Answer:f(x)=-16(x-1)^2+22
Step-by-step explanation:
The equation for the trajectory of ball in the air is h(t) = -16t² + 32t + 6.
What is differentiation?The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = lim h --> 0 (f(x + h) - f(x)) /(x + h - x).
It can also be said as the slope of the tangent for the function at a given point.
Given that,
The maximum height reached by the ball after 1 sec is 22 ft above ground.
And, the height at which it is thrown is 6 ft above the ground.
Which implies at 0 sec the height is 6 ft.
The quadratic function for the height can be written as,
h(t) = at² + bt + c
Substitute t = 0 to gat,
f(0) = a × 0² + b × 0 + c
=> c = 6
Now, for maximum height,
h'(t) = 0
=> 2at + b = 0
At maximum height t = 1
Then, the above expression becomes,
2a × 1 + b = 0
=> a = -b/2
Substitute t = 1 in h(t) = at² + bt + c to get,
22 = a + b + c
=> 22 = -b/2 + b + 6
=> b/2 = 16
=> b = 32
Then, a = -b/2
= -32/2
=-16
Thus substituting the corresponding values the equation can be written as h(t) = -16t² + 32t + 6.
Hence, the required equation for the path of the ball in the air is h(t) = -16t² + 32t + 6.
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PLEASE HELP AND HURRY!!!!!
A square playground is covered with pebbles, except for two equal size triangular portions that have grass. How many square feet do the pebbles cover?
7ft
14ft
Answer:28\2
Step-by-step explanation:
7+7=14
7+7=14
14+14=28
Triangle A=1\2bh
So 28\2
The pebbles cover an area of 147 sq ft. We can use the Pythagorean theorem to find the solution.
What is Pythagoras theorem?
The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
Now, Let's call the length of the third side of the triangle "x".
Since the two triangles are equal in size, and they share two sides with the square, we can use the Pythagorean theorem to find x.
a² + b² = c²
7² + 7² = c²
49 + 49 = c²
98 = c²
c = √(98)
c = 7 √(2)
So, each triangle has a base of 7 ft and a height of 7 √(2) ft.
And, Area of each triangle = (base × height) / 2
= (7 × 7√(2)) / 2
= 24.5 ft²
Since, there are two triangles,
Hence, the total area of the grass is,
⇒ 24.5 sq ft × 2 = 49 sq ft
Hence, The square has an area of,
⇒ 14ft × 14ft = 196 sq ft
So, The pebbles cover an area of,
⇒ 196 sq ft - 49 sq ft = 147 sq ft.
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Find the area of this hexagon
Daniel deposits $8,000 into a continuously compounding interest account. After 18 years there is $13,006.40 in the account. What was the interest rate?
Answer:
r = 2.7%
Step-by-step explanation:
Interest rate compounded continuously
r = ln(A/P) / t
Where,
r = interest rate
A = future value
P = principal
t = time
r = ln(A/P) / t
r = ln(13,006.40/8,000) / 18
= ln(1.6258) / 18
= 0.4860000023303 / 18
= 0.0270000001294
Approximately
r = 0.027
Convert value of r to percentage
r = 0.27 × 100
r = 2.7%
in the diagram the measures of angle 1 and 4 is 100 the measure of 5 and 8 are 110 are c and d parallel
Answer:
no,because <1 and <5 are not congruent
Step-by-step explanation:
i did the test yw
WILL MARK BRAINLIEST IF CORRECT
Answer:
this is the 3rd one or second
Step-by-step explanation:
Read each statement then select whether it is true or false.
True
False
O
§ * (5 x 8) is one-third of 5 * 8.
24 is two times as much as (12 + 12) 5
5 * 6+5 is five times as much as 6 +5.
is five times as much as 3 + 4.
O
5x
Answer:
1) true
2) false
3) false
4)True
dos hermanos tienen una cuenta de ahorros de s/1920 lo que le corresponde al hermano mayor es 6 veces mas de lo que le corressponde al hermano menor mas un adicion de s/72 ¿ cuanto le corresponde alk hermano mayor
Answer:
le corresponde s/1656
Step-by-step explanation:
espero y te ayude
The perimeter of one square is given as 4x. Its perimeter is equal to the perimeter of a rectangle given as 2.5x + 3.75. Write an equation to determine the perimeter of each figure
Answer:
5
Step-by-step explanation:
it would be 5. x is 5 so if it is wrong sorry its best e a while since i done that kind of math
How many degrees are measured in the interior angles
of a triangle?
Answer:
180 degrees
Step-by-step explanation:
Answer:
180 °
Step-by-step explanation:
Essay on how to use math outside of school?
