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3 years ago

Is 21/23 bigger or smaller than 29/32

1 answer:

5 0

Think of a pie, if you cut it into 32 pieces the pieces would have to be small, and it you cut it into 23 pieces then the pieces would be bigger than the one cut I to 32 pieces. So 21/23 is bigger than 29/32

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Which equation has a solution of x = 13?

horsena [70]

Answer:

Step-by-step explanation:

(13) - 10 = 3

(x - 10 = 3)

Fill in x and see what it answers!

Hope this helps

5 0

3 years ago

Read 2 more answers

Probe that:<br><img src="https://tex.z-dn.net/?f=%20%5Csec%20%5Calpha%20%20%5Csqrt%7B1%20-%20%20%5Csin%28%20%7B%7D%5E%7B2%7D%20%

Nataly [62]

Step-by-step explanation:

<h3> $\sec \alpha \sqrt{1 - \sin ^{2} \alpha } = 1$ </h3>

Prove the LHS

Using trigonometric identities

That's

<h3> $\cos ^{2} \alpha = 1 - \sin^{2} \alpha$ </h3>

<u>Rewrite the expression</u>

We have

<h3> $\sec \alpha \sqrt{ \cos^{2} \alpha }$ </h3>

<h3> $\sqrt{ { \cos }^{2} \alpha } = \cos \alpha$ </h3>

So we have

<h3> $\sec \alpha \times \cos \alpha$ </h3>

Using trigonometric identities

<h3> $\sec \alpha = \frac{1}{ \cos \alpha }$ </h3>

<u>Rewrite the expression</u>

That's

<h3> $\frac{1}{\cos \alpha } \times \cos \alpha$ </h3>

Reduce the expression with cos a

We have the final answer as

As proven

Hope this helps you

7 0

3 years ago

Lynne was making cookies and she

charle [14.2K]

Answer:

4 cups of flour

Step-by-step explanation:

We just need to double 2. The phrase "double" means to multiply by 2 so the answer is 2 * 2 = 4 cups of flour.

3 0

3 years ago

Can you guys please help me

VARVARA [1.3K]

Answer:

Number 1 I think sorry if I am incorrect.

8 0

3 years ago

Read 2 more answers

A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures 3 centimeters by 5 centimeters. Six

Zarrin [17]

Answer:

The volume of the box is maximized when x = 0.53 cm

Therefore, x = 0.53 cm and the Maximum volume = 1.75 cm³

Step-by-step explanation:

Please refer to the attached diagram:

The volume of the box is given by

$V = Length \times Width \times Height \\\\$

Let x denotes the length of the sides of the square as shown in the diagram.

The width of shaded region is given by

$Width = 3 - 2x \\\\$

The length of shaded region is given by

$Length = \frac{1}{2} (5 - 3x) \\\\$

So, the volume of the box becomes,

$V = \frac{1}{2} (5 - 3x) \times (3 - 2x) \times x \\\\V = \frac{1}{2} (5 - 3x) \times (3x - 2x^2) \\\\V = \frac{1}{2} (15x -10x^2 -9 x^2 + 6 x^3) \\\\V = \frac{1}{2} (6x^3 -19x^2 + 15x) \\\\$

Take the derivative of volume and set it to zero.

$\frac{dV}{dx} = 0 \\\\\frac{dV}{dx} = \frac{d}{dx} ( \frac{1}{2} (6x^3 -19x^2 + 15x)) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\0 = \frac{1}{2} (18x^2 -38x + 15)\\\\18x^2 -38x + 15 = 0\\\\$

We may solve the quadratic equation using the quadratic formula.

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

The values of coefficients a, b, c are

$a = 18 \\\\b = -38 \\\\c = 15 \\\\$

Substituting the values into quadratic formula yields,

$x=\frac{-(-38)\pm\sqrt{(-38)^2-4(18)(15)}}{2(18)} \\\\x=\frac{38\pm\sqrt{(1444- 1080}}{36} \\\\x=\frac{38\pm\sqrt{(364}}{36} \\\\x=\frac{38\pm 19.078}{36} \\\\x=\frac{38 + 19.078}{36} \: or \: x=\frac{38 - 19.078}{36}\\\\x= 1.59 \: or \: x = 0.53 \\\\$

Volume of box when x = 1.59:

$V = \frac{1}{2} (5 - 3(1.59)) \times (3 - 2(1.59)) \times (1.59) \\\\V = -0.03 \: cm^3 \\\\$

Volume of box when x = 0.53:

$V = \frac{1}{2} (5 - 3(0.53)) \times (3 - 2(0.53)) \times (0.53) \\\\V = 1.75 \: cm^3$

As you can see, the volume of the box is maximized when x = 0.53 cm

Therefore, x = 0.53 cm and the Maximum volume = 1.75 cm³

8 0

3 years ago