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3 years ago

You are driving from Kansas City to Denver. The distance (in miles) you

Mathematics

1 answer:

ad-work [718]3 years ago

5 0

Answer:

The slope is 70

The slope represents the speed of your car

Step-by-step explanation:

The slope is 70, y = mx + c, where m is the slope

The slope represents the speed of your car

speed = distance/time

speed x time = distance

As y represents the distance you travel, x is the time, slope is the speed, you get the distance travelled.

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Prove algebraically that r = 10/2+2sinTheta is a parabola

Xelga [282]

Answer:

$y = - \frac{ 1 }{10} {x}^{2} + \frac{5}{2}$

Step-by-step explanation:

We want to prove algebraically that:

$r = \frac{10}{2 + 2 \sin \theta}$

is a parabola.

We use the relations

${r}^{2} = {x}^{2} + {y}^{2}$

and

$y = r \sin \theta$

Before we substitute, let us rewrite the equation to get:

$r(2 + 2 \sin \theta) = 10$

$r(1+ \sin \theta) = 5$

Expand :

$r+ r\sin \theta= 5$

We now substitute to get:

$\sqrt{ {x}^{2} + {y}^{2} } + y = 5$

This means that:

$\sqrt{ {x}^{2} + {y}^{2} }=5 - y$

Square:

${x}^{2} + {y}^{2} =(5 - y)^{2}$

Expand:

${x}^{2} + {y}^{2} =25 - 10y + {y}^{2}$

${x}^{2} =25 - 10y$

${x}^{2} - 25 = - 10y$

$y = - \frac{ {x}^{2} }{10} + \frac{5}{2}$

This is a parabola (0,2.5) and turns upside down.

4 0

3 years ago

What times what equals 59

sweet-ann [11.9K]

59 is a "prime number". It has no factors except ' 1 ' and itself.

So the only possibility is 1 x 59 .

5 0

3 years ago

A copy machine makes 28 copies per minute. How many copies does it make in 3 minutes and 45 seconds?

lina2011 [118]

<u>Convert minutes and seconds to minutes:</u>
$\text{3 mins 45 seconds} \longrightarrow 3 \dfrac{3}{4} \text{mins}$

<u>FInd 3 3/4 mins:</u>
$\text{1 min} \longrightarrow 28 \text{ copies}$

$3 \dfrac{3}{4} \text{ min} \longrightarrow 28 \times 3\dfrac{3}{4} \text{ copies}$

$3 \dfrac{3}{4} \text{ min} \longrightarrow 28 \times \dfrac{15}{4} \text{ copies}$

$3 \dfrac{3}{4} \text{ min} \longrightarrow 105 \text{ copies}$

Answer: It can make 105 copies.

4 0

4 years ago

What is m∠S? Enter your answer in the box. ° An isosceles triangle with vertices labeled R, S, and T. Side R T is the base. Side

yulyashka [42]

Answer:

m<S = 45°

Step-by-step explanation:

The sum of the measures of the angles of a triangle equals 180 deg.

m<R + m<S + m<T = 180

3x + 2x + 3x = 180

8x = 180

x = 22.5

m<S = 2x = 2(22.5) = 45

5 0

4 years ago

Write in scientific notation 57,000,000

oee [108]

Answer: 5.7 x 107

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers