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3 years ago

A.(2,1)

Mathematics

1 answer:

Alex17521 [72]3 years ago

4 0

Answer:

D(6, 3)

Step-by-step explanation:

The diagonals of a rectangle bisect each other, so the midpoint of AC is the same as the midpoint of BD. This means ...

(A +C)/2 = (B +D)/2 . . . . the midpoints are the same

A +C = B +D . . . . . . . . . multiply by 2

D = A +C -B = (2+5-2, 1+5-3) . . . . . solve for D, substitute given coordinates

D = (6, 3)

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The mass of the particles that a river can transport is proportional to the sixth power of the speed of the river. A certain riv

kari74 [83]

The river flows at 2 miles per hour. This is the speed of the current, or the speed at which the water itself is moving.

The mass of the particles moving in river is proportional to the sixth power of 2, or $2^6 = 64$ miles per hour. So, if x is the mass of the particle, then the speed is modeled by an inverse relationship $x * 2^6 = k$ , for some constant k.

For particles that are 15 times the usual mass, the speed of the river itself must increase for the particles to travel at the same speed as before. The mass of the particles is still proportional to the sixth power of the speed of the river, but the speed of the river can no longer be 2 miles per hour. It is some speed y, which we are solving for.

So, the key here is proportional. We can set up two proportions and cross multiply.

$\dfrac{x}{2^6} = \dfrac{15x}{y^6} \\ (x)(y^6)=(2^6)(15x)$

Cancelling our x's (because we don't need to solve for them), we have

$y^6 = 15(2^6) = 15(64)=960$

To solve for y, we must take the sixth root of both sides, or raise both sides to the one-sixth power.

$\sqrt[6]{y^6} = \sqrt[6]{960}$

Using a calculator, we see that $\sqrt[6]{960} = 3.14 \ miles \ per \ hour$ .

6 0

3 years ago

A washer and dryer cost a total of $924. The cost of the washer is two times the cost of the dryer. Find the cost of each item.

marshall27 [118]

Answer:

Washer = $616, Dryer = $308

Step-by-step explanation:

When something is twice the cost of something else but add up to be a total number that means 2/3rds is one item and 1/3 is the other.

924 / 3 = 308

308 * 2 = 616

308 + 616 = 924

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3 years ago

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false:

kondaur [170]

$\text{Proof by induction:}$
$\text{Test that the statement holds or n = 1}$

$LHS = (3 - 2)^{2} = 1$
$RHS = \frac{6 - 4}{2} = \frac{2}{2} = 1 = LHS$
$\text{Thus, the statement holds for the base case.}$

$\text{Assume the statement holds for some arbitrary term, n= k}$
$1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2} = \frac{k(6k^{2} - 3k - 1)}{2}$

$\text{Prove it is true for n = k + 1}$
$RTP: 1^{2} + 4^{2} + 7^{2} + ... + [3(k + 1) - 2]^{2} = \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2} = \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$

$LHS = \underbrace{1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2}}_{\frac{k(6k^{2} - 3k - 1)}{2}} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1)}{2} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2[3(k + 1) - 2]^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2(3k + 1)^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 18k^{2} + 12k + 2}{2}$
$= \frac{k(6k^{2} - 3k - 1 + 18k + 12) + 2}{2}$
$= \frac{k(6k^{2} + 15k + 11) + 2}{}$
$= \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$
$= \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2}$
$= RHS$

Since it is true for n = 1, n = k, and n = k + 1, by the principles of mathematical induction, it is true for all positive values of n.

3 0

3 years ago

What is the smallest fraction between 1/2

ki77a [65]

What do you mean by this?

4 0

3 years ago

It gets cut off but it says ' Write the number marked with an arrow on the number line below as an improper (top-heavy) fraction

Anit [1.1K]

Answer:

1.2

Step-by-step explanation:

it's 1.2 because

the marked parts on the number line represent a fraction of the whole

so in writing this

it will be decimals

and wen the marked lines between 0 and 1 are counted it is 4

so starting each marked line represent 2

0.2,0.4,0.6,0.8,1,1.2,1.4,......

so from 1 the next marked part is 1.2

so the answer is <u>1.2</u>

7 0

2 years ago