Answer:
Length of the shorter diagonal is 8.68 cm.
Step-by-step explanation:
Length of the side AB = 11 cm
Length of side BC = 5 cm
Angle between these sides, m∠ABC = 50°
By cosine rule in ΔABC,
AC² = AB² + BC² - 2AB.BC.cos B
AC² = (11)² + 5² - 2(11)(5)cos50°
AC² = 121 + 25 - 70.71
AC = √(75.29)
AC = 8.68 cm
By the property of parallelogram,
m∠B + m∠C = 180° [Interior consecutive angles]
50° + m∠C = 180°
m∠C = 130°
Similarly, In ΔBCD,
BD² = BC² + CD² - 2BC.CD.cos130°
BD² = (5)² + (11)² - 2(5)(11)cos130°
BD² = 25 + 121 + 70.71
BD² = 216.71
BD = 14.72 cm
Therefore, length of the shorter diagonal will be 14.72 cm.
Answer:
Step-by-Step Solution
0.4 = 2/5 as a fraction
To convert the decimal 0.4 to a fraction, just follow these steps:
Step 1: Write down the number as a fraction of one:
0.4 = 0.41
Step 2: Multiply both top and bottom by 10 for every number after the decimal point:
As we have 1 numbers after the decimal point, we multiply both numerator and denominator by 10. So,
0.41 = (0.4 × 10)(1 × 10) = 410.
Step 3: Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(4,10) = 2. So,
(4÷2)(10÷2) = 2/5 when reduced to the simplest form.
<span>Rate of pump A: 1/8 of a pool per hour
Rate of pump B: 1/9 of a pool per hour
Combined rate: 1/8+1/9 = 17/72 +1/9 = 25/72
So if they work together, the two pumps have a combined rate of 25/72 of a pool per hour (i.e in one hour, the two pumps will empty 25/72 of the pool)
</span><span>But we want to empty ONE pool (not 25/72 of one). So we need to multiply 25/72 by some number x to get 1.
</span>
<span>Now solve for x
x=2.88
</span><span>It will take the two pumps 2.88 hours to empty the pool.
2 hours 52 minutes 50 seconds</span>
yes, they are all proportional
Answer:
are u sure thet write the question right?
