h (t) = -4t^2 + 24t = -4 (t² - 6t)
= -4 [(t - 3)² - 3²]
= -4 (t - 3)² + 36
max (3 ; 36)
(t - 3)² = t² - 2*t*3 + 3² = t² - 6t + 9
so it's why t² - 6t = (t - 3)² - 9
The maximum height of the projectile is 36 feet.
It is given that the projectile on a planet in our solar system at a given time t in seconds is represented by the function:
[tex]\rm h(t) = -4t^2+24t[/tex] can be written as a function:
[tex]\rm h(t) = a(t-h)^2+k\\[/tex]
It is required to determine the maximum height of the projectile.
What are maxima and minima?Maxima and minima of a function are the extrema within the range, in other words, the maximum value of a function at a certain point is called maxima and the minimum value of a function at a certain point is called minima.
The given function:
[tex]\rm h(t) = -4t^2+24t[/tex] for the maximum height of the projectile differentiate the given function with respect to 't' and equate it to zero.
[tex]\rm h(t) = -4t^2+24t\\[/tex]
[tex]\frac{\mathrm{d} }{\mathrm{d} x} [h(t)] = \frac{\mathrm{d} }{\mathrm{d} x}(-4t^2+24t)\\[/tex]
[tex]\frac{\mathrm{d} }{\mathrm{d} x} [h(t)] = \frac{\mathrm{d} }{\mathrm{d} x}(-4t^2)+\frac{\mathrm{d} }{\mathrm{d} x}(24t)\\[/tex]
[tex]\frac{\mathrm{d} }{\mathrm{d} x} [h(t)] = -8t+24\\[/tex]
[tex]\frac{\mathrm{d} }{\mathrm{d} x} [h(t)] = 0 \Rightarrow-8t+24=0\\[/tex]
[tex]\rm -8t+24=0\\\rm t= 3 \ sec[/tex]
Here, [tex]\rm \frac{\mathrm{d}^2 }{\mathrm dx^2} \leq 0[/tex]
It means that at t=3, we get the maximum height of the projectile.
[tex]\rm h(3)= -4(3)^2+24(3)\\\rm h(3) = -36+72\\\rm h(3)= 36 \ Feet[/tex]
Thus, the maximum height of the projectile is 36 feet.
Know more about the maxima and minima here:
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If a ∥ b and m∠1 = 65°, what is m∠2?
Answer:
65 degrees
Step-by-step explanation:
the angles are corresponding, and corresponding angles always have the same angle measures
If a ∥ b and m∠1 = 65°, The measure of m∠2 will be 65°.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called an "Angle." when a transverse line crosses two straight lines, corresponding angles are formed.
When two lines are crossed by a third line, these angles are generated at equivalent corners or corners corresponding to the transversal.
It is given that, a ∥ b and m∠1 = 65.
If the transversal meets two parallel lines, the corresponding angles theory asserts that the corresponding angles are congruent. In other words, the angles formed when a transversal crosses two parallel lines will always be equal.
Since corresponding angles always have the same angle measures, the angles are said to be corresponding.
As a result,
m∠1 =m∠2
m∠1 = 65°
m∠2=65°
Thus, if a ∥ b and m∠1 = 65°, The measure of m∠2 will be 65°.
Learn more about the angle here:
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What is he measure of the indicated angle? Hint: What angle pair relationship is being modeled?
Which set of side lengths would create a unique triangle?
a. 4 cm, 8 cm, 4 cm
b. 12 in, 8 in, 15 in
c. 2 ft, 9 ft, 12 ft
d. All of the above
Answer:
the set of side length would be 4cm, 8cm,4cm
Tylen and his friends perform an investigation in math class where they record the color of candy they pull out of a bag 15 times in order to predict how
many total pieces of each color are in the bag.
Once they pull
out a candy, they put it back in the bag before they pull another one.
They pull 9 red candies and 6 blue candies.
