PLEASE HELPPP!!!
San Francisco is well known for its fog: very thick, low-lying clouds that hide its hills. One foggy day, Penelope is practicing kicking a football. Once she kicks the football so high that it disappears into the fog! The height of the ball (in feet) can be represented at time (in seconds) by the equation h(t)=−16t2+64t . The ball disappears into the fog when it is 40 feet high.
a) Write an inequality that represents the times during which the ball was not visible.
b) Solve the inequality and represent your solution algebraically and on a number line. Also, write a sentence explaining your answer in the context of the problem.
c) How high does Penelope kick the football?
d) When does it reach its maximum height?
Answers
Answer:
a) [tex]-16t^{2}+64t\geq40[/tex]
b)[tex][2-\frac{\sqrt{6}}{2} , 2+\frac{\sqrt{6}}{2}][/tex]
(see attached picture for the number line)
This interval means that from about 0.78s to about 3.22s the ball will not be visible because it will be higher than 40 feet high.
c) [tex]h_{max}=64ft[/tex]
d) t=2s
Step-by-step explanation:
a)
Basically the ball will disappear when it is higher than 40 ft, so we can build the inequality like this:
[tex]-16t^{2}+64t\geq40[/tex]
this is because the function represents it's height, so when the function is greater than or equal to 40, then the ball will disappear.
b) to solve the inequality, first we need to turn the ≥ symbol to an = symbol and solve for t, so we get:
[tex]-16t^{2}+64t =40[/tex]
we can move the 40 to the other side of the equation so we get:
[tex]-16t^{2}+64t-40=0[/tex]
we can factor the equation so it's easier to solve, so we get:
[tex]-8(2t^{2}-8t+5) =0[/tex]
which simplifies to:
[tex]2t^{2}-8t+5=0[/tex]
and we can use the quadratic formula to solve this equation, so we get:
[tex]t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}[/tex]
so we get:
[tex]t=\frac{-(-8)\pm\sqrt{(-8)^{2}-4(2)(5)}}{2(2)}[/tex]
which yields:
[tex]2\pm \frac{\sqrt{6}}{2}[/tex]
and next we need to test the posible intervals to see which one makes the inequality true, the possible intervals are:
[tex](-\infty, 2-\frac{\sqrt{6}}{2}][/tex] for a test value of 0
[tex][2-\frac{\sqrt{6}}{2},2+\frac{\sqrt{6}}{2}][/tex] for a test value of 1
[tex][2+\frac{\sqrt{6}}{2},\infty)[/tex] for a test value of 4
so next we test each of the values in the original inequality and see if the inequality is true:
[tex](-\infty, 2-\frac{\sqrt{6}}{2}][/tex] for a test value of 0
[tex]-16(0)^{2}+64(0)\geq40[/tex]
[tex]0\geq40[/tex] false
so this is not an answer.
[tex][2-\frac{\sqrt{6}}{2},2+\frac{\sqrt{6}}{2}][/tex] for a test value of 1
[tex]-16(1)^{2}+64(1)\geq40[/tex]
[tex]48\geq40[/tex]
true, so this is an answer.
[tex][2+\frac{\sqrt{6}}{2}, \infty)[/tex] for a test value of 4
[tex]-16(4)^{2}+64(4)\geq40[/tex]
[tex]-16(16)+64(4)\geq40[/tex]
[tex]-256+256\geq40[/tex]
[tex]0\geq40[/tex]
false, so this is no answer.
So the answer is the interval:
[tex][2-\frac{\sqrt{6}}{2},2+\frac{\sqrt{6}}{2}][/tex]
This interval means that from about 0.78s to about 3.22s the ball will not be visible because it will be higher than 40 feet high.
c) In order to find how high Penelope kick the football, we must find the vertex of the parabola which is gotten when graping the given function (see attached picture)
so we can use the following formula to find the t-value for this maximum height:
[tex]t=-\frac{b}{2a}[/tex]
so we substitute the corresponding values:
[tex]t=-\frac{64}{2(-16)}[/tex]
which yields:
t=2s
next, we can substitute this time into the original function to find the maximum height, so we get:
[tex]h=-16(2)^{2}+64(2)[/tex]
which yields:
h=64 ft
d) We found the answer for d on the previous part where we got that t=2s
Related Questions
HELP 17 POINTS Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. What value of p makes the equation true?