Answer:
Mathematics is everywhere and is used by everyone, even a basic form of it. Some jobs require just simple maths, some require advanced maths. There are many uses of it from business to culinary. Simply counting is doing maths. Retracing back or adding time is doing maths. Mathematics is used to build cars to buildings. It is inevitable that you will be using maths any time now.
if a half a gallon of milk costs $1.24 then whats the cost per pint?
Answer:
Step-by-step explanation:
It costs . 31 cents for 1 pint of milk.
Answer:
1 pint would be ($1.25/4 pints) = $0.31
Step-by-step explanation:
There are eight pints in a US gallon, and thus four in half a gallon.
That comes to four pints of milk.
That's $1.24/(half gallon), or $2.48/gallon.
Since half a gallon (4 pints) is $1.25, 1 pint would be ($1.25/4 pints) = $0.31
Walden’s family is shopping for a reclining chair. The chair the family decided on has a retail price of $800 plus 5% sales tax at four stores. Each store is offering a different promotion.
Store
Promotional Offer
A
$75 instant rebate
B
10% off sale
C
5% off sale plus store pays sales tax
D
a “no tax” sale—the store pays the tax
Which store has the best deal?
Answer: B is the correct answer
Step-by-step explanation:
If you do the math for each question to get a price a leaves you with 725 and b leaves you with 720 and c leaves you with 760 while d leaves you paying 800 so the lowest amount would be B.
Answer: B
Step-by-step explanation:
I'm pretty sure its B.
Since all 4 stores have a 5% sales tax already on them, we do:
800 x 5%
800 x 5/100
800 x 0.5 = 40
So now we go to all the stores and see which one is less than $40.
Answer A = 40 - 75 = -35 (Which is a price the store would have to pay but that's not a good option)
Answer B = 4
40 x 10%
40 x 10/100
40 x 0.10 = 4
Answer C = So if the store already pays sales tax which would be the 5% then our answer is $40
Answer D = This would just be $800 since the store says "no tax" and the store pays the 5%.
So, i'm pretty sure the answer is B instead of C. (i say this because a lot of people were saying it was C but C is completely wrong.)
Bob and his friends went out to lunch.
• They bought 3 sandwiches and 3 bottles of water.
The bottles of water cost $1.50 each.
• The total bill was $30.00.
How much does one sandwich cost if they cost the same amount?
Answer:
Each sandwich cost 8:50
Step-by-step explanation:
total 30$
total price of the waters 4:50
30-4:50=25:50
25:50÷3=8:50
HELP ITS URGENT PLS I GIVE POINTS
Answer:
each base angle is 70°
Step-by-step explanation:
this is an isosceles triangle because two sides are equal which means two angles are equal
the left, right base angle is also 'x'
so, x + x + 40 = 180
2x = 140
x = 70
here are four fractions 2/5 2/3 1/14 1/10 look at the number line below write the letter for each fraction in the correct box help plz
Answer:
First box: 1/10
Second box: 2/5
Third box: 1/4
Fourth box: 2/3
In the image attached the correct order of letter for each fraction in the correct box are : Option D, C and A.
What is the fractions about?Note that:
A= 2/5
= 0.4
B =2/3
= 0.67
C = 1/14
= 0.25
D= 1/10
= 0.1
Therefore, In the image attached the correct letter for each fraction in the correct box are : Option D, C and A.
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The Question is in the png
Answer:
$30.69
Step-by-step explanation:
If z = -7, what is the value of (-8z) - z?
Answer:
63
Step-by-step explanation:
you will plug in -7 for both z's
(-8(-7) - (-7)
following PEMDAS you will do multiplication first
(-8(-7) = 56
now we have 56 - (-7)
since - and - make a positive it will be
56 + 7 = 63
I know the answer to this question but how many solutions does it have?
Answer:Hence, x = 5, y = 0 is the required solution.
Step-by-step explanation:
Answer:
There is only one solution
Step-by-step explanation:
Help plz I will give brainliest
Answer:
i think that it is C
Step-by-step explanation:
if im incorrect i apologize
Simplify the expression. Write your answer as a power.
(-4).(-4)
The simplified expression is
Answer:
(-4).(-4) = 4^2
Step-by-step explanation:
First, some rules that we need to remember:
if A is a positive number, then:
-A = (-1)*A
Also:
A*A = A^2
We also should remember that we can multiplicate in any order we want, this is:
A*B*C = (A*B)*C = A*(B*C)
And we also can change the order of the numbers:
A*B = B*A
And finally, we need to remember the sign rules for multiplication.
(+)*(+) = (+)
(+)*(-) = (-)
(-)*(+) = (-)
(-)*(-) = (+)
Ok, now let's look at our expression.
