Help me with the 3 of them

△ABC is inscribed in a circle. Find the angle between the tangents to the circle at points B and C, if m∠CAB=50°.

Daniel [21]

$DB,DC \: are \: tangents \: to \: (O) \: at \: B,C\\\Rightarrow DB\perp OB \: at \: B, DC\perp OC \: at \: C\Rightarrow \widehat{DBO}=\widehat{DCO}=90° \\ \widehat{BOC}=2\widehat{BAC}=2\times 50°=100°\\\widehat{BDC}=360°-\widehat{BOC}-\widehat{DBO}-\widehat{DCO}=360°-100°-90°-90°=80°$

5 0

4 years ago

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Which is best estimate for the length of the short leg a if the hypotenuses c is about 10 cm 15 points!!

iVinArrow [24]

Answer:

A)4

Step-by-step explanation:

Assuming all edges are integral values

The most basic right angles triangle with integral edges is

(3,4,5)

as it obeys pythogores theorem

which is

$a^{2}+ b^{2} =c^{2} \\\text{where c is the hypotenuse}\\\text{and a and b are the other side}$

$3^{2} +4^{2} =5^{2}$

Now, double each edge,it will still remain a right angled triangle since it will still obey pythogores theorem

so the edges are (4,6,10)

⇒4 cm is the short leg of a integral right triangle with hypotenuse 10 cm

3 0

3 years ago

I have another question 8x−8≤−72. please help

AnnyKZ [126]

First move the -8 on the left to the right. this makes the inequality become 8x≤-64. Then you want to isolate the x by dividing 8x by 8, and make sure to do the same to -64. This makes it become x<span>≤-8, which is your final answer! Hope this helped :)</span>

8 0

4 years ago

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determine (a) the volume and (b) the surface area of the three-dimensional figure. when appropriate, use pi key on your calculat

lawyer [7]

Answer:

$Volume = 150 yd^3$

$Surface Area = 150 yd^2$

Step-by-step explanation:

Going by the dimensions of the given three-dimensional figure, we can conclude that the figure is that of a cube. The height, length and width are equal.

Volume of a cube is given as $a^3$ , while surface area of a cube is given as $6a^2$

Where, a = the side length = 5 yards

$Volume = a^3 = 5^3$

$Volume = 150 yd^3$

$Surface Area = 6a^2 = 6(5)^2$

$Surface Area = 150 yd^2$

3 0

4 years ago

Circumference, radius, slant height, lateral area, and surface area are measurements of a cone. Given two of the measurements, f

USPshnik [31]

Answer:

LA = 21.7 ft²; C = 18.8 ft; h = 2.3 ft
h = 8 in; r = 7 in; SA = 330.1 in²

Step-by-step explanation:

Applicable relations are ...

C = 2πr . . . . . . . r = radius, C = circumference

LA = 1/2·Ch . . . . h = slant height, LA = lateral area

SA = πr² +LA . . . SA = total surface area

__

1. Given r and SA, we can find the other measures as ...

LA = SA -πr² = 50 ft² -π(3 ft)² ≈ 21.7 ft²

C = 2πr = 2π(3 ft) ≈ 18.8 ft

h = 2·LA/C ≈ 2·21.7 ft²/(18.8 ft) ≈ 2.3 ft

(Please note that for calculations using intermediate results, we used the full-precision values of those results, not the rounded ones. Rounding is always the last operation. Please note, too, that we have used a value for π sufficient to ensure accuracy in all the digits shown here.)

__

2. Given C and LA, we can find the other measures as ...

h = 2·LA/C = 2(176 in²)/(44 in) = 8 in

r = C/(2π) = (44 in)/(2π) ≈ 7.0 in

SA = LA +πr² = LA +rC/2 ≈ 176 in² +(7.0 in)(44 in)/2 ≈ 330.1 in²

4 0

3 years ago