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3 years ago

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A car is traveling at a speed of 81 miles per hour. What is the car's speed in feet per second? How many feet will the car trave

l in 15 seconds? In your computations, use the fact that 1 mile is equal to 5280 feet. Do not round your answers.

1 answer:

qaws [65]3 years ago

6 0

1 mile = 5280 feet

81 * 5280 = 427680 feet per hour

1 hour = 3600 seconds

427680 / 3600 = 118.8 feet per second

118.8 * 15 = 1782 feet in 15 seconds

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Find a point on the line y = 4 that is equidistant from the two points (0,1) and (5,6)

butalik [34]

Answer:

The point on the line $y=4$ that is equidistant from points (0,1) and (5,6) is (2, 4).

Step-by-step explanation:

Let be $y = 4$ , $A = (0,1)$ and $B = (5,6)$ . As we know that given function is a horizontal line, the condition of equidistance between that a point within that line and both points must be:

$r_{A/P} = r_{B/P}$

Where:

$r_{A/P}$ - Distance of point A with respect to P.

$r_{B/P}$ - Distance of point B with respect to P.

We expand this equivalence by Pythagorean Theorem:

$\sqrt{(x_{A}-x_{P})^{2}+(y_{A}-y_{P})^{2}} = \sqrt{(x_{B}-x_{P})^{2}+(y_{B}-y_{P})^{2}}$

$(x_{A}-x_{P})^{2} + (y_{A}-y_{P})^{2} = (x_{B}-x_{P})^{2}+(y_{B}-y_{P})^{2}$

$x_{A}^{2}-2\cdot x_{A}\cdot x_{P}+x_{P}^{2} + y_{A}^{2}-2\cdot y_{A}\cdot y_{P}+y_{P}^{2} = x_{B}^{2}-2\cdot x_{B}\cdot x_{P}+x_{P}^{2} + y_{B}^{2}-2\cdot y_{B}\cdot y_{P}+y_{P}^{2}$

$x_{A}^{2}-2\cdot x_{A}\cdot x_{P} + y_{A}^{2}-2\cdot y_{A}\cdot y_{P} = x_{B}^{2}-2\cdot x_{B}\cdot x_{P} + y_{B}^{2}-2\cdot y_{B}\cdot y_{P}$

And we get this expression:

$x_{A}^{2}+y_{A}^{2}-x_{B}^{2}-y_{B}^{2} - 2\cdot (x_{A}-x_{B})\cdot x_{P}-2\cdot (y_{A}-y_{B})\cdot y_{P} = 0$

If we know that $x_{A} = 0$ , $y_{A} = 1$ , $y_{P} = 4$ , $x_{B} = 5$ and $y_{B} = 6$ , the expression is reduced to this:

$0^{2}+1^{2}-5^{2}-6^{2}-2\cdot (0-5)\cdot x_{P} -2\cdot (1-6)\cdot (4) =0$

$10\cdot x_{P}-20=0$

The remaining component of the point within the line is:

$x_{P} = 2$

The point on the line $y=4$ that is equidistant from points (0,1) and (5,6) is (2, 4).

6 0

3 years ago

What is the volume of the cylinder below?

Diano4ka-milaya [45]

Answer:

Volume = 252π units³

Step-by-step explanation:

We have been given an obliques cylinder (a cylinder having its bases parallel to each other but are not aligned).

The volume of an oblique cylinder can be found similarly to that of a regular cylinder, with using the formula:

Volume = Base · Height

Where the height in the regular cylinder is taken as the distance from one base to another base, but for oblique cylinder, the height is taken as the perpendicular distance from one base to another base, which in the given diagram, is shown as 7

So, for the given cylinder:

Height = 7

Radius = 6

Volume = Base · Height

Volume = πr² · h

Volume = π(6)² · 7

Volume = 252π units³

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4 years ago

Which characteristics of a graph tell you that it represents<br> a proportional relationship?<br> I

SVEN [57.7K]

Answer: is a straight line that passes through the orgin hope it helps

Step-by-step explanation:

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3 years ago

For the water balloon toss the parent teacher organization needs to buy eight bags of balloons each bag is 175 balloons in it an

Black_prince [1.1K]

Answer:

1400 individual balloons

Step-by-step explanation:

Total bags of balloons needed = 8 bags

Each balloon bag contains 175 balloons.

Thus,

175 balloons × 8 = 1400 balloons.

Hence, the parent teacher association need to buy 1400 individual balloons.

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4 years ago

Simplify : 5y-2y+4=10

Mnenie [13.5K]

Answer:

See below.

Step-by-step explanation:

5y - 2y + 4 = 10

5y - 2y = 6

3y = 6

y = 2

Check:

5y - 2y + 4 = 10

5(2) - 2(2) + 4 = 10

10 - 4 + 4 = 10

6 + 4 = 10

10 = 10

The value of y = 2

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3 years ago

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