A ball is thrown into the air with an upward velocity of 32 ft/s. Its height h in feet after t seconds is given by the function h = –16t2 + 32t + 6. a. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. b. What is the ball’s maximum height?
Answers
but how do you show it
well do you know what a derivative is?
h=-32t + 32 + 0
t= 1
then plug into h(1)= -16(1)^2 + 32(1)+ 6
max height is 22
if you dont, then i will have to solve another way
a) It will reach the maximum in 1 second;
b) the maximum height is 22 feet.
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We find the maximum by finding the vertex.
We first find the axis of symmetry, whose equation is,
x = -b/2a
x = -32/2(-16)
x = -32/-32
x = 1
This gives us that it reaches the maximum in 1 second.
And, To find the y-coordinate, the maximum height, we substitute this into the equation:
h(1) = -16(1²)+32(1)+6
h(1) = -16+32+6 = 22
Hence, It reaches a height of 22 feet.
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Related Questions
The equilateral triangle shown is rotated about line a. Each side of the triangle measures 20 mm. What shape is created by the rotation and what is the approximate circumference of the base? Circumference of a circle: C = 2πr a cylinder with a circumference of about 63 mm a cylinder with a circumference of about 126 mm a cone with a base circumference of about 63 mm a cone with a base circumference of about 126 mm
Answers
The shape and the circumference of the base created by the rotation is; Cone and Circumference of 63 mm
What shape is created by rotation?We are given;
Each side of equilateral triangle = 20 mm
Now, when the triangle is rotated about the line ‘a’ which passes through the midpoint of any of the 3 sides of the equilateral triangle we will get a conical shape.
The distance from the line a which cuts one side of a triangle to one vertex of the triangle is the radius = 10 mm
We know that;
Circumference of a circle = 2πr
Thus;
C = 2 × 3.14 × 10
C = 6.28 × 10
C = 62.8 mm
C = 63 mm
Thus, the approximate circumference of the base is 63 mm.
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Which of the following is the prime factored form of the lowest common denominator of?
A.2 x 2 x 2 x 3
B.2 x 4 x 2 x 3
C.8 x 6
D.2 x 12
Answers
2 x 2 x 2 x 3 factored form is the prime factored form.
What is a prime number?"A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers."
The given factored forms are:
A. 2 x 2 x 2 x 3
Here, all the numbers are prime numbers.
Therefore, this factored form is the prime factored form.
B. 2 x 4 x 2 x 3
Here, all the numbers are not prime numbers.
Therefore, this factored form is not the prime factored form.
C. 8 x 6
Here, not a single number is prime number.
Therefore, this factored form is not the prime factored form.
D. 2 x 12
Here, all the numbers are not prime numbers.
Therefore, this factored form is not the prime factored form.
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help me pls i need to pass
Answers
The surface area (S) of a rectangular prism is given in terms of its length (L), width (W), and height (H) as
... S = 2(LW +WH + LH)
Substitute your numbers and do the arithmetic.
... S = 2(7.2·10 + 10·6.3 + 7.2·6.3)
... = 2(72 + 63 + 45.36)
... = 2·180.36
... = 360.72 . . . . square inches
You own a coffee shop where a cup of coffee costs $2.10. Your cost on the cup of coffee is $0.30. Calculate the margin per cup of coffee.
Answers
Profit margin = 1.8/2.1 x 100 = 85.71%
Answer: 85.71%
the cost of internet access at a cafe is a function of time the cost for 8, 25, and 40 minutes are shown write the equation in slope-intercept form that represents the function then find the cost of surfing the web at the cafe for one hour
Answers
Answer:
?
Step-by-step explanation:
Where is the graph?
If a bank has total deposits of $7,700 and reserves of $2,100: instructions: round to the nearest whole number. (a) what is its current reserve ratio? % (b) how large is its loan portfolio (outstanding loans)? %
Answers
b.What is the total amount of loans? _Loans = $7,500 - $2,000 = $5,500_
Calculate the taxes based on the following taxable income amounts
I really need help on this fast please!
I need the estimated taxes for each problem at the bottom is the table needed.
