Amy and Ben share £21 between them in the ratio 5 : 2. How much does Amy get?
1 answer:
Answer:
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Let us consider , there are 30 boys and 40 girls in a school. So, the ratio of number of boys to number of girls = and read as 3 is to 4. We can say , the ratio compares two of more quantities of same unit. Until two quantities have same units , it is meaningless to compare by ratio. So, to find the ratio of two quantities , it is necessary to express them in same unit or of same kind. Since , they are in division form. So ,ratio is unit less quantity. Thus , the ratio is a comparison of two quantities of the same kind in division which doesn't have any units. For example :
is a ratio and is read as ' a is to b ' in which ' a : is antecedent and ' b ' is called consequent.
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£ 21 is to be divided between Amy and Ben in the ratio 5 : 2. So, let Amy get £ 5x and Ben get £ 2x.
Then , According to the question ,
Solve for x :
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The value of x is 3. Now , substitute the value of x in 5x :
Amy received £ 5x = 5 × 3 = £ 15 .
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Answer:
3.27 meters
Step-by-step explanation:
The given equation gives a y(0) = 0, for the deflection of 3 cm. Then for a deflection of 2.5 cm, we want y(x) = 0.005, half a centimeter above the low point on the beam. Using this value, we can solve for x:
0.005 = 3/6400x^2
32/3 = x^2
4√(2/3) = x ≈ 3.26599 ≈ 3.27 . . . . meters
The deflection of the beam is 2.5 cm at a distance of 3.27 meters from center.
Answer:
Step-by-step explanation:
Adjacent angles of parallelogram are supplementary.
∠A + ∠D = 180
Divide both sides by 2
∠A +
∠D = 90
∠PAD + ∠ADP = 90 --------------------(I)
IN ΔPAD,
∠PAD + ∠ADP + ∠APD = 180 {angle sum property of triangle}
90 + ∠APD = 180 {from (I)}
∠APD = 180 - 90
∠APD = 90
∠SPQ = ∠APD {vertically opposite angles}
∠SPQ = 90°
Similarly, we can prove ∠PQR = 90° ; ∠QRS = 90° and ∠RSP = 90°
In a quadrilateral if each angle is 90°, then it is a rectangle.
PQRS is a rectangle.