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2 years ago

11

How long will it take for $6400 to grow to $43,800 at an interest rate of 3.4% if the interest is compounded continuously?

1 answer:

andrew-mc [135]2 years ago

7 0

Answer:

57.53years to the nearest hundredth

Step-by-step explanation:

For compound interest,A=P(1+r/100)^t

where r=rate of interest

t= investment tenor

$43800=6400(1+3.4/100)^t

which simplifies to 57.5250≈57.53 to the nearest hundredth

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Find f(12) = 3/4 x + 2

AlekseyPX

Answer:

f(12) = 11

Step-by-step explanation:

To solve this question:

Substitute x = 12 into the equation: f(12) = 3/4 (12) + 2
Simplify: 3/4 × 12 = 36/4 which is 9 → f(12) = 9 + 2

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2 years ago

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Look at this cylinder:

Sedbober [7]

Height=h=8cm
Radius=r=4cm

We know

$\boxed{\sf \star TSA_{(Cylinder)}=2\pi r(h+r)}$

$\\ \sf\longmapsto TSA_{(Old\:Cylinder)}=2\times \dfrac{22}{7}\times 4(8+4)$

$\\ \sf\longmapsto TSA_{(Old\:Cylinder)}=\dfrac{176}{7}(12)$

$\\ \sf\longmapsto TSA_{(Old\:Cylinder)}=\dfrac{2112}{7}$

$\\ \sf\longmapsto TSA_{(Old\:Cylinder)}=301.7cm^2$

Now

New Radius=2(4)=8cm
New Height=2(8)=16cm

$\\ \sf\longmapsto TSA_{(New\:Cylinder)}=2\times \dfrac{22}{7}\times 8(16+8)$

$\\ \sf\longmapsto TSA_{(New\:Cylinder)}=\dfrac{352}{7}(24)$

$\\ \sf\longmapsto TSA_{(New\:Cylinder)}=\dfrac{8448}{7}$

$\\ \sf\longmapsto TSA_{(New\:Cylinder)}=1204.7cm^2$

So

$\\ \sf\longmapsto \dfrac{TSA_{(New\:Cylinder)}}{TSA_{(Old\:Cylinder)}}=\dfrac{1204.7}{301.7}$

$\\ \sf\longmapsto \dfrac{TSA_{(New\:Cylinder)}}{TSA_{(Old\:Cylinder)}}=\dfrac{4}{1}$

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2 years ago

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OLEGan [10]

Answer:

Consider matrix A.

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Step-by-step explanation:

Consider matrix A.

What is the inverse of A? Fill in the missing elements in the matrixs.

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3 years ago

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Given the statement 11^(n -6) is divisible by 5 for every positive integer n. What must be shown in the induction step?

Lilit [14]

Answer:

Proved

Step-by-step explanation:

The given data is:

$11^n - 6$ not $11^{n - 6$

Required

Prove by induction that it is divisible by 5

Assume $n = k$

So, we have:

$11^k - 6 = 5p$ where p is a positive digit

Rewrite as:

$11^k = 5p + 6$

To solve further, we have to prove that $11^k - 6$ is true for $n=k+1$

So, we have:

$11^{k+1} - 6$

$11^{k+1} - 6 = 11^k * 11 - 6$

Add 0

$11^{k+1} - 6 = 11^k * 11 - 6 + 0$

Replace 0 with $-5 +5$

$11^{k+1} - 6 = 11^k * 11 - 6 - 5 + 5$

$11^{k+1} - 6 = 11^k * 11 - 11- 5$

Factorize

$11^{k+1} - 6 = 11 (11^k - 1)- 5$

Substitute $11^k = 5p + 6$

$11^{k+1} - 6 = 11 (5p + 6- 1)- 5$

$11^{k+1} - 6 = 11 (5p + 5)- 5$

Factorize

$11^{k+1} - 6 = 11 *5(p + 1)- 5$

Factorize

$11^{k+1} - 6 = 5[11(p + 1)- 1]$

<em>The 5 outside the bracket implies that it is divisible by 5</em>

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3 years ago