A ball is thrown from a height of 157 feet with an initial downward velocity of 9/fts . The ball's height h (in feet) after t se
conds is given by the following. =h−157−9t-16tsquared How long after the ball is thrown does it hit the ground? Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)
1 answer:
Answer:
2.86 seconds
Step-by-step explanation:
We presume the height is measured above the ground, so the height when the ball hits the ground is 0 feet. Putting that into the equation and solving for t, we get ...
0 = 157 -9t -16t^2
We can use the quadratic formula with a=-16, b=-9, c=157 to find the solution.
t = (-b -√(b^2 -4ac))/(2a) . . . . . we are not interested in the negative solution
t = (-(-9) -√((-9)^2 -4(-16)(157)))/(2(-16))
t = (9 -√10129)/-32 = (9 -100.6429)/-32 ≈ 2.86384
The ball will hit the ground about 2.86 seconds after it is thrown.
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The flagpole is vertical and is at 90° to the ground. This makes a right-angle to the ground, which is flat.
Since we have two sides of the triangle already, and they are in a ratio of ?? : 16 : 20 = ?? : 4 : 5, that means that because the triangle is a right-angled triangle, the third and last side must be 3 to complete the ratio! (This is called 'Pythagoras')
Since the other sides were divided by 4 to get the simple ratio, we must multiply 3 to get the actual ratio! 3 × 4 = 12 ft tall flagpole.
The flagpole is vertical and is at 90° to the ground. This makes a right-angle to the ground, which is flat.
Since we have two sides of the triangle already, and they are in a ratio of ?? : 16 : 20 = ?? : 4 : 5, that means that because the triangle is a right-angled triangle, the third and last side must be 3 to complete the ratio! (This is called 'Pythagoras')
Since the other sides were divided by 4 to get the simple ratio, we must multiply 3 to get the actual ratio! 3 × 4 = 12 ft tall flagpole.
Answer:
The 45% off discount saves an additional $10 compared to the 15% discount for a total of $15 off regular price.
Step-by-step explanation:
We can find the original price of the game through a proportion. A proportion is an equation where two ratios or fractions are equal. The ratios or fractions compare like quantities. For example, we will compare percent over percent to an equal ratio of $ to $. Since 15% of 100% is the same ratio as $5 to the unknown original $ price, I write:
I can now cross-multiply by multiplying numerator and denominator from each ratio.
I now solve for y by dividing by 15.
The original price was $33.34.
Now, we can find the amount if 45% off and then then compare the two discounts. To find the percent off I can multiply by 0.45(33.34)=15. The 45% off discount saves an additional $10 compared to the 15% discount.