The distance that Kirsten and Molly need to bike on their third day is obtained by subtracting the sum of the distances they have traveled after two days from the length of the entire route.

distance left = 156 miles - (64 miles + 45 miles)
= 47 miles
Thus, Kirsten and Molly need to bike 47 miles on their third day.

3 0

4 years ago

Find an equation equivalent to r = 10 sinθ in rectangular coordinates

Flura [38]

Answer:

$x^{2} + y^{2} - 10\cdot y = 0$

Step-by-step explanation:

The following expressions are used to transform from polar into rectangular form:

$r = \sqrt{x^{2}+y^{2}}$

$\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}$

Now, the variables are substituted and equation is finally simplified:

$\sqrt{x^{2}+y^{2}} = 10\cdot \frac{y}{\sqrt{x^{2}+y^{2}} }$

$x^{2}+y^{2} = 10\cdot y$

The equivalent equation in rectangular coordinates is:

$x^{2} + y^{2} - 10\cdot y = 0$

8 0

3 years ago

Solve log8 12=x-2. Round your answer to four decimal places.

olganol [36]

Answer:

$\large\boxed{x\approx3.1950}$

Step-by-step explanation:

$\log_ab=c\iff a^c=b\\\\\log_812=x-2\iff8^{x-2}=12\\\\(2^3)^{x-2}=4\cdot3\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{3(x-2)}=2^2\cdot3\qquad\text{use the distributive property}\\\\2^{3x-6}=2^2\cdot3\qquad\text{divide both sides by}\ 2^2\\\\\dfrac{2^{3x-6}}{2^2}=3\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\2^{3x-6-2}=3\\\\2^{3x-8}=3\qquad\text{logarithm of both sides}\\\\\log_22^{3x-8}=\log_23\qquad\text{use}\ \log_aa^n=n\\\\3x-8=\log_23\qquad\text{add 8 to both sides}$

$3x=\log_23+8\qquad\text{divide both sides by 3}\\\\x=\dfrac{\log_23+8}{3}\\\\\log_23\approx1.5849625\\\\x\approx\dfrac{1.5849625+8}{3}\approx3.1950$

4 0

3 years ago