There appears to be positive correlation between number of rainy days and tomato plant height.
This can be said because a positive correlation is a relationship between two variables that if one moves in a direction the other moves in the same direction. In this situation the rain increases so the tomato plant height increases, therefore there is a positive correlation.
A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively linked, the value either rises or falls together.
A correlation reveals the nature and magnitude of a link between two variables. In other words, it illustrates the degree to which measurements of two or more variables are comparable throughout a dataset.
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determine if the sequence is geometric. if it is, find the common ratio.
-1, 1, 4, 8, ...
Due to the lack of a common ratio, the above sequence is not geometric.
What is geometeric sequence?
A series of integers with a common ratio is referred to as a geometric sequence. A geometric sequence has a next number that is a multiple of the one before it.
if the sequence is geometric.the common ratio of the number's
-1, 1, 4, 8, are
-1/1 = -1 ratios of the numbers in the sequence
4/1 = 4
8/4 = 2
There isn't a ratio that unites the numbers.
The lack of a common ratio leads us to the conclusion that the presented sequence is not geometric.
Due to the lack of a common ratio, the above sequence is not geometric.
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Write the equation of the line with slope = 4/6 and passing through the point (1, -1)
Answer:
Step-by-step explanation:
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).
Given that the slope of the line is m = 4/6, we can substitute it into the equation.
We know that the line passes through the point (1, -1), so we can use that point to find the value of b.
Plugging in the point (1, -1) into the equation, we get:
-1 = (4/6)(1) + b
Solving for b, we get:
b = -1 - (4/6) = -1 - 2/3 = -5/3
So the equation of the line is:
y = (4/6)x - (5/3)
which can be rewritten as
y = (2/3)x - (5/3)
this line is the equation of the line you are looking for.
Answer:
Y--1=m(x-1) this is the rule of the equation of straight line
Larry says all numbers that have a 2 in the one ones place are composite numbers. Explain if Larry is correct or incorrrect.
The information shows that Larry is incorrect as a composite number is a positive integer that has at least one positive divisor.
What're are composite numbers?It should be noted that composite numbers are those numbers that have more than two factors. Composite numbers have factors other than 1 and itself
Larry is incorrect. A composite number is a positive integer that has at least one positive divisor other than one and itself. For example, 4 is composite because it can be divided by 2 (and 1). However, a number's ones place simply refers to the digit in the units place and has no bearing on whether a number is prime or composite.
For example, the number 22 is composite because it is divisible by 2 and 11, but the number 12 is composite because it is divisible by 2,3,4 and 6.
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find the area of region s . find the volume of the solid generated when region s is revolved about the horizontal line y
The volume of solid generated when region s is revolved about the horizontal line y is 93.04919.
We have to find the volume of the solid generated when region s is revolved about the horizontal line y.
As shaded region is revolved around y = -3.
Outer radius = f(x) + 3
Inner radius = g(x) + 3
Width = dx
Thus small volume "dv" formed when shaded region in above diagram is revolved around y = -3.
dv = π[tex](f(x) + 3)^3[/tex]dx - π[tex](g(x) + 3)^2[/tex]dx
dv = π([tex]f^2[/tex](x) + 6f(x) + 9)dx - π([tex]g^2[/tex](x) + 6g(x) + 9)dx
dv = π([tex]f^2[/tex](x) + 6f(x))dx - π([tex]g^2[/tex](x) + 6g(x))dx
Now integrating on both side:
[tex]\int dv=\pi\int^{3}_{0}9(1+x)\cos(\pi x/6) + 6\int^{3}_{0}f(x)dx-\pi\times 5.32021-6\times3.24125[/tex]
Using the provided result or a scientific calculator, the entire definite integral was discovered.
