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3 years ago

If the circumference of a circle is 11 what’s the area?

Mathematics

1 answer:

Ivan3 years ago

5 0

Circumference = 2 π r = 11
r = 11 / 2π = 1.75
Area = π r² = π (1.75)² = 9.625 square units

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If f(x) = 3x2 − 8x, 0 ≤ x ≤ 3, evaluate the Riemann sum with n = 6, taking the sample points to be right endpoints.

denis23 [38]

Split up the interval [0, 3] into 6 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], [3/2, 2], [2, 5/2], [5/2, 3]

The right endpoints are given by the arithmetic sequence,

$r_i=0+\dfrac i2=\dfrac i2$

with $1\le i\le6$ .

We approximate the integral of $f(x)$ on the interval [0, 3] by the Riemann sum,

$\displaystyle\int_0^3f(x)\,\mathrm dx=\sum_{i=1}^6f(r_i)\Delta x_i$

$\displaystyle=\frac{3-0}6\sum_{i=1}^6\left(3{r_i}^2-8r_i\right)$

$\displaystyle=\frac12\sum_{i=1}^6\left(\frac{3i^2}4-4i\right)$

$\displaystyle=\frac38\sum_{i=1}^6i^2-2\sum_{i=1}^6i$

Recall the formulas,

$\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2$

$\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$

Then the value of the integral is approximately

$\displaystyle=\frac38\cdot\frac{6\cdot7\cdot13}6-2\cdot\frac{6\cdot7}2=\boxed{-\frac{63}8}=-7.875$

Compare to the exact value of the integral, -9.

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3 years ago

Jason has a box that is 10 inches by 6 inches by 16 inches. He has an object that is 20 inches long. Will it fit in his box? Why

Norma-Jean [14]

Answer:

Step-by-step explanation:

because the length,width,or height have to be 20 inches or longer for Jason's object to fit

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4 years ago

A polynomial multiplied by a polynomial is a polynomial

Kruka [31]

Answer:

True

Step-by-step explanation:

I looked it up since I'm not good at explanations so here you go, sorry if this is a late reply;

"True: the product of two polynomials will be a polynomial regardless of the signs of the leading coefficients of the polynomials. When two polynomials are multiplied, each term of the first polynomial is multiplied by each term of the second polynomial."

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3 years ago

Line L has equation 2x - 3y = 5. Line M passes through the point (2, -10) and is perpendicular to line L. Determine the equation

Whitepunk [10]

C has to be the right one

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4 years ago

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A meteorologist reports that the temperature today will be colder than −1° Fahrenheit. The inequality is t < −1. The variable

Bad White [126]

Answer:

$-2$

Step-by-step explanation:

Given: The inequality is $t$ where t represents the temperature. A number line going from $-2$ to $2$ .

To find: Solutions of the inequality

Solution:

A number line is a line on which numbers are marked at equal intervals, used to show simple arithmetic operations.

An inequality is a mathematical relationship that compares two values to show less than or equal to, less than, not equal to, greater than, greater than or equal to.

In the given question solution of the inequality $t$ is $-2$ as a number line is going from $-2$ to $2$ .

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3 years ago

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