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2 years ago

In circle O, RT and SU are diameters. If m = m, what is m? 47° 52° 64° 87°

2 answers:

8 0

From the given figure, it can be seen that 13x = 15x - 8 because they are vertical angles and thus are equal.

13x = 15x - 8
15x - 13x = 8
2x = 8
x = 8/2 = 4

Thus, 15x - 8 = 15(4) - 8 = 60 - 8 = 52.

RT is a diameter, which means that mRT = 180

mRV + mVU + 52 = 180

mRV + mVU = 180 - 52 = 128

Now, given that mRV = mVU,

Thus, 2mVU = 128

Therefore, mVU = 128 / 2 = 64°

algol [13]2 years ago

6 0

Answer:

Step-by-step explanation:

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A steel pipe 100 cm long has an outside diameter of 2 cm and an inside diameter of 1.8 cm. If thee density of the steel is 7.8 g

ELEN [110]

Answer:

The mass of the pipe is $465\ g$

Step-by-step explanation:

step 1

Find the volume of the steel pipe

The volume is equal to the area of outside circle minus the area of inside circle, multiplied by the length of the pipe

$V=\pi [r2^{2}-r1^{2}]L$

we have

$r2=2/2=1\ cm$ ---> the radius is half the diameter

$r1=1.8/2=0.9\ cm$ ---> the radius is half the diameter

$L=100\ cm$

$\pi=3.14$

substitute

$V=(3.14)[1^{2}-0.9^{2}](100)=59.66\ cm^{3}$

step 2

Find the mass

The mass is equal to the density multiplied by the volume

$m=7.8(59.66)=465\ g$

8 0

2 years ago

Two planes, A and B, start from the same place and move in different directions, making an angle of 50º between them. The speed

cluponka [151]

Answer: The distance between them is 230.65 miles.

Step-by-step explanation:

Since we have given that

Speed of plane A (b) = 200 miles per hour

Speed of plane B (c) = 300 miles per hour

Angle between them = 50°

So,

We will use the "Cosine formula", we get

$a^2=b^2+c^2-2bc\cos A\\\\a^2=200^2+300^2-2\times 200\times 300\cos 50\textdegree\\\\a^2=40000+90000-120000\cos 50\textdegree\\\\a^2=130000-120000\times 0.64\\\\a^2=130000-76800\\\\a^2=53200\\\\a=\sqrt{53200}\\\\a=230.65\ miles\ per\ hour$

So, distance between the two planes after one hour will be

$Distance=\frac{Speed}{time}=\frac{230.65}{1}=230.65\ miles$

So, the distance between them is 230.65 miles.

6 0

2 years ago

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A lake near the Arctic Circle is covered by a sheet of ice during the cold winter months. When spring arrives, the ice starts to

hichkok12 [17]

Answer: 1.5 meters

Step-by-step explanation:

Given: A lake near the Arctic Circle is covered by a sheet of ice during the cold winter months. S

S(t) models the ice sheet's thickness (in meters) as a function of time t (in weeks) $S(t)=-0.25t+4$

if we put x=0, then

$S(0)=-0.25(0)+4\\=4\ meters$

So 4 meters is the initial thickness

To find the thickness after 6 weeks, put x=6 we get

$S(6)=-0.25(6)+4\\=-1.5+4=2.5\ meters$

Decrease in thickness every 6 weeks= $4-2.5=1.5\ meters$

3 0

2 years ago

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Evelyn believes that if she flips a coin 480 times, it will land tails up exactly 240 times. What would you tell Evelyn about he

iragen [17]

Answer:

Step-by-step explanation:

I'd tell her that if (and only if) her prediction is correct, the probability of getting tails is 0.5. Actually, the probability of getting heads would be the same, 0.5.

In real life she would not necessarily get 240 tails out of 480 tosses, but the mean value of the number of tails would indeed be close to 0.5.

3 0

2 years ago

Julia is standing 2 feet away from a lamppost. If she casts a shadow of 5 feet and the light makes a 20° angle relative to the g

givi [52]

Answer:

2.5477 feet

Step-by-step explanation:

Refer the image attached to understand my solution.

BC = height of lamppost.

DE = Julia

AD = shadow of Julia

BD = 2 feet. AD = 5 feet

BA = BD + AD

= 2 + 5 = 7 feet

In ΔABC

tan 20° = $\frac{BC}{BA} = \frac{BC}{7}$

BC = 7 * tan 20°

BC = 2.5477 feet

SO the height of lamppost = 2.5477 feet

5 0

2 years ago