Ill mark brainlist plss help

(5CQ) Use the comparison test to determine whether the series 25/3+125/9+625/27+... is convergent or divergent.

olya-2409 [2.1K]

The terms in the sum are given by the sequence

$\left\{\dfrac{5^{n+1}}{3^n}\right\}_{n\ge1}$

We have

$\dfrac{5^{n+1}}{3^n}>\dfrac{5^n}{3^n}=\left(\dfrac53\right)^n>1$

for all $n$ , and the series $1+1+1+\cdots$ clearly diverges, so $\dfrac{25}3+\dfrac{125}9+\cdots$ must also diverge.

4 0

3 years ago

Whats the factorization of x2+3x−18

Alexeev081 [22]

Answer:

(X+6)x(X-3)

Step-by-step explanation:

X^2+6X-3X-18

Xx(X+6)-3(X+6)

(X+6)x(X-3)

big X is the variable

small x is multiplication sign

4 0

3 years ago

Find the surface area of the surface given by the portion of the paraboloid z=3x2+3y2 that lies inside the cylinder x2+y2=4. (hi

natta225 [31]

Parameterize the part of the paraboloid within the cylinder - I'll call it $S$ - by

$\mathbf r(u,v)=\langle x(u,v),y(u,v),z(u,v)\rangle=\left\langle u\cos v,u\sin v,3u^2\right\rangle$

with $0\le u\le2$ and $0\le v\le2\pi$ . The region's area is given by the surface integral

$\displaystyle\iint_S\mathrm dS=\int_{u=0}^{u=2}\int_{v=0}^{v=2\pi}\|\mathbf r_u\times\mathbf r_v\|\,\mathrm du\,\mathrm dv$
$=\displaystyle\int_{v=0}^{v=2\pi}\int_{u=0}^{u=2}u\sqrt{1+36u^2}\,\mathrm du\,\mathrm dv$
$=\displaystyle2\pi\int_{u=0}^{u=2}u\sqrt{1+36u^2}\,\mathrm du$

Take $w=1+36u^2$ so that $\mathrm dw=72u\,\mathrm du$ , and the integral becomes

$=\displaystyle\frac{2\pi}{72}\int_{w=1}^{w=145}\sqrt w\,\mathrm dw$
$=\displaystyle\frac\pi{36}\frac23w^{3/2}\bigg|_{w=1}^{w=145}$
$=\dfrac\pi{54}(145^{3/2}-1)\approx101.522$

7 0

3 years ago

Match each set of conditions with the corresponding relationship between ∆abc and ∆xyz and the criterion (if any) that proves th

sveta [45]

Answer: After matching each set of conditions with the corresponding relationship between ∆ABC and ∆XYZ and the criterion that proves the relationship the matched pairs are as follows:

1 . AB = XY ,BC = YZ and ∠B ≅ ∠Y ⇒ ΔABC ≅ ΔXYZ by SAS criterion.

2 . AB = XY and ∠A ≅ ∠X and ∠B ≅ ∠Y⇒ ΔABC ≅ ΔXYZ by ASA criterion.

3 . ∠A=∠X,∠B=∠Y and ∠C=∠Z⇒ ΔABC and ΔXYZ are not necessarily congruent.[by AAA similarity criteria both triangles are similar but may not congruent ∵ every congruent triangles have equal sides and equal angles]

4 . AB = XY, BC = YZ and CA = ZX ⇒ ΔABC ≅ ΔXYZ by the SSS criterion.

4 0

3 years ago

Read 2 more answers

Gerald graphs the function f(x) = (x – 3)2 – 1. Which statements are true about the graph? Check all that apply.

Andru [333]

Statement 1 is false because the domain of f is all real numbers since the function is quadratic.

Statement 2 is true.

Statement 3 is true because when we graph f, it is a parabola opening upwards with vertex (3, -1). Since it is opening upward, then the value of x from -∞ to 3 is decreasing while increasing from 3 to ∞.

Statement 4 is false because we just stated above that f is decreasing from -∞ to 3. Hence, f is also decreasing from -1 to 3. Hence, f is not increasing from -1 to ∞.

Statement 5 is false because the axis of symmetry is x = 3.

Statement 6 is true.

3 0

4 years ago

Read 2 more answers