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3 years ago

A parallelogram with sides of 6 and 10 has an area of 30. Find the measure of the small angle of the parallelogram.

1 answer:

4 0

<span>A = 2 * (0.5ab) + b (10 - a) = ab + 10b - ab = 10b

10b = 30√2; b = 3√2

sin α = 3√2 / 6; α = 45 degrees

Small angle: 45°; Large angle: 135°</span><span>
</span>

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If a cup of coffee has temperature 97Â°C in a room where the ambient air temperature is 25Â°C, then, according to Newton's Law o

FinnZ [79.3K]

Answer:

The average temperature is $T_{a} = 81.95^oC$

Step-by-step explanation:

From the question we are told that

The temperature of the coffee after time t is $T(t) = 25 + 72 e^{[-\frac{t}{45} ]}$

Now the average temperature during the first 22 minutes i.e fro $0 \to 22$ minutes is mathematically evaluated as

$T_{a} = \frac{1}{22-0} \int\limits^{22}_{0} {25 +72 e^{[-\frac{t}{45} ]}} \, dx$

$T_{a} = \frac{1}{22} [25 t + 72 [\frac{e^{[-\frac{t}{45} ]}}{-\frac{1}{45} } ] ] \left| 22} \atop {0}} \right.$

$T_{a} = \frac{1}{22} [25 t - 3240e^{[-\frac{t}{45} ]} ] \left | 45} \atop {{0}} \right.$

$T_{a} = \frac{1}{22} [25 (22) - 3240e^{[-\frac{22}{45} ]} - (- 3240e^{0} )]$

$T_{a} = \frac{1}{22} [550 - 1987.12 + 3240]$

$T_{a} = 81.95^oC$

8 0

2 years ago

Can someone please help me?

yaroslaw [1]

3√24= 3√2^2*6 = 3*2√6 = 6√6

2√384= 2√8^2*6 = 2*8√6 = 16√6

√96= √4^2*6 = 4√6

6√6 -16√6- 4√6 = -14√6

Final answer: -14√6

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3 years ago

If 3(x -4) = 12, then x = 24

Alenkinab [10]

Answer:

Step-by-step explanation:

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daser333 [38]

Answer:

31 and a quarter week (31.25)

Step-by-step explanation:

First find the rate. There is no need to do cross multiplication because it's already a unit rate (per 1 week).

2. Divide

156.25 / 5 = 31.25

3. Answer

31.25 weeks

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3 years ago

Bob Tina and Hadley went running. Bob ran for 3/8 hour, Tina ran for 3 4/9 hours, and Hadley ran for 4 19/29 hours. Which runnin

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Answer: 3 4/9 and 4 19/29

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