Isolate the variable by dividing each side by factors that don't contain the variable.
x = 2
![\sqrt[7]{(7x^3y^2)^{2} } = \sqrt[7]{(49x^6y^4)}](https://tex.z-dn.net/?f=%20%5Csqrt%5B7%5D%7B%287x%5E3y%5E2%29%5E%7B2%7D%20%7D%20%3D%20%5Csqrt%5B7%5D%7B%2849x%5E6y%5E4%29%7D%20)
In a fractional exponent the denominator tells what root it is (7th root in this case) and the numerator tells what the value in the parenthesis is raised to (2nd power in this case)
Answer:
- 5.8206 cm
- 10.528 cm
- 23.056 cm^2
Step-by-step explanation:
(a) The Law of Sines can be used to find BD.
BD/sin(48°) = BD/sin(50°)
BD = (6 cm)(sin(48°)/sin(60°)) ≈ 5.82064 cm
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(b) We can use the Law of Cosines to find AD.
AD^2 = AB^2 +BD^2 -2·AB·BD·cos(98°) . . . . . angle ABD = 48°+50°
AD^2 ≈ 110.841
AD ≈ √110.841 ≈ 10.5281 . . . cm
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(c) The area of ∆ABD can be found using the formula ...
A = ab·sin(θ)/2 . . . . . where a=AB, b=BD, θ = 98°
A = (8 cm)(5.82064 cm)sin(98°)/2 ≈ 23.0560 cm^2
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Angle ABD is the external angle of ∆BCD that is the sum of the remote interior angles BCD and BDC. Hence ∠ABD = 48° +50° = 98°.
Lynn mixes 39 pounds of water with 48 pounds of brick dust, so the mixture has a total weight of 39 + 48 = 87 pounds.
13 pounds are spilled during mixing, so she's left with 87 - 13 = 74 pounds to turn into bricks.
7 pounds are needed for 1 brick, so she can make 10 bricks because 7 • 10 = 70 and 7 • 11 = 77, and 70 < 74 < 77.
If she uses the mixture to make 10 bricks, she uses up 70 pounds of it, which leaves 4 pounds to be washed out.
Check the picture below.
surely, you'd know how much that is.
