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Talja [164]
3 years ago
6

On a string of red and blue lights, the red lights blink everyb3 seconds, and the blue lights blink every 5 seconds. How many ti

mes will they blink at the same time in one minute?
Mathematics
1 answer:
yuradex [85]3 years ago
5 0
When will they blink together?
what is the smallest number they both mutiply to
3*5=15
so every 15 seconds
so at 15, 30, 45, 60 seconds
so 4 times if you count the time exactly at 1 minute
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Duffy was analyzing the trajectory made after throwing a football. his coach was able to measure that his throw reached a maximu
gregori [183]

Answer:

4.35 seconds.

Step-by-step explanation:

Let x represent the time the independent variable and y be dependent variable (height of the ball).

We are told that Duffy figured that the ball left his hand at a height of 5 feet. This means at x equals 0, y was 5 or initial height of ball is 5 feet.

We have been given that Duffy's coach measured that his throw reached a maximum height of 18 feet after 2 seconds. This means that at x equals 2 y was 18.

As point (2,18) represents maximum height of ball, so it will be vertex of parabola.  

Since initial height of ball is less than maximum height, so our parabola will be downward opening and leading coefficient will be negative.

We know that vertex form of a downward opening parabola is in form: y=-a(x-h)^2+k

y=-a(x-2)^2+18

Let us find value of a using point (0,5).

5=-a(0-2)^2+18

5=-a*4+18

5-18=-a*4+18-18

-13=-4a

\frac{-13}{-4}=\frac{-4a}{-4}

\frac{13}{4}=a

Therefore, the equation y=-(\frac{13}{4})(x-2)^2+18 can be used to find the height of ball after x seconds.

To find the time it will take the ball to hit the ground, we will substitute y equals 0 in our equation.

0=-(\frac{13}{4})(x-2)^2+18

0-18=-(\frac{13}{4})(x-2)^2+18-18

0-18=-(\frac{13}{4})(x-2)^2

-18*(\frac{4}{13})=-(x-2)^2

\frac{72}{13}=(x-2)^2

Taking square root of both sides of our equation we will get,

\sqrt{\frac{72}{13}}=x-2

x-2\pm 2.35339

x-2=2.35339\text{ (or) } x-2=2.35339

x-2+2=2.35339+2\text{ (or) } x-2+2=-2.35339+2

x=4.35339\text{ (or) } x=-0.35339

x\approx 4.35\text{ (or) } x\approx -0.35

Since time can not be negative, therefore, the ball will hit the ground approximately after 4.35 seconds.  

7 0
3 years ago
What are the common factors of 49 and72?
-Dominant- [34]
There are no common factors except 1
8 0
3 years ago
Read 2 more answers
Use the magnitudes​ (Richter scale) of the 120 earthquakes listed in the accompanying data table. Use technology to find the​ ra
Bas_tet [7]

Answer:

2.90

Step-by-step explanation:

im not completly shous though

5 0
2 years ago
Which of the following ratios has the same ratio value as 4:6?
Strike441 [17]

Answer:

6:9

Step-by-step explanation:

the answer is 6:9 because 4:6' equivalent is 2:3, which is the same as 6:9

8 0
3 years ago
Which of these numbers is a prime number: 1, 11, 21, 51?
statuscvo [17]

Answer:

11 and 51

Step-by-step explanation:

1 technically isn't a prime since a prime can only be divided by two things (itself and 1) and 1 can only be divided by 1.

21 can be divided by 1, 3, 7, and 21 so it is not prime.

Hope this helps!

5 0
3 years ago
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