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3 years ago

-4y + 7 = 35y - 6 Need Help

Mathematics

1 answer:

makkiz [27]3 years ago

4 0

Answer:

$y=\frac{1}{3}$

Step-by-step explanation:

Subtract $7$ from both sides of the equation:

$-4y+7=35y-6$

$-4y+7$ $-7=35y-6$ $-7$

Simplify:

Subtract the numbers:

$-4y+7$ $-7=35y-6-7$

$-4y=35y-6-7$

Subtract the numbers:

$-4y=35y$ $-6$ $-7$

$-4=35y$ $-13$

$-4y=35y-13$

Subtract $35y$ from both sides of the equation:

$-4y=35y-13$

$-4y$ $-35y=35y-13$ $-35y$

Simplify:

Combine like terms:

$-4$ $-35y=35y-13-35y$

$-39y=35y-13-35y$

Combine like terms:

$-39y=35y-13$ $-35y$

$-39y=-13$

Divide both sides of the equation by the same term:

$-39y=-13$

$\frac{-39y}{-39} =\frac{-13}{-39}$

Simplify:

Cancel terms that are in both the numerator and denominator:

$\frac{-39y}{-39} =\frac{-13}{-39}$

$y=\frac{-13}{-39}$

Divide the numbers:

$y=\frac{-13}{-39}$

$y=\frac{1}{3}$

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SOMEONE HELP

pantera1 [17]

Answer:

Step-by-step explanation:

Given y varies directly as x and z then the equation relating them is

y = kxz ← k is the constant of variation

To find k use the condition y = $\frac{8}{3}$ when x = 1 and z = 4 , then

$\frac{8}{3}$ = k × 1 × 4 = 4k ( divide both sides by 4 )

$\frac{2}{3}$ = k

y = $\frac{2}{3}$ xz ← equation of variation

When x = 6 and z = 3 , then

y = $\frac{2}{3}$ × 6 × 3 = $\frac{2}{3}$ × 18 = 2 × 6 = 12

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3 years ago

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The measure of an ____ angle of a tringle is equal to the sum of the measures of its remote interior angles

Aleonysh [2.5K]

Answer:

Exterior.

Step-by-step explanation:

A triangle has three sides. According to the theorem of exterior angles, the sum of two opposite interior angles is equal to the exterior angle of the triangle.

The sum of angle of triangle is equal to 180 degrees.

ATQ,

The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.

7 0

3 years ago

(a) Suppose anxn has finite radius of convergence R and an ≥ 0 for all n. Show that if the series converges at R, then it also c

valina [46]

Answer:

a) See the proof below.

b) $\sum \frac{(-x)^n}{n}$

Step-by-step explanation:

Part a

For this case we assume that we have the following series $\sum a)n x^n$ and this series has a finite radius of convergence $R$ and we assume that $a_n \geq 0$ for all n, this information is given by the problem.

We assume that the series converges at the point $x= R$ since w eknwo that converges, and since converges we can conclude that:

$\sum a)n R^n < \infty$

For this case we need to show that converges also for $x=-R$

So we need to proof that $\sum a_n (-R)^n < \infty$

We can do some algebra and we can rewrite the following expression like this:

$\sum a_n (-R)^n = \sum (-1)^n a)n R^n$ and we see that the last series is alternating.

Since we know that $\sum a_n x^n$ converges then the sequence { $a_n R^n$ } must be positive and we need to have $lim_{n\to \infty} a^n R^n = 0$

And then by the alternating series test we can conclude that $\sum a_n (-R)^n$ also converges. And then we conclude that the power series $a_n x^n$ converges for $x=-R$ ,and that complete the proof.

Part b

For this case we need to provide a series whose interval of convergence is exactly (-1,1]

And the best function for this $\frac{(-x)^n}{n}$

Because the series $\sum \frac{(-x)^n}{n}$ converges to $-ln(1+x)$ when $|x|$ using the root test.

But by the properties of the natural log the series diverges at $x=-1$ because $\sum \frac{1}{n} =\infty$ and for $x=1$ we know that converges since $\sum \frac{-1}{n}$ is an alternating series that converges because the expression tends to 0.