Question:Five Coat Colors In Mice Are Agouti, Cinnamon, Black, Chocolate And Albino. (A) List All Of The Possible Different Crosses Between Different Phenotypes. (B) Verify The Number Of Different Crosses By Applying The Combination Formula. This problem has been solved! See the answer
Five coat colors in mice are agouti, cinnamon, black, chocolate and albino.
(a) List all of the possible different crosses between different phenotypes.
(b) Verify the number of different crosses by applying the combination formula.
· Pythagoras Theorem: It is a basic relation in Euclidean geometry among the sides of a right-angled triangle. Pythagoras Theorem is commonly used to find the length of an unknown side in a right-angled triangle. It describes the interrelationship between the base, perpendicular and hypotenuse of a right-angled triangle. The converse of Pythagoras Theorem is used to check whether a triangle is a right-angled triangle or not. Statement of Pythagoras Theorem The Pythagoras Theorem states that in a right-angled triangle the sum of square of the base and square of the perpendicular is equal to the square of the hypotenuse To prove: PR2=PQ2+QR2PR2=PQ2+QR2 Construction: Draw a perpendicular line QDQD meeting PRPR at D. Proof: we know that ΔRDQ∼ΔRQPΔRDQ∼ΔRQP So, RDQR=QRPRRDQR=QRPR (Corresponding sides of similar triangles) ⇒QR2=RD×PR⇒QR2=RD×PR —(i)(i) Also, ΔQDP∼ΔRQPΔQDP∼ΔRQP So, PDPQ=PQPRPDPQ=PQPR (Corresponding sides of similar triangles) ⇒PQ2=PD×RP⇒PQ2=PD×RP —(ii)(ii) Adding the equation (i)(i) and (ii)(ii) we get, QR2+PQ2=RD×PR+PD×PRQR2+PQ2=RD×PR+PD×PR ⇒QR2+PQ2=PR(RD+PD)⇒QR2+PQ2=PR(RD+PD) From the figure, RD+PD=PRRD+PD=PR From the figure, PR2=PQ2+QR2PR2=PQ2+QR2 Hence, the Pythagoras Theorem is proved. Application of the Pythagoras Theorem Some of the applications of the Pythagoras Theorem are: · Pythagoras Theorem is commonly used to find the lengths of sides of a right-angled triangle. · The Theorem is used to find the length of diagonal of a rectangle, square, etc. · Pythagoras Theorem is used in trigonometry to find the trigonometric ratios like ,cos,tan,cosec,sec,cot.sin,cos,tan,sec,cot.. · Pythagoras Theorem is used in security cameras for face recognition. · The technique of Pythagoras Theorem is used by architects for engineering and construction fields.