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miskamm [114]
3 years ago
11

Fred begins walking toward John house at 3 mi/h. John leaves his house at the same time and walks toward Fred's house on the sam

e path at a rate of 2 mi/h. How long will it be before they meet if the distance between the houses is 4 miles?
Mathematics
1 answer:
Tcecarenko [31]3 years ago
7 0
Let us assume as at when they meet, the time elapsed is x hours.

Fred  3 mi/h
John  2 mi/h

Distance = speed * time

Fred = 3x
John = 2x

Houses are 4miles apart. 
So:            3x + 2x  = 4    5x = 4

x = 4/5 hour =  0.8 hour or 0.8*60 = 48 minutes

Time elapsed is 0.8 hour or 48 minutes.
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Find the range of p in equation p(x+1) (x-3)=x-4p-2 has no real roots. ​
Tanya [424]

Answer:

\displaystyle p > \frac{1}{4}.

Step-by-step explanation:

Expand the left-hand side of this equation:

p\, (x + 1)\, (x - 3) = p\, \left(x^2 - 2\, x - 3\right) = p\, x^2 - 2\, p\, x - 3\, p.

Collect the terms, so that this quadratic equation is in the form a\, x^2 + b\, x+ c = 0:

p\, x^2 - 2\, p\, x - 3\, p = x - 4\, p - 2.

p\, x^2 - (2\, p + 1)\, x + (p + 2) = 0.

In this equation:

  • a = p.
  • b = -(2\, p + 1).
  • c = p + 2.

Calculate the quadratic discriminant of this quadratic equation:

\begin{aligned}b^2 - 4\, a\, c &= (-(2\, p + 1))^2 - 4\, p\, (p + 2) \\ &= 4\, p^2 + 4\, p + 1 - 4\, p^2- 8\, p = -4\, p + 1\end{aligned}.

A quadratic equation has no real root if its quadratic discriminant is less then zero. As a result, this quadratic equation will have no real root when -4\, p + 1 < 0. Solve for the range of p:

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4 0
4 years ago
Linda calculated that the saucer for her teacup has an area of 50.24 square centimeters. What is the saucer's circumference?
Brilliant_brown [7]

Answer:

The saucer's circumference is <u>25.12 centimeter</u>.

Step-by-step explanation:

Given:

Linda calculated that the saucer for her tea cup has an area of 50.24 square centimeters.

Use 3.14 for π.

Now, to find the saucer's circumference.

So, we get the radius first by putting the formula of area:

Area = 50.24 square centimeters.

Let radius be r.

Area = \pi r^2.

Area = \pi\times r^2.

As given we use 3.14 for π.

50.24 = 3.14\times r^2.

<em>Dividing both sides by 3.14 we get:</em>

16=r^2.

<em>Using square root on both sides we get:</em>

4=r

r=4

Thus, the radius = 4 centimeters.

Now, to get the circumference we put formula:

Circumference=2\pi r

Circumference=2\times \pi \times r

Circumference=2\times 3.14\times 4

Circumference=25.12

Circumference = 25.12 centimeter.

Therefore, the saucer's circumference is 25.12 centimeter.

3 0
4 years ago
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