Answer:
5 cm
Step-by-step explanation:
If AB is tangent to the circle k(O), then radius OB is perpendicular to segment AB.
If BC is tangent to the circle k(O), then radius OC is perpendicular to segment AC.
Consider two right triangles ABO and ACO. In these triangles:
- AO is common hypotenuse;
- ∠OBA=∠OCA=90°, because AB⊥OB, AC⊥OC;
- OB=OC as radii of the circle k(O).
By HL theorem, triangles ABO and ACO are congruent. Then
- ∠OAB=∠OAC=30°;
- AC=AB=5 cm.
Hence, ∠BAC=∠OAB+∠OAC=30°+30°=60°.
Consider triangle ABC, this triangle is isosceles triangle. In isosceles triangles angles adjacent to the base are congruent, thus
∠CBA=∠BCA=1/2(180°-60°)=60°.
Therefore, triangle ABC is an equilateral triangle, so BC=AB=AC=5 cm.
You can round 375 up to 380 (because the ones is 5 or greater). 147 would be rounded to 150. Then add 380 and 150 and that will give you 530. 375+147≈530
Answer:
The sides of the first quadrilateral are 60 in, 40 in, 30 in and 12,5 in
The sides of the second quadrilateral are 24 in, 16 in, 12 in and 5 in
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor
Arrange the sides of each quadrilateral from largest to smallest
<u><em>First quadrilateral </em></u> <u><em>Second quadrilateral</em></u>
Longest side=60 in Longest side=c in
Second side=40 in Second side=16 in
Third side= a in Third side= 12 in
Fourth side=b in Fourth side=5 in
so
<em>Find the value of c</em>
<em>Find the value of a</em>
<em>Find the value of b</em>
Answer:
At a point when r = 6 ft
The rate of change of Area with time is given as
(dA/dt) = 36π = 113.1 ft²/min
Step-by-step explanation:
Area of a circle, A = πr²
A = πr²
(dA/dt) = (dA/dr) × (dr/dt)
(dA/dr) = 2πr, (dr/dt) = 3
(dA/dt) = 2πr × 3 = 6πr
At a point when r = 6 ft
(dA/dt) = 6πr = 6π × 6 = 36π = 113.1 ft²/min
In a trapezoid, with bases 
and 
and height 
, the area is given by
In your case:
so, the formula becomes
Since the area is 
, we have
