Please help me with this!!

Mathematics

1 answer:

bearhunter [10]2 years ago

6 0

Answer:

8.06

Step-by-step explanation:

Use the Pythagorean theorem:

$a^{2} +b^{2} =c^{2}$

The hypotenuse is always the slanted side, or c (x in this picture), but the other numbers can be interchanged. Doesn't matter.

Plug the numbers 4 and 7 into the formula.

$4^{2} +7^{2} =c^{2} \\$

Now evaluate them to get $c^2$

16+49=65

To get c, take the square root of 65

$\sqrt{65} = 8.06$

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Solve for x, 0 ≤ x ≤2π (2cosx-1)(2sinx+√3 ) = 0

vladimir1956 [14]

Answer:

x = π/3, x = 5π/3, x = 4π/3

Step-by-step explanation:

Let's split the given equation (2cosx-1)(2sinx+√3 ) = 0 into two parts, and solve each separately. These parts would be 2cos(x) - 1 = 0, and 2sin(x) + √3 = 0.

$2\cos \left(x\right)-1=0,\\2\cos \left(x\right)=1,\\\cos \left(x\right)=\frac{1}{2}$

Remember that the general solutions for cos(x) = 1/2 are x = π/3 + 2πn and x = 5π/3 + 2πn. In this case we are given the interval 0 ≤ x ≤2π, and therefore x = π/3, and x = 5π/3.

Similarly:

$\:2\sin \left(x\right)+\sqrt{3}=0,\\2\sin \left(x\right)=-\sqrt{3},\\\sin \left(x\right)=-\frac{\sqrt{3}}{2}$