1) income of 90,714.00
2) income of 63,036.00
3) income of 220,596.00
4) income of 166,904.00
5) income of 220,770.00
6) income of 97,266.00
7) income of 207,264.00
8) income of 479,956.00
9) income of 511,195.00
10) income of 511,104.00
11) income of 212,817.00
12) income of 435,045.00
13) income of 655,952.00
14) income of 739,334.00
15) income of 322,335.00
Income range Taxes
From To Tax rate. Plus
0.00 8,925.00 10.0%.
8925.00 36,250.00 15.0% 892.50
36,250.00 87,850.00 25.0% 5,437.50
87,850.00 183,250.00 28.0% 21,962.50
183,250.00 398,350.00 33.0% 51,310.00
398,350.00 400,000.00 35.0%. 131,455.50
400,000.000 - 39.6%. 140.000.00
Answers
2.) Taxable income is 12,140.75
3.) Taxable income is 63,634.18
4.) Taxable income is 44,097.62
5.) Taxable income is 63,691.60
6.) Taxable income is 24,598.98
7.) Taxable income is 59,234.62
8.) Taxable income is 171,662.58
9.) Taxable income is 184,033.22
10.) Taxable income is 183,997.18
11.) Taxable income is 61,067.11
12.) Taxable income is 153,877.82
13.) Taxable income is 241,356.99
14.) Taxable income is 274,376.26
15.) Taxable income is 97,208.05
Note: Use the "from" amount as the basis, so if the income is 10,000 then you'll deduct 8,925 (basis) from 10,000 (since 10,000 is more than 8,925 but less than 36,250)
Q10 Q2.) Find the standard form of the equation of the parabola satisfying the given conditions.
Answers
1. You have that the standard form of the equation of the parabola must satisfy the following conditions given in the exercise above:
Focus: (-1,4) and Directrix: y=2
2. Therefore you have:
√(x0-(-1))²+(y0-4)²=|y0-2|
(x0+1)²+(y0-4)²=(y0-2)²
3. When you simplify the expression above and clear y0, you obtain:
y0=y
y=1/4(x²+2x+13)
y=(x²/4)+(x/2)+(13/4)
Therefore, the answer is: y=(x²/4)+(x/2)+(13/4)
what is the equation for horizontal line through the point (0,3)?
Answers
The y-intercept is three and there is no slope.
Hope this helps!
ΔABC and ΔXYZ are similar triangles. If BC = x + 7, AC = x + 6, YZ = 4 − x, and XZ = 3 − x, find the value of x.
Answers
Answer:
-3/2 or -1.5
Step-by-step explanation:
-3/2 = -1.5
BC = -1.5 + 7 = 5.5
AC = -1.5 + 6 = 4.5
YZ = 4 - (-1.5) = 5.5
XZ = 3 - (-1.5) = 4.5
A package of three compact discs cost $24.96. How much does each disc cost?
Answers
24.96/3 =8.32
A test has forty questions worth 100 points.The test consists of True/False questions worth 3 points each and multiple choice questions worth 2 points each. How many multiple choice questions are on the test?
Answers
Answer:
20 multiple choice questions
Step-by-step explanation:
I hope this help you out
given that ABCD= PQRS, find AD
A.3
B.5
C.6
D.10
Answers
AD=SP
plugging in the values we obtain:
3m-9=2m-4
solving for m we get:
3m-2m=-4+9
m=5
thus the value of AD will be:
AD=3m-9=3(5)-9=15-9=6
The answer is AD=6
which constant term would mean that the expression is completely factored x ^ 2 - 3x +
-10
0
10
Answers
To completely factorize [tex]\(x^2 - 3x + c\),[/tex]the correct constant term is 10. With this, the expression becomes [tex]\((x - 2)(x - 5)\),[/tex] achieving complete factorization.
To find the correct constant term that would allow for complete factorization of the quadratic expression [tex]\(x^2 - 3x + c\),[/tex] let's consider what it means to factorize a quadratic expression:
A quadratic expression can be factored if it can be represented in the form [tex]\((x - a)(x - b)\),[/tex] where a and b are the roots of the expression. Given the original expression [tex]\(x^2 - 3x + c\),[/tex] we can expand [tex]\((x - a)(x - b)\)[/tex] and then compare coefficients to determine the constant term c.
