Calculate the area of quad. ABCD, given in til (ii) Calculate the area of trap. PQRS,
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The angles of a quadrilateral ABCD are `x^(@),(x+1)^(@),(x+2)^(@)` and `(x+3)^(@)`, taken in the same order. Then the quadrilateral ABCD is necessaril
Correct Answer - Trapezium
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एक किसान के पास समांतर चतुर्भुज PQRS के रूप का एक खेत था । उसने RS पर स्थित कोई बिंदु A लिया और उसे P और Q से मिला दिया खेत कितने भागों में विभाजित हो
Correct Answer - गेहू `Delta APQ ` ,में और दाल अन्य दो त्रिभुजों में या दाल `Delta APQ ` में और गेहू अन्य दो त्रिभुजों में ।
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If the roots of the equation \( a x^{2}+b x+c=0 \) are equal then \( c=? \) \( \quad \) 1) \( -\frac{b}{2 a} \) 2) \( \frac{b}{2 a} \) 3) \( -\frac{b^{2}}{4 a} \) 4) \( \frac{b^{2}}{4 a} \)
b^2 -4ac = 0 (as roots are equal ) b^2 =4ac b^2/4a = c
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Area of rectangle PQRS in sq. units
Correct option is C) √3 – √2
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Find the Inverse?\[A=\left[\begin{array}{lll}2 & 1 & 1 \\3 & 2 & 1 \\2 & 1 & 2\end{array}\right] \quad A^{-1}=?\]
We have A = IA \(\begin{bmatrix}2&1&1\\3&2&1\\2&1&2\end{bmatrix}=\) \(\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}\)A Applying R3 → R3 — R1 R2 → 2R2 — 3R1 \(\begin{bmatrix}2&1&1\\0&1&-1\\0&0&1\end{bmatrix}=\)\(\begin{bmatrix}1&0&0\\-3&2&0\\-1&0&1\end{bmatrix}\)A Applying R2 → R2 + R3 \(\begin{bmatrix}2&1&1\\0&1&0\\0&0&1\end{bmatrix}=\)\(\begin{bmatrix}1&0&0\\-4&2&1\\-1&0&1\end{bmatrix}\)A Applying R1 → R1 — R2 — R3 \(\begin{bmatrix}2&0&0\\0&1&0\\0&0&1\end{bmatrix}=\) \(\begin{bmatrix}6&-2&-2\\-4&2&1\\-1&0&1\end{bmatrix}\)A Applying R1 → \(\frac{R_1}2\) \(\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}=\)\(\begin{bmatrix}3&-1&-1\\-4&2&1\\-1&0&1\end{bmatrix}\)A Hence A-1 = \(\begin{bmatrix}3&-1&-1\\-4&2&1\\-1&0&1\end{bmatrix}\)
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In □ABCD; AB = DC and AD = BC also ∠A = 90° then □ABCD is a
Correct option is A) rectangle
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The opposite vertices of the quadrilateral PQRS are
Correct option is (D) Q, S P & R and Q & S are opposite vertices in quadrilateral PQRS.
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The opposite vertices of the quadrilateral PQRS are
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Use the definition of Odd and Even functions to determine whether each of the following functions is Odd, Even, or neither. Must show your work for credit II! 1) \( f(x)=\frac{x}{1-x^{3}} \) 2) \( f(x)=\frac{x^{2}}{1+x} \) 3) \( \quad f(x)=x-|x| \)
(1) f(x) = \(\frac{x}{1-x^3}\) f(-x) = \(\frac{-x}{1-(-x)^3}\) = \(\frac{-x}{1+x^3}\) ≠ -f(x) or f(x) ∴ f(x) is neither even nor odd function. (2) f(x) = \(\frac{x^2}{1+x}\) ∴ f(-x) = \(\frac{(-x^2)}{1+(-x)}\) = \(\frac{x^2}{1-x}\) ≠ -f(x) or f(x). (3) f(x) = x-|x| ∴ f(-x) = -x-|-x| = -x-|x| = -(x+|x|) ≠ -f(x)...
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