Answer:
you would use 1.5 cups of flour
A person standing close to the edge on top of a 72-foot building throws a ball vertically upward. The
quadratic function h = - 16ť+ 136t + 72 models the ball's height about the ground, h, in feet, t seconds after it was thrown.
a) What is the maximum height of the ball?
feet
b) How many seconds does it take until the ball hits the ground?
seconds
Answer:
I hope this helps.
Step-by-step explanation:
h(t) = -16t2 + 108t + 28
(a)
Maximum height occurs at the vertex of the height-vs.-time parabola, which is at
t = -108/[2(-16)] sec = ? sec
Evaluate h(t) at this value of t to get hmax.
(b)
Set h(t) = 0 and solve the quadratic equation for t. You will get a positive and a negative solution. Discard the negative solution, since time starts at t = 0.
The quadratic function, h = -16t + 136t + 72, gives us:
a) The maximum height of the ball is 360 feet.
b) The time taken by the ball to hit the ground is 9 seconds.
What is a quadratic function?A quadratic function is a function over a quadratic expression, that is, over an expression having degree 2.
How to solve the question?In the question, we are informed that a person standing close to the edge of a 72-foot building throws a ball vertically upward. The quadratic function h = -16t² + 136t + 72 models the ball's height above the ground, h in feet, t seconds after it was thrown.
We solve the following:-
a) What is the maximum height of the ball?
The maximum height of the ball can be obtained by differentiating the given quadratic function, h = -16t² + 136t + 72.
Differentiating both sides. we get:
[tex]\frac{\delta h}{\delta t} = -32t + 136[/tex] .
To get point of inflection, we equate this to 0, to get:
[tex]\frac{\delta h}{\delta t} = -32t + 136 = 0[/tex],
or, -32t + 136 = 0,
or, t = 136/32 = 4.5.
To check whether the value of h is maximum/minimum at t = 4.5, we differentiate [tex]\frac{\delta h}{\delta t} = -32t + 136[/tex] again, to get:
[tex]\frac{\delta^{2} h}{\delta t^{2} } = -32[/tex] , which is < 0, which that implies, h is maximum at t = 4.5.
Now, we calculate the maximum height, by putting in t = 4.5, in the equation, to get:
h = -16(4.5)² + 136(4.5) + 72,
or, h = -16(20.25) + 612 + 72,
or, h = -324 + 684 = 360.
Therefore, The maximum height of the ball is 360 feet.
b) How many seconds does it take until the ball hits the ground?
The time taken can be calculated by putting the value of h = 0, and solving the quadratic function h = -16t² + 136t + 72, as the height of the ball at the ground is 0.
Therefore, it can be written as:
0 = -16t² + 136t + 72.
or, 16t² - 136t - 72 = 0.
Solving this using the quadratic equation, we get:
[tex]t = \frac{-(-136)\pm \sqrt{(-136)^{2} - 4(16)(-72)}}{2(16)}[/tex] ,
or, [tex]t = \frac{136\pm \sqrt{18496 + 4608}}{32}[/tex] ,
or, [tex]t = \frac{136\pm \sqrt{23104}}{32}[/tex] ,
or, [tex]t = \frac{136\pm 52}{32}[/tex]
Therefore, either t = (136+152)/32 = 9,
or, t (136 - 152)/32 = -0.5.
Since t represents time, we won't take the negative value, and hence t = 9.
Therefore, The time taken by the ball to hit the ground is 9 seconds.
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It's for middle School PLZZZZ HELPPPP.
Lauren and her brother are buying their mom a watch for her birthday. The original price of the watch is $50, but the store is having a 25% off sale on watches. The sales tax in Lauren’s state is 6%.
How much will Lauren and her brother pay for the watch including tax? How much will each sibling pay if they split the cost equally?
Answer:
$20
Step-by-step explanation:
To find out sale
50 x .25 = 12.5
To find out tax
37.5 x .06 = 2.25
Then final price
37.5 + 2.25 = 39.75
If they spilt price
$19.88
Answer:
1. $37.5 without tax
2. Split bill with tax: $19.88
3. Split bill withput tax: $18.25
Step-by-step explanation:
Make an equation first.
y=.25 (50)
This would help solve the amount for the discpunt sale.
The discout is $12.5 off.
50-12.5=37.5
Now we have tp solve for the tax amount.
y=0.06 (37.5)
y=2.25
2.25 is the tax amount.
We have to add these all together to get the answer for part 1.
