Find, corrrect to the nearest degree, the three angles of the triangle with the given vertices. D(0,1,1), E(-2,4,3), C(1,2,-1)

Mathematics

1 answer:

Sholpan [36]3 years ago

4 0

Answer:

The three angles of the triangle given above are 23, 73 and 84 correct to the nearest degree. The concept of dot product under vectors was applied in solving this problem. The three positions forming the triangle were taken as positions vectors. The Dot product also known as scalar product is a very good way of finding the angle between two vectors. ( in this case the sides of the triangle given above). Below is a picture of the step by step procedure of the solution.

Step-by-step explanation:

The first thing to do is to treat the given positions in space as position vectors which gives us room to perform vector manipulations on them. Next we calculate the magnitude of the position vector which is the square root of the sun of the square of the positions of the vectors along the three respective axes). Then we calculate the dot product. After this is calculated the angle can then be found easily using formula for the dot product.

Thank you for reading this and I hope it is helpful to you.

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Find the geometric mean of the pair of numbers

Svetach [21]

Answer: a. 55

Step-by-step explanation:

The formula to find the geometeric mean between two numbers a and b is given by :-

$G.M. =\sqrt{ab}$

The given numbers are : 275 and 11

The geometric mean of 275 and 11 is given by :-

$G.M.=\sqrt{275\times11}\\\\\Rightarrow\ G.M. =\sqrt{3025}\\\\\Rightarrow\ G.M.=\sqrt{55\times55}\\\\\Rightarrow\ G.M.=\sqrt{55^2}\\\\\Rightarrow\ G.M.=55$

Hence, the geometric mean of 275 and 11 is 55.

So , the correct option is a. 55 .

4 0

3 years ago

Helppppp god bless u

Vanyuwa [196]

Lets be a price of the calculator - $ a
then , after using the coupon, you need to pay $(a-18)
and after using 15% discount , you need to pay (1-0.15)a=0.85a

then, if
(a-18) will be more than 0.85a, you should prefer 0.15 % discount, because it will be cheaper,

a-18> 0.85a
a-0.85a>18
0.15a > 18
a>120, that means that if the price of the calculator more than $120, 15% discount is better,
but if the price of the calculator is less than $120, you should choose $ 18 coupon.

for example, we have the price of the calculator $100
100-18=82,
100*0.85 =85, coupon is better.

If the price of the calculator $200
200-18=182,
200*0.85=170, so 15% discount is better

if price of the calculator is $120,
120-18=102
120*0.85=102,
it will not matter, what you are going to use, because you are going to pay the same amount of money

5 0

3 years ago

Read 2 more answers

Let ABC be an isosceles triangle with AB = AC and ∠BAC=30°. Side AB and the median AD contain points Q and P respectively (point

Svet_ta [14]

Answer:

15°

Step-by-step explanation:

Since P is on the median of ΔABC, it is equidistant from points B and C as well as from C and Q. Thus, points B, C, and Q all lie on a circle centered at P. (See the attached diagram.)

The base angles (B and C) of triangle ABC are (180° -30°)/2 = 75°. This means arc QC of the circle centered at P has measure 150°. The diameter of circle P that includes point Q is defined to intersect circle P at R.

Central angle RPC is the difference between arcs QR and QC, so is 180° -150° = 30°. Inscribed angle RQC has half that measure, so is 15°. Angle PQC has the same measure as angle RQC, so is 15°.

Angle PQC is 15°.