Answer:
Step-by-step explanation:
p(A) = a^3 + 3a^2 + 9a + 27
put brackets around the 1st and second terms and another set around the 3rd and 4th
P(a)= (a^3 + 3a^2) + (9a + 27)
Using the distributive property, pull out the common factor for each of the 2 terms that contain the brackets.
P(a) = a^2 ( a + 3) + 9(a + 3)
Let a + 3 = x
P(a) = a^2x + 9x
Put brackets around these 2 terms
P(a)= x(a^2 + 9)
Substitute a + 3 for x
P(a) = (a + 3) ( a^2 + 9)
Answer:
q = r
Step-by-step explanation:
<u><em>Explanation:-</em></u>
Given 2q – r = 4p ...(i)
2r = q...(ii)
r = 2p ...(iii)
Substitute 2r = q in equation (i)
<em> 2(2r) – r = 4p </em>
3 r = 4 p
<em> 2 r + r = 4 p</em>
2 r + 2 p = 4 p
2 r = 2 p
<em> q = r</em>
<span>P(at least 1 ) = 1 - P(exactly none) = 1 - (4/5)^6 = .738
Hope this helps!!!:)</span>
Answer:
Step-by-step explanation:
(a) radius is the bottom leg of the right triangle formed by the slopped edge and the vertical line from the tip to the center of the base. So that's easy enough with the pythagorean theorem.
15^2 + b^2 = 34^2
b = sqrt(1156 - 225)
b = 30.512
(b) The surface area can be looked at as the surface area of the circular base + the surface area of the actual cone.
area of a circle is pi*r^2 and the surface area of the cone, excluding the base, is pi*r*s, where s is the slant height. If you want to know where that one comes from it kinda takes some calculus to understand but I can link a video to explain it.
pi*r^2 + pi*r*s
pi(r^2+rs) I factored out pi to make things a little easier.
pi(931+30.512*34)
1968.408pi Feel free to multiply out pi.
(c) Volume for a cone (or any kind of pyramid) is area of the base times the height all divided by 3.
so since we know the area of the base we can just plug in.
(pi*r^2*h)/3
(pi*931*15)/3
4655pi
Let, the integers = x,(x+1)
x*(x+1) = 56
x²+x = 56
x²+x-56 = 0
x²+8x-7x-56=0
x(x+8)-7(x+8)=0
x+8= 0 OR x-7=0
x = -8 OR x = 7
it would be -8 & -7 or 7 & 8
