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Mathematics

1 answer:

Alexandra [31]4 years ago

7 0

<span>2% of 50 → 2 per cent of 50 = 0.02 × 50 = 1 → 1 book .... so Alexa Read 51 books

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What does the discriminant determine?

devlian [24]

The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.

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3 years ago

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A hemispherical dome of a building needs to be painted. If the circumference of the base of the

soldier1979 [14.2K]

Answer:

The cost of painting the hemispherical dome is 110880 unit

Step-by-step explanation:

Given as for a hemispherical dome :

The circumference of base = 17.6 m

The cost of painting it = 5 unit per 100 cm²

∵ circumference of base = circumference of circle = 2× $\pi$ ×radius

So ,17.6 m = 2× $\pi$ ×radius

Or, Radius = $\frac{17.6\times 7}{2\times 22}$

Or, Radius = $\frac{123.2}{44}$ = 2.8 m

Or, R = 280 cm

So, Total surface area of hemispherical dome = 3× $\pi$ ×radius²

or, Total surface area of hemispherical dome = 3× $\pi$ ×280²

Or, Total surface area of hemispherical dome = $\frac{3\times 22\times 280\times 280}{7}$

Or, Total surface area of hemispherical dome = $\frac{5174400}{7}$

∴ Total surface area of hemispherical dome = 739200 cm²

Now, The cost of painting 100 cm² is 15 unit

So, The cost of painting 739200 cm² = $\frac{15\times 739200}{100}$

Or, The cost of painting 739200 cm² = 110880 unit

Hence The cost of painting the hemispherical dome is 110880 unit Answer

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3 years ago

Using the Law of Cosines, in triangle DEF, if e=18yd, d=10yd, f=22yd, find measurement of angle D

Ivahew [28]

Check the picture below.

$\bf \textit{Law of Cosines}\\ \quad \\
c^2 = {{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)\implies 
c = \sqrt{{{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)}
\\\\\\
\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}=cos(C)\implies cos^{-1}\left(\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}\right)=\measuredangle C\\\\
-------------------------------\\\\
\begin{cases}
d=10\\
e=18\\
f=22
\end{cases}\implies cos^{-1}\left(\cfrac{{{ 18}}^2+{{ 22}}^2-10^2}{2(18)(22)}\right)=\measuredangle D$

$\bf \implies cos^{-1}\left(0.893\overline{93}\right)=\measuredangle D\implies 26.63^o\approx \measuredangle D$