Answer:
Step-by-step explanation:
1) The center lies on the vertical line x = -5 and the the circle is tangent to (touches in one place only) the y-axis. Thus, the radius is 5.
2) Starting with (x - h)^2 + (y - k)^2 = r^2 and comparing this to the given
(x - 4)^2 + (y + 3)^2 = 6^2
we see that h = 4, k = -3 and r = 6. The center is at (4, -3) and the radius is 6.
3) Notice that A and B have the same x-coordinate, x = 15. The center of the circle is thus (15, -2), where that -2 is the halfway point between the two given points in the vertical direction. Arbitrarily choose A(15, 4) as one point on the circle. Then the equation of this circle is
(x - 4)^2 + (y + 3)^2 = r^2 = 6^2, where the 6 is one half of the vertical distance between A(15, 4) and B(15, -8) (which is 12).
Step-by-step explanation:
a) determine the rate in km/L
==> 9.5 L/100km = 10.526316 km/L
b) how far can the car travel with 475L petrol
==> 0.210526315789473km/l
c) how many litres of petrol do they need to travel 350 km
==>Liters per km (l/km)2.86×10-3
Liters per 10 km (l/10 km)0.03
Liters per 100 km (l/100km)0.29
Kilometer per liter (km/l)350
Answer:
y = 8
x = 8√5
z = 4√5
Step-by-step explanation:
Using the formula (which is a geometric mean):
a y
---- = -----
x a
Where a is the altitude (y), x is a projection (16), and y is the other projection (4):
y 4
---- = -----
16 y
Cross multiply:
y² = 16 (4)
y² = 64
√y² = √64
y = 8
To find x and z, use the Pythagorean Theorem:
16² + y² = x²
256 + 8² = x²
256 + 64 = x²
320 = x²
√320 = √x²
√64√5 = √x²
8√5 = x
x = 8√5
4² + y² = z²
16 + 64 = z²
80 = z²
√80 = √z²
√16√5 = √z²
4√5 = z
z = 4√5
Plug in 12 for t in the given equation and solve
Answer:
88/7 ft = 12.6 ft (nearest tenth)
Step-by-step explanation:
Circumference of a circle = 2
r
<u>Radius of inner circle</u>
Given:
- circumference of inner circle = 22ft
- = 22/7
⇒ 22 = 2 x (22/7) x r
⇒ r = 3.5
So the radius of the inner circle is 3.5 ft
<u>Radius of outer circle</u>
If the distance between the inner circle and the outer circle is 2 ft, then the radius of the outer circle = 3.5 + 2 = 5.5
<u>Circumference of outer circle</u>
Therefore, circumference of outer circle:
= 2 x (22/7) x 5.5
= 242/7 ft
<u>Difference between circumferences</u>
Difference = outer circle circumference - inner circle circumference
= 242/7 - 22
= 88/7 ft
= 12.6 ft (nearest tenth)