37.5+2.25= $39.75
HELP AGAIN PLSSSSSSSS
Answer:
5x5 = 25
hope this helps (again) :D
x + 6 >10 or 3x + 11 ≤ −7
Answer:
x>4 or x≤-6
Step-by-step explanation:
x+6>10 or 3x+11≤-7
x>4 or 3x≤-18
x>4 or x≤-6
Given the function g(x)=41x^3+a for some constant a, which describes the inverse function g^-1(x)
Answer:
[tex]g^{-1}(x)=\sqrt[3]{\frac{x-a}{41}}[/tex]
Step-by-step explanation:
The inverse of a function has [tex]x[/tex] and [tex]y[/tex] values switched from the original function. Therefore, simply switch [tex]x[/tex] and [tex]y[/tex] and isolate [tex]y[/tex] to get your inverse function:
Original function: [tex]g(x)=41x^3+a[/tex]
Switching [tex]x[/tex] and [tex]y[/tex], then isolating [tex]y[/tex]:
[tex]x=41y^3+a,\\x-a=41y^3,\\\frac{x-a}{41}=y^3,\\y=\sqrt[3]{\frac{x-a}{41}}[/tex].
Therefore, the inverse of the [tex]g(x)=41x^3+a[/tex] is:
[tex]\fbox{$g^{-1}(x)=\sqrt[3]{\frac{x-a}{41}}$}[/tex].
4 pounds of grapes cost $11.52. what is the unit rate?
Answer: 2.88/1
Step-by-step explanation:
If fx) = -3x - 5 and g(x) = 4x - 2, find (f - g)(x).
Chose the ratio that forms a proportion with the ratio 3/8?
Answer:
well i donk know
so but just trying to get points
Jack is shopping. Last week he bought $10 of groceries and ended up paying $10.07 after taxes. This week he's buying $15 of groceries. If the tax rate remains the same, how much will he end up paying after taxes?
Answer:
16.05
Step-by-step explanation:
first I realized 7 cents is .07% of 10 the I multiplied .07 times 15 then I added them up and got the answer
Given the expression m - 5w + 3m +4n + 2w, Jeriche rewrote it as 4m - 3w + 4n while John rewrote it as 8mn - 3w Who is operatorname correct? What did the other do wrong?
Answer:
eJeriche is correct, the answer is 4m - 3w + 4n, John didn't collect the like terms correctly
Step-by-step explanation:
Answer: 4m - 3w + 4n - this is the right decision.
Step-by-step explanation:
m - 5w + 3m + 4n + 2w = m + 3m - 5w + 2w + 4n = 4m - 3w + 4n
Jericho wrote correctly, and John - not.
John put together various variables n and m, which is not allowed.
The following inequality has a solution in the form X > A. Solve the inequality and place the correct value of A into the box.
-17x - 10 > 7 - 20x
Answer: x > ______
Enter your answer as an integer or a reduced fraction in the form A/B.
JELPPPPP it’s due in 5 mins
The answer is 65
Step-by-step explanation:
all you had to do was divide
A dolphin travels through the water at a speed of 25 kilometers per hour. Which representation shows the distance a dolphin can travel at this rate
Answer:
B
Step-by-step explanation:
Refer to the diagram shown.
35°
25
t
DE
M
4
N
R
6
Q
What is m 2 MNT?
m2 MNT =
Answer:
what subject?
Step-by-step explanation:
The measure of <MNT = 142.17
What is Trigonometry?The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
PR= 6+ 4= 10 unit
So, using trigonometry
tan 25 = PT/ PR
0.466 = PT / 10
PT= 4.66 unit
Now, In ΔNPT
tan <TNP = P/ B
tan <TNP = 4.66/6
tan <TNP = 0.7766
<TNP = 37.83
Now, <MNT + <TNP = 180 {Linear pair}
<MNT = 142.17
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AC =
Round your answer to the nearest hundredth.
?
С
70°
4
B
Answer:
huh? im confused on the question
Step-by-step explanation:
!!
Answer: 3.76
Step-by-step explanation:
trust
Rewrite the following without an exponent. 6^-2
Please answer ASAP!
Answer:
Rewriting [tex]6^{-2}[/tex] without an exponent we get [tex]\mathbf{\frac{1}{36}}[/tex]
Step-by-step explanation:
We need to rewrite the following without an exponent. [tex]6^{-2}[/tex]
We need to solve the exponent to find the result.
