Answer:
The correct answer will be "0.756596 m²".
Step-by-step explanation:
The given values are:
The radius of an umbrella,
r = 0.4 m
The height of an umbrella,
h = 0.45 m
As we know,
The lateral surface of an umbrella will be:
⇒ ![\pi r\sqrt{r^2+h^2}](https://tex.z-dn.net/?f=%5Cpi%20r%5Csqrt%7Br%5E2%2Bh%5E2%7D)
On substituting the values, we get
⇒ ![\pi \times 0.4\sqrt{(0.4)^2=(0.45)^2}](https://tex.z-dn.net/?f=%5Cpi%20%5Ctimes%200.4%5Csqrt%7B%280.4%29%5E2%3D%280.45%29%5E2%7D)
⇒ ![0.756596 \ m^2](https://tex.z-dn.net/?f=0.756596%20%5C%20m%5E2)
So that the amount of fabric needed will be "0.756596 m²".
Step-by-step explanation:
It is given that,
The height of the sail on a boat is 7 feet less than 3 times the length of its base.
Let the length of the base is x.
ATQ,
Height = (3x-7)
Area of the sail is 68 square feet.
Formula for area is given by :
![A=lb\\\\68=x(3x-7)\\\\3x^2-7x=68\\\\3x^2-7x-68=0](https://tex.z-dn.net/?f=A%3Dlb%5C%5C%5C%5C68%3Dx%283x-7%29%5C%5C%5C%5C3x%5E2-7x%3D68%5C%5C%5C%5C3x%5E2-7x-68%3D0)
x = 8 feet and x = -3.73 feet
So, length is 8 feet
Height is 3(8)-7 = 17 feet.
So, its height and the length of the base is 17 feet and 8 feet respectively.
Answer:
arc VW=218°
Step-by-step explanation:
∠VWY is an inscribed angle.
An inscribed angle is always half of the corresponding arc
109x2=218
Therefore...
arc VW=218°
Answer:
Step-by-step explanation:
What you are being told is that 3x - 7 is twice as big as x. You can see that because ST (for example) is cut into 2 equal parts. So is UT (cut into two equal parts). So the parts of the Big Triangle (SUT) are twice as Big as the parts of the small triangle DET
So multiply x by 2
3x - 7 = 2x Add 7 to both sides
3x - 7 + 7 = 2x + 7
3x = 2x + 7 Subtract 2x from both sides
3x-2x = 7
x = 7
Answer:
The equation is:
![S=\frac{a_n*r-a_1}{r-1}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7Ba_n%2Ar-a_1%7D%7Br-1%7D)
![S=\frac{\frac{16}{243}*\frac{2}{3}-\frac{1}{3}}{\frac{2}{3}-1}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7B%5Cfrac%7B16%7D%7B243%7D%2A%5Cfrac%7B2%7D%7B3%7D-%5Cfrac%7B1%7D%7B3%7D%7D%7B%5Cfrac%7B2%7D%7B3%7D-1%7D)
The sum is:
![S=\frac{211}{243}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7B211%7D%7B243%7D)
--------------------------------------------------------------------
If the sequence is infinite, the formula is:
![S = \frac{a_1}{1-r}](https://tex.z-dn.net/?f=S%20%3D%20%5Cfrac%7Ba_1%7D%7B1-r%7D)
-------------------------------------------------------------------
Step-by-step explanation:
We must calculate the radius of the geometric series
![r =\frac{a_{n+1}}{a_n}\\\\r=\frac{\frac{2}{9}}{\frac{1}{3}}\\\\r=\frac{2}{3}](https://tex.z-dn.net/?f=r%20%3D%5Cfrac%7Ba_%7Bn%2B1%7D%7D%7Ba_n%7D%5C%5C%5C%5Cr%3D%5Cfrac%7B%5Cfrac%7B2%7D%7B9%7D%7D%7B%5Cfrac%7B1%7D%7B3%7D%7D%5C%5C%5C%5Cr%3D%5Cfrac%7B2%7D%7B3%7D)
The first term of the series is: ![a_1=\frac{1}{3}](https://tex.z-dn.net/?f=a_1%3D%5Cfrac%7B1%7D%7B3%7D)
The last term of the series is: ![a_n=\frac{16}{243}](https://tex.z-dn.net/?f=a_n%3D%5Cfrac%7B16%7D%7B243%7D)
If the sequence is finite then the formula is:
![S=\frac{a_n*r-a_1}{r-1}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7Ba_n%2Ar-a_1%7D%7Br-1%7D)
![S=\frac{\frac{16}{243}*\frac{2}{3}-\frac{1}{3}}{\frac{2}{3}-1}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7B%5Cfrac%7B16%7D%7B243%7D%2A%5Cfrac%7B2%7D%7B3%7D-%5Cfrac%7B1%7D%7B3%7D%7D%7B%5Cfrac%7B2%7D%7B3%7D-1%7D)
![S=\frac{211}{243}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7B211%7D%7B243%7D)
If the sequence is infinite then by definition as the radius are
then the formula for the sum of the geometric sequence is:
![S = \frac{a_1}{1-r}\\\\S = \frac{\frac{1}{3}}{1-\frac{2}{3}}\\\\S =1](https://tex.z-dn.net/?f=S%20%3D%20%5Cfrac%7Ba_1%7D%7B1-r%7D%5C%5C%5C%5CS%20%3D%20%5Cfrac%7B%5Cfrac%7B1%7D%7B3%7D%7D%7B1-%5Cfrac%7B2%7D%7B3%7D%7D%5C%5C%5C%5CS%20%3D1)