Kato buys a recliner on Saturday. If the original price is 350 dollars, how much does he get off the original price?

The amount of a 500 g sample of a radioactive substance that remains over time is given by the equation , where d is the number

Vlada [557]

Non-linear

The line should be an exponential function, as it halves in mass every time a certain amount of time has passed.

4 0

3 years ago

Please help me with these, oh sweet jesus

Lelechka [254]

Answer:

77. $\cot^{6} x = \cot^{4} x \csc^{2}x - \cot^{4} x$ Proved

78. $\sec^{4}x \tan^{2} x = \sec^{2}x [\tan^{2}x + \tan^{4}x ]$ Proved

79. $\cos^{3} x\sin^{2} x = [\sin^{2}x - \sin^{4}x] \cos x$ Proved.

80. $\sin^{4}x - \cos^{4}x = 1 - 2\cos^{2}x + 2 \cos^{4} x$ Proved.

Step-by-step explanation:

77. Left hand side

= $\cot^{6} x$

= $\cot^{4} x \times \cot^{2} x$

= $\cot^{4}x [\csc^{2}x - 1]$

{Since we know, $\csc^{2} x - \cot^{2}x = 1$ }

= $\cot^{4} x \csc^{2}x - \cot^{4} x$

= Right hand side (Proved)

78. Left hand side

= $\sec^{4}x \tan^{2} x$

= $\sec^{2} x [1 + \tan^{2}x] \tan^{2} x$

{Since $\sec^{2}x - \tan^{2}x = 1$ }

= $\sec^{2}x [\tan^{2}x + \tan^{4}x ]$

= Right hand side (Proved)

79. Left hand side

= $\cos^{3} x\sin^{2} x$

= $\cos x[1 - \sin^{2} x] \sin^{2} x$

{Since $\sin^{2}x + \cos^{2} x = 1$ }

= $[\sin^{2}x - \sin^{4}x] \cos x$

= Right hand side

80. Left hand side

= $\sin^{4}x - \cos^{4}x$

= $[\sin^{2}x + \cos^{2}x]^{2} - 2\sin^{2} x \cos^{2}x$

{Since $\sin^{2}x + \cos^{2} x = 1$ }

= $1 - 2\cos^{2} x[1 - \cos^{2}x ]$

= $1 - 2\cos^{2}x + 2 \cos^{4} x$

= Right hand side. (Proved)

7 0

3 years ago

All of the functions shown below are either exponential growth or decay functions.

AlekseyPX

Answer:

Step-by-step explanation:

If an exponential function is in the form of y = a(b)ˣ,

a = Initial quantity

b = Growth factor

x = Duration

Condition for exponential growth → b > 1

Condition for exponential decay → 0 < b < 1

Now we ca apply this condition in the given functions,

1). $y=3.2(1+0.45)^{2x}$

Here, (1 + 0.45) = 1.45 > 1

Therefore, It's an exponential growth.

2). $y=(0.85)^{3x}$

Here, (0.85) is between 0 and 1,

Therefore, it's an exponential decay.

3). y = (1 - 0.03)ˣ + 4

Here, (1 - 0.03) = 0.97

And 0 < 0.97 < 1

Therefore, It's an exponential decay.

4). y = 0.5(1.2)ˣ + 2

Here, 1.2 > 1

Therefore, it's an exponential growth.

5 0

2 years ago

WILL GIVE BRAINLIEST What is the perimeter of the track, in meters? Use π = 3.14 and round to the nearest hundredth of a meter.

Ivenika [448]

Answer:

Perimeter = 317 m

Step-by-step explanation:

Given track is a composite figure having two semicircles and one rectangle.

Perimeter of the given track = Circumference of two semicircles + 2(length of the rectangle)

Circumference of one semicircle = πr [where 'r' = radius of the semicircle]

= 25π

= 25 × 3.14

= 78.5 m

Length of the rectangle = 80 m

Perimeter of the track = 2(78.5) + 2(80)

= 157 + 160

= 317 m

Therefore, perimeter of the track = 317 m

7 0

3 years ago

f(x) = 32g(x) = V48xFind (f.g)(x). Assume x20.O A. (f.g)(x) = 72.O B. (f.g)(x) = V51xO c. (f.g)(x) = 12/xO D. (fºg)(x) = 12xSUBM

QveST [7]

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

f(x) = √3x

g(x) = √48x

(f . g)(x) = ?

Step 02:

(f . g)(x) :

$\text{ (f.g)(x) = }\sqrt[]{3(\sqrt[]{48x)}}$ $(f.g)(x)\text{ = }\sqrt[]{3(48x)^{\frac{1}{2}}}\text{ }$

(f.g)(x) = 12 √ x

The answer is:

(f.g)(x) = 12 √ x

3 0

9 months ago