We know the exponent rule: [tex]a^{-b}=\frac{1}{a^b}[/tex]
Now using this rule to solve the equation:
[tex]6^{-2}\\=\frac{1}{6^2}\\We \:know \:that\:6^2 = 6\times 6=36\\=\frac{1}{36}[/tex]
So, Rewriting [tex]6^{-2}[/tex] without an exponent we get [tex]\mathbf{\frac{1}{36}}[/tex]
You roll a number cube twice. What is the probability of rolling a 2 first and then rolling an odd number?
12
Gel.
Answer:
50/50
Step-by-step explanation:
Graph the opposite of the opposite of 10 on the number line. Click on the number line to
identify the number's location.
Answer:
the opposite of 10 is -10 that's the best i could do for ya my bad hope this still helps.
Step-by-step explanation:
Answer:-10
Step-by-step explanation:
If BD bisects ∠ABC, find each value
Answer:
x=14
y=10
AD=19
CD=19
Step-by-step explanation:
x:
5x-6=64
+6 +6
5x=70
x=14
y:
3y-11=y+9
+11 +11
3y=y+20
-y -y
2y=20
y=10
AD:
3y-11
3(10)-11
30-11
19
CD:
y+9
(10)+9
19
Here is a easy one if you are low on points
Answer:
11x -21= 180
11x=201
18.2727273
Step-by-step explanation:
The distance in feet that Karina swims in a race is represented by 5d -5, where d is the distance for eac
What is an expression equivalent to 5d -5?
Choose the correct answer below.
A. 5d - 5 = 5(-5)
B. 5d -5 = -5 + 5d
C. 5d - 5 = 5-5d
D. 5d - 5 = -5(d+5)
Answer:
C. 5d - 5 = 5-5d
Step-by-step explanation:
Write the given percent of increase or decrease as a growth factor.
7% Increase
a.1.7
c. 7.1
c.1.007
d.1.07
Answer: D
Step-by-step explanation:
The median number of cars sold by 11 sales representatives in a certain month is 6. The range of number of cars
sold by those sales representatives that month is 4.
Determine if the following statement is true, is false, or does not contain enough information.
The fewest cars sold could be 0.
Choose 1 answers
True
False
Not enough information
Answer:
False
Step-by-step explanation:
Khan Academy
The given statement is False.
What is median?
'In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution.'
According to the given problem,
Median = 6
Total count = 11
Range = 0
Now, range is the difference between the highest value and the lowest value.
Since, the median is 6, the highest number must be greater than 6. This would not have been possible if the lowest value was 0. If the lowest count had been 0, then the highest count had to be 4.
Hence, we can conclude, the fewest cars sold cannot be 0.
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find the product of (−x−3)(2x2+5x+8)
The school says that no less than a third of the juniors went to prom. If 37 juniors went, what the minimum amount of juniors at the school?
Answer: 37 times 3 is 111. So there are 111 junior at that school.
1/3 times the # = the answer.
Given that the following is a Rhombus, find the missing angles.
Answer:
1. 90
2. 61
3. 29
4. 61
Step-by-step explanation:
1 is a 90 degree angle. Triangles = 180 degrees
(help me it is not much)
Which form of a linear equation should we use when given the y-intercept and the slope of
the line?
Point-Slope form
Slope-intercept form
Standard form?
Answer:
Slope Intercept Form
Step-by-step explanation:
its the basics
PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!
$4x-5$ is less than 25$
can someone help me please, i’ll give brainly. (10 points)
Answer:
Gradient of Line A: 0.75
Gradient of Line B: 0.8
Therefore the lines ARE NOT parallel.
Step-by-step explanation:
Find the gradient (slope) of line A and B respectively.
Line A Gradient:
Equation of line A is 3x - 4y = 5
Rewrite this in slope-intercept form as y = mx + b, where m is the gradient (slope).
Thus,
3x - 4y - 3x = -3x + 5
-4y = -3x + 5
Divide both sides by -4
y = ¾x + ⁵/4
The gradient = ¾ = 0.75
Line B Gradient:
Gradient of line passing through (4, 7) and (-1, 3)
[tex] m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 7}{-1 - 4} = \frac{-4}{-5} = \frac{4}{5} [/tex]
Gradient (m) = ⅘ = 0.8
Since both lines do not have the same gradient, therefore the lines are not parallel.
A 1 : 6
B 1 : 3
C 2:1
D 3:1
Answer:
B)1:3
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