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Anna35 [415]
2 years ago
13

The path of a ball is modelled by the quadratic function ℎ(t) = −5(t − 2)^2 + 23 where

Mathematics
2 answers:
Maru [420]2 years ago
8 0

Answer:

23

Step-by-step explanation:

the answer is the y intercept of the equation

sukhopar [10]2 years ago
7 0

Answer:

23m, at t=2s

Step-by-step explanation:

Putting the physics part aside, you can rewrite the height function as

h(t)= 23 - 5(t-2)^2. Now you have a fixed value, 23, and you're subtracting to it a quantity that, being a square, is at least zero. The maximum value of that sum you have when you're not subtracting anything, that is 23. That happens when 5(t-2)^2 = 0 \rightarrow t=2

Alternatively, if you know how to determine the velocity from that kind of motion, you can find out the speed, and the highest altitude you reach when the speed is zero, which leads to a bunch of calculation for the same result.

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A ball is thrown in the air from a height of 3 m with an initial velocity of 12 m/s. To the nearest tenth of a second, how long
stepladder [879]

Answer:  1.4 seconds

<u>Step-by-step explanation:</u>

The equation is: h(t) = at² + v₀t + h₀          where

  • a is the acceleration (in this case it is gravity)
  • v₀ is the initial velocity
  • h₀ is the initial height

Given:  

  • a = -9.81 (if it wasn't given in your textbook, you can look it up)
  • v₀ = 12
  • h₀ = 3

Since we are trying to find out when it lands on the ground, h(t) = 0

EQUATION:   0 = 9.81t² + 12t + 3

Use the quadratic equation to find the x-intercepts

                        a=-9.81, b=12, c=3

x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(12)\pm \sqrt{(12)^2-4(-9.81)(3)}}{2(-9.81)}\\\\\\x=\dfrac{-12\pm 16.2}{-19.62}\\\\\\x=\dfrac{-12+ 16.2}{-19.62}=-0.2\qquad x=\dfrac{-12- 16.2}{-19.62}=\large\boxed{1.4}\\

Note: Negative time (-0.2) is not valid

4 0
3 years ago
If the discriminant, b^2-4ac is ___, a quadratic will have two real roots, two points of intersection with the x-axis.
den301095 [7]

If the discriminant, b² - 4ac is<u> positive</u>

<h3>How to complete the statement?</h3>

From the question, we have the following equation of discriminant

The discriminant (d) is calculated as

d = b² - 4ac

The solutions of a quadratic equation are dependent on the following conditions

  • If d = 0, the quadratic equation has 1 real solution
  • If d < 0, the quadratic equation has imaginary solutions
  • If d > 0, the quadratic equation has 2 different real solutions

This means that "d > 0, the quadratic equation has 2 different real solutions" implies that the discriminant is positive

Hence, the complete statement is (b) positive

Read more about discriminant at

brainly.com/question/64103

#SPJ1

6 0
1 year ago
14) Simplify: -(16 - 5x) A) 5x - 16 B) 5x + 16 C) -5x - 16 D) - 5x + 16
VLD [36.1K]

Answer: 5x-16

<u>Switch operations</u>

Before: -(16 - 5x)

After: 5x-16

Before you switch operation you remove the subtraction sign where -(16) is.

5 0
3 years ago
HELP!
Flauer [41]

7/50 = 0.14 therefore In order to write it as a fraction out of 100 you move 2 decimal to the right.

Therefore, the answer for the first box is 14/100

The last box obviously being 0.14

6 0
3 years ago
Read 2 more answers
Find h (x) + g (x) h (x) = x2 + 6x and g (x) = -2x - 3 A. x2 - 4x - 3 B. x2 + 8x - 3 C. x2 + 4x - 3 D. x3 + 4x2 - 3​
skelet666 [1.2K]

Answer:

Step-by-step explanation:

x^2 + 6x - 2x - 3

x^2 + 4x - 3

answer is C

4 0
3 years ago
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