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ZanzabumX [31]
3 years ago
5

Let the function f be continuous and differentiable for all x. Suppose you are given that f(−1)=−3, and that f'(x) for all value

s of x. Use the Mean Value Theorem to determine the largest possible value of f(5).

Mathematics
1 answer:
Monica [59]3 years ago
8 0

Answer:

Step-by-step explanation:

By MVT,

f'(c) = \frac{f(5)-f(-1)}{5-1}

4f'(c)= f(5) + 3\rightarrow f(5) = 4f'(c) - 3

Moreover, f'(x)\leq 4~~~~~~ \forall x,

f(5) \leq 16 - 3 =13

Hence the largest possible value of f(5) is 13

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If a logo of 6 ft and he needs a quart of paint for every 22 square ft how many quarte will he need for the whole logo
bulgar [2K]

Complete Question

If a logo has dimensions of 6 ft and 11ft, he needs a quart of paint for every 22 square ft. How many quarts will he need for the whole logo?

Answer:

3 quarts of paint

Step-by-step explanation:

The Logo is rectangular in shape, hence:

The area of a rectangle = Length × Width

The logo has dimensions of 6 ft and 11ft.

Area of the Logo = 6ft × 11ft = 66ft²

He needs a quart of paint for every 22 square ft

Hence:

22 ft² = 1 quart of paint

66ft² = x

Cross Multiply

22 ft² × x = 66 ft² × 1 quart

x = 66 ft² × 1 quart/22 ft²

x = 3 quarts of paint

Therefore, he will need 3 quarts of paint for the whole logo.

7 0
3 years ago
LOTS OF POINTS ANSWER ASA P , painter is painting a rectangular wall that measures 25.1 ft by 18.5 ft. Each gallon can of paint
svlad2 [7]

Answer:

1.548 gallons

Step-by-step explanation:

Length of the rectangular wall = 25.1 ft.

Width of the rectangular wall = 18.5 ft.

Area of the rectangular wall = length * width = 25.1 * 18.5

= 464.35 square feet

300 square feet wall can be painted using 1 gallon of paint.

=> 1 square feet wall can be painted using \[\frac{1}{300}\] gallon of paint.

=> 464.35 square feet wall can be painted using \[\frac{1}{300} * 464.35\] gallon of paint.

= 1.548 gallons of paint

3 0
3 years ago
Read 2 more answers
ABCD is a rhombus, where m∠AED = 5x – 10. Use the properties of a rhombus to determine the value of x. Question 10 options: A) x
fomenos

Answer:

A) x = 20

Step-by-step explanation:

ABCD is a rhombus, AC and BD are diagonals which intersect each other at point E.

Since, diagonals of a rhombus are perpendicular bisector.

\therefore \: m \angle AED = 90 \degree \\  \therefore \: (5x - 10) \degree = 90 \degree \\ \therefore \: 5x - 10 = 90  \\ \therefore \: 5x  = 90 + 10  \\ \therefore \: 5x  = 100  \\ \\  \therefore \: x  = \frac{100}{5}  \\  \\ \huge \red{ \boxed{ \therefore \: x  =20}}

5 0
3 years ago
What is the base five representation of The number 219
ICE Princess25 [194]

assuming 219_{10}

Then the column values for base five here are

5³  5²  5^{1}  5^{0}

We can get 1 × 5³ = 125 → 219 - 125 = 94

We can get 3 × 5² = 75 → 94 - 75 = 19

We can get 3 x 5^{1} → 19 - 15 = 4

and 4 = 4 × 5^{0}

Thus 219_{10} = 1334_{5}

As a check

(1 × 125 ) + (3 × 25 ) + (3 × 5 ) + 4 = 219


3 0
3 years ago
Find the possibability of 1 head when flipping 3 coins
iogann1982 [59]
The probability of flipping 1 head when flipping 3 coins is 3/8.
Hope I helped!
3 0
3 years ago
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