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Trava [24]
3 years ago
12

Find dy/dx implicitly and find the largest interval of the form −a < y < a or 0 < y < a such that y is a differentia

ble function of x. cos y = x
Mathematics
1 answer:
mylen [45]3 years ago
6 0

Answer:

dy/dx = -1/√(1 - x²)

For 0 < y < π

Step-by-step explanation:

Given the function cos y = x

-siny dy = dx

-siny dy/dx = 1

dy/dx = -1/siny (equation 1)

But cos²y + sin²y = 1

=> sin²y = 1 - cos²y

=> siny = √(1 - cos²y) (equation 2)

Again, we know that

cosy = x

=> cos²y = x² (equation 3)

Using (equation 3) in (equation 2), we have

siny = √(1 - x²) (equation 4)

Finally, using (equation 4) in (equation 1), we have

dy/dx = -1/√(1 - x²)

The largest interval is when

√(1 - x²) = 0

=> 1 - x² = 0

=> x² = 1

=> x = ±1

So, the interval is

-1 < x < 1

arccos(1) < y < arxcos(-1)

= 0 < y < π

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Anna007 [38]

Both functions decrease at (-1, 2)

<h3>How to determine the decreasing intervals of the function?</h3>

The complete question is added as an attachment

The polynomial function f(x) is represented by the graph.

From the graph, the polynomial function decreases at (-2, 2)

The absolute function is given as;

f(x) = =5|x + 1| + 10

The vertex of the above function is

Vertex = (-1, 10)

Because a is negative (a= -5), the vertex is a maximum.

This means that the function decreases at (-1, ∞)

So, we have

(-2, 2) and (-1, ∞)

Combine both intervals

(-1, 2)

This means that both functions decrease at (-1, 2)

See attachment 2 for the number line that represents the interval where both functions are decreasing

Read more about function intervals at:

brainly.com/question/27831985

#SPJ1

3 0
1 year ago
Someone please please help me with this ! I would really appreciate it
Lubov Fominskaja [6]

Answer:

1. The right triangles pass the AA similarity congruence theorem.

2. s/q

Step-by-step explanation:

They are similar since they pass the AA( Angle-Angle) similarity theorem.

Similar triangles have corresponding proportional sides so side z corresponds with side s and side x corresponds with q so we would represent that as

s/q

5 0
2 years ago
H(x)={(-7,-1),(0,0),(5,8)} domain and range
Bingel [31]

Answer:

The domain is -7, 0, and 5

The range is -1, 0, and 8

Step-by-step explanation:

The domain of a set of points is the x-value. In this case the x-values are -7, 0, and 5 respectively. The range of a set of points is the y-value so in this case the range is -1, 0, and 8.

7 0
2 years ago
In Cos A = 0.4 Find The Value Of Cos 3 A.<br><br><br><br>Thenku ☃️<img src="https://tex.z-dn.net/?f=%20%5C%3A%20%5C%3A%20" id="T
s2008m [1.1K]
Answer:
- 0.944

Step-by-step explanation:
We know that,
cos 3A = 4 cos³A - 3 cos A (formula)

So,
If cos A = 0.4,

cos 3A = 4 cos³A - 3 cos A
cos 3A = 4 × (0.4)³ - 3 × (0.4)
cos 3A = 4 × 0.064 - 1.2
cos 3A = - 0.944


Hope it helps ⚜




3 0
2 years ago
Read 2 more answers
2 The Skoblickis are building a new home. The scale
yanalaym [24]

The actual width of the room is 20 ft and the actual length of the room is 15 ft

Since on the scale, 2 in : 5 ft and the width of the room on the drawing is 8 in.

Let the actual width of the room is w.

The ratio of the drawing to actual width is   8 in : w

So, 2 in : 5 ft = 8 in : w

2 in/5 ft = 8 in/w

So, w = 8 in × 5 ft/2 in

w = 4 × 5 ft

w = 20 ft

Also, the length of the room on the drawing on the drawing is 6 in.

Let the actual length of the room is L.

The ratio of the drawing to actual length is   6 in : L

So, 2 in : 5 ft = 6 in : L

2 in/5 ft = 6 in/L

So, L = 6 in × 5 ft/2 in

L = 3 × 5 ft

L = 15 ft

So, the actual width of the room is 20 ft and the actual length of the room is 15 ft.

Learn more about scale drawing here:

brainly.com/question/25324744

4 0
2 years ago
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