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agasfer [191]
2 years ago
7

If

"latex-formula">, prove that f(x) + f(x+1)=4f(x)
Mathematics
1 answer:
SOVA2 [1]2 years ago
8 0

$f(x)+f(x+1) \stackrel{1}{=} 3^x+3^{x+1} \stackrel{2}{=} 3^x+3^x\cdot3^1\stackrel{3}{=}3^x+3\cdot3^x\stackrel{4}{=}4\cdot3^x\stackrel{5}{=}4\cdot f(x)

1) Substitution from definition.

2) We use $x^{a+b}=x^a\cdot x^b

3) We are changing the order of 3 and 3^x.

4) We add 1 and 3 3^x and we get 4\cdot 3^x

5) Substitution from definition (but the other way than at the beginning).

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What is the length of the hypotenuse
Viefleur [7K]

Answer:

15ft

Step-by-step explanation:

a^2 + b^2 = c^2

12 or 9 can equal to b or a

12^2 + 9^2 = c^2

144 + 81 = c ^2

225 = c^2

Square root of 225

15 = c

4 0
3 years ago
Read 2 more answers
Can someone help me <br> 14. Determine the arc length. Give your answer to two decimal places.
Paul [167]

Answer:

19.48 m

Step-by-step explanation:

The formula that is used to find arc length is:

arc length = 2πr (\frac{angle}{360})

In this question, r = 9m and the angle (θ) = 124°. Substitute the values into the formula.

arc length = 2 × π × 9 ×(\frac{124}{360})

= 2 × π × 9 × 0.3444

= 19.48 m

8 0
2 years ago
You need to design a rectangle with a perimeter of 14.2 cm. The length must be 2.4 cm. What is the width of the
irina1246 [14]

Part (a)

<h3>Answer: 2(2.4+w) = 14.2</h3>

--------------

Explanation:

L = 2.4 = length

W = unknown width

The perimeter of any rectangle is P = 2(L+W)

We replace L with 2.4, and replace P with 14.2 to get 14.2 = 2(2.4+w) which is equivalent to 2(2.4+w) = 14.2

========================================================

Part (b)

<h3>Answer:   w = 4.7</h3>

--------------

Explanation:

We'll solve the equation we set up in part (a)

2(2.4+w) = 14.2

2(2.4)+2(w) = 14.2

4.8+2w = 14.2

2w = 14.2-4.8

2w = 9.4

w = 9.4/2

w = 4.7

The width must be 4.7 cm.

4 0
3 years ago
Can anyone tell me what the answer please please
marishachu [46]

Answer:

where is the photo?

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 3x2 − 2x + 1, [0, 2] Yes, it do
expeople1 [14]

Answer:

Yes , function is continuous in [0,2] and is differentiable (0,2) since polynomial function are continuous and differentiable

Step-by-step explanation:

We are given the Function

f(x) =3x^2 -2x +1

The two basic hypothesis of the mean valued theorem are

  • The function should be continuous in [0,2]
  • The function should be differentiable in (1,2)

upon checking the condition stated above on the given function

f(x) is continuous in the interval [0,2] as the functions is quadratic and we  can conclude that from its graph

also the f(x) is differentiable in (0,2)

f'(x) = 6x - 2

Now the function satisfies both the conditions

so applying MVT

6x-2 = f(2) - f(0) / 2-0

6x-2 = 9 - 1 /2

6x-2 = 4

6x=6

x=1

so this is the tangent line for this given function.

   

4 0
2 years ago
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