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3 years ago

5

Which link between two elements could you remove from the relation so that it becomes a function? 1 and c or 3 and a 4 and d or

5 and d 2 and e or 4 and d 2 and b or 2 and e

2 answers:

shtirl [24]3 years ago

8 0

It would make more sense to remove 4 and D

sertanlavr [38]3 years ago

7 0

Answer: 2 and E or 4 and D

Step-by-step explanation:

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The sum of the first three terms of a convergent geometric series is 19. the sum of the series is 27. find the first term and th

NikAS [45]

1st,since this GP is convergent that means the common ratio r <1
2nd, sum of a GP = a₁(1-rⁿ)/(1-r), where a₁ = 1st term and n=number of terms
3rd, for any convergent GP, r<1 and the sum of all terms =a₁/(1-r): Why?
[since r<1 → lim rⁿ when n→∞, =0 in the formula of the 2nd)]
Now let's solve :

a) Sum = a₁(1-r³)/(1-r) = 19 (sum of the first 3 terms)
b) Σ(Sum) = a₁/(1-r) = 27 (sum of all terms of this CONVERGENT GP)

Divide a) by b):

[a₁(1-r³)/(1-r)] / [a₁/(1-r)] = 19 /27 ↔ [a₁(1-r³)/(1-r)] x [(1-r)/a₁]=19/27.
Simplify:
(1-r³) = 19/27
-r³ = 19/27 - 1
r³ = 8/27

r = ∛(8/27)

r = 2/3 and a₁ = 9 (Plug r in the Σ sum)
Hence first term a₁ = 9
and common ration r =2/3

4 0

3 years ago

4+8+12+... + 4n=2n(n+1)

Blababa [14]

4 + 8 + 12 + 4n = 2n(n + 1)
      24 + 4n = 2n(n) + 2n(1)
      24 + 4n = 2n² + 2n
   <u> -2n -2n</u>
      24 = 2n²
      <u>24</u> = <u>2n²
</u>   <u /> 2 2
      12 = n²
      √12 = n
        √4 × 3 = n
       √4 √3 = n
   2 √3 = n
<u />

4 0

3 years ago

What is 34,567.992 rounded to nearest thousandth

lesya692 [45]

The 2 on the end is the thousandths place. In order to know whether it should remain a '2' or increase to a '3', we would need to know what comes after it.

-- If there's nothing after it, then it's already written to the nearest thousandth.

-- If there <em>is</em> more after it, we don't know what that is, so we have nothing to base a decision on.

4 0

3 years ago

Find the values of c such that the area of the region bounded by the parabolas y = 4x2 − c2 and y = c2 − 4x2 is 32/3. (Enter you

Misha Larkins [42]

Answer:

-2,2

Step-by-step explanation:

Let

$y_1=4x^2-c^2$

$y_2=c^2-4x^2$

We have to find the value of c such that the are of the region bounded by the parabolas =32/3

$y_1=y_2$

$4x^2-c^2=c^2-4x^2$

$4x^2+4x^2=c^2+c^2$

$8x^2=2c^2$

$x^2=c^2/4$

$x=\pm \frac{c}{2}$

Now, the area bounded by two curves

$A=\int_{a}^{b}(y_2-y_1)dx$

$A=\int_{-c/2}^{c/2}(c^2-4x^2-4x^2+c^2)dx$

$\frac{32}{3}=\int_{-c/2}^{c/2}(2c^2-8x^2)dx$

$\frac{32}{3}=2\int_{-c/2}^{c/2}(c^2-4x^2)dx$

$\frac{32}{3}=2[c^2x-\frac{4}{3}x^3]^{c/2}_{-c/2}$

$\frac{32}{3}=2(c^2(c/2+c/2)-4/3(c^3/8+c^3/28))$

$\frac{32}{3}=2(c^3-\frac{4}{3}(\frac{c^3}{4}))$

$\frac{32}{3}=2(c^3-\frac{c^3}{3})$

$\frac{32}{3}=2(\frac{2}{3}c^3)$

$c^3=\frac{32\times 3}{4\times 3}$

$c^3=8$

$c=\sqrt[3]{8}=2$

When c=2 and when c=-2 then the given parabolas gives the same answer.

Therefore, value of c=-2, 2

7 0

2 years ago

Identify the word problem that represents the algebraic expression πr²(3r).

Olegator [25]

Answer:

the volume of a cylindrical-shaped corn silo with a height that is 3 times the radius

Step-by-step explanation:

i took test

8 0

3 years ago