What is 5x =25 what is x
2 answers:
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Option A: The vessel has sailed 34 miles South
Explanation:
Given that the vessel sails 41 miles S 35° E.
We need to determine the how far south the vessel has sailed.
Let us use the Pythagorean theorem to find the distance of the vessel has sailed.
Thus, we have,
Substituting ,
and
Hence, we get,
Simplifying, we have,
Multiplying both sides by 41, we have,
Rounding off to the nearest integer, we have,
Thus, the vessel has sailed 34 miles South.
Therefore, Option B is the correct answer.
Answer:
The dimensions are 13.92inches by 36.92inches by 5.04inches
Volume is 2590.18 inches³
Step-by-step explanation:
see attachment for the figure
supposing 'h' is side length of the square and also the height of the box
then, According to the question
Length of the box 'L'= 47 - 2h
Width of the box 'w'= 24 - 2h
Volume of the box 'V'= hLw
Substituting the values of 'L' and 'w' in above equation
V= h(47 - 2h)(24 - 2h)
V=(47h - 2h²)(24 - 2h) => 1128h - 94h²-48h²+4h³
V= 4h³ -142h²+1128h -->eq(1)
Taking derivative on both sides.
V' = 12h² - 284h + 1128
Setting the equation to zero, we will have
0=12h² - 284h + 1128
0= 3h² - 71h + 282
Using Quadratic formula to find h
h= (-b+-√b²-4ac) / 2a
= 71+-√71² - (4 x 3 x 282) / (2 x 3)=> 71+-√5041- 3384 / 6
h =(71+- 40.706)/ 6
EITHER h= 18.6
OR h=5.04
By substituting the value of 'h' in eq(1)
(1)=>V(18.6)= 4(18.6)³ -142(18.6)²+1128(18.6) => -2406.096
(1)=>V(5.04)= 4(5.04)³ -142(5.04)²+1128(5.04) => 2590.18
By ignoring the negative value, we will have h=5.04
Therefore,
L= 47 - 2h => 47 -2(5.04) =>36.92
w= 24 - 2h=> 24- 2(5.04)=> 13.92
The dimensions are 13.92inches x 36.92inches x 5.04inches
Volume is 2590.18 inches³
Answer:
Step-by-step explanation:
Use the exterior angle theorem of a triangle.
According to this theorem; an exterior angle is equal to the sum of the two opposite interior angles (35+58).
Simplify;