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agasfer [191]
3 years ago
12

Use a graphing calculator to solve the equation -3 cost= 1 in the interval from . Round to the nearest hundredth.

Mathematics
1 answer:
RSB [31]3 years ago
8 0
In place of t, or theta, I'm going to utilize x instead. So the equation is -3*cos(x) = 1. Get everything to one side and we have -3*cos(x)-1 = 0

Let f(x) = -3*cos(x)-1. The goal is to find the root of f(x) in the interval [0, 2pi]

I'm using the program GeoGebra to get the task done of finding the roots. In this case, there are 2 roots and they are marked by the points A and B in the attachment shown

A = (1.91, 0)
B = (4.37, 0)

So the two solutions for theta are
theta = 1.91 radians
theta = 4.37 radians

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An isosceles trapezoid has base angles equal to 45 and bases of lengths 6 and 12. Find the area of the trapezoid.
swat32

Answer:

First option: 27 square units.

Step-by-step explanation:

The formula for calculate the area of a trapezoid is:

A=\frac{h}{2}(B+b)

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Observe the figure of the trapezoid called ABCD. The length of the larger base (AB) is 12 units and the lenght of the smaller base (CD) is 6 units, but the height h is unknown, so you need to find it.

You can observe in the figure that two equal right triangles are formed, whose opposite side is the height "h". If you calculate the opposite side of one of those triangles, you will  obtain the height of the trapezoid.

For this, you can use the identity tan\alpha=\frac{opposite}{adjacent}.

Identify the opposite side, the adjacent side and the angle \alpha:

opposite=h\\adjacent=\frac{12units-6units}{2}=3units\\\alpha=45\°

Substitute and solve for the height h:

tan(45\°)=\frac{h}{3}\\(3)(tan(45\°)=h\\3units=h

Finally substitute into A=\frac{h}{2}(B+b):

A=\frac{3units}{2}(12units+6units)=27units^2

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Answer:

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Step-by-step explanation:

Percentage solution with steps:

Step 1: We make the assumption that 9 is 100% since it is our output value.

Step 2: We next represent the value we seek with $x$.

Step 3: From step 1, it follows that $100\%=9$.

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