18 less than the product of 42 and x write as an algebraic expression

Find the derivative of sinx/1+cosx, using quotient rule

Mrrafil [7]

Answer:

f'(x) = -1/(1 - Cos(x))

Step-by-step explanation:

The quotient rule for derivation is:

For f(x) = h(x)/k(x)

$f'(x) = \frac{h'(x)*k(x) - k'(x)*h(x)}{k^2(x)}$

In this case, the function is:

f(x) = Sin(x)/(1 + Cos(x))

Then we have:

h(x) = Sin(x)

h'(x) = Cos(x)

And for the denominator:

k(x) = 1 - Cos(x)

k'(x) = -( -Sin(x)) = Sin(x)

Replacing these in the rule, we get:

$f'(x) = \frac{Cos(x)*(1 - Cos(x)) - Sin(x)*Sin(x)}{(1 - Cos(x))^2}$

Now we can simplify that:

$f'(x) = \frac{Cos(x)*(1 - Cos(x)) - Sin(x)*Sin(x)}{(1 - Cos(x))^2} = \frac{Cos(x) - Cos^2(x) - Sin^2(x)}{(1 - Cos(x))^2}$

And we know that:

cos^2(x) + sin^2(x) = 1

then:

$f'(x) = \frac{Cos(x)- 1}{(1 - Cos(x))^2} = - \frac{(1 - Cos(x))}{(1 - Cos(x))^2} = \frac{-1}{1 - Cos(x)}$

4 0

3 years ago

When the following quadratic equation is written in standard form, what is the value of "c"?

Nikolay [14]

Answer:

Then value is 2

Step-by-step explanation:

standard of quadratic is A $x^{2}$ +Bx+C=0

and 2 is where C is.

sorry for the bad explanation but, trust me I did this type of question in class yesterday

7 0

2 years ago

With compound interest, what happens when you start compounding more and more frequently?

VLD [36.1K]

Your money grows faster because the interest is added back into the principle and then the next time it compounds you get interest on the new principle amount. So for example, you deposit $100 in an account that gets 5% interest compounded semiannually. The first time it compounds you get $5 added to your account so your new balance is $105. The next time it compounds you get 5% on $105 so you get $5.25 added and so on. If this is only happening semi-annually that would be all you get for the year. But if it happens quarterly you would get would get deposits of $5.51 and $5.79 as well. If it compounds monthly or even daily your money would grow more and more. Hope this helps.

7 0

3 years ago

You buy Apple stock for $120 per share over a period of time the stock value increased at a weekly rate of 5% you sell the stock

Rainbow [258]

Answer:

8.31 weeks

Step-by-step explanation:

Given that the cost of one share of Apple stock, C=$120

Rate is the increment of the stock value, R= 5%/week=0.05 / week.

Assuming that after t week, the stock has been sold for $180.

Since the stock value increased at 5% every week, so, the interest is compounded weekly, so

$S=C\left(1+R\right)^t \\\\ \Rightarrow 180 = 120\left(1+0.05\right)^t \\\\ \Rightarrow 180 = 120\left(1.05 )^t \\\\$

$\Rightarrow \frac{180}{120}=1.05^t \\\\\Rightarrow 1.5=1.05^t$

$\Rightarrow \ln(1.5)=t \ln(1.05)$ [taking log both sides]

$\Rightarrow t=\frac {\ln(1.5)}{\ln(1.05)}=8.31$ weeks

Hence, after 8.31 weeks the stock has been sold for $180.

6 0

3 years ago

Two liquids Kaylin mixed two liquids for science experiment one container had 7/8 Cup and the other health 9/10 cup what is the

seraphim [82]

Answer:

Step-by-step explanation:

<em>Step 1: Determine quantity per liquid</em>

liquid 1=7/8 cup

liquid 2=9/10 cup

<em>Step 2: Derive expression to calculate total amount of mixture</em>

The expression below can be derived;

T=a+b

where;

T=total amount of mixture

a=total amount of liquid 1

b=total amount of liquid 2

In our case;

a=7/8 cup

b=9/10 cup

replacing;

T=(7/8)+(9/10)=1 31/40 cups

The total amount of mixture=1 31/40 cups

3 0

2 years ago