Solution: If $b>0, \sqrt{a+i b}=\pm\left[\left(\frac{a+\sqrt{a^{2}+b^{2}}}{2}\right)^{\frac{1}{2}}+i\left(\frac{-a+\sqrt{a^{2}+b^{2}}}{2}\right)^{\frac{1}{2}}\right]$ If $b<0, \sqrt{a+i...
Find the square root of the following complex numbers.
Find the square root of the following complex numbers.
(i) 8 – 15i
(ii) -11 – 60√-1
Solution: If $b>0, \sqrt{a+i b}=\pm\left[\left(\frac{a+\sqrt{a^{2}+b^{2}}}{2}\right)^{\frac{1}{2}}+i\left(\frac{-a+\sqrt{a^{2}+b^{2}}}{2}\right)^{\frac{1}{2}}\right]$ If $b<0, \sqrt{a+i...
Find the square root of the following complex numbers.
(i) 1 – i
(ii) – 8 – 6i
Solution: If $b>0, \sqrt{a+i b}=\pm\left[\left(\frac{a+\sqrt{a^{2}+b^{2}}}{2}\right)^{\frac{1}{2}}+i\left(\frac{-a+\sqrt{a^{2}+b^{2}}}{2}\right)^{\frac{1}{2}}\right]$ If $b<0, \sqrt{a+i...
Find the square root of the following complex numbers.
(i) – 5 + 12i
(ii) -7 – 24i
Solution: If $b>0, \sqrt{a+i b}=\pm\left[\left(\frac{a+\sqrt{a^{2}+b^{2}}}{2}\right)^{\frac{1}{2}}+i\left(\frac{-a+\sqrt{a^{2}+b^{2}}}{2}\right)^{\frac{1}{2}}\right]$ If $b<0, \sqrt{a+i...
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?
Think about the accompanying graph Volume of water that streams in t minutes from pipe \[=\text{ }t\times 0.5\pi \text{ }m^3\] Volume of water that streams in t minutes from pipe = \[t\times 0.5\pi...
Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?
It is given that the waterway is the state of a cuboid with measurements as: Broadness (b) = 6 m and Height (h) = 1.5 m It is additionally given that The speed of waterway = 10 km/hr Length of...
A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.
The outline will be as- Given, Tallness $(h_1)$ of tube shaped piece of the pail = 32 cm Range $(r_1)$ of roundabout finish of the pail = 18 cm Tallness of the cone like pile $(h_2)$ = 24 cm...
How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?
It is realized that the coins are round and hollow fit. Along these lines, tallness (h1) of the chamber = 2 mm = 0.2 cm Range (r) of roundabout finish of coins \[=\text{...
A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
Number of cones will be = Volume of chamber/Volume of frozen treat For the chamber part, Range = 12/2 = 6 cm Stature = 15 cm ∴ Volume of chamber \[=\text{ }\mathbf{\pi }\times \mathbf{r2}\times...
A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
The state of the well will be tube shaped as given underneath. Given, Depth $(h_1)$ of well = 14 m Distance across of the roundabout finish of the well =3 m Thus, Radius $(r_1)$ = 3/2 m Width of the...
A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.
t is given that the state of the well is looking like a chamber with a width of 7 m In this way, span = 7/2 m Likewise, Depth (h) = 20 m Volume of the earth uncovered will be equivalent to the...
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.
For Sphere 1: Span (r1) = 6 cm ∴ Volume (V1) \[=\text{ }\left( 4/3 \right)\times \pi \times r13\] For Sphere 2: Span (r2) = 8 cm ∴ Volume (V2) \[=\text{ }\left( 4/3 \right)\times \pi \times r23\]...
A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.
It is given that range of the circle (R) = 4.2 cm Likewise, Radius of chamber (r) = 6 cm Presently, let stature of chamber = h It is given that the circle is liquefied into a chamber. Along these...