The large triangle is an isosceles since both angles at the base each equal 42°.
In an isosceles triangle the altitude z is at the same time median , then it bisects the opposite side in the middle . So w = 120/2 = 60
Now let's calculate z:
tan 42° = (opposite side) / (adjacent side) = z/60
tan 42° = 0.9,
0.9 = z/60 and z = 54
Answer:
The limit of this function does not exist.
Step-by-step explanation:
![\lim_{x \to 3} f(x)](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%203%7D%20f%28x%29)
![f(x)=\left \{ {{9-3x} \quad if \>{x \>< \>3} \atop {x^{2}-x }\quad if \>{x\ \geq \>3 }} \right.](https://tex.z-dn.net/?f=f%28x%29%3D%5Cleft%20%5C%7B%20%7B%7B9-3x%7D%20%5Cquad%20if%20%5C%3E%7Bx%20%5C%3E%3C%20%5C%3E3%7D%20%5Catop%20%7Bx%5E%7B2%7D-x%20%7D%5Cquad%20if%20%5C%3E%7Bx%5C%20%5Cgeq%20%5C%3E3%20%7D%7D%20%5Cright.)
To find the limit of this function you always need to evaluate the one-sided limits. In mathematical language the limit exists if
![\lim_{x \to a^{-}} f(x) = \lim_{x \to a^{+}} f(x) =L](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20a%5E%7B-%7D%7D%20f%28x%29%20%3D%20%5Clim_%7Bx%20%5Cto%20a%5E%7B%2B%7D%7D%20f%28x%29%20%3DL)
and the limit does not exist if
![\lim_{x \to a^{-}} f(x) \neq \lim_{x \to a^{+}} f(x)](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20a%5E%7B-%7D%7D%20f%28x%29%20%5Cneq%20%5Clim_%7Bx%20%5Cto%20a%5E%7B%2B%7D%7D%20f%28x%29)
Evaluate the one-sided limits.
The left-hand limit
![\lim_{x \to 3^{-} } 9-3x= \lim_{x \to 3^{-} } 9-3*3=0](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%203%5E%7B-%7D%20%7D%209-3x%3D%20%5Clim_%7Bx%20%5Cto%203%5E%7B-%7D%20%7D%209-3%2A3%3D0)
The right-hand limit
![\lim_{x \to 3^{+} } x^{2} -x= \lim_{x \to 3^{+} } 3^{2}-3 =6](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%203%5E%7B%2B%7D%20%7D%20x%5E%7B2%7D%20-x%3D%20%5Clim_%7Bx%20%5Cto%203%5E%7B%2B%7D%20%7D%203%5E%7B2%7D-3%20%3D6)
Because the limits are not the same the limit does not exist.
Answer:
x = 35 feet.
Step-by-step explanation:
Given that,
The height of the person is 5 feet.
The height of the flag and the eye is (x-5) feet.
We can calculate using trigonometry.
![\tan\theta=\dfrac{(x-5)}{30}\\\\\tan(45)=\dfrac{(x-5)}{30}\\\\(x-5)=30\\\\x=30+5\\\\x=35\ ft](https://tex.z-dn.net/?f=%5Ctan%5Ctheta%3D%5Cdfrac%7B%28x-5%29%7D%7B30%7D%5C%5C%5C%5C%5Ctan%2845%29%3D%5Cdfrac%7B%28x-5%29%7D%7B30%7D%5C%5C%5C%5C%28x-5%29%3D30%5C%5C%5C%5Cx%3D30%2B5%5C%5C%5C%5Cx%3D35%5C%20ft)
So, the value of x is equal to 35 feet. The correct option is (c).
CEVAP:....................
She used 1221 wrapping paper for 21 gifts, so to find the individual amount, you would do:
1221/21
She used about 58.143 ft² of wrapping paper for each gift.