$\text{If } a_n=1.5(a_n-1) \text{ this is a geometric sequence with a ratio of 1.5. The first term is 40. }a_n=40(1.5)^{n-1},\ a_5=40(1.5)^4=202.5$

3 0

3 years ago

Plot the foci of the hyperbola represented by the equation x^2/625 − y^2/3600 =1 100pts

Pavel [41]

The attached image represents the foci of the hyperbola

<h3>How to determine the foci?</h3>

The equation of the hyperbola is given as:

$\frac{x^2}{625} - \frac{y^2}{3600} = 1$

Rewrite as:

$\frac{x^2}{25^2} - \frac{y^2}{60^2} = 1$

A hyperbola is represented as:

$\frac{(x - h)^2}{b^2} - \frac{(y - k)^2}{a^2} = 1$

This means that:

h = 0

k = 0

b = 25

a = 60

Next, calculate c the distance from the center to the focus using:

$c = \sqrt{a^2 -b^2}$

This gives

$c = \sqrt{60^2 -25^2}$

Evaluate

$c = \pm \sqrt{2975}$

This means that:

Foci = (0, -√2975) and (0, √2975)

See attachment for the hyperbola and the foci

Read more about hyperbola at:

brainly.com/question/16735067

#SPJ1

3 0

2 years ago

A cuboid has a length of 25cm, a width of 5cm and height of (x-2)cm

mr Goodwill [35]

Step-by-step explanation:

Hi there!

From above question;

A cuboid has a length of 25cm, a width of 5cm and height of (x-2)cm.

Length (l) = 25cm

width (b) = 5cm

height (h) = (x-2)cm.

a).

Volume= l*b*h

V = 25*5*(x-2)

V = 125(x-2)

V = 125x - 250 → Answer

b).

(i)

V = 750cm³

V = 125x - 250

750 = 125x - 250..........(i)

(ii)

The equation (i) is: 750 = 125x - 250

or, 125x = 750+250

or, 125x = 1000

or, X = 1000/125

Therefore, X= 8cm.

(iii)

Height (h) = x-2

= 8-2

= 6

Therefore, height is 6cm.

<u>Hope</u><u> it</u><u> helps</u><u>!</u>

6 0

3 years ago

What is the slope of the line perpendicular to 2x-3y=8

Elanso [62]

Answer:

X=11/2

Step-by-step explanation:

2x=8+3

2x=11

x=11/2

5 0

2 years ago

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