Expanding [tex]\((x - a)(x - b)\)[/tex] :
- [tex]\((x - a)(x - b) = x^2 - (a + b)x + a \cdot b\).[/tex]
Comparing Coefficients :
- By comparing with [tex]\(x^2 - 3x + c\),[/tex] we can identify that [tex]\(a + b = 3\)[/tex] (the coefficient for [tex]\(x\)[/tex] and [tex]\(a \cdot b = c\)[/tex] (the constant term).
- Given \(a + b = 3\), let's find possible values for a and b that would yield a correct factorization:
- Consider [tex]\(a = 1\), \(b = 2\):[/tex] Then [tex]\(a \cdot b = 1 \times 2 = 2\),[/tex] which is different from the given constant \(c\).
- Consider [tex]\(a = -2\), \(b = -5\):[/tex] Then [tex]\(a \cdot b = -2 \times -5 = 10\),[/tex] suggesting that [tex]\(c = 10.[/tex]
- Consider [tex]\(a = 5\), \(b = 2\):[/tex] Then [tex]\(a \cdot b = 5 \times 2 = 10\),[/tex] also suggesting [tex]\(c = 10\).[/tex]
Considering this process, the correct answer that would allow for complete factorization of the given expression [tex]\(x^2 - 3x + c\)[/tex] is 10:
Thus, the factorization of [tex]\(x^2 - 3x + 10\)[/tex] results in [tex]\((x - 2)(x - 5)\),[/tex] suggesting that the constant term in question should be 10.
The complete question is : Which constant term in the expression [tex]\(x^2 - 3x + c\)[/tex] would allow it to be completely factored? Consider the possible values of c and determine which would result in a fully factored form. Options: -10, 0, 10.
The correct constant term that completes the factoring of the expression [tex]\( x^2 - 3x + \ ? \)[/tex] is 10.
To find the constant term that completes the factoring of the quadratic expression [tex]\( x^2 - 3x + \ ? \)[/tex], we can follow these steps:
Understand that when factoring a quadratic expression of the form [tex]\( ax^2 + bx + c \)[/tex], we are looking for two numbers that multiply to ( ac ) and add to ( b ).
In our case, ( a = 1 ), ( b = -3 ), and ( c ) is the constant term we're looking for.
Since ( a ) is 1, we need to find two numbers that multiply to ( c ) and add up to ( -3 ).
These two numbers are the factors of ( c ).
Given that the constant term ( c ) is the term that doesn't include ( x ), it will be the product of these two factors.
To find the constant term, we can factorize the expression ( ac ), where ( a = 1 ) and ( c ) is the constant term.
Once we find the factors of ( c ), we can test different values until we find the correct one that makes the expression factorable.
Let's start by factoring ( ac ):
Since ( a = 1 ), and ( b = -3 ), we have ( ac = c ).
Given that the product of the factors should be ( c ), and the factors should add up to ( -3 ), we can find the factors of ( c ) by trial and error.
Let's try different values of ( c ) and see which one works:
If ( c = 10 ), the factors of ( c ) would be 1 and 10. However, 1 + 10 = 11, not -3.
If ( c = -10 ), the factors of ( c ) would be -1 and 10. However, -1 + 10 = 9, not -3.
If ( c = -10 ), the factors of ( c ) would be 1 and -10. However, 1 + (-10) = -9, not -3.
If ( c = 10 ), the factors of ( c ) would be -1 and -10. However, -1 + (-10) = -11, not -3.
If ( c = 0 ), the factors of ( c ) would be 0 and 0. However, 0 + 0 = 0, not -3.
Based on these trials, we see that none of the values satisfy the condition of adding up to -3.
Therefore, the correct constant term that completes the factoring of the expression [tex]\( x^2 - 3x + \ ? \)[/tex] is 10.
Which of the points listed is the same distance from the y-axis as the point (−1.5, 6)?
Answers
we know that
the distance from a point to line (y-axis) is the perpendicular line against y-axis, which is the absolute value of x-coordinates
in this problem
the point (−1.5, 6)
the absolute value of x-coordinates is 1.5
hence
the distance is 1.5
therefore
the answer is
the option B) the point (1.5,-3)
3^2·3^5·3^-3 Please help.
