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Mathematics

1 answer:

taurus [48]3 years ago

7 0

Answer:

x = 44°

Step-by-step explanation:

2x - 6 = 82

2x = 82 +6

2x = 88

divide through by 2

x = 44°

similar triangle

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John has a pet hamster, Apollo. The base of the hamster’s home is 336 inches and 18 inches tall. Solve the total volume of the c

Brrunno [24]

Answer:

the total volume of the cage is 6,048

Step-by-step explanation:

336*18=6,048

hope this helps

5 0

4 years ago

Please Help!!!

algol [13]

$f\left(\dfrac\beta2\right)=\sin\dfrac\beta2$

Recall the half-angle identity:

$\sin^2\dfrac\beta2=\dfrac{1-\cos\beta}2\implies\sin\dfrac\beta2=\pm\sqrt{\dfrac{1-\cos\beta}2}$

So in order to find $f\left(\dfrac\beta2\right)$ , we only need to know the value of $\cos\beta$ . But there are two possible values. To decide which to take, we use the given information: we know that $\beta$ lies in quadrant III, which means $\pi$ , so $\dfrac\pi2$ , which places $\dfrac\beta2$ in quadrant II. In this quadrant, the sine of angle is positive, and so

$\sin\dfrac\beta2=\sqrt{\dfrac{1-\cos\beta}2}$

$\beta$ is an angle of a ray whose terminal point, $\left(-\dfrac13,y\right)$ lies on the circle $x^2+y^2=1$ . The $x$ -coordinate is all we need to know in order to find that $\cos\beta=-\dfrac13$ . So,

$\sin\dfrac\beta2=\sqrt{\dfrac{1-\left(-\frac13\right)}2}=\sqrt{\dfrac46}=\dfrac{\sqrt2}{\sqrt3}=\dfrac{\sqrt6}3$