Answers
Answer:
0.125
Step-by-step explanation:
First, remove the 1/8 by subtracting 1/8 on both sides
-3p = -3/8
Then, isolate the variable by diving each side by -3
p = 0.125
Answer:
0.125
Step-by-step explanation:
did the test and got it right!!
When a number is decreased by 4%, the result is 66. What is the original number to the nearest tenth?
Answers
Answer:
68.8
Step-by-step explanation:
100% = x number
96% = 66
so 100%
= 68.75
to the nearest tenth is 68.8
solve for x- 5(x+4)=30
Answers
Answer: x= -12.5
Step-by-step explanation:
Start with distributing-5(x+4) or you get
x-5x-20=30
Add x and -5x to get -4x
Thank you add 20 to each side and get
-4x = 50
Divide by -4 on each side to get x=-12.5
Answer:
x=-25/2 is the answer.
Step-by-step explanation:
Below are the steps for solving the equation:
Step 1: Simplify, combine like terms, and distribute:
x−5(x+4)=30
x+(−5)(x)+(−5)(4)=30
x+−5x+−20=30
(x+−5x)+(−20)=30
−4x+−20=30
−4x−20=30
Add 20 to each side:
−4x−20+20=30+20
−4x=50
Divide each side by -4:
-4x/-4=50/-4
x=-25/2, which is -12.5 as a decimal.
So, your answer is x=-25/2 as a fraction, which is also -12.5 as a decimal.
To the nearest tenth, what is the value of x?
A. 3.5
B. 4.8
C. 5.9
D. 7.3
E. 9.8
Answers
Answer:
D, I think, pls don't report if im wrong
Step-by-step explanation:
Write 27 as a product of primes.
Use index notation when giving your answer.
Answers
Answer:
3, 9, 3 and 3
Step-by-step explanation:
27
3 and 9
3 and 3
I don't know how to do index notation. I apologize.
how to solve -2(v-2)=-3-2v i need it step by step
Answers
Answer:O0
Step-by-step explanation:
2*(v-2)-(-3-2*v)=0
STEP
1
:
Equation at the end of step 1
(0 - 2 • (v - 2)) - (-2v - 3) = 0
STEP
2
:
Equation at the end of step 2
7 = 0
STEP
3
:
Equations which are never true:
3.1 Solve : 7 = 0
Answer:
No solution
Step-by-step explanation:
Given: -2(v-2)=-3-2v
Distribute -2 at the left side of the equal sign:
-2v+4=-3-2v
Put all like terms in one side:
-2v+2v=-3-4
Combine all like terms:
0=-12
Answer: No solution
If you have less than $10.00 in dimes and quarters. Which of the following is a
possible combination of dimes and quarters that satisfy the inequality. *
a. 50 dimes and 20 quarters
b. 20 dimes and 50 quarters
c. 50 dimes and 30 quarters
d. 40 dimes and 20 quarters
Answers
Answer:
D. 40 dimes and 20 quarters
Step-by-step explanation:
40 dimes= $4 because 10 dimes= $1
20 quarters= $5 because 4 quarters= $1
The other options are above $10. I hope this helps!!!! :D
Using a layaway plan, Bill bought a set of golf clubs for $1700. He has 6 months to pay off his balance after paying a down payment. The store does not charge a fee for their program. If Bill makes payments of $201 a month, how much did he need to use as a down payment in order to pay for the clubs
Answers
Answer:
$494
Step-by-step explanation:
Given that:
Cost of golf club = $1700
Number of months taken to balance payment after down payment = 6 months
Amount paid per month = $201
The down payment made :
Cost of golf clubs - (monthly payment * number of months)
$1700 - ($201 * 6)
$1700 - $1206
= $494
Hence, the downpayment made = $494
help if you have time !
Answers
Answer:
72 Bricks would be needed.
Step-by-step explanation:
24 * 2 = 48
12 * 2 = 24
48 + 24 = 72
plzplPzlpzlzpzl .......i beg u do this easy question for me ....
Answers
Answer: [tex]-p^2-(q+r)^2[/tex]
Work Shown:
I'm assuming your teacher wants you to factor as much as possible.
