Since 6/1.5 is 4. It increased 400%.
Answer:
In the step by step
Step-by-step explanation:
Graph 1 : k(x)=(1/4)^x
Graph 2: f(x)=-(1/4)^x
Graph 3: g(x)=4^x
Graph 4: h(x)=-4^x
Answer:
c. 6 cups
Step-by-step explanation:
The proportion is 1 cup of sugar for 1 dozen cookies (1/1). So if you multiply the denominator by 6 you must multiply the numerator by 6, and 6*1=6. Therefore you need 6 cups of sugar to make 6 dozen cookies.
Step-by-step explanation:
I'll do the first one as an example.
"What are the coordinates of the point on the directed line segment from K(-5,-4) to L(5,1) that partitions the segment into a ratio of 3 to 2?"
Let's call the point we're trying to find P. Ratio of 3 to 2 means that the distance from K to P divided by the distance from P to L is 3/2.
KP / PL = 3 / 2
Which also means the horizontal distances and vertical distances between the points have a ratio of 3:2.
KxPx / PxLx = 3 / 2
KyPy / PyLy = 3 / 2
First, let's use the x coordinates:
(x − (-5)) / (5 − x) = 3 / 2
(x + 5) / (5 − x) = 3 / 2
2 (x + 5) = 3 (5 − x)
2x + 10 = 15 − 3x
5x = 5
x = 1
And now with the y coordinates:
(y − (-4)) / (1 − y) = 3 / 2
(y + 4) / (1 − y) = 3 / 2
2 (y + 4) = 3 (1 − y)
2y + 8 = 3 − 3y
5y = -5
y = -1
So the point P is at (1,-1).
Answer:
4 feet
Step-by-step explanation:
Since the whispering gallery is 15 feet high and 60 feet wide, it forms an ellipse with major axis along the width of the gallery and minor axis along the height of the gallery.
Using the equation of an ellipse with major axis along the x-axis, we have
x²/a² + y²/b² = 1 where a = midpoint of the width = 60/2 = 30 feet and b = 15 feet.
c² = a² - b² where c = focus of the ellipse.
So, c² = a² - b²
= 30² - 15²
= 900 - 225
= 675
c = ±√675 = ±25.98 feet
So, the coordinate of the focus is thus (0, ±c) = (0, ±25.98) and the coordinate of the vertex is (0, ±a) = (0, ±30)
So, the distance between the foci and the vertex is the distance from the wall at which each of them should be positioned at the foci.
So, d = a - c
= 30 ft - 25.98 ft
= 4.02 feet
≅ 4 feet
