Answer:
Step-by-step explanation:
Given the expression cosec (x) = 4 and tan(x)< 0
since cosec x = 1/sinx
1/sinx = 4
sinx = 1/4
From SOH, CAH TOA
sinθ = opposite/hypotenuse
from sinx = 1/4
opposite = 1 and hypotenuse = 4
to get the adjacent, we will use the Pythagoras theorem
adj² = 4²-1²
adj² = 16-1
adj ²= 15
adj = √15
cosx = adj/hyp = √15/4
tanx = opposite/adjacent = 1/√15
since tan < 0, then tanx = -1/√15
From double angle formula;
sin2x = 2sinxcosx
sin2x = 2(1/4)(√15/4)
sin2x = 2√15/16
sin2x = √15/8
for cos2x;
cos2x = 1-2sin²x
cos2x = 1-2(1/4)²
cos2x = 1-2(1/16)
cos2x= 1-1/8
cos2x = 7/8
for tan2x;
tan2x = tanx + tanx/1-tan²x
tan2x = 2tanx/1-tan²x
tan2x = 2(-1/√15)/1-(-1/√15)²
tan2x = (-2/√15)/(1-1/15)
tan2x = (-2/√15)/(14/15)
tan2x = -2/√15 * 15/14
tan2x = -30/14√15
tan2x = -30/7√15
rationalize
tan2x = -30/7√15 * √15/√15
tan2x = -30√15/7*15
tan2x = -2√15/7
<h3>One possible set for the base area and height of the pyramid is 570 cm and 1 cm respectively</h3><h3>Other possible set for the base area and height of the pyramid is 285 cm and 2 cm respectively</h3>
<em><u>Solution:</u></em>
<em><u>The volume of rectangular pyramid is given as:</u></em>
Given that,
<em><u>Rectangular pyramid has a volume of 190 cubic centimeters</u></em>
<em><u></u></em>
<em><u></u></em>
<em><u>Substitute, base area = 570 and height = 1</u></em>
Then we get,
Thus one possible set for the base area and height of the pyramid is 570 cm and 1 cm respectively
<em><u>Substitute, base area = 285 and height = 2</u></em>
Thus other possible set for the base area and height of the pyramid is 285 cm and 2 cm respectively
Answer:
Cougar population was 790 at the beginning
830-790=40
The answer is to your question is 1. You must replace t with 12 and then follow the rule of PEMDAS to solve this equation.