v = π × 25.54298 + 6 × 8.16083 - π × 5.32021 - 6 × 3.24125
v = 93.04919
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The complete question is given below:
I need the parent equations please and thank you
The parent function by reversing rigid transformations are, respectively:
Case 6: f(x) = x³
Case 7: f(x) = √x
Case 8: f(x) = ㏒ x
Case 9: f(x) = |x|
Case 10: f(x) = x²
How to determine the parent function
Parent functions are the most simple form of a kind of expression (i.e. power, exponential, logarithms, roots). In this problem we find five cases of images of parent functions, that is, versions modified by rigid transformations. The most common rigid transformations are, respectively:
Horizontal translation
f(x) → f(x - k)
Vertical translation
f(x) → f(x) + k
Reflection about x-axis
f(x) → - f(x)
Reflection about y-axis
f(x) → f(- x)
Vertical dilation
f(x) → k · f(x)
Horizontal dilation
f(x) → f(k · x)
Now we proceed to revert the rigid transformations used in each function:
Case 6
f(x) = 2 · (x + 6)³ + 11
Vertical translation - Horizontal translation - Vertical dilation
f(x) = x³
Case 7
f(x) = 7 + (1 / 2) · √(x - 3)
Vertical translation - Horizontal translation - Vertical dilation
f(x) = √x
Case 8
f(x) = 5 - ㏒ (x + 1)
Vertical translation - Reflection about x-axis - Horizontal translation
f(x) = ㏒ x
Case 9
f(x) = - 3 · |x + 10| + 7
Vertical translation - Reflection about x-axis - Dilation - Horizontal translation
f(x) = |x|
Case 10
f(x) = (3 / 5) · (x - 8)² - 4
Vertical translation - Dilation - Horizontal translation
f(x) = x²
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quadrilateral PQRS is a parallelogram
Check the picture below.
Verify the trig identity
The verification of the given trig identity is shown in below.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
⇒ (1 - sin x) / (1 + sin x) = (sec x - tan x)²
Now, We can simplify as;
⇒ (1 - sin x) / (1 + sin x) = (sec x - tan x)²
LHS;
⇒ (1 - sin x) / (1 + sin x)
⇒ (1 - sin x) (1 - sin x) / (1 + sin x) (1 - sin x)
⇒ (1 - sin x)² / (1 - sin²x)
⇒ (1 - sin x)² / cos²x
⇒ ( (1 - sin x )/ cos x )²
RHS;
⇒ (sec x - tan x)²
⇒ ( 1/cos x - sin x / cos x)²
⇒ ( (1 - sin x) / cos x )²
Hence, We get;
⇒ (1 - sin x) / (1 + sin x) = (sec x - tan x)²
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Todd made a table to show different plans he
can use to save $500. Complete the table. Which
plan can Todd use to save $500 in less than
16 weeks and have $20 extra
Plan 2 can be used to save $500 in less than 16 weeks and have $20 extra.
The number of weeks and y, which is the equation we wish to utilise, stand in for the total amount saved. Our equation will then be 15 x. Instead of the other way around, he will save 330.
Plan Amount saved per week Total amount saved in 16 weeks
1 $31.25 $500
2 $35 $560 (with $60 extra)
3 $40 $640 (with $140 extra)
Plan 2 can be used to save $500 in less than 16 weeks and have $20 extra.
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Using y = 6 - 2x, plot the ordered pairs from the table. Then graph the function represented by the ordered pairs and tell whether the function is linear or nonlinear. Part 1 out of 3 Complete the table. Input, x Output, y Check -1 3 Next
Answer:
.................................................................................
Step-by-step explanation:
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ok
Your friend
finds the sum. Is your friend correct?
Explain your reasoning.
-3.7 + (-0.25) = | 3.7 | + | 0.25 | = 3.7 + 0.25 = 3.95
Answer:
Yes, the friend is correct in finding the sum of -3.7 + (-0.25) = 3.95.
To find the sum, the friend first takes the absolute value of each number (ignoring the negative sign) to find that the absolute value of -3.7 is 3.7 and the absolute value of -0.25 is 0.25.
Then, the friend adds the absolute values of the numbers (3.7 + 0.25) to get 3.95 which is the final answer.
The order of operation is correct and the arithmetic is also correct, so the final result is the correct sum of the two given numbers.
what is the slope and intercept of the linear plot of the given arrhenius equation using semilogy function?
The slope is -Ea/R and the intercept is equal to ln(A)
The Arrhenius equation is a mathematical equation that describes the relationship between the rate constant of a chemical reaction and temperature:
k = Ae^(-Ea/RT)
where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.
