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2 years ago

5

On a coordinate grid, the coordinates of vertices P and Q for Polygon PQRS are P(5, 4) and Q(−2, 4). What is the length of Side

PQ of the polygon?
A. 2 units
B. 3 units
C. 7 units
D. 8 units

2 answers:

Sedaia [141]2 years ago

7 0

The answer is c. 7 units .

earnstyle [38]2 years ago

6 0

The answer would be C:7 units

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A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 31 ft/s. (a) A

julsineya [31]

Answer:

a) -13.9 ft/s

b) 13.9 ft/s

Step-by-step explanation:

a) The rate of his distance from the second base when he is halfway to first base can be found by differentiating the following Pythagorean theorem equation respect t:

$D^{2} = (90 - x)^{2} + 90^{2}$ (1)

$\frac{d(D^{2})}{dt} = \frac{d(90 - x)^{2} + 90^{2})}{dt}$

$2D\frac{d(D)}{dt} = \frac{d((90 - x)^{2})}{dt}$

$D\frac{d(D)}{dt} = -(90 - x) \frac{dx}{dt}$ (2)

Since:

$D = \sqrt{(90 -x)^{2} + 90^{2}}$

When x = 45 (the batter is halfway to first base), D is:

$D = \sqrt{(90 - 45)^{2} + 90^{2}} = 100. 62$

Now, by introducing D = 100.62, x = 45 and dx/dt = 31 into equation (2) we have:

$100.62 \frac{d(D)}{dt} = -(90 - 45)*31$

$\frac{d(D)}{dt} = -\frac{(90 - 45)*31}{100.62} = -13.9 ft/s$

Hence, the rate of his distance from second base decreasing when he is halfway to first base is -13.9 ft/s.

b) The rate of his distance from third base increasing at the same moment is given by differentiating the folowing Pythagorean theorem equation respect t:

$D^{2} = 90^{2} + x^{2}$

$\frac{d(D^{2})}{dt} = \frac{d(90^{2} + x^{2})}{dt}$

$D\frac{dD}{dt} = x\frac{dx}{dt}$ (3)

We have that D is:

$D = \sqrt{x^{2} + 90^{2}} = \sqrt{(45)^{2} + 90^{2}} = 100.63$

By entering x = 45, dx/dt = 31 and D = 100.63 into equation (3) we have:

$\frac{dD}{dt} = \frac{45*31}{100.63} = 13.9 ft/s$

Therefore, the rate of the batter when he is from third base increasing at the same moment is 13.9 ft/s.

I hope it helps you!

4 0

2 years ago

Read 2 more answers

Which statement is true about the difference 2 square root of 7 − square root of 28?

3241004551 [841]

<span> 2 square root of 7 − square root of 28
= 2</span>√7 - √28
= 2√7 - 2√7
= 0

4 0

3 years ago

Read 2 more answers

Can you conclude that the parallelogram is a rhombus,a rectangle, or a square

Tems11 [23]

Answer:

No

Step-by-step explanation:

Parallelogram has opposite sides equal and parallel

Square and rhombus have all sides equal

Rectangle has all angles = 90, which is not a condition for parallelograms

8 0

3 years ago

What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive?

NeX [460]

Answer:

letter C: 100

Step-by-step explanation:

This problem can be configured as an arithmetic progression:

The first value is 10, the ratio is also 10 (the multiples of ten are 20, 30, 40, ...) and the number of terms is 19 (10, 20, 30, ... , 180, 190 -> total of 19 numbers).

So, we can use the following formula to calculate the sum of all these numbers:

Sn = n(a1 + an) /2

where Sn is the sum, n is the number of terms, a1 is the first term and an is the last one.

The result we want is the average of the sum, so we need to divide Sn by n:

Average = Sn/n = n(a1 + an) /2n = (a1 + an) /2 = (10+190)/2 = 200/2 = 100

The correct option is letter C.

7 0

2 years ago

I'll give brainliest to the most reliable and well-explained answer.

lapo4ka [179]

Answer:

Option B. 5.5 ft²

Step-by-step explanation:

Perimeter of the square piece of land = length of fence required

4(length of a side of the square) = 24 ft

Length of a side = 6 ft

Area of the square land = (Side)²

= 6²

= 36 square ft

Area of the side walk = Area of the square - [Area of two triangles separated by the sidewalk]

= 36 - [1/2 (Area Of The Sqaure) + 1/2 (Base) (Height) ]

= 36 - [36/2 + 1/2 (6 - 1) (6 - 1)]

= 36 - (18 + 12.5)

= 36 - 30.5

= 5.5 ft²

Therefore, Option B. is the correct answer.

4 0

2 years ago

Read 2 more answers