Ask question

Ask question

All categories

riadik2000 [5.3K]

3 years ago

6

6 is 15% of what number

1 answer:

larisa [96]3 years ago

4 0

40 is the answer 15% of 40=6

You might be interested in

I have 30 ones, 82 thousand, 60tens and 100 hundreds

Neporo4naja [7]

That creates the number 82,190

6 0

3 years ago

Please help. will give points

Snezhnost [94]

(x² + 10)(6x - 5)
6x³ - 5x² + 60x - 50 or the second option

6 0

3 years ago

Problem 4: Solve the initial value problem

pishuonlain [190]

Separate the variables:

$y' = \dfrac{dy}{dx} = (y+1)(y-2) \implies \dfrac1{(y+1)(y-2)} \, dy = dx$

Separate the left side into partial fractions. We want coefficients a and b such that

$\dfrac1{(y+1)(y-2)} = \dfrac a{y+1} + \dfrac b{y-2}$

$\implies \dfrac1{(y+1)(y-2)} = \dfrac{a(y-2)+b(y+1)}{(y+1)(y-2)}$

$\implies 1 = a(y-2)+b(y+1)$

$\implies 1 = (a+b)y - 2a+b$

$\implies \begin{cases}a+b=0\\-2a+b=1\end{cases} \implies a = -\dfrac13 \text{ and } b = \dfrac13$

So we have

$\dfrac13 \left(\dfrac1{y-2} - \dfrac1{y+1}\right) \, dy = dx$

Integrating both sides yields

$\displaystyle \int \dfrac13 \left(\dfrac1{y-2} - \dfrac1{y+1}\right) \, dy = \int dx$

$\dfrac13 \left(\ln|y-2| - \ln|y+1|\right) = x + C$

$\dfrac13 \ln\left|\dfrac{y-2}{y+1}\right| = x + C$

$\ln\left|\dfrac{y-2}{y+1}\right| = 3x + C$

$\dfrac{y-2}{y+1} = e^{3x + C}$

$\dfrac{y-2}{y+1} = Ce^{3x}$

With the initial condition y(0) = 1, we find

$\dfrac{1-2}{1+1} = Ce^{0} \implies C = -\dfrac12$

so that the particular solution is

$\boxed{\dfrac{y-2}{y+1} = -\dfrac12 e^{3x}}$

It's not too hard to solve explicitly for y; notice that

$\dfrac{y-2}{y+1} = \dfrac{(y+1)-3}{y+1} = 1-\dfrac3{y+1}$

Then

$1 - \dfrac3{y+1} = -\dfrac12 e^{3x}$

$\dfrac3{y+1} = 1 + \dfrac12 e^{3x}$

$\dfrac{y+1}3 = \dfrac1{1+\frac12 e^{3x}} = \dfrac2{2+e^{3x}}$

$y+1 = \dfrac6{2+e^{3x}}$

$y = \dfrac6{2+e^{3x}} - 1$

$\boxed{y = \dfrac{4-e^{3x}}{2+e^{3x}}}$

7 0

2 years ago

Elis [28]

Answer:

2 ≤ x < 9 or x = [2, 9)

Step-by-step explanation:

<u>Negative four is at least six less than a number</u>

-4 ≤ x - 6 ⇒ x ≥ 2

<u>Sum of a negative two & nine times a number is less than seventy nine</u>

-2 + 9x < 79 ⇒ 9x < 81 ⇒ x < 9

<u>Combined inequality:</u>

2 ≤ x < 9 or x = [2, 9)

3 0

3 years ago

Which equation can be used to find the unknown length, b, in this triangle?

Romashka-Z-Leto [24]

The equation for finding the hypotneus of a right triangle is
${a }^{2} + {b}^{2} = c {}^{2}$
so we know that 4²+b²=5²
so that would simplify as 16+b=25
so x=25-16
which is 9
so therefore we can conclude that
$b = 9inches$

3 0

3 years ago

Read 2 more answers