Answer:
5.567764363 or rounded off to two decimal places 5.57
Step-by-step explanation:
Calculator
A) Let x = cost of t-shirt:
x= 22.95-12.25
B) x = 22.95 -12.25 = 10.70
C) the t-shirt cost $10.70
The cylinder is a clue to use cylindrical coordinates. Taking
![x=3\cos\theta](https://tex.z-dn.net/?f=x%3D3%5Ccos%5Ctheta)
and
![y=3\sin\theta](https://tex.z-dn.net/?f=y%3D3%5Csin%5Ctheta)
, we then are forced to use
![z=3\cos\theta+3](https://tex.z-dn.net/?f=z%3D3%5Ccos%5Ctheta%2B3)
. So the parameterization of the intersection of the plane and cylinder is
![\mathbf s(\theta)=(3\cos\theta,3\sin\theta,3\cos\theta+3)](https://tex.z-dn.net/?f=%5Cmathbf%20s%28%5Ctheta%29%3D%283%5Ccos%5Ctheta%2C3%5Csin%5Ctheta%2C3%5Ccos%5Ctheta%2B3%29)
To get the surface, we can introduce a second parameter
![r](https://tex.z-dn.net/?f=r)
that "contracts" the elliptical intersection to a point. The simplest way to do this is to use
![\mathbf s(r,\theta)=(3r\cos\theta,3r\sin\theta,3r\cos\theta+3)](https://tex.z-dn.net/?f=%5Cmathbf%20s%28r%2C%5Ctheta%29%3D%283r%5Ccos%5Ctheta%2C3r%5Csin%5Ctheta%2C3r%5Ccos%5Ctheta%2B3%29)
with
![0\le r\le1](https://tex.z-dn.net/?f=0%5Cle%20r%5Cle1)
and
![0\le\theta\le2\pi](https://tex.z-dn.net/?f=0%5Cle%5Ctheta%5Cle2%5Cpi)
.
Answer: Kate = £102
Sanjeev = £153
Step-by-step explanation:
From the question, we are informed that for every £2 that kat collects, sanjeev collects £3. This csn be represented in a fraction as:
Kat = 2/5
Sanjeev = 3/5
The amount that each collects will be:
Kat = 2/5 × £255
= 2 × £51
= £102
Sanjeev = 3/5 × £255
= 3 × £51
= £153
Answer:
<em>The height of the monument is 124.8 ft</em>
Step-by-step explanation:
<u>Right Triangles</u>
The ratios of the sides of a right triangle are called trigonometric ratios. The tangent ratio is defined as:
![\displaystyle \tan\theta=\frac{\text{opposite leg}}{\text{adjacent leg}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctan%5Ctheta%3D%5Cfrac%7B%5Ctext%7Bopposite%20leg%7D%7D%7B%5Ctext%7Badjacent%20leg%7D%7D)
The figure attached below shows the different distances involved in the problem. We heed to find the value of h, the height from Daniel's eyes. Then we'll add it to the 6 ft where his eyes are located from the ground.
Taking the angle of 68° as a reference:
![\displaystyle \tan 68^\circ=\frac{h}{48}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctan%2068%5E%5Ccirc%3D%5Cfrac%7Bh%7D%7B48%7D)
Solving for h:
![\displaystyle h=48\tan 68^\circ](https://tex.z-dn.net/?f=%5Cdisplaystyle%20h%3D48%5Ctan%2068%5E%5Ccirc)
Calculating:
h = 118.8 ft
The height of the monument is 118.8 ft + 6 ft = 124.8 ft