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10. A wire is of length 264 cm. It is bent into a circle. What is the radius of the circle so obtained. If it

Luden [163]

Answer:

$r = 42$ --- radius

$L = 66$ -- Length of the square

Step-by-step explanation:

Given

$Length = 264cm$

Solving (a): Find the radius (when it formed a circle).

The length of the wire represents the circumference (C) of the wire.

So, we have:

$C = 2\pi r$

Make r the subject

$r = \frac{C}{2\pi}$

Substitute 264 for C

$r = \frac{264}{2\pi}$

$r = \frac{132}{\pi}$

Take $\pi$ as 22/7

$r = \frac{132}{22/7}$

$r = \frac{132*7}{22}$

$r = \frac{924}{22}$

$r = 42$

Solving (b): Find the side length (when it formed a square).

The length of the wire represents the perimeter (P) of the wire.

So, we have:

$P = 4L$

Make L the subject

$L = \frac{1}{4}P$

Substitute 264 for P

$L = \frac{1}{4}*264$

$L = 66$

4 0

3 years ago

Only IAS and PCS are civil services jobs ? or IAS or PCS

OLga [1]

"The exponential growth in popularity of administrative jobs among the Indian youth is clearly seen with the surging number of applicant appearing in UPSC IAS exam which is around 5 lakh every year and many more applicants trying their luck in the respective State PCS exams also. Although the chances of success in UPSC IAS Exam and State Civil Service exams are abysmally low (less than 1% at times) but the prestige and privileges attached to this job profile still manages to attract a huge intelligentsia.

Let’s understand the basic difference in service code of IAS and PCS officers."

-Jagran Josh

8 0

3 years ago

I don't really understand how to put anything into standard form. If anyone could help that would be great...thanks.

zalisa [80]

I believe you would first distribute within the parentheses and then make it so A and B are the only things on the left side and I and the other random characters are on the right.

5 0

3 years ago

Degree of inverse tangent of 0.83

exis [7]

Answer:

39.69 degrees

Step-by-step explanation:

Let

x ----> the measure of the angle

we have that

$tan(X)=0.83$

using a calculator

$m\angle X=tan^{-1}(0.83)=39.69^o$

4 0

3 years ago

Verify that the points are the vertices of a parallelogram and find its area. (2,-1,1), (5, 1,4), (0,1,1), (3,3,4)

Gelneren [198K]

Answer:

Area = 13.15 square units

Step-by-step explanation:

Let the given vertices be represented as follows:

A(2, -1, 1) = 2i - j + k

B(5, 1, 4) = 5i + j + 4k

C(0, 1, 1) = 0i + j + k

D(3, 3, 4) = 3i + 3j + 4k

(i) Let's calculate the vectors of all the sides:

$\\$ AB = B - A = (5i + j + 4k) - (2i - j + k)

AB = 5i + j + 4k - 2i + j - k [Collect like terms]

AB = 3i + 2j + 3k

BC = C - B = (0i + j + k) - (5i + j + 4k)

BC = 0i + j + k - 5i - j - 4k [Collect like terms]

BC = -5i + 0j - 3k

CD = D - C = (3i + 3j + 4k) - (0i + j + k)

CD = 3i + 3j + 4k - 0i - j - k [Collect like terms]

CD = 3i + 2j + 3k

DA = A - D = (2i - j + k) - (3i + 3j + 4k)

DA = 2i - j + k - 3i - 3j - 4k [Collect like terms]

DA = -i - 4j - 3k

AC = C - A = (0i + j + k) - (2i - j + k)

AC = 0i + j + k - 2i + j - k [Collect like terms]

AC = -2i + 2j

BD = D - B = (3i + 3j + 4k) - (5i + j + 4k)

BD = 3i + 3j + 4k - 5i - j - 4k [Collect like terms]

BD = -2i + 2j

(ii) From the results in (i) above, we can deduce that;

AB = CD This implies that AB || CD [AB is parallel to CD]

AC = BD This implies that AC || BD [AC is parallel to BD]

(iii) Therefore, ABDC is a parallelogram since opposite sides (AB and CD) are parallel. Hence, the points are vertices of a parallelogram

Now let's calculate the area

To find the area of the parallelogram, we find the magnitude of the cross product of any two adjacent sides.

In this case, we'll choose AB and AC

Area = |AB X AC|

Where;

$AB X AC = \left[\begin{array}{ccc}i&j&k\\3&2&3\\-2&2&0\end{array}\right]$

AB X AC = i(0 - 6) - j(0 + 6) + k(6 + 4)

AB X AC = - 6i - 6j + 10k

|AB X AC| = $\sqrt{(-6)^2 + (-6)^2 + (10)^2}$

|AB X AC| = $\sqrt{172}$

|AB X AC| = 13.15

Area = 13.15 square units.

PS: ACBD is also a parallelogram. The diagram has also been attached to this response.

6 0

3 years ago