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Sholpan [36]
2 years ago
12

PLEASE HELP Christine walks 0.5 miles around the lake in 10 minutes.

Mathematics
1 answer:
grin007 [14]2 years ago
4 0

Answer:

Her speed is 0.05 miles per minute

Step-by-step explanation:

The unit rate of her speed in miles per minute is given by the number of miles divided by the number of minutes. So:

0.5 miles in 10 minutes. So

0.5/10 = 0.05 miles per minute

Her speed is 0.05 miles per minute

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Consider the curve defined by the equation y=6x2+14x. Set up an integral that represents the length of curve from the point (−2,
torisob [31]

Answer:

32.66 units

Step-by-step explanation:

We are given that

y=6x^2+14x

Point A=(-2,-4) and point B=(1,20)

Differentiate w.r. t x

\frac{dy}{dx}=12x+14

We know that length of curve

s=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}dx

We have a=-2 and b=1

Using the formula

Length of curve=s=\int_{-2}^{1}\sqrt{1+(12x+14)^2}dx

Using substitution method

Substitute t=12x+14

Differentiate w.r t. x

dt=12dx

dx=\frac{1}{12}dt

Length of curve=s=\frac{1}{12}\int_{-2}^{1}\sqrt{1+t^2}dt

We know that

\sqrt{x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{1}{2}\ln(x+\sqrt {x^2+a^2})+C

By using the formula

Length of curve=s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}

Length of curve=s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}

Length of curve=s=\frac{1}{12}(\frac{(12+14)\sqrt{1+(26)^2}}{2}+\frac{1}{2}ln(26+\sqrt{1+(26)^2})-\frac{12(-2)+14}{2}\sqrt{1+(-10)^2}-\frac{1}{2}ln(-10+\sqrt{1+(-10)^2})

Length of curve=s=\frac{1}{12}(13\sqrt{677}+\frac{1}{2}ln(26+\sqrt{677})+5\sqrt{101}-\frac{1}{2}ln(-10+\sqrt{101})

Length of curve=s=32.66

5 0
3 years ago
7
LUCKY_DIMON [66]

The answer is B. 15 cm

5 0
3 years ago
*PLEASE ANSWER TY* What is the area of minor sector DFE?
FinnZ [79.3K]

Answer:

x ≈ 34.88 square cm

Step-by-step explanation:

Solve by proportional formula:

Area of a sector/area of circle* = sector central arc measure/360

*area of a circle = πr²

x/(53.29π) = 75/360

x/53.29π = 0.2083

x = 11.1020833π

x = 34.8782233

x ≈ 34.88 square cm

8 0
3 years ago
Scientists estimate between 10,000,000 and 50,000,000 monarch
frozen [14]

Answer:

Step-by-step explanation:The Monarch Butterfly Biosphere Reserve is a World Heritage Site containing most of the ... The monarch butterflies migration patterns are altered by climate change. During migration ... This area is predominantly covered in forests. ... These colonies are dense, with between six and sixty million butterflies per hectare.

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2 years ago
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Ashley is making cookies for
allochka39001 [22]

Answer:

1.6 cups of sugar

Step-by-step explanation:

0.4 cups per batch.

4 batches.

Total sugar required = 0.4 x 4

= 1.6 cups of sugar

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3 years ago
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