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aleksley [76]
3 years ago
10

A playground is in the shape of a square . If the perimeter of the playground is 60 feet , find the diagonal distance across the

park , leave your answer in simplest radical form .
Mathematics
1 answer:
puteri [66]3 years ago
4 0

The perimeter is the sum of the 4 sides of the square. Divide the perimeter by 4 to find the length of one side:

60/4 = 15

Now using the Pythagorean theorem find the diagonal:

Diagonal = √(15² + 15²)

Diagonal = 15√2 ( or 21.213 as a decimal answer)

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Stan has a rectangular piece of carpet with an area of 23.4 square meters. The piece of carpet is 13 meters long. What is the wi
Sholpan [36]

<u>A</u><u>n</u><u>s</u><u>w</u><u>e</u><u>r</u><u>:</u>

The breadth of rectangular carpet is 1.8 m.

<u>S</u><u>t</u><u>e</u><u>p</u><u>-</u><u>b</u><u>y</u><u>-</u><u>s</u><u>t</u><u>e</u><u>p</u><u> </u><u>e</u><u>x</u><u>p</u><u>l</u><u>a</u><u>n</u><u>a</u><u>t</u><u>i</u><u>o</u><u>n</u><u>:</u>

We have,

  • The area of rectangular carpet that is 23.4 m²
  • The length of carpet is 13 m.

We know that,

= Area of rectangle = Length × Breadth

= 23.4 = 13 × Breadth

= 23.4/13 = Breadth

= 234/130 = Breadth

= 1.8 m = Breadth

<h2>__________________________</h2>
3 0
3 years ago
Show with work please.
kolbaska11 [484]

Answer:

$\csc \left(\theta-\frac{\pi }{2}\right)=0.73$

Step-by-step explanation:

The identity you will use is:

$\csc \left(x\right)=\frac{1}{\sin \left(x\right)}$

So,

$\csc \left(\theta-\frac{\pi }{2}\right)$

$\csc \left(\theta-\frac{\pi }{2}\right)=\frac{1}{\sin \left(-\frac{\pi }{2}+\theta\right)}$

Now, using the difference of sin

Note: state that \text{sin}(\alpha\pm \beta)=\text{sin}(\alpha) \text{cos}(\beta) \pm \text{cos}(\alpha) \text{sin}(\beta)

$\csc \left(\theta-\frac{\pi }{2}\right)=\frac{1}{-\cos \left(\theta\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(\theta\right)}$

Solving the difference of sin:

$-\cos \left(\theta\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(\theta\right)$

-\cos \left(\theta\right) \cdot 1+0\cdot \sin \left(\theta\right)

-\text{cos} \left(\theta\right)

Then,

$\csc \left(\theta-\frac{\pi }{2}\right)=-\frac{1}{\cos \left(\theta\right)}$

Once

\text{sec}(-\theta)=\text{sec}(\theta)

And, \text{sec}(\theta)=-0.73

$-\frac{1}{\cos \left(\theta\right)}=-\text{sec}(\theta)$

$-\frac{1}{\cos \left(\theta\right)}=-(-0.73)$

$-\frac{1}{\cos \left(\theta\right)}=0.73$

Therefore,

$\csc \left(\theta-\frac{\pi }{2}\right)=0.73$

3 0
3 years ago
The sides of a square field are 28 meters. A sprinkler in the center of the field sprays a circular area with a diameter that co
Stella [2.4K]
If a field is 900 meters squared and one side is twice as big as the other how big is each side
6 0
2 years ago
4. Allison's vegetable garden is in shape of rectangle with an area of 10 feet^2. The width of
inna [77]

Answer:

33333

Step-by-step explanation:

6 0
3 years ago
If a given data point is (1,4) and the line of best fit is y = 1.5x + 3.25, what's the residual value?
Svetlanka [38]

Answer:

The residual value is -0.75

Step-by-step explanation:

we know that  

The residual value is the observed value minus the predicted value.

RESIDUAL VALUE=[OBSERVED VALUE-PREDICTED VALUE]

where

Predicted value.--> the predicted value given the current regression equation

Observed value. --> The observed value for the dependent variable.

in this problem

we have the point (1,4)

so

The observed value is 4

<em>Find the predicted value  for x=1 </em>

y =1.5(1)+3.25=4.75

predicted value is 4.75

so

RESIDUAL VALUE=(4-4.75)=-0.75

4 0
3 years ago
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