The steps to convert 37 over 4 to a decimal are shown below

Determine the length of the hypotenuse of a right triangle if the legs have lengths 12 inches and 16 inches?

tiny-mole [99]

Answer:

c = 20 inches

Step-by-step explanation:

To find the sides of a right triangle, you use the Pythagorean Theorem.

a² + b² = c²

You know a and b, and you need to find c, the hypotenuse.

Plug in a and b.

(12)² + (16)² = c²

Simplify by solving the exponents.

144 + 256 = c²

Combine the constants.

400 = c²

Take the square root of both sides.

√400 = √c²

Solve the √

±20 = c

The length cannot be negative, so you can eliminate that as an option.

So, c = 20

5 0

3 years ago

Find dy/dx for y=log (tan2x)

nekit [7.7K]

Answer:

$\frac{dy}{dx} = \frac{2}{sin2x cos2x}$

Step-by-step explanation:

y = log (tan 2x)

Applying chain rule:

$\frac{dy}{dx} = \frac{d}{dx} (1st function) . \frac{d}{dx} (2nd function). \frac{d}{dx}(3rd function)$

$\frac{dy}{dx} = \frac{d}{dx} log(tan 2x) . \frac{d}{dx} tan2x. \frac{d}{dx} 2x$

$\frac{dy}{dx} = \frac{1}{tan2x} \times sec^{2}2x \times 2$

$\frac{dy}{dx} = \frac{2sec^{2}2x }{tan2x}$

Now since $sec^{2}x = \frac{1}{cos^{2}x } \ and\ tanx = \frac{sinx}{cosx}$

∴ $\frac{dy}{dx} = \frac{2cos2x }{sin2x cos^22x}$

∴ $\frac{dy}{dx} = \frac{2}{sin2x cos2x}$

7 0

4 years ago

Which is independent and dependent

Mademuasel [1]

Answer:

The variables in a study of a cause-and-effect relationship are called the independent and dependent variables. The independent variable is the cause. ... The dependent variable is the effect. Its value depends on changes in the independent variable.

Step-by-step explanation:

4 0

3 years ago

Given the following equation where A = Area of a rectangle and w = width of the rectangle, what value of 'w' would maximize the

Papessa [141]

Answer:

the second option : w should be 25 units

Step-by-step explanation:

the area of the rectangle is length×width = L×W

the perimeter of a rectangle = 2L + 2W

now, we know that the perimeter is 100 units.

and we have to find the best length of W, that will then define L (to keep the 100 units of perimeter) and maximizes the area of the rectangle.

in other words, what is the maximum area of a rectangle with perimeter of 100 (and what are the corresponding side lengths)?

now, w = 625 is impossible. that side alone would be bigger than the whole perimeter.

W = 0 would render the whole rectangle to a flat line with L = 50 because of

100 = 2L + 2W = 2L + 0 = 2L

L = 50

and A = L×W = 50×0 = 0

an area of 0 is for sure not the largest possible area.

w = 50 would cause L = 0

100 = 2L + 2W = 2L + 2×50 = 2L + 100

0 = 2L

L = 0

and with L = 0 the same thing happens as with W = 0 : a flat line with 0 area.

so, the only remaining useful answer is W = 25

100 = 2L + 2W = 2L + 2×25 = 2L + 50

50 = 2L

L = 25

A = L×W = 25×25 = 625 units²

and indeed, the maximum area for a given perimeter is achieved by arranging the sides to create a square.

8 0

3 years ago

I want to be a teacher some day and i know this question----------What is -15 -(-8)=? remember a negitive plus a negitive equals

irina [24]

Answer is -7 because -15+8=-7

8 0

4 years ago