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3 years ago

12

Wyatt is paying back a loan with a nominal interest rate of 13.62%. If the interest is compounded quarterly, how much greater is

Wyatt’s effective interest rate than his nominal interest rate?

1 answer:

PilotLPTM [1.2K]3 years ago

6 0

0.71 percentage points

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Verify the identity. cot(x - pi/2) = -tan(x)

gizmo_the_mogwai [7]

Answer:

See below.

Step-by-step explanation:

$\cot(x-\frac{\pi}{2})=-\tan(x)$

Convert the cotangent to cosine over sine:

$\frac{\cos(x-\frac{\pi}{2} )}{\sin(x-\frac{\pi}{2})} =-\tan(x)$

Use the cofunction identities. The cofunction identities are:

$\sin(x)=\cos(\frac{\pi}{2}-x)\\\cos(x)=\sin(\frac{\pi}{2}-x)$

To convert this, factor out a negative one from the cosine and sine.

$\frac{\cos(-(\frac{\pi}{2}-x ))}{\sin(-(\frac{\pi}{2}-x))} =-\tan(x)$

Recall that since cosine is an even function, we can remove the negative. Since sine is an odd function, we can move the negative outside:

$\frac{\cos((\frac{\pi}{2}-x ))}{-\sin((\frac{\pi}{2}-x))} =-\tan(x)\\-\frac{\sin(x)}{\cos(x)} =-\tan(x)\\-\tan(x)\stackrel{\checkmark}{=}-\tan(x)$

8 0

3 years ago

The men s clothing buyer had a group of 50 jackets priced at $250 each that was selling very slowly. To stimulate sales of these

erastovalidia [21]

Answer:

The answer is $3000.

Step-by-step explanation:

The men's clothing buyer had a group of 50 jackets priced at $250 each.

Total price of jackets = $50\times250=12500$ dollars

The buyer reduced the price of the jackets in that group to $200 and 40 jackets were sold.

So, the price for selling 40 jackets is = $40\times200=8000$ dollars

Remaining jackets = $50-40=10$

These were sold at $150 each, totaling to = $10\times150=1500$ dollars

So, overall money earned by reducing prices both time = $8000+1500=9500$ dollars

And the markdown in dollars = (original price before reducing) minus (educed total price)

= $12500-9500=3000$ dollars

So, the answer is $3000.

3 0

2 years ago

Which of the following could be the system of nonlinear inequalities graphed below?

Ivan

Answer:

Option A.

Step-by-step explanation:

step 1

we know that

The equation of the solid line is

$y=5$

The solution is the shaded area above the solid line

so

The equation of the first inequality is

$y\geq 5$

step 2

The equation of the dashed line is

$y=x^{2} -5x+6$

The solution is the shaded area above the dashed line

so

The equation of the second inequality is

$y>x^{2} -5x+6$

therefore

The system of inequalities could be

$y\geq 5$

$y>x^{2} -5x+6$

4 0

3 years ago

write the equation of a line in slope intercept form that is parallel to the line x+5y=10 and goes through the point (-5,6)

lilavasa [31]

Answer:

The equation would be y = -1/5x + 5

Step-by-step explanation:

To find the equation of this new line, we first need to identify the slope of the first line. We do this by putting it into slope intercept form.

x + 5y = 10

5y = -x + 10

y = -1/5x + 2

In slope-intercept form, the slope is always the coefficient of x. This makes the slope of the first equation -1/5. Since parallel lines have the same slope, our new slope will also be -1/5.

Given that and the point, we can solve for the equation using point-slope form.

y - y1 = m(x - x1)

y - 6 = -1/5(x + 5)

y - 6 = -1/5x - 1

y = -1/5x + 5

4 0

3 years ago

I need some math help

Kobotan [32]

This is an answer should help you

8 0

2 years ago