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2 years ago

9

What is the present value of $3,000 per year for 9 years discounted back to the present at 10 percent?

1 answer:

Studentka2010 [4]2 years ago

3 0

Answer:

$17,277.07

Step-by-step explanation:

Present value of annuity is the present worth of cash flow that is to be received in the future, if future value is known, rate of interest is r and time is n then PV of annuity is

PV of annuity = $\frac{P[1-(1+r)^{-n}]}{r}$

= $\frac{3000[1-(1+0.10)^{-9}]}{0.10}$

= $\frac{3000[1-(1.10)^{-9}]}{0.10}$

= $\frac{3000[1-0.4240976184]}{0.10}$

= $\frac{3000(0.5759023816)}{0.10}$

= $\frac{1,727.7071448}{0.10}$

= 17,277.071448 ≈ $17,277.07

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WILL MARK BRAINLIEST PLEASE HELP

Marrrta [24]

Answer:

$f(x)=-\frac{1}{8}(x-4)^2+3$

Step-by-step explanation:

The directrix given to us has equation,

$y=5$ and the focus is $(4,1)$ .

This means that the axis of symmetry of the parabola is parallel to the y-axis and has equation $x=4$ , because it must go through the focus.

This axis of symmetry of the parabola will meet the directrix at $(4,5)$ .

The vertex of this parabola is the midpoint of the point of intersection of the axis of symmetry and the focus.

Thus,

$V(h,k)=(\frac{4+4}{2},\frac{5+1}{2})$

$V(h,k)=(4,3)$ .

The equation is given by $(x-h)^2=4p(y-k)$ .

$(x-4)^2=4p(y-3)$ .

$|p|$ is the distance between the vertex and the focus, which is 2.

This implies that,

$p=-2$ or $p=2$

But the position of the directrix and the vertex implies that the parabola opens downwards.

$\therefore p=-2$ .

The equation of the parabola now becomes;

$(x-4)^2=4(-2)(y-3)$ .

$(x-4)^2=-8(y-3)$

We solve for y to obtain,

$y=-\frac{1}{8}(x-4)^2+3$

or

$f(x)=-\frac{1}{8}(x-4)^2+3$

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2 years ago

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k0ka [10]

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8 0

2 years ago

Can someone please help me it's due by tomorrow.

ikadub [295]

Answer:

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Step-by-step explanation:

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2 years ago

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Answer:

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Step-by-step explanation:

2700/90 = 30

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2 years ago

Does anyone know the answer?

motikmotik

Answer:

We conclude that the area of the right triangle is:

$A\:=p^2-2p-3$

Hence, option A is correct.

Step-by-step explanation:

From the given right-angled triangle,

Base = p+1

Perpendicular = 2p-6

Using the formula to determine the area of the right-angled triangle

Area of the right triangle A = 1/2 × Base × Perpendicular

$=\frac{1}{2}\left(p+1\right)\left(2p-6\right)$

Factor 2p-6: 2(p-3)

$=\frac{\left(p+1\right)\times \:2\left(p-3\right)}{2}$

Divide the number: 2/2 = 1

$=\left(p+1\right)\left(p-3\right)$

$\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$

$=pp+p\left(-3\right)+1\cdot \:p+1\cdot \left(-3\right)$

$=pp-3p+1\cdot \:p-1\cdot \:3$

$=p^2-2p-3$

Therefore, we conclude that the area of the right triangle is:

$A\:=p^2-2p-3$

Hence, option A is correct.

3 0

2 years ago