-
Part A: Based on the boys'investigation, how many red candies will they expect to find in a bag of 120? (1 point
Answer:
I think they expect to find 40 red candies.
whats 4/9 divided by 3/7 equal
Answer:
1.03703703704
Step-by-step explanation:
i d k if this is what ur looking for but hope this helped :)
A cellphone company charges a monthly fee of $34.00, plus $0.05 per text message. If you have at most $52 to spend, how many text messages can you send?
Answer:
360 text messages
Step-by-step explanation:
52 - 34 = 18
0.05 = 1 text message
0.05 * 360 = 18$
Hope this helps!
Answer:
52-34=18
18/0.05=360
360 text messages per month
Step-by-step explanation:
Analyze each situation. Identify a reasonable domain and range for each situation. Explain.
a. A bowler pays $2.75 per game.
b. A car travels 25 miles using 1 gallon of gas.
Answer: A The domain is all positive integers, because the bowler could not play a fractional or negative number of games.
The range is multiples of 2.75.
B The domain is all positive real numbers, since a portion of a gallon of gas could be used.
The range is all positive real numbers.
A rectangular lawn has area 140 square yards. Its length is six less than twice the width. What are the width and length of the lawn?
Answer:
width = let width be w
area = 140
length = 2w-6
Area of a rectangle = l*b
⇒ 2w-6*w=140
⇒ [tex]2w^2-6=140\\2w^2 = 146\\w^2 = 146/2\\w^2 = 73\\w = \sqrt{73}[/tex]
Rhonda went out to dinner.
• The price of her meal was
$15.55.
• The sales tax was 7% of the
price of the meal.
• The tip was 18% of both the
meal and the sales tax.
How much money did Rhonda
pay for the meal, including tax
and tip?
Answer:
18.54
Step-by-step explanation:
15.55 X 7% = 1.0885
15.55 + 1.0885 = 16.6385 X 18% = 2.99493
15.55 + 2.99493 =18.54493
can you help me please?
Answer: D. $12.00
Step-by-step explanation:
Looking at the table you will see that the increment from 3 to 4 is $12.00
You can find this by subtracting 3 from 4.
48-36 = 12
If you fill in the table with $12.00, you will see it is consistent with the other values.
I hope this helps.
Answer:
$24
Step-by-step explanation:
You have to multiply the hours worked by 12
pls mark brainliest
what are the answers to all of these
Answer/Step-by-step explanation:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[tex]\frac{1}{3}\times\frac{2}{4}[/tex]
[tex]\mathrm{Cancel\:the\:numbers:}\:\frac{2}{4}=\frac{1}{2}[/tex]
[tex]=\frac{1}{3}\cdot \frac{1}{2}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}[/tex]
[tex]=\frac{1\cdot \:1}{3\cdot \:2}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:1\cdot \:1=1[/tex]
[tex]=\frac{1}{3\cdot \:2}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:3\cdot \:2=6[/tex]
[tex]=\frac{1}{6}[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[tex]\frac{1}{6}\times\frac{4}{9}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}[/tex]
[tex]=\frac{1\cdot \:4}{6\cdot \:9}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:1\cdot \:4=4[/tex]
[tex]=\frac{4}{6\cdot \:9}[/tex]
[tex]\mathrm{Factor\:the\:number:\:}\:4=2\cdot \:2[/tex]
[tex]=\frac{2\cdot \:2}{6\cdot \:9}[/tex]
[tex]\mathrm{Factor\:the\:number:\:}\:6=2\cdot \:3[/tex]
[tex]=\frac{2\cdot \:2}{2\cdot \:3\cdot \:9}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:2[/tex]
[tex]=\frac{2}{3\cdot \:9}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:3\cdot \:9=27[/tex]
[tex]=\frac{2}{27}[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[tex]\frac{2}{3}\times\frac{7}{8}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}[/tex]
[tex]=\frac{2\cdot \:7}{3\cdot \:8}[/tex]
[tex]\mathrm{Factor\:the\:number:\:}\:8=2\cdot \:4[/tex]
[tex]=\frac{2\cdot \:7}{3\cdot \:2\cdot \:4}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:2[/tex]
[tex]=\frac{7}{3\cdot \:4}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:3\cdot \:4=12[/tex]
[tex]=\frac{7}{12}[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[tex]\frac{2}4\times\frac{2}{5}[/tex]
[tex]\mathrm{Cancel\:the\:numbers:}\:\frac{2}{4}=\frac{1}{2}[/tex]
[tex]=\frac{1}{2}\cdot \frac{2}{5}[/tex]
[tex]\mathrm{Cross-cancel\:common\:factor:}\:2[/tex]
[tex]=\frac{1}5[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Code: 6 2 12 1
~Learn with Lenvy~
eight to the power of 2 plus three to the power of 2
Answer: 73
Step-by-step explanation:
8² = 64 3² = 9 64 +9 = 73
8 to the power of 2 means 8 × 8 that is 64
3 to the power of 2 means 3 × 3 that is 9
The price of a sweater was reduced from $20 to $12. By what percentage was the price of the sweater reduced.
