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Andrews [41]
3 years ago
5

The area of a square is 729 square feet.What is the length of the side?

Mathematics
1 answer:
Art [367]3 years ago
7 0

To find the length of the side of a square when the area is known, find the square root of the area:


Side length = √729

Side Length = 27 feet.

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Let g be the function given by g(x)=limh→0sin(x h)−sinxh. What is the instantaneous rate of change of g with respect to x at x=π
lorasvet [3.4K]

The <em>instantaneous</em> rate of change of <em>g</em> with respect to <em>x</em> at <em>x = π/3</em> is <em>1/2</em>.

<h3>How to determine the instantaneous rate of change of a given function</h3>

The <em>instantaneous</em> rate of change at a given value of x can be found by concept of derivative, which is described below:

g(x) =  \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}

Where h is the <em>difference</em> rate.

In this question we must find an expression for the <em>instantaneous</em> rate of change of g if f(x) = \sin x and evaluate the resulting expression for x = \frac{\pi}{3}. Then, we have the following procedure below:

g(x) =  \lim_{h \to 0} \frac{\sin (x+h)-\sin x}{h}

g(x) =  \lim_{h \to 0} \frac{\sin x\cdot \cos h +\sin h\cdot \cos x -\sin x}{h}

g(x) =  \lim_{h \to 0} \frac{\sin h}{h}\cdot  \lim_{h \to 0} \cos x

g(x) = \cos x

Now we evaluate g(x) for x = \frac{\pi}{3}:

g\left(\frac{\pi}{3} \right) = \cos \frac{\pi}{3} = \frac{1}{2}

The <em>instantaneous</em> rate of change of <em>g</em> with respect to <em>x</em> at <em>x = π/3</em> is <em>1/2</em>. \blacksquare

To learn more on rates of change, we kindly invite to check this verified question: brainly.com/question/11606037

4 0
2 years ago
Convert (20 possible points)
Sergeeva-Olga [200]

Answer:

9.7*10^9 or 9,700,000,000

Step-by-step explanation:

To find the answer, multiply 9.7 * 10^6 by 1000 times becasue 1kg = 1000g, we got:

9.7 * 10^6 * 1000 = 9.7*10^9 or 9,700,000,000

Hope this help you :3

8 0
2 years ago
Read 2 more answers
I need to help with that
Bingel [31]
The ratio of people that can be served to milligrams of baking soda needed is:

Serving : Baking Soda
2 : 1600mg

Since you want 10 people, you can multiply this ratio by 5:5 to get 

10 people served = 8000mg needed

8000mg = 8 grams
3 0
3 years ago
Of the 850 runners in a race, 137 are men and the rest are women. What is the ratio of the number of female runners to the total
Masteriza [31]

Answer:

Unsimplified answer

713:850

Step-by-step explanation:

850-137=713

713:850

6 0
3 years ago
Read 2 more answers
What is the area of the medal platform?
Pani-rosa [81]
The total area is 78 sq. ft.

Since the medal platform has different measurements, we need to individually compute the area of each polygon.

The top polygon is a square. Its sides measure 3 ft. 

A₁ = a²
A₁ = 3 ft²
A₁ = 9 ft²

The middle polygon is a rectangle. 

Its total width can be derived by adding the widths given and the width of the square above.

w = 3 ft + 3 ft + 3 ft
w = 9 ft

A₂ = width * height
A₂ = 9 ft * 2 ft
A₂ = 18 ft²

The bottom polygon is also a rectangle.

w = 4 ft + 9 ft + 4 ft
w = 17 ft

A₃ = width * height
A₃ = 17 ft * 3 ft
A₃ = 51 ft²

Total Area = A₁ + A₂ + A₃
T.A. = 9 ft² + 18 ft² + 51 ft²
T.A. = 78 ft²
3 0
3 years ago
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