Answer:
The answer is "Pattern B showed number 40; each pattern is also increased as per the rule".
Step-by-step explanation:
In every sequence pattern, it recalls that rule, it adds 15 in this need to build from the specified initial estimate each sequence.
In Pattern A.
5+20+35+50+......
In Pattern B.
10+25+40+55+70+.....
In Pattern C.
15+30+45+60....
In this, pattern option B is correct because it will give 40.
Width = w
length = w+2
f(w) =w(w+2) = w^2 + 2w.
Please, let me know whether the procedure is clear for you.
The answer is f(w)=w^2 + 2w.
2x+5x+5=180 so x has to be 25
Answer:
5in by 5in by 5in
Step-by-step explanation:
We are not told wat to find but we can as well find the dimension of the prism that will minimize its surface area.
Given
Volume = 125in³
Formula
V = w²h ..... 1
S = 2w²+4wh ..... 2
w is the side length of the square base
h is the height of the prism
125 = w²h
h = 125/w² ..... 3
Substitute eqn 3 into 2 as shown
S = 2w²+4wh
S = 2w²+4w(125/w²)
S = 2w²+500/w
To minimize the surface area, dS/dw = 0
dS/dw =4w-500/w²
0= 4w-500/w²
Multiply through by w²
0 = 4w³-500
-4w³ = -500
w³ = 500/4
w³ =125
w = cuberoot(125)
w = 5in
Get the height
125 =w²h
125 = 25h
h = 125/25
h = 5in
Hence the dimension of the prism is 5in by 5in by 5in
Answer:
-1
Step-by-step explanation:
We need to find the value of tan² 70° -sec² 70°.
We know that,
...(1)
We can write the given expression as :
tan² 70° -sec² 70° = -(-tan² 70° +sec² 70°)
=-(sec² 70°-tan² 70°)
Using identity (1)
=-(1)
= -1
Hence, the value of the given expression is -1.