▪ Answer:
40%
▪ Step-by-step explanation:
Hi there !
$20 ........ 100%
$12 ..............x %
x = 12×100/20
= 1200/20
= 60%
100% - 60% = 40%
Good luck !
Mary sells fruit with four of her friends If the earnings are divided evenly how much must the business make in order for each person to earn 30?
In a case whereby Mary sells fruit with four of her friends If the earnings are divided evenly the amount they must make in order for each person to earn 30 is 150.
How can the earningbe calculated?Since 4 of them wereinto the business aimimg to share the profit in erqual amount then the business should make [30*(1+4) ]= (30*5 )= 150 dollars total earnings.
Therefore, If the profits from selling fruit with Mary's four friends are divided equally, they will need to make 150 in order for each individual to make $30.
Learn more about selling at:
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Answer:
150
Step-by-step explanation:
You have to find the total number of fruits so multiply 30 by 4. However, Mary is included too so add another 30
Kelly is on a four-person relay team. The team's total time for its last race was 41.37 seconds. Giselle ran her part in 9.36 seconds. Sarah took 9.71 seconds to run her part of the race, and Aliyah ran her part in 10.57 seconds. How long did Kelly take to run her portion of the race?
Answer: 11.73 seconds
Step-by-step explanation:
To solve the question, we have to add the time used by Giselle, Sarah and Aliyah and then subtract from 41.37 seconds to determine the time used by Kelly. This will be:
= 41.37 - (9.36 + 9.71 + 10.57)
= 41.37 - 29.64
= 11.73 seconds
Kelly used 11.73 seconds
Find the value of x. (8x-1)° (4x+7)°
Answer:
X = -1/2 or X = 0.50
Step-by-step explanation:
8x - 1 + 4x + 7
Combine like terms
12x + 6 = 0
Isolate X
12x + 6 = 0
- 6 = 0
12x = -6
12x/12 = -6/12
X = -1/2
Hope this helps :)
100 POINTS!!!
Company A and B are cleaning
companies. Who has a lower initial
value?
A. Company A
B. Company B
EXPLAIN
Answer:company b
Step-by-step explanation:
it would cost $75 to hire company b and $90 to hire company a.
The area of a circle is 16π m². What is the circumference, in meters? Express your answer in terms of pi
*hint 8 isnt the answer *
brainlest
pls hurry
Solution:
We know that:
Area of circle = πr² = 16π
Let's undo this equation by dividing π both sides. Then, take a square root to find the radius.
=> πr² = 16π=> πr²/π = 16π/π=> r² = 16=> √r² = √16=> r = 4Now, let's find the circumference by substituting the radius in the circumference formula.
=> 2πr = Circumference=> (2)(π)(r) = Circumference=> (2)(π)(4) = Circumference=> 8π meters = CircumferenceSince the question says to leave the circumference in terms of π, 8π meters is the circumference of the circle.
Thus, the circumference is 8π meters
Pls help with this is laws of exponents pls help
These are the laws of exponent.
