Use the Pythagorean Theorem to find the missing length and then round the result to the nearest tenth.

PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!

Kisachek [45]

Answer: (A) vertical asymptote: x = 2, horizontal asymptote: y = 1

Step-by-step explanation:

$f(x) = \dfrac{1}{x-2}+1$

Vertical Asymptote is the restriction on the x-value. The denominator cannot be zero, so x - 2 ≠ 0 ⇒ x ≠ 2

The restricted value on x is when x = 2 which is the vertical asymptote

Horizontal Asymptote (H.A.) is the restriction on the y-value. This is a comparison of the numerator (n) and denominator (m). There are 3 rules that will help you:

n > m No H.A. (use long division to find slant asymptote)
n = m H.A. is the coefficient of n divided by coefficient of m
n < m H.A. is 0

In the given problem, n < m so y = 0, however there is also a vertical shift of up 1 so the H.A. also shifts up. This results in H.A. of y = 1

5 0

3 years ago

Write an equation for a circle with a diameter that has endpoints at (7, –4) and (1, –10). Round to the nearest tenth if necessa

Black_prince [1.1K]

The standard form for the equation of a circle is :

(x−h)^2+(y−k)^2=r2 ----------- EQ(1)
where handk are the x and y coordinates of the center of the circle and r is the radius.
The center of the circle is the midpoint of the diameter.

So the midpoint of the diameter with endpoints at (7,-4)and(1,-10) is :

((7+(1))/2,(-4+(-10))/2)=(4,-7)

So the point (4,-7) is the center of the circle.

Now, use the distance formula to find the radius of the circle:

r^2=(7−(4))^2+(-4−(-7))^2=9+9=18

⇒r=√18

Subtituting h=4, k=-7 and r=√18 into EQ(1) gives :

(x-4)^2+(y+7)^2=18

7 0

3 years ago

A box is to be made where the material for the sides and the lid cost $0.20 per square foot and the cost for the bottom is $0.

Reika [66]

Answer:

The dimension of the box is l×w×h = (2.274 × 2.274 × 1.934) ft³

Step-by-step explanation:

From the given information;

Let a be the cost of the box

Let b be one side of the square base ; &

h to be the height of the box

We know that the volume of the box = 10 cubic feet

Then;

a²h = 10

h = 10/a²

The base = (0.65)a²

The top = (0.2)a²

The side = (0.2) a × 25/a²

= 5/a

For the four sides of the box now ;

= (0.2) 4a × 25/a²

= 0.8 × 25/a

= 20 /a

The total cost of the box is:

b = 0.65a² + 0.2a² + 20 /a

b = 0.85 a² + 20 /a

Taking differential of b with respect to a ;we have:

db/da = 1.7a - 1/a²(20) = 0

1.7 a³ - 20 = 0

1.7 a³ = 20

a³ = 20/1.7

a³ = 11.77

a = $\sqrt[3]{11.77}$

a = 2.274 ft

Thus; the cost for the base of the box = (0.65)a²

the cost for the base of the box =(0.65) × ( 2.274)²

the cost for the base of the box = 3.362

The top of the box = (0.2)a²

The top of the box = (0.2)× ( 2.274)²

The top of the box = 1.034

The four sides of the box = 20 /a

The four sides of the box = 20/2.274

The four sides of the box = 8.795

the total cost = b = 0.85 a² + 20 /a

the total cost = 0.85 (2.274)² + 20 /2.274

the total cost = 4.395 + 8.795

the total cost = 13.19

Recall that:

the volume of the box = 10 cubic feet

Then;

a²h = 10

h = 10/a²

h = 10/ 2.274²

h 1.934

The dimension of the box is l×w×h = (2.274 × 2.274 × 1.934) ft³

7 0

3 years ago

Please help me!! Due today

klasskru [66]

Answer:

Step-by-step explanation:

y = (-1/4)x - 4 has a y-intercept of (0, -4). Place a dark dot at (0, -4).

Now we use the info from the slope, -1/4:

Starting with your pencil point on the dot (0, -4), move the pencil point 4 units to the right and then 1 unit down. You will now be at (4, -5). Place a dark dot there.

Then draw a straight, solid line through (0, -4) and (4, -5).

6 0

3 years ago

In Panama City in January high tide was at midnight. The water level at high tide

Ivanshal [37]

The water levels at high tide was 9 feet and 1 foot at low tide

7 0

2 years ago