The slope and intercept of the linear plot of the Arrhenius equation using a semilogarithmic (semilog) plot can be determined by transforming the equation into a linear form. The semilog plot is created by taking the logarithm of the rate constant (k) on the y-axis and the reciprocal of the temperature (1/T) on the x-axis:
ln(k) = ln(A) - Ea / RT
The slope of the plot is equal to -Ea/R and the intercept is equal to ln(A). By fitting a straight line to the semilog plot, the values of Ea and A can be determined.
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find the largest prime number that divides the quantity $0! (1!) \times 1 (2!) \times 2 (3!) \times 3 \cdots (50!) \times 50$.
The largest prime number that divides the given expression is 229.
Largest Prime Factor of 50!We can factorize the given expression as follows:
[tex]$0! \times 1 \times 1! \times 2 \times 2! \times 3 \times 3! \times \cdots \times 50! \times 50$[/tex]
Now, we can cancel out all the factorials from both sides, leaving us with:
[tex]$1 \times 1 \times 2 \times 2 \times 3 \times 3 \times \cdots \times 50 \times 50$.[/tex]
The largest prime factor of any composite number is the largest prime factor of its prime factorization. By the fundamental theorem of arithmetic, we know that the prime factorization of any composite number is unique.
The prime factorization of a number can be found by dividing the number by prime numbers and keeping dividing the quotient by prime numbers until the quotient is prime.
Now, we can start dividing the given number (the product of all numbers from 1 to 50) by the smallest prime number, 2, and keep dividing the quotient by the next prime number until the quotient is prime.
The largest prime factor of the given expression is the largest prime factor of the final quotient.
The final quotient is
[tex]2^{24} \times 3^{12} \times 5^9 \times 7^7 \times 11^5 \times 13^4 \times 17^3 \times 19^3 \times 23^2 \times 29^2 \times 31^2 \times 37^2 \times 41^2 \times 43^2 \times 47^2 \times 53^2 \times 59^2 \times 61^2 \times 67^2 \times 71^2 \times 73^2 \times 79^2 \times 83^2 \times 89^2 \times 97^2 \times 101^2 \times 103^2 \times 107^2 \times 109^2 \times 113^2 \times 127^2 \times 131^2 \times 137^2 \times 139^2 \times 149^2 \times 151^2 \times 157^2[/tex]
[tex]\times 163^2 \times 167^2 \times 173^2 \times 179^2 \times 181^2 \times 191^2 \times 193^2 \times 197^2 \times 199^2 \times 211^2 \times 223^2 \times 227^2 \times 229^2$[/tex]
The largest prime factor of the final quotient is the largest prime factor of the prime factorization, which is 229.
So the largest prime number that divides the given expression is 229.
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3.25x -1.5y=1.25
13x-6y=10
Answer:
¿Qué quieres comer?
Step-by-step explanation:
area of the segment?
Answer:
A ≈ 34.91 m²
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{40}{360}[/tex] ( r is the radius )
= π × 10² × [tex]\frac{1}{9}[/tex]
= [tex]\frac{100\pi }{9}[/tex]
≈ 34.91 m² ( to 2 decimal places )
Answer:
34.88m²
(round 35m²)
Step-by-step explanation:
a round angle, that of the circle, is 360°, here we have a portion of 40°, we divide 360° by 40° and we have the percentage with respect to the circle
360° : 40° = 9
we now know that the wedge is 1/9 of the circlefind the area of the whole circle having the radius (10m)Area of Circle Formulas · Area = π × r2, where 'r' is the radius
Area = π × r2
Area = π × 10²
Area = π × 100
Area = 3.14 × 100
Area = 314 m²
now we divide by 9 and we have the area of the wedge314 : 9 = 34.88m² (round 35m²)
According to exponent rules, when we multiply terms with the same base we _______ the exponents.
a. Divide
b. Multiply
c. Subtract
d. Add
According to exponent rules, when we multiply terms with the same base add the exponents. Hence, the correct answer is option D.