[tex]-p^2-q^2-r^2-2qr\\\\-p^2-q^2-2qr-r^2\\\\-p^2-(q^2+2qr+r^2)\\\\-p^2-(q+r)^2\\\\[/tex]
In the last step, I used the rule that [tex](a+b)^2 = a^2+2ab+b^2[/tex]
We cannot factor any further. If the first term was [tex]p^2[/tex] instead of [tex]-p^2[/tex], then we could use the difference of squares factoring rule.
A rectangular computer monitor is measured by the length and width of its display resolution. Three different monitors are described below. Monitor A has a display resolution of 640 pixels by 480 pixels. Monitor B has a display resolution of 800 pixels by 600 pixels. Monitor C has a display resolution of 1,280 pixels by 800 pixels. Which of the monitors are similar, based on their display resolution
Answers
Answer: Monitors A and B
Step-by-step explanation:
The similar monitors based on display resolution are those with similar ratios.
Take the ratios to their simplest forms to see which are similar.
Monitor A
= 640 : 480
= 16 : 12
= 4 : 3
Monitor B
= 800 : 600
= 8 : 6
= 4 : 3
Monitor C
= 1,280 : 800
= 32 : 20
= 8 : 5
Monitors A and B are similar as they have the same display ratio.
A line has slope m=3/4 and passes through the point (0,-5) what is the equation of the line?
Answers
Write an equation in point slope form of the line that passes through the point (2,-8) and had a slope of 4
Answers
Plug those in
Solution: y + 8 = 4(x - 2)
The equation of a line in point-slope form is (y + 8) = 4(x - 2).
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given, A line passes through the point (x₁, y₁) ⇒ (2,-8) and had a slope of 4.
We know the equation of a line in point-slope form is (y - y₁) = m(x - x₁).
∴ The equation of this line is (y + 8) = 4(x - 2).
learn more about lines and slopes here :
https://brainly.com/question/3605446
#SPJ2
i need help!
number 14
Answers
Answer:
I’m gonna edit This answer give me a sec to do the work
Step-by-step explanation:
Answer:
1. One Solution
2. No Solution
3. Infinitely Many
Hope this helps :)
What is the unit rate for cats per dog if there's 72 cats and 12 dogs
Answers
Answer:
6 dogs
Step-by-step explanation:
72 divided by 12=6
Please mark brainliset
Answer:
6:1, 6/1, or 6 to 1
Step-by-step explanation:
72/12
72/12=6
12/12=1
6/1
Papyrus or Undyne? YEET
Answers
Answer:
Papyrus. it is the only thing to pick! :) also YEET TO YOU TO
Answer:
:)
Step-by-step explanation:
Papyrus
lol
yeet to you too my good sir/madam
How can you determine the sale price if you are given the regular price and the percent of markdown? (List the steps)
Answers
Answer:
The sale price is $34
Step-by-step explanation:
If we are given the regular price P and the markdown percentage r, we follow these steps:
1) Calculate the markdown or discount amount M.
M = P*r/100
2) Subtract it from the regular price:
S = P - M
S is the sale price.
Example: The regular price is $40 and the markdown percentage is 15%. Thus:
1) M = $40*15/100 = $6
2) S = $40 - $6 = $34
The sale price is $34
Which angle or side combinations can make a triangle? Select all that apply. Angles measuring 90°, 45°, and 45°. Angles measuring 27°, 35°, and 108°. Angles measuring 82°, 41°, and 57°. Sides measuring 8 cm, 12 cm, and 5 cm. Sides measuring 7 in., 4 in., and 13 in. Sides measuring 43 cm, 41 cm, and 58 cm.
Answers
Answer:
Angles measuring 90°, 45°, and 45°: Can make triangle
Angles measuring 27°, 35°, and 108°: Can not make triangle
Angles measuring 82°, 41°, and 57°: Can make triangle
Sides measuring 8 cm, 12 cm, and 5 cm: Can make triangle
Sides measuring 7 in., 4 in., and 13 in: Can not make triangle
Sides measuring 43 cm, 41 cm, and 58 cm: Can make triangle
Step-by-step explanation:
For the angles to form a triangle, there sum must be equal to 180°
Angles measuring 90°, 45°, and 45°
Sum of Angles = 90° + 45° +45° = 180°
Hence, this combination can make triangle.
Angles measuring 27°, 35°, and 108°
Sum of Angles = 27° + 35° + 108° = 170° ≠ 180°
Hence, this combination can not make triangle.
