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2 years ago

3. A pitcher of water contains 1/4 liters of water. The water is poured equally into 5 glasses.

Mathematics

1 answer:

Nuetrik [128]2 years ago

5 0

Answer:

A pitcher of water containes 1/4 liters of water.

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An island is 1 mi due north of its closest point along a straight shoreline. A visitor is staying at a cabin on the shore that i

Elanso [62]

Answer:

The visitor should run approximately 14.96 mile to minimize the time it takes to reach the island

Step-by-step explanation:

From the question, we have;

The distance of the island from the shoreline = 1 mile

The distance the person is staying from the point on the shoreline = 15 mile

The rate at which the visitor runs = 6 mph

The rate at which the visitor swims = 2.5 mph

Let 'x' represent the distance the person runs, we have;

The distance to swim = $\sqrt{(15-x)^2+1^2}$

The total time, 't', is given as follows;

$t = \dfrac{x}{6} +\dfrac{\sqrt{(15-x)^2+1^2}}{2.5}$

The minimum value of 't' is found by differentiating with an online tool, as follows;

$\dfrac{dt}{dx} = \dfrac{d\left(\dfrac{x}{6} +\dfrac{\sqrt{(15-x)^2+1^2}}{2.5}\right)}{dx} = \dfrac{1}{6} -\dfrac{6 - 0.4\cdot x}{\sqrt{x^2-30\cdot x +226} }$

At the maximum/minimum point, we have;

$\dfrac{1}{6} -\dfrac{6 - 0.4\cdot x}{\sqrt{x^2-30\cdot x +226} } = 0$

Simplifying, with a graphing calculator, we get;

-4.72·x² + 142·x - 1,070 = 0

From which we also get x ≈ 15.04 and x ≈ 0.64956

x ≈ 15.04 mile

Therefore, given that 15.04 mi is 0.04 mi after the point, the distance he should run = 15 mi - 0.04 mi ≈ 14.96 mi

$t = \dfrac{14.96}{6} +\dfrac{\sqrt{(15-14.96)^2+1^2}}{2.5} \approx 2..89$

Therefore, the distance to run, x ≈ 14.96 mile

6 0

2 years ago

12/30 and 18/45 <br> Whats the relationship between these two? Proportional or Not Proportional?

Ann [662]

Proportional

Both equal 6/15

6 0

2 years ago

Read 2 more answers

you want to purchase a new pair of jeans that cost $48 but on sale for 15% off. what's the sale price?

jekas [21]

40.8 because u take 15 percent of 48 and subtract it from 48

7.2 - 48 = 40.8

3 0

2 years ago

The quantity r varies jointly with t and u and inversely with s when t= -12, u= -7, and s= -4, r= -126. Find r when t= -8, u= 8,

vichka [17]

Answer:

r = 64

Step-by-step explanation:

r = (k*t*u)/s

Where,

k = constant of proportionality

t = -12,

u= -7,

s= -4,

r= -126.

r = (k*t*u)/s

-126 = (k*-12*-7)/-4

-126 * -4 = 84k

504 = 84k

k = 504/84

k = 6

Find r when t= -8, u= 8, and s= -6.

r = (k*t*u)/s

= (6*-8*8) / -6

= -384 / -6

= 64

r = 64

6 0

2 years ago

SOMEONE HELPPPPPPPPP!!!!!!

Finger [1]

Answer:

104 yd^2.

Step-by-step explanation:

Area of the 2 circles = 2 * π r^2

= 2 * π * 4^2

= 32 π yd^2.

Area of the side of the cylinder = 2 π r h

= 2 π * 4 * 9

= 72 π yd^2.

Total surface area = 32 + 72

= 104 yd^2.

6 0

3 years ago

Read 2 more answers