H23=3H23=3 what does H equal ?

The region bounded by y=x^2+1, y=x, x=-1, x=2 with square cross sections perpendicular to the x-axis.

VLD [36.1K]

Answer:

The bounded area is 5 + 5/6 square units. (or 35/6 square units)

Step-by-step explanation:

Suppose we want to find the area bounded by two functions f(x) and g(x) in a given interval (x1, x2)

Such that f(x) > g(x) in the given interval.

This area then can be calculated as the integral between x1 and x2 for f(x) - g(x).

We want to find the area bounded by:

f(x) = y = x^2 + 1

g(x) = y = x

x = -1

x = 2

To find this area, we need to f(x) - g(x) between x = -1 and x = 2

This is:

$\int\limits^2_{-1} {(f(x) - g(x))} \, dx$

$\int\limits^2_{-1} {(x^2 + 1 - x)} \, dx$

We know that:

$\int\limits^{}_{} {x} \, dx = \frac{x^2}{2}$

$\int\limits^{}_{} {1} \, dx = x$

$\int\limits^{}_{} {x^2} \, dx = \frac{x^3}{3}$

Then our integral is:

$\int\limits^2_{-1} {(x^2 + 1 - x)} \, dx = (\frac{2^3}{2} + 2 - \frac{2^2}{2}) - (\frac{(-1)^3}{3} + (-1) - \frac{(-1)^2}{2} )$

The right side is equal to:

$(4 + 2 - 2) - ( -1/3 - 1 - 1/2) = 4 + 1/3 + 1 + 1/2 = 5 + 2/6 + 3/6 = 5 + 5/6$

The bounded area is 5 + 5/6 square units.

3 0

2 years ago

Kedar earns a monthly salary if $2,200 plus a 3.75% commission on the amount of his sales at a men's clothing store. What would

ryzh [129]

Monthly salary of Kedar = $2000
Percentage commission on the amount of his sales = 3.75%
Amount of money for which clothing sold by Kedar = $4500
Amount of interest earned by Kedar this month = (3.75/100) * 4500
= 3.75 * 45
= 168.75 dollars
So
The total amount earned by Kedar this month = (2200 + 168.75) dollars
= 2368.75 dollars
So Kedar earned a total amount of $2368.75 this month.I hope the procedure is absolutely clear to you.

7 0

3 years ago

2(3/5x+3). How would I get that answer

Airida [17]

Answer: $\frac{6}{5}$ x + 6

Step-by-step explanation:

We will use the order of operations, also known as PEMDAS. See attached. Please note that we cannot do what is in the parentheses first because we have a variable, so we will distribute the 2 into it. Since this is an expression, I do not believe we can fully solve for x, but can only simplify.

Given:

2(3/5x+3)

Distribute:

2 * (3/5x) + (2 * 3)

6/5x + 6

Answer:

$\frac{6}{5}$ x + 6

5 0

2 years ago

Find the density of a 40 gram pyramid with rectangular base 5 x 6 cm and height 8 cm.

e-lub [12.9K]

Density is <u>mass</u>
volume
With those dimensions, the volume of the pyramid is;
V = lw(h/3)
V = (5)(6)(8/3)
V = 80 cm^3

D = <u> 40 g </u> = 1 g/cm^3
80 cm^3

3 0

3 years ago

Read 2 more answers

PLSSS HELPPPP MEEEEEE I NEED HELP HOENSTLYY I DONT UNDETRSTAND THIS

olasank [31]

Step-by-step explanation:

Hey so ok, Ill explain this the best I can.

So you see the 10/2 (10/2 is the fraction just you cant type it in that way)

So 10/2 is litterally 10÷2, which is 5 just imagine that the line inbetween is a division symbol, and it goes from top to bottom, so for example 5/2 would be 5÷2... NOT 2÷5

With this said, to simplify 10/2, just divide the numerator, (Top) by the denominator (bottom) so --> 10÷2 = 5,

so Wednesday would equal 5 (and 5 is the same as 5/1 because 5÷1=5)

Do the same for Thursday 18÷3 = 6

So Thursday would equal 6 (and 6 is the same as 6/1 because 6÷1=6)

and since 6 > 5, (aka 6/1 > 5/1) She ran a longer distance per mile on Thursday, therefore she ran faster on Thursday.

Hopefully I answered your question in the right way.

8 0

2 years ago