How to find angle acb

Let A be a non-empty set of rational numbers and B = {a+1 : a ∈ A} (sometimes denotes A + 1). Prove carefully that sup(B) = sup(

liraira [26]

Answer:

a is an element of A; a is a rational number

(a+1) is element of B

Step-by-step explanation:

(a+1) = sup(A), which are the elements of B.

(a+1) + 1 = sup(B)

Recall a+1 = sup(A),

Therefore,

sup(A )+ 1 = sup(B)

sup(B) = sup(A) + 1 ___proved

Sup(A) means supremum of set A. It means least element of another set (say set B), that is greater than every element in set A

8 0

4 years ago

Evaluate the integral Find the volume of material remaining in a hemisphere of radius 2 after a cylindrical hole ofradius 1 is d

algol13

You want to find the volume inside the hemisphere $x^2+y^2+z^2=4$ (i.e. inside the sphere but above the plane $z=0$ ) and outside the cylinder $x^2+y^2=1$ . Call this region $R$ .

In cylindrical coordinates, we have

$\displaystyle\iiint_R\mathrm dV=\int_0^{2\pi}\int_1^2\int_0^{\sqrt{4-r^2}}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$

$\displaystyle=2\pi\int_1^2 r\sqrt{4-r^2}\,\mathrm dr$

$\displaystyle=-\pi\int_3^0\sqrt u\,\mathrm du$

(where $u=4-r^2$ )

$\displaystyle=\pi\int_0^3\sqrt u\,\mathrm du$

$=\dfrac{2\pi}3u^{3/2}\bigg|_0^3=2\sqrt3\,\pi$

7 0

4 years ago

The table shows the weight gain of a kitten over a

stepan [7]

Answer:

The rate of change of the weight of kitten A is greater than the rate of change of the weight of kitten B

Step-by-step explanation:

The rate of change of the linear relationship is the slope of the line which represent this relationship

The rule of the slope is m = $\frac{y2-y1}{x2-x1}$ , where (x1, y1) and (x2, y2) are 2 points on the line

∵ The table shows the weight gain of kitten A

→ Choose two points from the table to find the slope

∵ Points (0, 3) and (1, 7) are two points in the table

∴ x1 = 0 and y1 = 3

∴ x2 = 1 and y2 = 7

→ Substitute them in the rule of the slope above

∵ m = $\frac{7-3}{1-0}$ = $\frac{4}{1}$ = 4

∵ The slope is the rate of change

∴ The rate of change of the weight of kitten A is 4 oz/week

∵ The graph shows the weight gain of kitten B

→ Choose two points on the line to find the slope

∵ Points (0, 4) and (2, 10) lies on the line

∴ x1 = 0 and y1 = 4

∴ x2 = 2 and y2 = 10

→ Substitute them in the rule of the slope above

∵ m = $\frac{10-4}{2-0}$ = $\frac{6}{2}$ = 3

∵ The slope is the rate of change

∴ The rate of change of the weight of kitten B is 3 oz/week

→ By comparing the two rates

∵ The rate of change of kitten A is 4 oz per week

∵ The rate of change of kitten B is 3 oz per week

∴ The rate of change of the weight of kitten A is greater than

the rate of change of the weight of kitten B

7 0

3 years ago

In one month, the median home price in the Northwest rose from \$198,500 to $200,800 . Find the percent increase. Round to the n

krek1111 [17]

Answer:

1.16% decreases

Step-by-step explanation:

200,800 - 198,5000 = 2300

divided by og number

2300/198,500 = .01158

in percent and rounded = 1.16%

8 0

2 years ago

Savings account A and savings account B both offer APRs of 4%, but savings account A compounds interest quarterly, while savings

Digiron [165]

The answer is b because theres more transactions with mothly that quarterly

6 0

4 years ago

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