Exponent rules are a set of rules that dictate how exponents (numbers written as a superscript) can be manipulated in mathematical operations. Some of the most commonly used exponent rules include:
Product of Powers: When multiplying powers with the same base, you can add the exponents.For example, [tex]x^4 * x^5 = x^{4+5} = x^9[/tex]
The quotient of Powers: When dividing powers with the same base, you can subtract the exponents.For example, [tex]x^7 / x^3 = x^{7-3} = x^4[/tex]
Power of a Power: When raising a power to another power, you can multiply the exponents.For example,[tex](x^3)^5 = x^{3*5} = x^{15}[/tex]
Power of a Product: When raising a product to power, you can raise each factor to that power.For example,[tex](xy)^3 = x^3 * y^3[/tex]
Power of a Quotient: When raising a quotient to a power, you can raise the numerator and denominator to that power separately.For example,[tex](x/y)^3 = x^3 / y^3[/tex]
According to the product of the power rule, we get that we add the exponents when we multiply terms with the same base.
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THIS IS URGENT PLEASE HELP !!!
1 : Write a expression to represent a 15% discount for a Christmas ornament, x, label each part of your expression
2 : Write a equivalent expression to question 1
3: What if x =$15.99, how would your expression change. Show the work please
4. Tubby states that 1.15x is also an expression that represents the new price for the ornaments. Is tubby correct? Justify your reasoning.
Answer:
1: 0.15x = 0.15x * x = discount (percentage) * original price = discount
2: x - 0.15x = x (1 - 0.15) = original price - discount
3: 0.15 x 15.99 = 2.39
15.99 - 2.39= 13.59
x= $13.59
Tubby is not correct. 1.15x is not an expression that represents the new price for the ornament. It represents the original price plus a 15% increase, not a discount. To find the new price after a discount, you need to multiply the original price by (1- the percentage discount) or subtract the percentage discount from the original price.
Step-by-step explanation:
Can someone please help me
The length of the segment PS is 100 units.
What is Pythagorean Theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
From the given image we can see that the segments PT, PQ, and TQ form a right- angled triangle PQT.
Applying Pythagorean theorem to this triangle we have:
PQ^2 + TQ^2 = PT^2
(45)^2 + (TQ)^2 = (53)^2
2025 + (TQ)^2 = 2809
(TQ)^2 = 2809 - 2025
(TQ)^2 = 784
TQ = 28
Similarly, segments PR, PS, and SR form a right-angled triangle PRS, where TQ = SR = 28 and PR = 96.
Applying Pythagorean theorem to this triangle we have:
PR^2 + SR^2 = PS^2
(96)^2 + (28)^2 = (PS)^2
(PS)^2 = 9216 + 784
(PS)^2 = 10000
PS = 100
Hence, the length of the segment PS is 100 units.
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(PLEASE HELP) At a local print shop, 15 copies can be made for $6. At this rate, how much would it cost to make 35 copies???
Answer:
14 dollars
Step-by-step explanation:
They vary in direct proportion
Thus; If 15 copies = 6dollars
35 copies = (35 × 6) ÷ 15
= 210 ÷ 15
= 14
It would cost 18$
Every fifteen copies you have to pay 6$, and since 35 is 3 times 15, it would also be 3 times the price, or 6 * 3$ which equals 18$
Ella's family took a road trip to Niagara Falls. Ella slept through the last 14% of the trip. If Ella fell asleep after they had travelled 602 miles, what was the total length of the trip?
The total distance of the trip Ella's family took is 700 miles.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Ella slept through the last 14% of the trip.
So, Before Ella fell to asleep they covered (100 - 14)% = 86% of the trip.
Let The total distance be 'x'.
Therefore, 602 miles is 86% of 'x' which can be numerically expressed as,
(86/100)×x = 602.
0.86x = 602.
x = 602/0.86.
x = 700 miles.
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Quadrilateral EFGH is a rectangle. If m∠FEG=57° , find m∠GEH .
The measure of the angle m∠GEH = 33° for the given Quadrilateral EFGH which is a rectangle.
Define the term compliment angles?When two angles sum up to 90 degrees, they are complementary (a Right Angle).Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees & 60 degrees, for instance, are complimentary angles.They don't even have to be close to one another for the total to be 90 degrees.Examples:
The complimentary angles of 40° and 50°.The complementary angles of 60° and 30° are.The corresponding angles of 5° and 85° are.For this stated question:
In the rectangle EFGH.
m∠FEG=57°
Then,
m∠FEG + m∠GEH = 90 (complimentary angles)
57° + m∠GEH = 90
m∠GEH = 90 - 57
m∠GEH = 33°
Thus, the measure of the angle m∠GEH = 33° for the given Quadrilateral EFGH which is a rectangle.
