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2 months ago

6

Do you think mr. carpenter should Use a rectangle to arrange the 29 quilt squares, if not, what shape should he use?

1 answer:

Zina [12.3K]2 months ago

3 0

Response:

hey, did you assist anyway?

Detailed breakdown:

You might be interested in

The total time T (in hours) needed to fly from New York to Los Angeles and back can be modeled by the equation below, where d is

tester [12383]

Answer:

Step-by-step explanation:

There are two distinct issues to address, correct?

1, The overall duration T required to fly from New York to Los Angeles:

Time = Distance/average speed

2, The problem related to the race:

A) The total duration of the race would be:

$t=\frac{0.5}{r} +\frac{22}{15r} + \frac{6}{r+5}$

B) For swimming at an average pace of 2 miles per hour, this means r=2.

Substituting r=2 allows us to calculate the total time needed as follows:

$t=\frac{0.5}{2} +\frac{22}{15*2} + \frac{6}{2+5}= 0.25 + 0.73333+ 0.85714=1.84047$

When rounding the result: 1.84047 hours rounds to 110 minutes

7 0

2 months ago

Find the point on the circle x^2+y^2 = 16900 which is closest to the interior point (30,40)

Leona [12618]

Response-

(78,104) represents the point closest to the interior.

Explanation-

The equation defining the circle,

$\Rightarrow x^2+y^2 = 16900$

$\Rightarrow y^2 = 16900-x^2$

$\Rightarrow y = \sqrt{16900-x^2}$

Since the point lies on the circle, its coordinates must be,

$(x,\sqrt{16900-x^2})$

The distance "d" from the point to (30,40) can be calculated as,

$=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$=\sqrt{(x-30)^2+(\sqrt{16900-x^2}-40)^2}$

$=\sqrt{x^2+900-60x+16900-x^2+1600-80\sqrt{16900-x^2}}$

$=\sqrt{9400-60x-80\sqrt{16900-x^2}}$

Next, we need to determine the value of x for which d is minimized. The minimum distance occurs when $9400-60x-80\sqrt{16900-x^2}$ is at its lowest value.

Let’s set up the equation,

$\Rightarrow f(x)=9400-60x-80\sqrt{16900-x^2}$

$\Rightarrow f'(x)=-60+80\dfrac{x}{\sqrt{16900-x^2}}$

$\Rightarrow f''(x)=\dfrac{1352000}{\left(16900-x^2\right)\sqrt{16900-x^2}}$

We find the critical points,

$\Rightarrow f'(x)=0$

$\Rightarrow-60+80\dfrac{x}{\sqrt{16900-x^2}}=0$

$\Rightarrow 80\dfrac{x}{\sqrt{16900-x^2}}=60$

$\Rightarrow 80x=60\sqrt{16900-x^2}$

$\Rightarrow 80^2x^2=60^2(16900-x^2)$

$\Rightarrow 6400x^2=3600(16900-x^2)$

$\Rightarrow \dfrac{16}{9}x^2=16900-x^2$

$\Rightarrow \dfrac{25}{9}x^2=16900$

$\Rightarrow x=\sqrt{\dfrac{16900\times 9}{25}}=78$

$\Rightarrow x=78$

Then,

$\Rightarrow f''(78)=\dfrac{1352000}{\left(16900-78^2\right)\sqrt{16900-78^2}}=\dfrac{125}{104}=1.2$

Since f''(x) is positive, the function f(x) achieves its minimum at x=78

When x is set to 78, the corresponding y value will be

$\Rightarrow y = \sqrt{16900-x^2}=\sqrt{16900-78^2}=104$

This leads us to conclude that the closest point is (78,104)

5 0

2 months ago

An equiangular triangle has one side of length six inches. What is the height of the triangle, drawn from that side, to the near

AnnZ [12381]

The height of the triangle measures 5.2 inches. An equiangular triangle has equal measures for all interior angles, which means it is equivalent to an equilateral triangle. Since all angles equal 60 degrees, applying the Pythagorean theorem enables us to calculate the height based on the provided side length.

5 0

1 month ago

Which would best display the following data if you wanted to display the numbers which are outliers as well as the mean? [4, 1,

AnnZ [12381]

Organizing the data in increasing order to find the outlier and compute the mean

Detailed explanation:

The provided data consists of: [4, 1, 3, 10, 18, 12, 9, 4, 15, 16, 32]

Arranging it in ascending sequence

[1, 3, 4, 4, 9, 10, 12, 15, 16, 18, 32 ]

The outlier is identified as 32

Calculating the mean;

Mean=total of data set/quantity of data set

Total= 1 + 3+ 4+ 4+ 9+ 10+ 12+ 15+ 16+ 18+ 32=124

Quantity of data set=11

Mean=124/11=11.27

3 0

3 months ago