Answer:
6
Step-by-step explanation:
-The different ways of two head and two tails in 4 tosses can be determined by drawing the sample space:
![THTH\\HTHT\\THHT\\TTHH\\HTTH\\HHTT](https://tex.z-dn.net/?f=THTH%5C%5CHTHT%5C%5CTHHT%5C%5CTTHH%5C%5CHTTH%5C%5CHHTT)
-The sample space of the four tosses is as above. Hence, they are 6 different ways to get 2 heads and 2 tails.
Answer:
a- x = 5/3, or x = -7/2
b- 675
c - 5·x + 2
Step-by-step explanation:
The polynomial representing the capital of the two partners = 6·x² + 11·x - 35
a. The total share is the capital of the two partners together = 6·x² + 11·x - 35
∴ When their total share is equal to 0, we have;
6·x² + 11·x - 35 = 0
Factorizing the above equation with a graphing calculator gives;
(3·x - 5)·(2·x + 7)
Therefore;
x = 5/3, or x = -7/2
b- The total expenditure, when x = 10 is given by substituting the value of <em>x </em>in the polynomial 6·x² + 11·x - 35, as follows;
When x = 10
6·x² + 11·x - 35 = 6 × 10² + 11 × 10 - 35 = 675
The total expenditure of Vicky and Micky when x = 10 is 675
c - The sum of their expenditure is (3·x - 5) + (2·x + 7) = 5·x + 2
I’d say 6 I’m not very sure
Answer:
lateral surface area of the cone =49π
Step-by-step explanation:
y= x/4
dx/dy = 4
Given x range as from 0 ≤ x ≤ 7 ⇒ x ranges between (a,b)
a= x/4 = 0/4 = 0
b = x/4= 7/4
lateral surface area of the cone
![\int\limits^b_a {2\pi x\sqrt{1 + (\frac{dx}{dy})^2 } } \, dx \\\\= \int\limits^{\frac{7}{4}}_0 {2\pi (4y)\sqrt{1 + (4)^2 } } \, dx \\\\= 32\pi \int\limits^{\frac{7}{4}}_0 { y } \, dx \\\\= 32\pi [\frac{y^2}{2}]|^\frac{7}{4}_0](https://tex.z-dn.net/?f=%5Cint%5Climits%5Eb_a%20%7B2%5Cpi%20x%5Csqrt%7B1%20%2B%20%28%5Cfrac%7Bdx%7D%7Bdy%7D%29%5E2%20%7D%20%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%3D%20%5Cint%5Climits%5E%7B%5Cfrac%7B7%7D%7B4%7D%7D_0%20%7B2%5Cpi%20%284y%29%5Csqrt%7B1%20%2B%20%284%29%5E2%20%7D%20%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%3D%2032%5Cpi%20%5Cint%5Climits%5E%7B%5Cfrac%7B7%7D%7B4%7D%7D_0%20%7B%20y%20%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%3D%2032%5Cpi%20%5B%5Cfrac%7By%5E2%7D%7B2%7D%5D%7C%5E%5Cfrac%7B7%7D%7B4%7D_0)
=32π * 49/(16 *2)
=49π