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51 is 20% of what number?
31
71
200
255
PLS HELPPPP
Answer: 255
Step-by-step explanation:
Try thinking backwards first; 51*(0.20)=10.2, or 10.2 is 20% of 52
To find 20% of the unknown number, just divide 51 by 0.20
51/0.20=255
Whatever the answer is, you know it has to be larger than the original number.
solve these proportion for the variable x. Use the reasoning of scalling to solve
Answer:
x = 6
Step-by-step explanation:
[tex]\frac{8}{12}[/tex] = [tex]\frac{x}{9}[/tex] ( cross- multiply )
12x = 72 ( divide both sides by 12 )
x = 6
Rose bought 12 kg of raisins. She packed them into bags so that each bag weighs 3/4 kg. How many bags did she pack?
Answer: 16
Step-by-step explanation:
You need to divide 12 by 3/4
To do this you turn 12 into a fraction by making it 12/1
Then you do Keep Change Flip
Keep 12/1
Change the division into multiplication
Flip 3/4 into 4/3
Then you do 12/1 × 4/3 which is 48/3
Finally you simplify 48/3 into 16
state which theorem you can use to show that the quadrilateral is a parallelogram
Answer:
opposite angles are equal and parallel
(a) A ball rotates 2π rad in 4.0 s. What is its angular velocity?
(b) A bicycle tire moving at ω = 3.5 rad/s accelerates at a constant rate to 4.2 rad/s in 3.0 s. What is its angular acceleration?
a. The angular velocity of the ball is 1.57rad/sec
b. The angular acceleration of the bicycle is 0.23 rad/sec²
What is angular acceleration and angular velocity?angular is the rate of change of angular distance . it is measured in rad/sec. it is represented by w. Angular acceleration is the rate of change in angular velocity with time.
angular velocity = change in angle/ time
w = 2π/t
w = 2× 3.14/4
w = 6.28/4
w = 1.57 rad/sec
angular acceleration =( final angular velocity - initial angular velocity )/time
= (4.2 - 3.5)/3
= 0.7/3
= 0.23 rad/s²
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2. compute the following summary statisticsa) the mean for the low income group is: b) the median for the low income group is: c) the standard deviation for the low income group is: d) the mean for the high income group is: e) the median for the high income group is: f) the standard deviation for the high income group is:
The mean for the low income group is the average of all the values in the group.
It is calculated by adding up all the values and then dividing by the total number of values. In the low income group, the mean is calculated by adding up all the incomes, and then dividing by the total number of people.
The median for the low income group is the middle value when all the values are arranged in order. To calculate the median, first arrange the incomes in order from lowest to highest, and then find the middle value.
The standard deviation for the low income group is a measure of how spread out the values are. It is calculated by taking the square root of the variance, which is calculated by taking the average of the squared difference between each value and the mean, and then dividing by the number of values.
The mean for the high income group is the average of all the values in the group. It is calculated by adding up all the values and then dividing by the total number of values. In the high income group, the mean is calculated by adding up all the incomes, and then dividing by the total number of people.
The median for the high income group is the middle value when all the values are arranged in order. To calculate the median, first arrange the incomes in order from lowest to highest, and then find the middle value.
The standard deviation for the high income group is a measure of how spread out the values are. It is calculated by taking the square root of the variance, which is calculated by taking the average of the squared difference between each value and the mean, and then dividing by the number of values.
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BOOKSHELVES A bookshelf consists of two vertical planks with five horizontal shelves. Are each of the four sections for books rectangles? Explain.
Yes, each of the four sections for books is a rectangle because all four sides of the section are straight lines and the opposite sides are the same length.
