Given the ratio, you know that:
length = 6x
width = 2x
height = 7x
Because the sum of the length and the width is 24 cm, you can write the equation:
6x + 2x = 24
Solve:
8x = 24
x = 3
Plug the 3 back into the expressions written earlier for length, width, and height.
length = 18 cm
width = 6 cm
height = 21 cm
Use the formula SA = 2B + Ph to solve for the surface area.
Surface Area = 2(area of the base) + (perimeter of the base)(height)
I'm going to plug in l, w, and h as variables for length, width, and height to show the exact way to solve for the B and P.
SA = 2lw + 2(l + w)h
SA = 2(18)(6) + 2(18 + 6)(21)
SA = 216 + 2(24)(21)
SA = 216 + 1008
SA = 1224
The surface area is 1,224 cm^2.
From the given equation above, F = ma, acceleration may be calculated by slightly modifying the equation into a = F / m. Substituting the known values for force and mass,
a = 2,050,000 N / 40,000 kg = 51.25 m/s²
Thus, the acceleration achieved is 51.25 m/s².
Answer:
x = 21° or 339°
Step-by-step explanation:
We are given that cos x = 0.9341.
So, cosine of x is positive and then x can be in first quadrant or fourth quadrant.
Now, ≈ 21° (to the nearest degree)
So, x = 21° or (360 - 21)° = 339° (Answer)
Answer:
Step-by-step explanation:
we know that
In a rhombus the diagonals are perpendicular
so
The triangle ABE is a right triangle
see the attached figure to better understand the problem
Applying the Pythagoras Theorem to the right triangle ABE
where
AB is the hypotenuse of the right triangle (greater side)
AE and BE are the legs of the right triangle
we have
substitute
solve for BE
Answer:
x=5
y=−1
Step-by-step explanation:
x+y=4
2x−5y=15
In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.
x+y=4,2x−5y=15
To make x and 2x equal, multiply all terms on each side of the first equation by 2 and all terms on each side of the second by 1.
2x+2y=2×4,2x−5y=15
Simplify.
2x+2y=8,2x−5y=15
Subtract 2x−5y=15 from 2x+2y=8 by subtracting like terms on each side of the equal sign.
2x−2x+2y+5y=8−15
Add 2x to −2x. Terms 2x and −2x cancel out, leaving an equation with only one variable that can be solved.
2y+5y=8−15
Add 2y to 5y.
7y=8−15
Add 8 to −15.
7y=−7
Divide both sides by 7.
y=−1
Substitute −1 for y in 2x−5y=15. Because the resulting equation contains only one variable, you can solve for x directly.
2x−5(−1)=15
Multiply −5 times −1.
2x+5=15
Subtract 5 from both sides of the equation.
2x=10
Divide both sides by 2.
x=5
The system is now solved.
x=5,y=−1