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4 years ago

13

Twenty-four 4-inch wide square posts are evenly spaced with 5 feet between adjacent posts to enclose a square field, as shown. W

hat is the outer perimeter, in feet, of the fence? Express your answer as a mixed number.

2 answers:

Nata [24]4 years ago

4 0

Answer:

492 0/10

Step-by-step explanation:

We have that the perimeter is 4 times the length of the side, now we know that this side "l" is given by:

l = 4 in * 24 + 23 * 5 ft

l = 96 in + 115 ft

Now, we pass the inches to pes, knowing that 1 foot equals 12 inches, so

96 in * 1 ft / 12 in = 8 ft

therefore replacing it remains:

l = 8 ft + 115 ft

l = 123 ft

now the perimeter:

p = 123 * 4

p = 492

to change to a mixed number:

4920/10 = 492 0/10

Nadusha1986 [10]4 years ago

4 0

Answer:

129 1/3

Step-by-step explanation:

According to Alcumus, "There are 20 square posts which are not on a corner, so there are $20/4=5$ square posts on each side, not including the corner posts. Including the corner posts, there are 7 posts on a side, which means that there are 6 five-foot gaps between posts. Altogether the length of a side is $7\left(\frac{1}{3}\right)+6(5)=32\frac{1}{3}$ feet. The perimeter of the square is four times the side length, so the perimeter is $4\cdot 32\frac{1}{3}=\boxed{129\frac{1}{3}}$ feet."

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Determine the equation of the line that is parallel to the given line, through the given point

bixtya [17]

The equation of the line that is parallel to the given line, through the given point is y = -5x - 7

Given equation,

y = -5x + 1

Slope = m

= -5

For two lines to be parallel, slope is equal.

Therefore, m = -5 for another line.

Let the equation of the line be y = mx + c

This line passes through A(-2,3)

Therefore, 3 = -5(-2) + c

3 = 10 + c

c = 3 - 10

= -7

Hence, equation of line is y = -5x - 7.

To learn more about equation of the line here:

brainly.com/question/21511618

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1 year ago

A news item is spreading by word of mouth through a population of size 12,000 people. After t days, the number of people (in tho

Lilit [14]

Answer:

a) 2.303

b) $f'(t)=\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}$

c) 1.3609

e) $\frac{dy}{dx}=0.04y(12-y)$

f) 4.5 thousand people(smaller)

7.5 thousand people (larger)

e) t=7.93 days (smaller)

t=10.06 days (larger)

g) 1.44

Step-by-step explanation:

The given function is $y=f(t)=\frac{12}{1+75e^{-0.48t}}$

To find how many thousand people have heard the news after 6 days, we substitute to get:

$f(6)=\frac{12}{1+75e^{-0.48*6}}=2.303$ thousands.

b) We rewrite to get: $f(t)=12(1+75e^{-0.48t})^{-1}$

We differentiate using the chain rule to obtain:

$f'(t)=-12(1+75e^{-0.48t})^{-2}\cdot 75e^{-0.48t}\cdot -0.48$

This simplifies to:

$f'(t)=432e^{-0.48t}(1+75e^{-0.48t})^{-2}$

We rewrite as positive index to get:

$f'(t)=\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}$

c) To find the rate at which the news is spreading after 8 days, we substitute t=8 into $f'(t)=\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}$ to get:

$f'(8)=\frac{432e^{-0.48\cdot 8}}{(1+75e^{-0.48\cdot 8})^{2}}=1.3609$

d) The solution to the logistic differential equation:

$\frac{dy}{dt}=ky(M-y)$

is

$y=\frac{M}{1+be^{-Mkt}}$

By comparison, M=12, and $Mk=0.48$

$12k=0.48\\k=0.04$

The differential equation is:

$\frac{dy}{dx}=0.04y(12-y)$

e) To how many people have heard the news when its rate of spread is 1.35 thousand per day, we equate the differential equation to 1.35 and so for t first.

$\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}=1.35$

This gives us: t=10.06 ot t=7.93

We substitute the times into the function to get:

$f(7.93)=\frac{12}{1+75e^{-0.48\cdot7.93}}$ =4.5 thousand: smaller value

$f(10.06)=\frac{12}{1+75e^{-0.48\cdot10.06}}=7.5$ thousand: Larger value

f) The two times that the news is spreading at rate 1.35 thousand people per day are:

$t=7.93$ days: Smaller value

$t=10.06$ : Larger value

g) To find the fastest rate at which the news spread we take the second derivative and equate it to zero.

$f''(t)=0$

This corresponds to where the horizontal line is tangent to

$f'(t)=\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}$

From the graph the point of tangency is:

(8.99,1.44)

Therefore the fastest rate at which the news spread is 1.44

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3 years ago

What is the solution for the following equation 3(2x+3)=2(3x+4)?

ki77a [65]

Answer:

<h2><u><em>no solution, the equation is false</em></u></h2>

Step-by-step explanation:

what is the solution for the following equation 3(2x+3)=2(3x+4)?

3 * (2x + 3) = 2 * (3x + 4)

6x + 9 = 6x + 8

6x - 6x = -9 + 8

0 = ±1

the equation is false

7 0

2 years ago

Read 2 more answers

A school wishes to accept 2000 students for their freshman class, and they expect 20,000 applications. In order to make their ad

vovangra [49]

Answer:

456

Step-by-step explanation:

Let X be the SATscore scored by the students

Given that X is normal (1000,200)

By converting into standard normal variate we can say that

$z=\frac{x-1000}{200}$ is N(0,1)

To find the top 10% we consider the 90th percentile for z score

Z 90th percentile = 1.28

$X= 200+1.28(200)\\= 200+256\\=456$

i.e. only students who scored 456 or above only should be considered.

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4 years ago

Graph the image of this triangle after a dilation with a scale factor of 2 centered at the origin.

Svet_ta [14]

Answer:

Since, the coordinates of the given triangle are (0,0), (4,-4) and (-4,-2)

In the dilation by the scale factor k with centered at origin,

$(x,y)\rightarrow (kx,ky)$

Thus, If the dilation occurs by the scale factor of 2 with centered at origin,

New coordinates of the triangles are,

$(0,0)\rightarrow (2\times 0, 2\times 0)$

$(-4,4)\rightarrow (2\times -4, 2\times 4)$

$(-4,-2)\rightarrow (2\times -4, 2\times -2)$

Thus, the coordinates of new triangle are,

(0,0) ( -8, 8) and (-8,-4)

7 0

3 years ago