Answer:
-20
Step-by-step explanation:
First, you divide both sides by -2/5, which would get you c = 8 * -5/2 (Because when you divide, you multiply by the reciprocal). 8 * -5/2 is equal to -20. The answer is -20.
9514 1404 393
Answer:
31.243 units
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationships between sides and angles in a right triangle. Using the attached figure, it is convenient to find the length of BE as an intermediate step in the solution.
Sin = Opposite/Hypotenuse
sin(30°) = BE/100
BE = 100·sin(30°)
Then ...
Tan = Opposite/Adjacent
tan(58°) = BE/x
x = BE/tan(58°) = 100·sin(30°)/tan(58°)
x ≈ 31.243 . . . . units
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<em>Comment on the figure</em>
The intermediate problem in creating the figure was to locate point D. That was accomplished by locating point C on a line at an angle of 58° CCW from the horizontal, using point B as a center. Then D is the intersection of BC with the x-axis. BE is drawn perpendicular to the x-axis.
Answer:
x = 51
Step-by-step explanation:
Here, we want to find the value of x
To do this, we are going to use the appropriate trigonometric identity
We have the side facing the right angle ( hypotenuse) and the side facing the angle given (opposite)
The trigonometric identity that links both is the sine and it is the ratio of the opposite to the hypotenuse
Thus, we have it that;
sine x = 7/9
x = arisine (7/9)
x = 51
Answer:
V(max) = 8712.07 in³
Dimensions:
x (side of the square base) = 16.33 in
girth = 65.32 in
height = 32.67 in
Step-by-step explanation:
Let
x = side of the square base
h = the height of the postal
Then according to problem statement we have:
girth = 4*x (perimeter of the base)
and
4* x + h = 98 (at the most) so h = 98 - 4x (1)
Then
V = x²*h
V = x²* ( 98 - 4x)
V(x) = 98*x² - 4x³
Taking dervatives (both menbers of the equation we have:
V´(x) = 196 x - 12 x² ⇒ V´(x) = 0
196x - 12x² = 0 first root of the equation x = 0
Then 196 -12x = 0 12x = 196 x = 196/12
x = 16,33 in ⇒ girth = 4 * (16.33) ⇒ girth = 65.32 in
and from equation (1)
y = 98 - 4x ⇒ y = 98 -4 (16,33)
y = 32.67 in
and maximun volume of a carton V is
V(max) = (16,33)²* 32,67
V(max) = 8712.07 in³