(-4)*(-4)
First, we can rewrite this as:
( (-1)*4)*((-1)*4)
And we can rearrange the numbers to:
(-1)*(-1)*4*4
Now let's multiplicate the first two ones, because of the sign rule, we know that the outcome will be positive, and 1 times 1 is equal to 1,
(-1)*(-1) = 1
Then:
(-1)*(-1)*4*4 = 1*4*4 = 4*4
And we know that when a number is multiplied by itself we can rewrite it as:
4*4 = 4^2
Then:
(-4).(-4) = 4^2
The simplified expression is 4^2
People use water to cook, clean, and drink every day. An estimate of 15.5% of the water used each
day is for cooking. If a family uses 68.2 gallons of water a day for cooking, how many gallons do they use every day?
Answer:
260 gallons
Step-by-step explanation:
An estimate of 26.5% of the water used each day is for cleaning and a family uses 68.9 gallons of water a day for cleaning,
Percentage of water used for cleaning= 26.5%
Gallons of water used for cleaning= 68.9
Let the number of gallons used everyday be represented by g. This will give:
26.5% of g = 68.9
26.5/100 × g = 68.9
0.265 × g = 68.9
0.265g = 68.9
Divide both side by 0.265
0.265g/0.265 = 68.9/0.265
g= 260
260 gallons of water are used everyday
11. What is the positive solution to this equation?
4x2+ 12 x= 28
Answer:
x = sqrt(37)/2 - 3/2
approximately 1.54
Step-by-step explanation:
Solve for x over the real numbers:
4 x^2 + 12 x = 28
Divide both sides by 4:
x^2 + 3 x = 7
Add 9/4 to both sides:
x^2 + 3 x + 9/4 = 37/4
Write the left hand side as a square:
(x + 3/2)^2 = 37/4
Take the square root of both sides:
x + 3/2 = sqrt(37)/2 or x + 3/2 = -sqrt(37)/2
Subtract 3/2 from both sides:
x = sqrt(37)/2 - 3/2 or x + 3/2 = -sqrt(37)/2
Subtract 3/2 from both sides:
Answer: |
| x = sqrt(37)/2 - 3/2 or x = -3/2 - sqrt(37)/2
ylan can run a mile in 9.5 minutes. Over the next 6 months, he wants reduce his time so he can run a mile in 8 minutes or less, Which equality can Dylan use to find t, the amount of time he must cut each honth to reach his goal?
Answer:
So I never really knew you
God, I really tried to
Blindsided, addicted
Felt we could really do this
But really I was foolish
Hindsight, it's obvious
Step-by-step explanation:
“What is 1/2 written as a...
percent”
Please help in lowkey lost
Which triangle is congruent to the figure below?
Answer:B
Step-by-step explanation: because it is trust me
Answer:
The answer is B
Wendy borrowed a 400-page book from the library. She read 50 pages. The book is due in 5 days. Complete the inequality to find x, the number of pages Wendy must read to finish the book ?
Answer:
350 Pages or 70 pages a day
Step-by-step explanation:
If the book is 400 pages long and she already read 50 pages she only needs to read 350 pages.
What is the value of log4 2?
Answer:
1/2
Step-by-step explanation:
type it into the calculator
The value of logarithm log base 4(2 is 1/2.
What is Logarithm?The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.
Given:
Rewrite as an equation.
log base 4(2)=x
and, Rewrite log base 4(2)=x in exponential form using the definition of a logarithm. If x and b are positive real then
log (base b) x= y equivalent to [tex]b^y[/tex] = x
Create expressions in the equation that all have equal bases.
log base 4(2)=x
[tex](2^2)^x[/tex] = 2
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
2x = 1
x= 1/2.
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Please help me. I will mark brainlest
NO LINKS OR I WILL REPORT
Thank you!
Answer:
2nd and 3rd
Step-by-step explanation:
2x+1: Term 1: 2x Term 2: +1
1-1/4x: Term 1: 1 Term 2: -1/4x
I need help now! Someone
Answer:
210
Step-by-step explanation:
Hi,
Split this up. Find the area of the rectangle first. To find the area of the rectangle, you need to multiply the L x W
So...
L x W
18 x 10
Area: 180
Now, you need to find the area of the two right triangles. For the first one, to find the area, it's 1/2bh.
So...
We know that 24 - 18 will give us the length of the right triangle. We get... 6 ft.
So...
1/2 (6) (5)
We get 15.
Since both right triangles are the exact same, the other right triangle will also equal 15ft.
Now, add all of the shapes.
15 + 15 + 180 = 210
Your total area is 210.
I hope this helps :)
In ΔXYZ, ∠Y=90° and ∠X=73°. ∠ZWY=80° and XW=80. Find the length of ZY to the nearest 100th
Answer:
618.2203≈618.22
Step-by-step explanation:
618.2203≈618.22