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kumpel [21]
3 years ago
9

The height of a rocket launched upward from a 160 foot cliff is modeled by the function h(t)= -16t^2+48t+160, where h is height

in feet and t is time in seconds. Find the time it takes the rocket to reach the ground at the bottom of the cliff.
Mathematics
1 answer:
aliina [53]3 years ago
6 0

Answer:

5 seconds

Step-by-step explanation:

In order to find the time when it landed, we will have to find the x-intercepts.

Equation given to us : -16t² + 48t + 160

Let's take the GCD, which is -16.

-16( t² - 3t - 10 )

Factoring what's inside the brackets, we get the x-intercepts.

What multiples to -10 but adds up to -3? The numbers are -5 and 2

-16 ( t - 5 ) ( t - 2 )

X-intercepts are t - 5 and t - 2

Which is 5 and 2 seconds. But one of this is an extraneous solution and that is 2.

If we substitute the value of 2 in the equation, we will not get 0.

During the x-intercept, the x has a value and y is 0. If we substitute 5 ans x. we will get y as 0.

Hence, the answer is 5 seconds.

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2 years ago
Prove that the sum of ab and ba is divisible by the sum of a and b
Likurg_2 [28]

Answer:

It is divisible by 11 and (a + b) !

Step-by-step explanation:

Given a two digit number $ ab $, the digits written in reverse order is $ba $.

Note that a two digit number ab  = 10a + b.

For example: 24 = 10(2) + 4

Similarly, ba = 10(b) + a

Now, the sum of the numbers ab and ba = 10a + b + 10b + a

= 11a + 11b

= 11(a + b)

Hence, the sum of any two digit number ab and the reverse of the number ba,  is divisible by 11 and (a + b).

Hence, proved.

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3 years ago
Evaluate - 2y + x(-3)<br> When x = -5 y = 3
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Answer:

27

Step-by-step explanation:

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4 0
3 years ago
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A fruit punch contains 0.125 liter of grape juice. This is 6.25% of the amount of juice in the punch. How much punch was made? A
kupik [55]
C b/c you divide the two numbers
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3 years ago
Erin is flying a kite. She knows that 260 feet of the kite
lianna [129]

Answer:

100 ft high

Step-by-step explanation:

We know that Erin, the kite, and her friend create a right triangle since the friend is standing directly under the kite and in front of Erin.  

Thus, we can use the Pythagorean theorem to find the height of the kite.

We can let the side the distance be at represents Erin and the kite's distance be EK (aka the hypotenuse), the side that represents Erin and her friend's distance be EF and the side that represents the kite and the friend's distance be KF.

The theorem says that a^2 + b^2 = c^2, where a and b are the two shortest sides and c is the hypotenuse.

We already have the measure of the hypotenuse (260 ft) and one of the shorter sides (240), so we have:

KF^2+240^2=260^2\\KF^2+57600=67600\\KF^2=10000\\\sqrt{(KF^2=10000)} \\KF=100

7 0
2 years ago
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