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bekas [8.4K]
2 years ago
13

The distances covered by each of two runners during the first 21 minutes of a race are

Mathematics
2 answers:
777dan777 [17]2 years ago
8 0

Answer:

t = 10.5 minutes

Step-by-step explanation:

Curves on the graph show the distance covered by two runners during the first 21 minutes of a race.

These curves intersect each other at a point which shows a common location of both the runners on the graph.

This common point is at the mid of t = 9 and 12 seconds

Therefore, time at which both the runners passes the other will be,

t = 9+\frac{12-9}{2}

 = 9 + 1.5

 = 10.5 minutes

erica [24]2 years ago
5 0

Answer:

It's either 10.5 or 11

Step-by-step explanation:

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You mix 1-3 teaspoon of baking soda with 3 teaspoon of salt.what is the value of the ratio of baking soda to salt?
erastova [34]

Answer:1-3:3

Step-by-step explanation:

8 0
2 years ago
The function f(x) = x2 has been translated 9 units up and 4 units to the right to form the function g(x). Which represents g(x)?
Alenkinab [10]

For this case, the parent function is given by:

f (x) = x ^ 2

We apply the following transformations:


Vertical translations:

Suppose that k> 0

To graph y = f (x) + k, move the graph of k units upwards:

For k = 9 we have:

h (x) = x ^ 2 + 9


Horizontal translations:

Suppose that h> 0

To graph y = f (x-h), move the graph of h units to the right

For h = 4 we have:

g (x) = (x-4) ^ 2 + 9

Answer:

The function g (x) is given by:

g (x) = (x-4) ^ 2 + 9

7 0
2 years ago
Read 2 more answers
You and a friend each randomly draw a card from a standard deck. What is the probability that at least one of you is holding a f
Andreyy89

Answer:

0.24

Step-by-step explanation:

Total cards = 52

Face cards = heart {K,Q,J} , Spade {K,Q,J} , Club {K,Q,J} , Diamond{K,Q,J} = 12

Now we are given that You and a friend each randomly draw a card from a standard deck.

Probability that no one getting face card:

Favorable events = total cards - face cards = 52 -12= 40

Total cards = 52

So, probability that no one is getting face card = \frac{40}{52} =0.76

Now we are supposed to find the probability that at least one of you is holding a face card

So, probability = 1 - probability that no one is getting face card

                        =1 - 0.76

                        = 0.24

So, probability that at least one of you is holding a face card is 0.24

8 0
2 years ago
Read 2 more answers
Find the dimensions of a rectangle with area 512 m2 whose perimeter is as small as possible. (If both values are the same number
Masja [62]

Answer:

<h2>√512 by √512 </h2>

Step-by-step explanation:

Length the length and breadth of the rectangle be x and y.

Area of the rectangle A = Length * breadth

Perimeter P = 2(Length + Breadth)

A = xy and P = 2(x+y)

If the area of the rectangle is 512m², then 512 = xy

x = 512/y

Substituting x = 512/y into the formula for calculating the perimeter;

P = 2(512/y + y)

P = 1024/y + 2y

To get the value of y, we will set dP/dy to zero and solve.

dP/dy = -1024y⁻² + 2

-1024y⁻² + 2 = 0

-1024y⁻² = -2

512y⁻² = 1

y⁻² = 1/512

1/y² = 1/512

y²  = 512

y = √512 m

On testing for minimum, we must know that the perimeter is at the minimum when y = √512

From xy = 512

x(√512) = 512

x = 512/√512

On rationalizing, x = 512/√512 * √512 /√512

x = 512√512 /512

x = √512 m

Hence, the dimensions of a rectangle is √512 m  by √512 m

5 0
2 years ago
Find dy/dx implicitly and find the largest interval of the form −a &lt; y &lt; a or 0 &lt; y &lt; a such that y is a differentia
mylen [45]

Answer:

dy/dx = -1/√(1 - x²)

For 0 < y < π

Step-by-step explanation:

Given the function cos y = x

-siny dy = dx

-siny dy/dx = 1

dy/dx = -1/siny (equation 1)

But cos²y + sin²y = 1

=> sin²y = 1 - cos²y

=> siny = √(1 - cos²y) (equation 2)

Again, we know that

cosy = x

=> cos²y = x² (equation 3)

Using (equation 3) in (equation 2), we have

siny = √(1 - x²) (equation 4)

Finally, using (equation 4) in (equation 1), we have

dy/dx = -1/√(1 - x²)

The largest interval is when

√(1 - x²) = 0

=> 1 - x² = 0

=> x² = 1

=> x = ±1

So, the interval is

-1 < x < 1

arccos(1) < y < arxcos(-1)

= 0 < y < π

6 0
2 years ago
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