Angles measuring 82°, 41°, and 57°
Sum of Angles = 82° + 41° +57° = 180°
Hence, this combination can make triangle.
For three sides to form a triangle the sum of the two sides must be greater than the length of third side.
Sides measuring 8 cm, 12 cm, and 5 cm
(8 cm + 12 cm) > 5 cm (True)
(8 cm + 5 cm) > 12 cm (True)
(12 cm + 5 cm) > 8 cm (True)
Hence, this combination can make triangle.
Sides measuring 7 in., 4 in., and 13 in
(7 in + 4 in) > 13 in (False)
Hence, this combination can not make triangle.
Sides measuring 43 cm, 41 cm, and 58 cm
(43 cm + 41 cm) > 58 cm (True)
(43 cm + 58 cm) > 41 cm (True)
(41 cm + 58 cm) > 43 cm (True)
Hence, this combination can make triangle.
Answer:
A- Angles measuring 90°, 45°, and 45°.
C- Angles measuring 82°, 41°, and 57°.
D- Sides measuring 8 cm, 12 cm, and 5 cm
F- Sides measuring 43 cm, 41 cm, and 58 cm.
Step-by-step explanation:
I got it wrong for you guys :D
There is the picture for proof, Have a Wonderful day to anyone who see's this
:)
Pls help me it is a simple function
Answers
Answer:
blank 1 = 4
blank 2 = 1
Step-by-step explanation:
The slope is how much the y changes for each x value.
have a great day!!!
x2 + 13x = -22 solve for x
Answers
Consider the triangle. Which statement is true about the length of the sides?
Each side has a different length.
Two sides have the same length, which is less than the length of the third side.
The three sides have the same length.
The sum of the lengths of two sides is equal to the length of the third side.
Answers
Answer:For this case we observe that the 2 angles of the triangle are equal. Also, we have by definition:
A triangle is , when the three sides are connected(in addition, the three internal angles measure 2 angles 45 degrees and 1 angle 90
Step-by-step explanation:
Please help i need to get this done asap !
Answers
Answer:
Step-by-step explanation:
Equation of line k is y = (-4/7)x + 1
point (-5,-10); m = -4/7
Line L is perpendicular to k so the perpendicular slope will be 7/4
Equation of line L is (y - y1) = m(x-x1)
y+10 = (7/4) (x +5)
4y + 40 = 7x + 35
4y = 7x - 5
y = (7/4)x - (5/4)
solve for the equation 3r = -24
Answers
Answer:
yes
Step-by-step explanation:
bc Quick maths
Answer:
r=-8
Step-by-step explanation:
Why is the first step when solving
2x – 15 - 4x = 3 to combine like terms?
Answers
Answer:
-9 is the final answer
Step-by-step explanation:
2x-4x=-2x
so the equation would be -2x-15=3
add 15 to both sides -2x=18
divide both sides by -2
Increase 130 by one fifth
Answers
Answer:
sorry i cant help
Step-by-step explanation:
Answer:
156.
Step-by-step explanation:
130/5 = 26.
130 + 26 = 156.
Can someone answer my English question, please :/ I will mark you brainliest
Answers
Answer:
Step-by-step explanation:
The temperature in Quebec City was 5 degrees Celsius at 4 pm. By midnight, the temperature dropped 15 degrees. A number line has points negative 20, blank, A, B, 0, 5, C, blank, D. Which point is a representation of the colder midnight temperature in degrees Celsius?
Answers
Answer: Point A
Step-by-step explanation:
The temperature at midnight is;
= 5 - 15
= -10°C
Looking at the number line, one can surmise that the scale is in multiples of 5. This means that C is 10, B is -5 and A is -10.
With point A being -10°C, it represents the colder midnight temperature.
Answer:
Point A
Step-by-step explanation:
We know that the temperature dropped 15 degrees, and that it was initially of 5°C. So, by midnight, the temperature will be of -10°C (5-15=-10).
We also know that the distance between points is of 5°C. So, the point that we have to mark is point A, which represents -10°C.
Can someone please help?!
Answers
.
....................
. .
. .
-3x + 7 (-6 – 5c)
C= 7
x = -9
Answers
Answer:
=−260
Step-by-step explanation:
What is the r-value of the following data to three decimal places?
Answers
Answer:
.953
Step-by-step explanation:
took it on a test and got it right
Answer:
.953
Step-by-step explanation: