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3 years ago

Th

Mathematics

1 answer:

Elodia [21]3 years ago

3 0

Answer:

Step-by-step explanation:

"There is a two-digit number such that the sum of its digits is 6"

The digits can be

0, 6 possible numbers: 06, 60

1, 5 possible numbers: 15, 51

2, 3 possible numbers: 23, 32

3, 3 possible numbers: 33

"the product of the digits is 1/3 of the original number"

That means we need a number that is 3 times the product of the digits.

0, 6 product of the digits: 0 3 times product: 0

1, 5 product of the digits: 5 3 times product: 15

2, 3 product of the digits: 6 3 times product: 18

3, 3 product of the digits: 9 3 times product: 27

The only number that appears with both conditions is 15.

Answer: 15

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If 5x - 2 = -12, then x =

yKpoI14uk [10]

Answer:

x = -2

Step-by-step explanation:

1) add 2 to both sides to eliminate -2.

5x = -10

2) divide both sides by 5.

x = -2

7 0

4 years ago

Read 2 more answers

Select the correct answer from each drop-down menu.

Oksi-84 [34.3K]

Answer:

$we \: have \: ohms \: law \: h = {i}^{2} rt \\ \frac{h}{t} = {i}^{2} rt \div t = p \\ p = {i}^{2} r....(1) \\ we \: have \: v = ir \\ i = \frac{v}{r} .....(2) \\ put \: (2) \: in \: (1) \\ then \: p = { (\frac{v}{r}) }^{2} r \\ p = \frac{ {v}^{2} }{r} \\ v = \sqrt{pr} = {(pr)}^{ \frac{1}{2} } \\ 2) \\ here \: r = 32 \: and \: p = .5 \\ then \: v = \sqrt{32 \times .5} \\ = \sqrt{16} = 4volt \\ thank \: you$

6 0

3 years ago

Carol has some dimes and quarters. If she has 31 coins worth a total of $4.30, how many of each type of coin does she have?

sasho [114]

Answer:

23 Dimes and 8 Quarter.

Step-by-step explanation:

Important info:

31 Coins worth a total of $4.30

Note:

Dimes = .10

Quarters = .25

10 Dimes = 1.00

4 Quarter = 1.00

Question to Answer:

How many of each type of coin does she have?

Solution:

Lets get rid of the .30 cent in $4.30 so

.30 = 3 Dimes

Now $4.00,

4.00-1.00 of quarter

3.00 and 4 quarter..

Right now we have 3 Dimes and 4 Quarter = $1.30.

And that 7 Coins worth of $1.30.

3.00-2.00= 1.00 and 20 Dimes so now we have

23 Dimes and 4 Quarter.

And that add up to 27.

1.00-1.00 of Quarter = 4 Quarter.

so 31 worth a total of $4.30.

So that's 23 Dimes and 8 Quarter.

Check Work:

23 Dimes = $2.30 and 8 Quarter = $2.00

$2.30 + $2.00 = 4.30

Hence, The Correct Answer is 23 Dimes and 8 Quarter.

~[ RevyBreeze }~

5 0

3 years ago

Xy′ = √(1 − y2 ), y(1) = 0

tigry1 [53]

Answer:

y=sin(ln(x))

Step-by-step explanation:

First, we have to order the terms as follows and express y' as dy / dx:

$x*\frac{dy}{dx} =\sqrt{(1-y^{2} )} \\\frac{x}{dx}=\frac{dy}\sqrt{(1-y^{2} )}}\\\frac{dx}{x}=\frac{dy}{\sqrt{(1-y^{2} )} }$

Then, we have to integrate

$\int{\frac{dx}{x}=\int{\frac{dy}{\sqrt{(1-y^{2} )} }$

with this solution after integration:

$ln(x)+C1=arcsin(y)+C2$

Then, we have to reorder

$arcsin(y)=ln(x)+C$

and applied Sin function on both sides

$sin(arcsin(y))=sin(ln(x)+C)\\y=sin(ln(x)+C)$

To define the value of C, we use the known point y(1)=0 and replace in the equation

$y=sin(ln(x)+C)\\0=sin(ln(1)+C)\\0=sin(0+C)\\0=sin(C)\\C=arcsin(0)\\C=0$

The function that proves that differential equation is

$y=sin(ln(x))$

6 0

3 years ago

Can someone please give me the answers to these 2 will add 40 points

Zielflug [23.3K]

Answer:

Step-by-step explanation:

Use sine and cosine.

$sine=\dfrac{opposite}{hypotenuse}$

$cosine=\dfrac{adjacent}{hypotenuse}$

Q8.

We have:

$opposite=y\\\\adjacent=x\\\\hypotenuse=18\\\\\alpha=18^o\\\\\sin18^o\approx0.309\\\\\cos18^o\approx0.9511$

Substitute:

$\dfrac{y}{18}=0.309$ <em> multiply both sides by 18</em>

$y=5.562\to y\approx5.6$

$\dfrac{x}{0.9511}=18$ <em>multiply both sides by 0.9511</em>

$x=17.1198\to x\approx17.1$

Q9.

We have:

$opposite=y\\\\adjacent=x\\\\hypotenuse=26\\\\\alpha=68^o\\\\\sin68^o\approx0.9272\\\\\cos68^o\approx0.3746$

Substitute:

$\dfrac{y}{26}=0.9272$ <em>multiply both sides by 26</em>

$y=24.1072\to y\approx24.1$

$\dfrac{x}{26}=0.3746$ <em>multiply both sides by 26</em>

$x=9.7396\to x\approx9.7$

7 0

3 years ago