Question

question 3(multiple choice worth 1 points) (08.04 mc) amir pitches a baseball at an initial height of 6 feet with a velocity of 73 feet per second. this can be represented by the function h(t)=-16t² + 73t + 6. if the batter misses, about how long does it take the ball to hit the ground? 4.64 seconds 2.94 seconds 2.28 seconds 0.06 seconds question 4(multiple choice worth 1 points) (08.04 mc) alexei wants to hang a mirror in his boat and put a frame around it. the mirror and frame must have an area of 19.25 square feet. the mirror is 3 feet wide and 5 feet long. which quadratic equation can be used to determine the thickness of the frame, x? 2x² + 8x - 19.25 = 0 3x² + 5x - 19.25 = 0 4x² + 16x - 4.25 = 0 4x² + 16x + 15 = 0

Explanation:

Question 3

Step1: Set height function to 0

When the ball hits the ground, $H(t)=0$. So we have the equation $- 16t^{2}+73t + 6=0$. Here, $a=-16$, $b = 73$, $c = 6$.

Step2: Use quadratic - formula

The quadratic formula is $t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute the values: $t=\frac{-73\pm\sqrt{73^{2}-4\times(-16)\times6}}{2\times(-16)}=\frac{-73\pm\sqrt{5329 + 384}}{-32}=\frac{-73\pm\sqrt{5713}}{-32}$.

Step3: Calculate the values of t

$\sqrt{5713}\approx75.6$. Then $t=\frac{-73\pm75.6}{-32}$. We have two solutions for $t$: $t_1=\frac{-73 + 75.6}{-32}=\frac{2.6}{-32}\approx - 0.08$ (rejected since time can't be negative) and $t_2=\frac{-73-75.6}{-32}=\frac{-148.6}{-32}\approx4.64$.

Step1: Find the dimensions of the mirror - and - frame

The width of the mirror and frame is $3 + 2x$ (where $x$ is the thickness of the frame) and the length is $5+2x$.

Step2: Calculate the area formula

The area $A=(3 + 2x)(5 + 2x)$. We know that $A = 19.25$. Expand $(3 + 2x)(5 + 2x)$: $(3 + 2x)(5 + 2x)=15+6x + 10x+4x^{2}=4x^{2}+16x + 15$.

Step3: Set up the quadratic equation

Since $4x^{2}+16x + 15=19.25$, then $4x^{2}+16x+15 - 19.25=0$, which simplifies to $4x^{2}+16x - 4.25=0$.

Answer:

4.64 seconds

Question 4