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3 years ago

What quadratic equation has roots 7 and -2/3

Mathematics

1 answer:

-BARSIC- [3]3 years ago

6 0

Answer:

(x-7)(x+2/3)

Step-by-step explanation:

To easily find an equation with said roots, use the intercept form:

y=a(x-p)(x-q), where p and q are your roots.

y=(x-7)(x-(-2/3) = y=(x-7)(x+2/3)

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Can you show the work for 444*31

marusya05 [52]

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3 years ago

Find the solution of the differential equation that satisfies the given initial condition. y' tan x = 3a + y, y(π/3) = 3a, 0 &lt

Paladinen [302]

Answer:

$y(x)=4a\sqrt{3}* sin(x)-3a$

Step-by-step explanation:

We have a separable equation, first let's rewrite the equation as:

$\frac{dy(x)}{dx} =\frac{3a+y}{tan(x)}$

But:

$\frac{1}{tan(x)} =cot(x)$

So:

$\frac{dy(x)}{dx} =cot(x)*(3a+y)$

Multiplying both sides by dx and dividing both sides by 3a+y:

$\frac{dy}{3a+y} =cot(x)dx$

Integrating both sides:

$\int\ \frac{dy}{3a+y} =\int\cot(x) \, dx$

Evaluating the integrals:

$log(3a+y)=log(sin(x))+C_1$

Where C1 is an arbitrary constant.

Solving for y:

$y(x)=-3a+e^{C_1} sin(x)$

$e^{C_1} =constant$

So:

$y(x)=C_1*sin(x)-3a$

Finally, let's evaluate the initial condition in order to find C1:

$y(\frac{\pi}{3} )=3a=C_1*sin(\frac{\pi}{3})-3a\\ 3a=C_1*\frac{\sqrt{3} }{2} -3a$

Solving for C1:

$C_1=4a\sqrt{3}$

Therefore:

$y(x)=4a\sqrt{3}* sin(x)-3a$

3 0

4 years ago

Can someone please help me? -r/3 ≤ 6

lozanna [386]

The answer would be $r \geq 2$

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4 years ago

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Setler [38]

Answer:

$\large{ \boxed{ \tt{ - 20a {z}^{2} - 2 {z}^{3} - 2 {a}^{3} + 11 {a}^{2} z }}}$

- Please see the attached picture for full solution!:)

----------------- HappY LearninG <3 --------------

3 0

2 years ago

Mary has saved $17.50 in the past 3 weeks.at This rate , how much will she save in 15 weeks ?

Oksanka [162]

Answer:

$87.60

Step-by-step explanation:

Assuming that mary is on a fixed income rate, we can calculate that Mary is making approximately $5.84 per week.

17.50 / 3 = 5.833333.... -> 5.84

Now we multiply this number by 15 to get the amount of money she saves over this time.

5.84 * 15 = 87.6

So, we can see that Mary has saved $87.60 in 15 weeks.

3 0

3 years ago