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2 years ago

7

Kala is building a fence around her garden. For every 4 feet of fencing. the cost is 36$ . Complete the table below showing the

length of the fence and the cost.
Length of fencing: (4) (6) (7) (_) (10)
Cost: (36) ( _ ) (_) 81 (_)

1 answer:

ExtremeBDS [4]2 years ago

4 0

Answer:

Length of fencing: 4, 6, 7, 9, 10

Cost: 36, 54, 63, 81, 90

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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,

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

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2 years ago

Find the length of the missing side. triangle with an 8 inch side and 12 inch side with a right angle 8.9 in. 104 in. 4 in 14.4

Mamont248 [21]

Given:

In a triangle, length of one side is 8 inches and length of another side is 12 inches, and an angle is a right angle.

To find:

The length of the missing side.

Solution:

In a right angle triangle,

$Hypotenuse^2=Perpendicular^2+Base^2$

Suppose the measures of sides adjacent to the right angle are 8 inches and 12 inches.

Substituting Perpendicular = 8 inches and Base = 12 inches, we get

$Hypotenuse^2=8^2+12^2$

$Hypotenuse^2=64+144$

$Hypotenuse^2=208$

Taking square root on both sides, we get

$Hypotenuse=\sqrt{208}$

$Hypotenuse=14.422205$

$Hypotenuse\approx 14.4$

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