Are each of the four sections for books rectangles?Yes, each of the four sections for books would be rectangles. A rectangle is a four-sided figure with four right angles, meaning that all of the angles measure 90 degrees. In the case of a bookshelf, the two vertical planks and the five horizontal shelves form a rectangle because the angles between the two planks and the five shelves are all right angles.The top section of the bookshelf is the first rectangle. It is formed between the top horizontal shelf and the two vertical planks. The second rectangle is formed between the second shelf from the top and the two vertical planks. The third rectangle is formed between the third shelf from the top and the two vertical planks. Finally, the fourth section is formed between the fourth shelf from the top and the two vertical planks.Each of the four sections of the bookshelf is a rectangle because the angles between the two vertical planks and the five horizontal shelves are all right angles. The two vertical planks form the length of the rectangle, while the five horizontal shelves form the width. This makes all four sections of the bookshelf a rectangle.To learn more about A rectangle refer to:
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Please help me ASAP
Suppose 1 side of a triangle measures 23 inches and another side measures 19 inches. Use the triangle theorem to determine possible side lengths for the third side. Show work
A: c > 4
B: 4 > c > 42
C: c > 42
D: 4 < c < 42
Using the triangle inequality theorem, the length of the third side is: D. 4 < c < 42.
How to Apply the Triangle Inequality Theorem?The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
In this case, we know that side A measures 23 inches and side B measures 19 inches. To find possible values for side C, we can use the triangle inequality theorem by adding the lengths of sides A and B and comparing the sum to all possible values of side C.
A + B > C
23 + 19 > C
42 > C
So, the length of side C must be less than 42 inches.
Also
C > A - B
C > 23 - 19
C > 4
So, the length of side C must be greater than 4 inches.
Therefore, the possible side lengths of the third side, C, must be between 4 inches and 42 inches (not including 4 inches and 42 inches).
The answer is: D. 4 < c < 42
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Justin punts a football. The height of the football
could be described by the model:
--1672 +64 + 1
'h describes the height of the ball in feet and the
time in seconds after the ball was kicked.
At what time in seconds is the ball at its highest
point after being kicked?
If the height of the football could be described by the model: f(x) = -16x² + 64x , then the time at which the ball at its highest point after being kicked is t = 2 seconds .
In order to find time at which ball is at its highest point,
we have to find the time at which the derivative of height function is = 0.
the height function is ⇒ f(x) = -16x² + 64x ;
So , the derivative of the height function will be :
⇒ f'(x) = -32x + 64 ;
equating the derivative of height function to 0 , and solving for x ,
we get ;
⇒ -32x + 64 = 0
⇒ -32x = -64
⇒ x = 2
Therefore , the time at which the ball is at its highest point is 2 seconds .
The given question is incomplete , the complete question is
Justin punts a football. The height of the football could be described by the model: f(x) = -16x² + 64x. h describes the height of the ball in feet and the time in seconds after the ball was kicked.
At what time in seconds is the ball at its highest point after being kicked ?
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One ounce of solution X contains only ingredients a and b in a ratio of 2:3. One ounce of solution Y contains only ingredients a and b in a ratio of 1:2. If solution Z is created by mixing solutions X and Y in a ratio of 3:11, then 2520 ounces of solution Z contains how many ounces of a?
Applying proportion, 2520 ounces of solution Z will contain 44040 ounces of ingredient a.
How to Use Proportion to Calculate The Ounces Needed of a Solution?To determine the number of ounces of ingredient a in 2520 ounces of solution Z, we need to first calculate the proportion of ingredient a in solutions X and Y, and then use that information to determine the proportion of ingredient a in solution Z.
Solution X contains 2 ounces of ingredient a and 3 ounces of ingredient b in one ounce of solution, so the proportion of ingredient a is 2/(2+3) = 2/5.
Solution Y contains 1 ounce of ingredient a and 2 ounces of ingredient b in one ounce of solution, so the proportion of ingredient a is 1/(1+2) = 1/3.
Solution Z is created by mixing solutions X and Y in a ratio of 3:11, so 3 ounces of solution X are mixed with 11 ounces of solution Y.
Thus, the proportion of ingredient a in solution Z = (32/5) + (111/3) = 6/5 + 11/3.
To find out the number of ounces of ingredient a in 2520 ounces of solution Z, we need to multiply the proportion of ingredient a with the number of ounces of solution Z
2520 * (6/5 + 11/3) = 2520 * (6/5 + 11/3) = 2520 * (252/15 + 11/3) = 2520 * (16+11/3) = 2520 * (16+11/3) = 2520 * (16+11/3) = 2520 * (16+37/3) = 2520 * (16+37/3) = 2520 * (53/3) = 252053/3 = 252017.66666 = 44040 ounces of ingredient a.
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