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3 years ago

4 pts

Mathematics

1 answer:

lubasha [3.4K]3 years ago

5 0

9514 1404 393

Answer:

=FV(4.5%/12,30*12,-150,0)
$113,907.92
$54,000
$59,907.92

Step-by-step explanation:

We have used the formula shown in Go.ogle Sheets to give the results shown. (We presume Excel has a similar function.)

The result is that the future value of the investment is $113,907.92.

The amount deposited is ($150/mo)(12 mo/yr)(30 yr) = $54,000.

The interest earned is the difference: $113,907.92 -54,000 = $59,907.92.

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A parabola has a focus of F(2, -0.5) and a directrix of y=-1.5 P(x,y) represents any point on the parabola, while D(x, -1.5) rep

prohojiy [21]

The sketch of the parabola is attached below

We have the focus $(a,b) = (2, -0.5)$
The point $P(x,y)$
The directrix, c at $y=-1.5$

The steps to find the equation of the parabola are as follows

Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates; $(2, -0.5)$ and $(x,y)$ .
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$

Step 2
Find the distance between the point P to the directrix $c$ . It is a vertical distance between y and c, expressed as $y-c$

Step 3
The equation of parabola is then given as
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$ = $y-c$
$(x-a)^{2}+ (y-b)^{2}= (y-c)^{2}$ ⇒ substituting a, b and c
$(x-2)^{2}+ (y--0.5)^{2} = (y--1.5)^{2}$
$(x-2)^{2}+ (y+0.5)^{2}= (y+1.5)^{2}$ ⇒Rearranging and making $y$ the subject gives

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

7 0

3 years ago

0.12 word form decimal

7nadin3 [17]

Answer:

0.12=zero point one two

Step-by-step explanation:

6 0

3 years ago

Louise measured the perimeter of her rectangular scrapbook to be 156 cm. If the scrapbook is 43 cm wide, how long is the scrapbo

Montano1993 [528]

Answer:

L=35cm

Step-by-step explanation:

Perimeter is 2(L+w)

156cm=2*(43+L)

L=35cm

8 0

3 years ago

If sin(A+B)=1/2 & sin(A-B)=1/3 find sin(2A)

timofeeve [1]

Answer:

sin(2A) = (2√2 + √3) / 6

Step-by-step explanation:

2A = (A+B) + (A−B)

sin(2A) = sin((A+B) + (A−B))

Angle sum formula:

sin(2A) = sin(A+B) cos(A−B) + sin(A−B) cos(A+B)

sin(2A) = 1/2 cos(A−B) + 1/3 cos(A+B)

Pythagorean identity:

sin(2A) = 1/2 √[1 − sin²(A−B)] + 1/3 √[1 − sin²(A+B)]

sin(2A) = 1/2 √(1 − 1/9) + 1/3 √(1 − 1/4)

sin(2A) = 1/2 √(8/9) + 1/3 √(3/4)

sin(2A) = 1/3 √2 + 1/6 √3

sin(2A) = (2√2 + √3) / 6

6 0

3 years ago

Help me please its geometry

Maslowich

Answer for the first dropdown box is CAF and EFH

Answer for the second dropdown box is because they are corresponding angles of parallel lines cut by a transversal

Answer for the third dropdown box is transitive property of congruence

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Explanation:

Angles CAF and EFH are corresponding angles because they are on the bottom side of the parallel lines, and on the right side as well. So they are congruent (due to the lines being parallel).

Since CAF = EFH and EFH = HFD, this means that CAF = HFD

It's similar to saying if x = y and y = z, then x = z. Think of it as a connecting chain. This is the transitive property.

4 0

3 years ago