Answers
A cyclist rides a bicycle with a wheel radius of 0.500 m across campus. a piece of plastic on the front rim makes a clicking sound every time it passes through the fork. if the cyclist counts 320 clicks between her apartment and the cafeteria, how far has she traveled? (a) 0.50 km (b) 1.5 km (c) 1.0 km (d) 0.80 km (e) 1.8 km
Answers
circumference=2*pi*r
for r=0.50 m
circumference=2*pi*0.50-----> pi m
1 click correspond to a length of--------> pi meter
320 click---------------> x
x=320*pi-----> x=1005.31 meters-------> 1 km
the answer is
the option (c) 1.0 km
The probabilities for four different simple events are given. Of the four, which is MOST LIKELY to occur?
A. 0.5
B. 0.9
C. 0.35
D. 0.0100
Answers
100%=1 so the number closes to 1 is the most likely
we can't have a probility of more than 1 so we can say that the greatest number is most likely
if we rank the numbers we get
0.9>0.5>0.35>0.00100
so the answer is B. 0.9 which is equivilent to an 90% chance of the event occuring
the circumference of an Oreo is 6.28 inches what is the area of the top cookie?
Answers
The circumference of an Oreo is 6.28 inches what is the area of the top cookie?
Solution:
Circumference= 6.28 inches
The formula of circle =2πr
So, 2πr=6.28
2*3.14*r=6.28
6.28r=6.28
To find the value of r, Let us divide by 6.28 on both sides
6.28 r /6.28 =6.28/6.28
r=1
Area of circle=πr²
=π1²
=π
=3.14 inches²
Area of the top cookie=3.14 inches²
What is the area of the figure?
Answers
The current size of an image on Samuel's computer is shown below: A rectangle is shown. The length of the rectangle is labeled as length equal to 8 inches and the width is labeled as width equal to 10 inches. What are the dimensions of the image at fraction 1 over 2 times its current size
Answers
You can just divide each by 2.
Answer:
The length and the width of image is 4 inches and 5 inches respectively
Step-by-step explanation:
Given : Length of rectangle is 8 inches
Width of rectangle is 10 inches
To Find: What are the dimensions of the image at fraction [tex]\frac{1}{2}[/tex] times its current size
Solution:
Length of rectangle is 8 inches
Since we are given that the dimensions of the image at fraction [tex]\frac{1}{2}[/tex] times its current size
So, Length of image = [tex]\frac{1}{2} \times 8 = 4[/tex]
Thus the length of image is 4 inches.
Width of rectangle is 10 inches
Since we are given that the dimensions of the image at fraction [tex]\frac{1}{2}[/tex] times its current size
So, width of image = [tex]\frac{1}{2} \times 10 = 5[/tex]
Thus the width of image is 5 inches.
Hence the length and the width of image is 4 inches and 5 inches respectively.
John likes 400 but not 300; he likes 100 but not 99; he likes 3600 but not 3700. Which does he like?
o 900
o 1000
o 1100
o 1200
Answers
Suppose that the demand equation for a certain item is 1p+1x2−160=0. evaluate the elasticity at 65:
Answers
Here, the question has omitted to define variables, so we will ASSUME
p=price
x=variable,
and we're given
p+x^2-160=0
We calculate
[tex]\delta{x}/\delta{p}[/tex] by implicit differentiation with respect to p:
1+2x (dx/dp)=0
=>
E(x)=(dx/dp)=-1/(2x)
Therefore the price elasticity at x=65 is
E(65)=1/(2*65) =-1/130 (approximately -0.00769)
The required value of elasticity at x = 65 is -0.007.
Given that,
The demand equation for a certain item is [tex]1p + 1x^{2} -160 = 0[/tex].
We have to determine,
The value of elasticity at 65.
According to the question,
The price elasticity of demand is calculated as the percentage change in quantity divided by the percentage change in price.
