On the first day of the fiscal year, a company issues $65,000, 6%, five-year installment

Mathematics

1 answer:

enot [183]3 years ago

7 0

Answer:

Dr cash $65,000

Cr Notes payable $65,000

repayment:

Dr Notes payable $11,531

Dr interest expense $3,900

Cr Cash $15,431

Step-by-step explanation:

Upon the issuance of the notes,the cash received would be debited to cash account and the same amount credited to notes payable account.

The payment of $15,431 as annual repayment on the notes payable would be credited to cash account as an outflow of cash from the business while the notes payable and interest expense accounts would be debited with $11,531 and$3,900 respectively

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Derek is planning on covering an entire drum in leather. The diameter of the drum is 10 inches, and the height of the drum is 16

fredd [130]

Answer: 694.4 in^2

Step-by-step explanation:

We have a cylinder with:

diameter = d = 10 inches

heigth = h = 16 inches.

The total surface of a cylinder is equal to:

S = h*2*pi*(d/2) + 2*pi*(d/2)^2

we can replace the numbers and get:

S = 16*2*3.14*(10/2) + 2*3.14*(10/2)^2 = 659.4 inches squared

5 0

3 years ago

[Will mark as brainliest]

Aleks04 [339]

The answer is: $f^{-1} = 4x^2-3,\quad\text{for } x \leq 0$

The inverse of a function $f(x)$ is another function, $f^{-1}(x)$ , with the following property:

$f(f^{-1}(x)) = f^{-1}(f(x)) = x$

In other words, the inverse of a function does exactly "the opposite" of what the original function does, and so if you compute them both in sequence you return to the starting point.

Think for example to a function that doubles the input, $f(x)=2x$ , and one that halves it: $f(x)= \frac{x}{2}$ . Their composition is clearly the identity function $f(x)=x$ , since you consider "twice the half of something", or "half the double of something".

In general, to invert a function $y=f(x)$ , you have to solve the expression for $x$ , writing an expression like $x = g(y)$ . If you manage to do so, then $g$ is the inverse of $f$ .

In your case, you have

$f(x) = y = -\frac{1}{2}\sqrt{x+3}$

Multiply both sides by $-2$ to get

$-2y = \sqrt{x+3}$

Square both sides to get

$4y^2 = x+3$

Finally, subtract 3 from both sides to get

$x = 4y^2 - 3$

Since the name of the variables doesn't really have a meaning, you can say that the inverse function is

$f^{-1}(x) = 4x^2 - 3$

As for the domain of the inverse function, remember what we said ad the beginning: if the original function goes from set A (domain) to set B (codomain), then the inverse function goes from set B (domain) to set A (codomain). This means that the inverse function is defined on an element in B if and only if that element belongs to the range of the original function, i.e. the set of the elements of the codomain $b \in B$ such that there exists $a \in A : f(a)=b$ . So, we need the range of $f(x)$ .

We know that the range of $g(x)=\sqrt{x}$ is $[0,\infty)$ . When you transform it to $g(x)=\sqrt{x+3}$ you simply translate the graph horizontally, so the range doesn't change. But when you multiply the function times $-\frac{1}{2}$ you affect both extrema of the range, turning it into $(-\infty,0]$ , which you can simply write as $x \leq 0$