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2 years ago

How much will 1,000.00 amount to in 2 years at 13%2% simple interest

Mathematics

1 answer:

Sonbull [250]2 years ago

3 0

For %13 in 2 years 1,000,000 will amount to 1,260,000

For %2 in 2 years 1,000,000 will amount to 1,040,000

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Differentiate with respect to X <img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B%20%5Cfrac%7Bcos2x%7D%7B1%20%2Bsin2x%20%7D%20

Mice21 [21]

Power and chain rule (where the power rule kicks in because $\sqrt x=x^{1/2}$ ):

$\left(\sqrt{\dfrac{\cos(2x)}{1+\sin(2x)}}\right)'=\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'$

Simplify the leading term as

$\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}$

Quotient rule:

$\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'=\dfrac{(1+\sin(2x))(\cos(2x))'-\cos(2x)(1+\sin(2x))'}{(1+\sin(2x))^2}$

Chain rule:

$(\cos(2x))'=-\sin(2x)(2x)'=-2\sin(2x)$

$(1+\sin(2x))'=\cos(2x)(2x)'=2\cos(2x)$

Put everything together and simplify:

$\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{(1+\sin(2x))(-2\sin(2x))-\cos(2x)(2\cos(2x))}{(1+\sin(2x))^2}$

$=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2\sin^2(2x)-2\cos^2(2x)}{(1+\sin(2x))^2}$

$=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2}{(1+\sin(2x))^2}$

$=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac{\sin(2x)+1}{(1+\sin(2x))^2}$

$=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac1{1+\sin(2x)}$

$=-\dfrac1{\sqrt{\cos(2x)}}\dfrac1{\sqrt{1+\sin(2x)}}$

$=\boxed{-\dfrac1{\sqrt{\cos(2x)(1+\sin(2x))}}}$

5 0

3 years ago

31% of 62 what is it i have been suffering

natita [175]

I’m pretty sure it’s 50%

3 0

2 years ago

The equation of a parabola is 1/32 (y−2)2=x−1 .

Andru [333]

The given equation of parabola is

$\frac{1}{32} (y-2)^2 = x-1$

Which can also be written as

$x = \frac{1}{32} (y-2)^2 +1$

Here vertex (h,k) is (1,2)

And value of a is

$a = \frac{1}{32}$

Formula of focus is

$(h+ \frac{1}{4a} , k)$

Substituting the values of h,k and a, we will get

$(1+ \frac{1}{4*(1/32) } , 2} = (1+ 8,2) = (9,2)$

Therefore the correct option is the last option .

6 0

3 years ago

Read 2 more answers

How many triangles can be constructed with sides measuring 15 cm, 7 cm, and 5 cm? Explain. Be sure to use complete sentences and

Hatshy [7]

Answer: No triangles can be formed.

Step-by-step explanation: Given Dimensions = 15cm , 7cm , 5cm

Inequality property = Sum of 2 shorter sides ≥ 3rd side

∴ 7 + 5 is not greater than 15

∴ No triangles can be formed.

3 0

3 years ago

What is the value of the expression when a = -1.4 and b = -2.7? |a| + b

Julli [10]

"a" is an absolute value, so that means that after whatever is in the brackets is solved as far as it can be, it becomes a positive value, no matter what it is. So, |-1.4| is equal to 1.4. The equation is 1.4+ (-2.7) or 1.4 - 2.7 which equals -1.3

5 0

3 years ago