What is the remainder when you find 298

ZanzabumX [31]

Consider the function $f(x)=x^{1/3}$ , which has derivative $f'(x)=\dfrac13x^{-2/3}$ .

The linear approximation of $f(x)$ for some value $x$ within a neighborhood of $x=c$ is given by

$f(x)\approx f'(c)(x-c)+f(c)$

Let $c=64$ . Then $(63.97)^{1/3}$ can be estimated to be

$f(63.97)\approxf'(64)(63.97-64)+f(64)$
$\sqrt[3]{63.97}\approx4-\dfrac{0.03}{48}=3.999375$

Since $f'(x)>0$ for $x>0$ , it follows that $f(x)$ must be strictly increasing over that part of its domain, which means the linear approximation lies strictly above the function $f(x)$ . This means the estimated value is an overestimation.

Indeed, the actual value is closer to the number 3.999374902...

4 0

3 years ago

Find (a) the perimeter and (b) the area of the figure. Use 3.14 or 22 22 for 1. Round your answer to the nearest hundredth, if n

Vedmedyk [2.9K]

Step-by-step explanation:

i dont know

3 0

3 years ago

Lou has a solid clay brick in the shape of a rectangular prism with a length of 8 inches, a width of 3.5 inches, and a height of

Rzqust [24]

The weight of solid clay brick is 66.465 ounces, if solid brick with a length of 8 inches, a width of 3.5 inches, and a height of 2.25 inches and the clay weighs 1.055 ounces per cubic inch.

Step-by-step explanation:

The given is,

A solid clay brick in the shape of a rectangular prism.

A length of 8 inches, a width of 3.5 inches, and a height of 2.25 inches.

The clay weighs 1.055 ounces per cubic

Step:1

Formula for volume of rectangular prism,

$Volume, V= whl$ ...................(1)

Where, w - Width of the rectangular prism

h - Height of rectangular prism

l - Length of rectangular prism

From the given,

w = 3.5 inches

h = 2.25 inches

l = 8 inches

Equation (1) becomes,

$= (3.5)(2.25)(8)$

$= (7.875)(8)$

$= 63$

Volume, V = 63 cubic inches

Step:2

Weight of brick = Volume of brick × Weight per cubic inch

$= (63) (1.055)$

= 66.465 ounces

Weight of brick = 66.465 ounces

Result:

The weight of solid clay brick is 66.465 ounces, if solid brick with a length of 8 inches, a width of 3.5 inches, and a height of 2.25 inches and the clay weighs 1.055 ounces per cubic inch.

7 0

3 years ago

Prove that the sum of the squares of two consecutive integers is odd

seraphim [82]

Answer:

Step-by-step explanation:

Start by breaking up the question into parts:'always an odd number' . An even number is any number divisible 2 e.g. 2n, an odd number is always 1 higher or lower than an even number e.g. 2n+1 or something similar. Getting an answer at the end of working of this form will prove the theory'any two consecutive integers' means two numbers that are next to each other on the number line.To prove this, we can do this in terms of n i.e. n and n+1'the squares' square the two terms we have just written down to give n2 and (n+1)2The 'sum of the squares' tells us to add these two parts together. We would then hope to work through this and get something similar to the idea of 2n+1 or something similarn2+(n+1)2=2n2+2n+1=2(n2+n) +1. The first part of this is even because it is divisible by 2. By adding 1 it must become odd.

4 0

3 years ago

Read 2 more answers

Given f(x)=9-2x, find f(10). A.-11 B.11 C.29 D.-29

zaharov [31]

The given function is a linear function that decreases as the value of the

input x increases.

The value of f(10), given f(x) = 9 - 2·x is option A. -11

Reasons:

The given function is f(x) = 9 - 2·x

The output of the function is the value of f(x) for a given input x of the function.

The input value, x is substituted into the function to obtain the output value, f(x).

Given that the input, x = 10

We have;

f(10) = 9 - 2×10 = -11

Therefore, the correct option for f(10) is A. -11

Learn more about functions here:

brainly.com/question/10781304

7 0

2 years ago

Read 2 more answers

What is the remainder when you find 298 - 3?