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Natasha2012 [34]
3 years ago
12

[Please, help me. I need it quickly]If cosA+sinA=√2, then prove A=45°.

Mathematics
1 answer:
Dmitrij [34]3 years ago
6 0

Step-by-step explanation:

Start by squaring both sides

cosA+sinA=\sqrt{2}

cos^2A+2cosAsinA+sin^2A=2

Apply Trig identity

cos^2x+sin^2x=1

2cosAsinA+1=2

2cosAsinA=1

Apply Trig Identity

2cosxsinx=sin(2x)

sin(2A)=1

2A=arcsin1

arcsin(1) is a known value \frac{\pi }{2}

2A=\frac{\pi }{2}

A=\frac{\pi }{4}

\pi radians=180^o

A=\frac{180^o}{4}=45^o

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Why true I had that problem and it was true.

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Which graph represents the equation -5x+4y&gt;-1?
galben [10]
<h3>Answer: Choice D</h3>

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Explanation:

The inequality sign has an "or equal to", which means the boundary line will be solid. We can rule out choices B and C because they have dashed boundary lines.

A solid boundary line means that points on the boundary are part of the solution set.

Now let's see what happens when we plug in a point like (x,y) = (4,0). This will tell us how to shade the blue region.

-5x + 4y \ge -1 \\\\-5(4) + 4(0) \ge -1 \\\\-20 \ge -1 \\\\

This is false because -20 is not larger than -1. It's the other way around.

This tells us the point (4,0) is not in the blue shaded region, and it's not on the boundary line either. We can rule out choice A because of this.

The only thing left is choice D, which is the final answer. I recommend plugging a point from this region into the inequality to confirm we have a true statement.

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3 years ago
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gregori [183]

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A triangular prism is 40 millimeters long and has a triangular face with a base of 24 millimeters and a height of 35 millimeters
abruzzese [7]

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Step-by-step explanation:

To find out how to solve this is that we first need to know that Triangular prisms have their own formula for finding surface area because they have two triangular faces opposite each other. The formula A=12bh is used to find the area of the top and bases triangular faces, where A = area, b = base, and h = height.

Also: To find the total surface area of a prism, you need to calculate the area of two polygonal bases, the top face and bottom face. And then calculate the area of lateral faces connecting the bases. Add up the area of the two bases and the area of the lateral faces to get the total surface area of a prism.

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3 years ago
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vitfil [10]

Answer:

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Step-by-step explanation:

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1) Move the graph 2 units to the right:

Let y = f (x-2) then y =(x-2) ^ 2 Notice that the cut point has been moved to x = 2.

2) Reflect on the x axis:

To reflect a graph on the x-axis we do y = -f(x) Then f (x) = -(x-2) ^ 2

3) Stretch according to factor 2.

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