What is 9.16 minus 6.59

) dy 2x<br> ------ = ---------------<br> dx yx2 + y

larisa86 [58]

Step-by-step explanation:

$\dfrac{dy}{dx} = \dfrac{2x}{y(x^2 + 1)}$

Rearranging the terms, we get

$ydy = \dfrac{2xdx}{x^2 + 1}$

We then integrate the expression above to get

$\displaystyle \int ydy = \int \dfrac{2xdx}{x^2 + 1}$

$\displaystyle \frac{1}{2}y^2 = \ln |x^2 +1| + k$

or

$y = \sqrt{2\ln |x^2 + 1|} + k$

where I is the constant of integration.

6 0

3 years ago

Diana has been saving nickels and dimes. She opened up her piggy bank and determined that it contained 48 coins worth $4.50. Det

tino4ka555 [31]

Answer:

6 Nickels

42 Dimes

Step-by-step explanation:

There are 48 coins in total (nickels and dimes). Let the number of nickels be "n" and the number of dimes be "d". So we can write:

n + d = 48

or

n = 48 - d

In dollars, we know nickels are worth 0.05 and dimes are worth 0.10. In total there is $4.50, so we can write:

0.05n + 0.10d = 4.50

Now replacing first equation [n = 48 - d] into 2nd, we get and equation in "d" and solve for d first:

$0.05n + 0.10d = 4.50\\0.05(48-d) + 0.10d = 4.50\\2.4-0.05d+0.10d=4.50\\0.05d=4.50-2.4\\0.05d=2.1\\d=\frac{2.1}{0.05}=42$

So, there are 42 dimes.

We know from before, n = 48 - d, so

n = 48 - 42 = 6

There are 6 nickels

3 0

3 years ago

The triangles ABC and DFG are similar and the ratio of their corresponding sides is 6:5. The area of the triangle ABC is greater

Naya [18.7K]

Answer:

The Area of Δ DFG is 175 cm²

The Area of Δ ABC is 252 cm²

Step-by-step explanation:

Given as :

The Δ ABC is similar to the Δ DFG

The area of the triangle ABC is greater than the area of the triangle DFG by 77 cm²

Let The area of Δ DFG = x cm²

So, The area of Δ ABC = ( 77 + x ) cm²

The ratio of corresponding sides of Δ ABC and Δ DEF = 6 : 5

Let The side AB = 6 y

And The side DE = 5 y

Now,<u> from The property of similar Triangles</u>

$\dfrac{area ABC}{area DFG}$ = $\dfrac{AB^{2} }{DE^{2} }$

I.e $\dfrac{77+x}{x}$ = $\dfrac{(6 y)^{2} }{(5y)^{2} }$

Or, $\dfrac{77+x}{x}$ = $\dfrac{36}{25}$

Or, 25 × (77 + x ) = 36 x

Or, 25 × 77 + 25 x = 36 x

Or, 25 × 77 = 36 x - 25 x

Or, 11 x = 25 × 77

∴ x = $\frac{25\times 77}{11}$

I.e x = 175 cm²

So,The Area of Δ DFG = x = 175 cm²

And The Area of Δ ABC = x + 77 = 175 + 77 = 252 cm²

Hence, The Area of Δ DFG is 175 cm²

And The Area of Δ ABC is 252 cm² Answer

4 0

3 years ago

Jennie's car gets 32.4 miles per gallon on the highway. If her car's fuel tank holds 12.7 gallons, how far can she drive on one

kozerog [31]

For this question, you simply multiply 32.4 by 12.7 to get the number of miles that Jennie can drive. The answer is 411.48, choice c.

Hope this helps!

4 0

3 years ago

Read 2 more answers

How do you reduce the ratio 104 to 1008

Helen [10]

Treat as fraction
104/1008
divide top and bottom by 2
52/504
divide by 2
26/252
divide by 2
13/126

13:126

8 0

4 years ago