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2 years ago

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A boat travels at a constant speed. After 20 minutes, the boat has traveled 2.5 miles. The boat travels a total of 10 miles to a

bridge.
a. How long does it take the boat to reach the bridge? Explain how you found it.

1 answer:

monitta2 years ago

6 0

In order to find the speed at which the boat is traveling, we divide the distance it has traveled by the time elapsed:

2.5/20=0.125 miles/minute

Next, we want to find how long it took for the boat to travel 10 miles. Since it travels 0.125 miles every minute, we just divide:

10/0.125=80

Thus, it took 80 minutes for the boat to reach the bridge

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ch4aika [34]

ANSWER

$2 \times 2$

EXPLANATION

The dimensions of a matrix is of the form:

$Row \times Column$

The dimensions of the first matrix is

$2 \times 3$

The dimensions of the second matrix is

$3 \times 2$

Since the inner products are the same,the outer products give the dimensions of the product of the two matrices.

$(2 \times 3)(3 \times 2) = 2 \times 2$

Therefore the dimensions of the product is a 2×2 matrix.

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Masteriza [31]

Answer:

(2,-5) and (2,1).

Step-by-step explanation:

We need to find the find all the points having an x coordinate of 2 whose distance from the point (-2,-4) is 5.

A circle with center (-2,-4) and radius 5 represents all the points whose distance from the point (-2,-4) is 5.

Standard form of a circle is

$(x-h)^2+(y-k)^2=r^2$

where, (h,k) is center and r is the radius.

$(x-(-2))^2+(y-(-4))^2=(5)^2$

$(x+2)^2+(y+2)^2=25$

Now, put x=2.

$(2+2)^2+(y+2)^2=25$

$(4)^2+(y+2)^2=25$

$(y+2)^2=25-16$

$(y+2)^2=9$

Taking square root on both sides.

$y+2=\pm\sqrt{9}$

$y+2=\pm3$

$y+2=-3\text{ or }y+2=3$

$y=-5\text{ or }y=1$

So, the y-coordinates of the points are -5 and 1.

Therefore, the required points are (2,-5) and (2,1).

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2 years ago

Regular hexagon ABCDEF has vertices at A(4, 4!3), B(8, 4!3), C(10, 2!3), D(8, 0), E(4, 0) and F(2, 2!3).

marissa [1.9K]

Since the given hexagon is a regular hexagon all it's sides will be of equal length. Now, we know that the Area of any regular hexagon is given by:

$A=\frac{3\sqrt{3}}{2} a^2$

Where $A$ is the area of the regular hexagon

$a$ is the side length of the regular hexagon

Also, it's Perimeter is given by:

$P=6a$

Thus, all that we need to do is to find the side length of any one of the sides and to do that let us have a look at at the data of vertices points given and find out which points are definitely adjacent to each other and are also easy to calculate.

A quick search will yield that D(8, 0) and E(4, 0) are definitely adjacent to each other.

Please check the attached file here for a better understanding of the diagram of the original regular hexagon. Points D and E indeed are adjacent to each other.

Let us now find the distance between the points D and E using the distance formula which is as:

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

Where $d$ is the distance.

$(x_1,y_1)$ and $(x_2,y_2)$ are the coordinates of points D and E respectively. (please note that interchanging the values of the coordinates will not alter the distance $d$ )

Applying the above formula we get:

$d=\sqrt{(8-4)^2+(0-0)^2} =\sqrt{4^2}=4$

$\therefore d=4$

We know that this distance is the side length of the given regular hexagon.

$\therefore d=a=4$

Now, if the sides of the given regular polygon are reduced by 40%, then the new length of the sides will be:

$a_{small}=4-\frac{40}{100}\times 4=2.4$

Thus, the area of the smaller hexagon will be:

$A_{small}=\frac{3\sqrt{3}}{2} a_{small}^2=\frac{3\sqrt{3}}{2} (2.4)^2\approx14.96$ unit squared

and the new smaller perimeter will be:

$P_{small}=6a_{small}=6\times 2.4=14.4$ unit

Which are the required answers.

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Step2247 [10]

Area = (h/2)(a +b)

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