Alan says that the distance from Hadley to Greenville is 16 miles. Is he correct?Explain

Mathematics

1 answer:

yuradex [85]3 years ago

8 0

Answer:

Step-by-step explanation:

Considering the complete question attached in figure.

Consider

Hadley = x

Parker = y

Greenville = z

Distance between Greenville and Parker = yz = 29

Given that distance between Hadley and Greenville is 13 miles less than the distance between Parker and Greenville.

xz = yz -13 --- (1)

Distance between hardley and greenville = xz = ?

From (1)

xz = 29 -13

xz = 16 miles

So Alan is right that distance between Hadley and Greenville is 16 miles

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The area of the sector formed by the 110 degree central angle is 50 units squared. What is the circumference of the circle

Mama L [17]

Answer:

The circumference of the circle is $C=45.346 \:units$ .

Step-by-step explanation:

A sector is the part of a circle enclosed by two radii of a circle and their intercepted arc. A pie-shaped part of a circle.

The area of a circle is given by $A_{circle}=\pi r^2$

The formula used to calculate the area of a sector of a circle is:

$A_{sector}=\frac{central \:angle}{360} \cdot {Area \:of \:whole \:circle}\\\\A_{sector}=\frac{\theta}{360} \cdot \pi r^2$

The circumference of a circle is the distance around the outside of the circle and its given by

$C=2\pi r$

We know the central angle $\theta$ = 110º and the area of the sector 50 units squared.

First, we use the formula to calculate the area of a sector to find the radius.

$50=\frac{110}{360} \cdot \pi r^2\\\\\frac{110}{360}\pi r^2=50\\\\\frac{11\pi }{36}r^2=50\\\\11\pi r^2=1800\\\\r^2=\frac{1800}{11\pi }\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\r=\sqrt{\frac{1800}{11\pi }},\:r=-\sqrt{\frac{1800}{11\pi }}$