Answer:32
Step-by-step explanation:96-64=32 half of 64 is 32 also equal to 50%
The markup percentage is .40778 -> 40.778%
$4015 = current price ; $2852 = original price
To find the mark up percentage:
First, find the difference between the current price and original price.
$4015 - $2852 = $1163
Second, divide the price difference by the current price to get the percentage.
1163/2852 = .40778
Check the math by multiplying the original price by the markup percentage and add the original price to it.
$2852 X .40778 + $2852 = $4015
Answer:
![Area = \infty](https://tex.z-dn.net/?f=Area%20%3D%20%5Cinfty)
Points of intersection: (1.225,-1.58) and (1.225,1.58)
Step-by-step explanation:
Given
![x = \sqrt{4 - y^2}](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%7B4%20-%20y%5E2%7D)
![y^2 = 1 + x^2](https://tex.z-dn.net/?f=y%5E2%20%3D%201%20%2B%20x%5E2)
Required
The region area
Plot the graphs of
and ![y^2 = 1 + x^2](https://tex.z-dn.net/?f=y%5E2%20%3D%201%20%2B%20x%5E2)
Make y the subject in both equations
![x = \sqrt{4 - y^2}](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%7B4%20-%20y%5E2%7D)
Square both sides
![x^2 = 4 - y^2](https://tex.z-dn.net/?f=x%5E2%20%3D%204%20-%20y%5E2)
Rewrite
![y^2 = 4 - x^2](https://tex.z-dn.net/?f=y%5E2%20%3D%204%20-%20x%5E2)
Take square roots
![y = \sqrt{4 - x^2](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%7B4%20-%20x%5E2)
So, we have:
![f(x) = \sqrt{4 - x^2}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%7B4%20-%20x%5E2%7D)
![y^2 = 1 + x^2](https://tex.z-dn.net/?f=y%5E2%20%3D%201%20%2B%20x%5E2)
Take square roots
![y = \sqrt{1 + x^2}](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%7B1%20%2B%20x%5E2%7D)
So, we have:
![g(x) = \sqrt{1 + x^2}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Csqrt%7B1%20%2B%20x%5E2%7D)
The point of intersection is:
![f(x) = g(x)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20g%28x%29)
![\sqrt{4 - x^2} = \sqrt{1 + x^2}](https://tex.z-dn.net/?f=%5Csqrt%7B4%20-%20x%5E2%7D%20%3D%20%5Csqrt%7B1%20%2B%20x%5E2%7D)
Square both sides
![4 - x^2 = 1 + x^2](https://tex.z-dn.net/?f=4%20-%20x%5E2%20%3D%201%20%2B%20x%5E2)
Collect like terms
![x^2 + x^2 = 4 - 1](https://tex.z-dn.net/?f=x%5E2%20%2B%20x%5E2%20%3D%204%20-%201)
![2x^2 = 3](https://tex.z-dn.net/?f=2x%5E2%20%3D%203)
Divide by 2
![x^2 = 1.5](https://tex.z-dn.net/?f=x%5E2%20%3D%201.5)
Take square roots
![x = 1.225](https://tex.z-dn.net/?f=x%20%3D%201.225)
![g(x) = \sqrt{1 + x^2}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Csqrt%7B1%20%2B%20x%5E2%7D)
![g(x) = \sqrt{1 + 1.5}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Csqrt%7B1%20%2B%201.5%7D)
![g(x) = \sqrt{2.5}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Csqrt%7B2.5%7D)
![g(x) = \±1.581](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5C%C2%B11.581)
So, the point of intersection is at: (1.225,-1.58) and (1.225,1.58)
<em>See attachment</em>
From the attached image, we can see that the curves do not enclose
Hence:
![Area = \infty](https://tex.z-dn.net/?f=Area%20%3D%20%5Cinfty)
Answer:
{(–4, 2), ( –2, 1), (2, 0), (4, 5)}
Step-by-step explanation: Look at the first number in each bracket for domain :)
Answer:
2
x
2
−
16
x
+
35
.
2
(
x
−
4
)
2
+
3
Set
y
equal to the new right side.
y
=
2
(
x
−
4
)
2
+
3
Use the vertex form,
y
=
a
(
x
−
h
)
2
+
k
, to determine the values of
a
,
h
, and
k
.
a
=
2
h
=
4
k
=
3
Find the vertex
(
h
,
k
)
.
(
4
,
3
)
Step-by-step explanation: