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3 years ago

Find the distance between the pair of points that given on the graph?

Mathematics

1 answer:

katen-ka-za [31]3 years ago

8 0

Answer:

$\displaystyle d = \sqrt{74}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Reading a coordinate plane
Coordinates (x, y)

Algebra Ii

Distance Formula: $\displaystyle d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$

Step-by-step explanation:

Step 1: Define

Find endpoints from graph

Point (-3, -3)

Point (4, 2)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Substitute in points [Distance Formula]: $\displaystyle d = \sqrt{(4- -3)^2+(2- -3)^2}$
[√Radical] (Parenthesis) Subtract: $\displaystyle d = \sqrt{7^2+5^2}$
[√Radical] Evaluate exponents: $\displaystyle d = \sqrt{49+25}$
[√Radical] Add: $\displaystyle d = \sqrt{74}$

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The volume of a spherical balloon is increasing at the constant rate of 8 cubic feet per minute. How fast is the radius incresin

OverLord2011 [107]

Answer:

Rate of increase of radius = 0.0064 ft/sec

Rate of increase of surface area = 1.61 $ft^2/sec$

Step-by-step explanation:

Given that:

Rate of change of volume of a spherical balloon = 8 cubic feet per minute

$\dfrac{dV}{dt} = 8 ft^3/min$

Radius, $r$ = 10 feet

To find:

The rate of change of radius at this moment and rate of change of surface area at this moment?

Solution:

First of all, let us have a look at the formula:

$1.\ V = \dfrac{4}{3}\pi r^3\\2.\ A =4\pi r^2$

Now, differentiating the volume and area, we get:

$\dfrac{dV}{dt} = \dfrac{4}{3}\times 3 \pi r^2 \dfrac{dr}{dt}\\\Rightarrow \dfrac{dV}{dt} = 4 \pi r^2 \dfrac{dr}{dt}$

$\dfrac{dA}{dt} = 4\pi \times 2 r \dfrac{dr}{dt}\\\Rightarrow \dfrac{dA}{dt} = 8\pi r \dfrac{dr}{dt}$

$\dfrac{dV}{dt} = 8 = 4\pi r^2 \dfrac{dr}{dt}\\\Rightarrow 8 = 4\times 3.14 \times 10^2 \dfrac{dr}{dt}\\\Rightarrow 2 = 3.14 \times 10^2 \dfrac{dr}{dt}\\\Rightarrow \dfrac{dr}{dt} = 0.0064\ ft/sec$

$\dfrac{dA}{dt} = 8\times \pi \times r \dfrac{dr}{dt}\\\Rightarrow \dfrac{dA}{dt} = 8\times 3.14 \times 10 \times 0.0064\\\Rightarrow \dfrac{dA}{dt} = \bold{1.61 \ ft^2/sec}$

7 0

3 years ago

A sum of Rs. 1800 borrowed for 2 years at the rate of 12 % per annum. Find the interest?

wel

Answer:

Step-by-step explanation:

principal (P)=1800

time(T)=2yrs

rate(R)=2%

SI=?

now,

SI=PTR÷100

= 1800×2×2÷100

=7200÷100

=72

so interest is 72.

hope this will help you :D

7 0

4 years ago

Miles draws three cards at random from a standard deck of 52 cards, without replacement.

o-na [289]

Answer:

P( red, red, red no replacement ) = 2/17

P( 3 cards with same rank, no replacement) = 1/425

Step-by-step explanation:

There are 52 cards, 26 are red

P( red) = red/total =26/ 52 = 1/2

Now draw the second card without replacement

There are 51 cards, 25 are red

P( red) = red/total =25/51

Now draw the third card without replacement

There are 50 cards, 24 are red

P( red) = red/total =24/50 = 12/25

P( red, red, red no replacement ) = 1/2 * 25/51 * 12/25 = 2/17

P ( all have the same rank)

There are 52 cards, 4 of each rank

We don't care what the first rank is, now the second and third draw have to have the same rank as the first

P( rank) = 1/1

Now draw the second card without replacement

There are 51 cards, 3 are left with the same rank

P( same rank) = cards with same rank/total = 3/51

Now draw the third card without replacement

There are 50 cards, 2 are left with the same rank

P( same rank) = cards with same rank/total = 2/50 = 1/25

P( 3 cards with same rank, no replacement) = 1 * 3/51*1/25 = 1/425

4 0

3 years ago

Two questions on Sum and Different right triangles (Last two questions)

Vlad1618 [11]

Answer:

do you want the full formula and explanation or just answer?

7 0

3 years ago

an airplane propeller turns at a constant rate of 3000 revolutions per minute find its angular velocity in radians per minute

iVinArrow [24]

1 revolution = 2 pi radians
2 revolutions = 2 x (2 pi) radians
3 revolutions = 3 x (2 pi) radians
4 revolutions = 4 x (2 pi) radians
.
.
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9 revolutions = 9 x (2 pi) radians
.
.
3000 revolutions = 3000 x (2 pi) radians = 6,000 pi radians

= 18,849.6 radians (rounded)

8 0

3 years ago