximumâ area? what is theâ area?
Mathematics
1 answer:
Nina [5.8K]3 years ago
6 0
You should have drawn1 - x-axis and y-axis in light pencil.2 - graphed a down-facing parabola with the top of the frown on the y-axis at y = 2.  It should be crossing the x-axis at ±√2.  This should be in dark pencil or another color.3 - In dark pencil or a completely new color, draw a rectangle with one of the horizontal sides sitting on top of the x-axis and the other horizontal side touching the parabola at each of the top corners of the rectangle. The rectangle will have half of its base in the positive x-axis and the other half on the negative x-axis.  It should be split right down the middle by the y-axis.  So each half of the base we will say is "x" units long.  So the whole base is 2x units long (the x units to the right of the y-axis, and the x units to the left of the y-axis)  I so wish I could draw you this picture...   In the vertical direction, both vertical edges are the same length and we will call that y.   The area that we want to maximize has a width 2x long, and a height of y tall. So A = 2xy     This is the equation we want to maximize (take derivative and set it = 0), we call it the "primary equation", but we need it in one variable. This is where the "secondary equation" comes in.  We need to find a way to change the area formula to all x's or all y's. Since it is constrained to having its height limited by the parabola, we could use the fact that y=2 - x2 to make the area formula in only x's.   Substitute in place of the "y", "2 - x2" into the area formula. A = 2xy = 2x(2 - x2)   then simplify A = 4x - 2x3     NOW you are ready to take the deriv and set it = 0 dA/dx = 4 - 6x2       0 = 4 - 6x2   6x2 = 4    x2 = 4/6 or 2/3 So x = ±√(2/3) Width remember was 2x.   So the width is 2[√(2/3)]Height is y which is 2 - x2 = 2 - 2/3  =4/3
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The product of two consecutive integers is 90. Which equation can be used to find the two integers?
joja [24]
Two consecutive integers would be x and x+ 1
if you multiply them you have x(x + 1) = x^2 + x
if you want the product to equal 90 you get x^2 + x = 90
The first option is correct.
3 0
3 years ago
How many cylindrical can of bottles 12 cm high and with 6 cm diameter could be filled from a tank containing 125 liters of deter
Orlov [11]

Answer:

368 cans.

Step-by-step explanation:

Volume of 1 can = π r^2 h.

Here h (height) = 12 and r (radius) = 1/2 * 6 = 3 cm.

So V =  π * 3^2 * 12

= 108π cm^3.

The tank hold 125 liters

=  125,000 cm^3, so:

Number of cans that could be filled = 125000/ 108 π

= 368.4.

4 0
3 years ago
Read 2 more answers
A laptop producing company also produces laptop batteries, and claims that the batteries
gregori [183]

Answer:

There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours. (P-value = 0).

The null and alternative hypothesis are:

H_0: \mu=4\\\\H_a:\mu< 4

Step-by-step explanation:

<em>The question is incomplete: To test this claim a sample or population standard deviation is needed.</em>

<em>We will estimate that the sample standard deviation is 2 hours, and use a t-test to test that claim.</em>

<em> NOTE (after solving): The difference between the sample mean and the mean of the null hypothesis is big enough to reject the null hypothesis, even when we have a sample standard deviation of 3.5 hours, which can be considered bigger than the maximum standard deviation for the sample.</em>

This is a hypothesis test for the population mean.

The claim is that the batteries power the laptops for significantly less than 4 hours.

Then, the null and alternative hypothesis are:

H_0: \mu=4\\\\H_a:\mu< 4

The significance level is 0.05.

The sample has a size n=500.

The sample mean is M=3.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.

The estimated standard error of the mean is computed using the formula:

s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2}{\sqrt{500}}=0.0894

Then, we can calculate the t-statistic as:

t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{3.5-4}{0.0894}=\dfrac{-0.5}{0.0894}=-5.5902

The degrees of freedom for this sample size are:

df=n-1=500-1=499

This test is a left-tailed test, with 499 degrees of freedom and t=-5.5902, so the P-value for this test is calculated as (using a t-table):

P-value=P(t

As the P-value (0) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours.

5 0
3 years ago
The sum of the measures of two adjacent angles is 72 degrees. The ratio of the smaller angle to the
Goryan [66]

Answer:

The larger angle is 54°

Step-by-step explanation:

Given

Let the angles be: θ and α where

θ > α

Sum = 72

α : θ = 1 : 3

Required

Determine the larger angle

First, we get the proportion of the larger angle (from the ratio)

The sum of the ratio is 1 + 3 = 4

So, the proportion of the larger angle is ¾.

Its value is then calculated as:.

θ = Proportion * Sum

θ = ¾ * 72°

θ = 3 * 18°

θ = 54°

4 0
2 years ago
CAN SOMEONE PLZZ HELP WIT THIS!!!!!
Shtirlitz [24]

Answer:

B

Step-by-step explanation:

b and a=40⁰ so if b+c is supplementary they equal 180⁰ together so 180-40= 150⁰

6 0
2 years ago
Read 2 more answers
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