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MrRissso [65]
3 years ago
7

The area of a square is increasing at a rate of 24 centimeters squared per second. Find the rate of change of the side of the sq

uare when it is 4 centimeters. The rate of change of the side is Number cm/sec.
Mathematics
1 answer:
velikii [3]3 years ago
8 0

Answer:

3cm/s

Step-by-step explanation:

Area of a square is expressed as:

A = L²

Rate of change of area is expressed as:

dA/dt = dA/dL•dL/dt

Given that

dA/dt = 24cm²/s

L = 4cm

Required

dL/dt

Since dA/dl = 2L

dA/dl = 2(4)

dA/dl = 8cm

Subatitute the given values into the formula

24 = 8 dL/dt

dL/dt = 24/8

dL/dt = 3cm/s

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Answer:

5.099

Step-by-step explanation:

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Evaluate the expression under the given conditions. tan(2); cos() = 5 13 , in quadrant i
Nataliya [291]

The solution to given expression tan(2θ) is 22.615°

For given question,

We have been given an expression tan(2θ)

Given that cos(θ) = 5/13, and θ is in quadrant 1.

We know that the trigonometric identity

sin²θ + cos²θ = 1

⇒ cos²θ = (5/13)²

⇒ sin²θ = 1 - 25/169

⇒ sin²θ = 169 - (25/169)

⇒ sin²θ = 144/169

⇒ sin(θ) = 12/13

We know that the identity cos(2x) = cos²x - sin²x

⇒ cos(2θ) = cos²θ - sin²θ

⇒ cos(2θ) = 25/169 - 144/169

⇒ cos(2θ) = -119/169

And sin(2x) = 2sin(x)cos(x)

⇒ sin(2θ) = 2sin(θ)cos(θ)

⇒ sin(2θ) = 2 × 12/13 × 5/13

⇒ sin(2θ) = 120/169

We know that, tan(x) = sin(x)/cos(x)

⇒ tan(2θ) = sin(2θ)/cos(2θ)

⇒ tan(2θ) = (120/169) / (-119/169)

⇒ tan(2θ) = 120 / (-119)

⇒ tan(2θ) = -1.008

Since θ is in quadrant 1, tan(2θ) = 1.008

⇒ 2θ = arctan(1.008)

⇒ 2θ = 45.23

⇒ θ = 22.615°

Therefore, the solution to given expression tan(2θ) is 22.615°

Learn more about the expression here:

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7 0
2 years ago
-½(x + 1¼) = - 3 + ¼x <br> Solve for x
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Answer:

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3 years ago
What is the equation of a circle with a center located at (-3, 4) and a diameter of 14?
AnnZ [28]

Answer: (x + 3)^2 + (y - 4)^2 = 49

Step-by-step explanation:

The equation of a circle given the center and radius: (x - h)^2 + (y - k)^2 = r^2

Given: center (-3,4) ; h = -3 and k = 4

diameter = 14

To find the radius: divide the diameter by 2 = 14/2 = 7 = r

Center: (-3,4) and radius: 7

Equation of a circle: (x - h)^2 + (y - k) ^2 = r^2

Substitute h = -3, k = 4, r = 7

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Answer:

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3 years ago
I need help please help me
Elan Coil [88]
Here’s the correct answer and how I got it :)

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