Hope it will help you......Melissa practiceted piano for 5/6 of an hour. On Monday and 8/9 of an hour on Tuesday. How many more minutes did she practice on Tuesday compared to monday
Answer:
24 hrs
Step-by-step explanation:
99594iu58
The number of minutes that she practiced on Tuesday compared to Monday will be 103 minutes.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
Melissa practiced piano for 5/6 of an hour on Monday and 8/9 of an hour on Tuesday.
The number of minutes that she practiced on Tuesday compared to Monday will be
⇒ (5/6) + (8/9)
⇒ 31/18
⇒ 103 minutes
The number of minutes that she practiced on Tuesday compared to Monday will be 103 minutes.
More about the Algebra link is given below.
https://brainly.com/question/953809
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Which relationship would form a graph that is not a straight line?
Answer:
D
Step-by-step explanation:
The last line is not a straight line because when you start from 1 and plug higher numbers, you see that forms a quadratic curve or parabola.
William writes a function
f(x)=−2x−10
. He uses an input-output table to represent the function.
What is the output of William’s function when the input is
−6?
Answer:
2
Step-by-step explanation:
f(-6) = -2(-6) - 10
f(-6) = 12 - 10
f(-6) = 2
what is the value of
[tex] \sqrt{(p { }^{2} } - 4q) \: if \: p = 6 \: and \: q = 5[/tex]
Answer:
4
Step-by-step explanation:
Given :-
p = 6
q = 5
√(p² - 4q)
To Find :-
Value of expression after evaluation
Solving :-
= √(6)² - 4(5)
= √36 - 20
= √16
= 4
Solution :-
4
Answer:
4
Step-by-step explanation:
Solving
Step 1: Plug in the values of p and q.
[tex]\sqrt{(6^2-4*5)}[/tex]Step 2: Solve exponents.
[tex]\sqrt{(6*6-4*5)}[/tex] [tex]\sqrt{(36-4*5)}[/tex]Step 3: Solve multiplication.
[tex]\sqrt{(36-20)}[/tex]Step 4: Subtract 20 from 36.
[tex]\sqrt{16}[/tex]Step 5: Solve square root.
[tex]\sqrt{16} = 4[/tex]Have a lovely rest of your day/night, and good luck with your assignments! ♡
Solve for p in the literal equation 9p + 7r = q.
Answer:
p = [tex]\frac{q-7r}{9}[/tex]
Step-by-step explanation:
Given
9p + 7r = q ( subtract 7r from both sides )
9p = q - 7r ( isolate p by dividing both sides by 9 )
p = [tex]\frac{q-7r}{9}[/tex]
Answer: p = q - 7r ÷ 9
Identify the exponent and the base in the expression 6^12
Given parameters:
Expression;
6¹²
Identify the exponent and the base in the expression;
6¹²
An exponent is a power to which a number or variable is raised.
Generally, it signifies the number of times a number should be repeatedly multiplied.
The base is the number that is being multiplied.
So, in this problem, exponent is 12 and base is 6.
please help me find mo
Answer:
MO = 25
Step-by-step explanation:
Point O between parallel lines PQ and MN divides segment PM in the same proportion that it divides segment QN.
MO/OP = NO/OQ
MO/20 = 20/16 . . . . . . use the given numbers
MO = 20(20/16) . . . . . multiply by 20
MO = 25
If 596 people voted in the election, how many were over 65 years old?
596 x 25% = 149
This implies 149 persons over the age of 65 voted.
I hope this helps.
Answer:
596 x 25% =149
149 people voted over age 65
Grayson is organizing textbooks on his bookshelf. He has an English textbook, a biology textbook, and a physics textbook. How many different ways can he line the textbooks up on his bookshelf?
Answer:
9
Step-by-step explanation:
you multiply the number of textbooks by itself to figure out how many lineups are possible
100000x444444444444444444
Answer: 4.4444???
Step-by-step explanation:
Answer: 2.65787 × 10²
plz mark brainliest:)
I need the answer right now. I’ll give 40 points
sorry its 13 1/8 lol