X is -1/2 . Using the Lambert W function.
x^2=16^x => x^2=(2^4)^x
x^2=2^4x => x=2^2x
x=(e^in(2))^2x => x=e^2in(2)x
e^2in(2)x1/x=1
xe^-2in(2)x=1 /*1
-xe^-2in(2)x=-1
-2in(2)xe^-2in(2)x=-2in(2)
W(-2in(2)xe^-2in2x)=W(-2in(2))
-2in(2)x=W(-2in(2))
X=-W(-2in(2))/2in(2)
Answer: The temperature of the object after one hour is 12.9°C to the nearest tenth of a degree
Step-by-step explanation:
Please see the attachments below
Answer:
a. ![x=4\sqrt{3}](https://tex.z-dn.net/?f=x%3D4%5Csqrt%7B3%7D)
b. ![m\angle B =60\°](https://tex.z-dn.net/?f=m%5Cangle%20B%20%3D60%5C%C2%B0)
Step-by-step explanation:
a. The sides of an Equilateral triangle are all equal.
Then, in this case:
![AB=BC=CA=8](https://tex.z-dn.net/?f=AB%3DBC%3DCA%3D8)
Based on this, you can identify that AD divides the side BC into two equal parts and the triangle into two equal Right triangles. Then:
![CD=BD=\frac{8}{2}=4](https://tex.z-dn.net/?f=CD%3DBD%3D%5Cfrac%7B8%7D%7B2%7D%3D4)
Knowing the length CD, you can find "x" using the Pythagorean Theorem. This is:
![a^2=b^2+c^2](https://tex.z-dn.net/?f=a%5E2%3Db%5E2%2Bc%5E2)
Where "a" is the hypotenuse and "b" and "c" are the legs.
In this case:
![a=8\\b=x\\c=4](https://tex.z-dn.net/?f=a%3D8%5C%5Cb%3Dx%5C%5Cc%3D4)
Substituting values and solving for "x", you get:
![8^2=x^2+4^2\\\\\sqrt{8^2-4^2}=x\\\\x=4\sqrt{3}](https://tex.z-dn.net/?f=8%5E2%3Dx%5E2%2B4%5E2%5C%5C%5C%5C%5Csqrt%7B8%5E2-4%5E2%7D%3Dx%5C%5C%5C%5Cx%3D4%5Csqrt%7B3%7D)
b. By definition, the measure of each interior angle of an Equilateral triangle is 60 degrees. Therefore:
![m\angle B =60\°](https://tex.z-dn.net/?f=m%5Cangle%20B%20%3D60%5C%C2%B0)