Therefore,
Price of elasticity = [tex]\frac{dp}{dx}[/tex]
Calculate change by differentiation with respect to p:
[tex]\dfrac{d(p+x^{2} -160)}{dx}\\\\1 + 2x\frac{dp}{dx} = 0\\[/tex]
Then,
[tex]E(x) = \frac{dp}{dx} = \frac{-1}{2x}[/tex]
Therefore, The elasticity at x = 65 is ,
[tex]E(65) = \frac{-1}{2(65)} = -0.007[/tex]
Hence, The required value of elasticity at x = 65 is -0.007.
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5-2i and 7+6i find the midpoint
Answers
So that would be ((5+7) / 2, (-2+6) / 2) = (6, 2)
So then answer would be 6+2i
The midpoint between the complex numbers 5-2i and 7+6i is 6 + 2i.
Explanation:To find the midpoint between two complex numbers, we can use the formula:
Midpoint = (Re(z1) + Re(z2))/2 + (Im(z1) + Im(z2))/2i
Applying the formula to the given complex numbers 5-2i and 7+6i, we have:
Midpoint = (5 + 7)/2 + (-2 + 6)/2i
Midpoint = 12/2 + 4/2i
Midpoint = 6 + 2i
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Can somebody solve this system equation using addition please?
-4x-5y=7
3x+5y=-14
I can’t solve it and it’s due tomorrow for my math class also please show work on how you’ve solved it
Answers
-4x - 5y = 7
3x + 5y = -14
You can add these two equations together straightaway since the y-terms have opposite coefficients.
-4x - 5y = 7
3x + 5y = -14
+___________
-x - 0 = -7
-x = -7
x = 7
Substitute 7 for x into either of the original equations and solve algebraically to find y.
3x + 5y = -14
3(7) + 5y = -14
21 + 5y = -14
21 = -14 - 5y
35 = -5y
-7 = y
Finally, check work by substituting both x- and y-values into both original equations.
-4x - 5y = 7
-4(7) - 5(-7) = 7
-28 + 35 = 7
7 = 7
3x + 5y = -14
3(7) + 5(-7) = -14
21 - 35 = -14
-14 = -14
Answer:
x = 7 and y = -7; (7, -7).
Paisley needs 32 in of ribbon for a hair bow. The ribbon is sold by centimeters. Givin that 1 in = 2.54 centimeters, how many centimeters of ribbon does she need.
Work Pls
Thx
Answers
Multiply 32 inches by 2.54 centimeters to find how many centimeters of ribbon Paisley needs.
(32)(2.54) = 81.28
Paisley needs 81.28 centimeters of ribbon for the hair bow.
Last year 40 people adopted a manatee through Fia's Foundation.This year 30% more people adopted a manatee. How many more people adopted a manatee this year ?
Answers
[tex]30 / 100 = 0.3[/tex]
The problem can be solved with the following equation:
[tex]0.3(40) = difference[/tex]
Multiply 0.3 by 40.
[tex]0.3 * 40 = 12[/tex]
12 more people adopted a manatee this year.
What is the value of y?
11.6 ft
12.5 ft
16.5 ft
17.5 ft
Answers
in the triangle BCD
cos C=8/14
C=arc cos (8/14)-----> C=55.15°
sin C=BD/14---------> BD=14*sin 55.15------> BD=11.49 ft
in the triangle ABC
180=∡A+∡B+∡C
∡A=180-(90+55.15)-----> ∡A=34.85°
tan A=BD/y-------> y=BD/tan A-----> y=11.49/tan 34.85----> y=16.50 ft
the answer is
y=16.50 ft
1. First, you must apply the Pythagorean Theorem to calculate the heigth of the triangle, as below:
a^2=b^2+c^2
b=√(a^2-c^2)
b=√(14)^2-(8)^2
b=√132
b=11.48
2. Now, you must calculate the angle ∠BC, as below:
Sin(α)^-1=opposite/hypotenuse
Sin(BC)^-1=8/14
∠BC=34.84°
3. Therefore, the angle ∠BA is:
∠BA=90°-34.84°
∠BA=55.15°
4. Then, you have:
Tan(55.15°)=y/11.48
y=16.48
Vicente is watching a movie that last 1 hour and 37 minutes you watch 52 minutes of our how many minutes are left in the movie
Answers
Hope this helps
a band that will be the opening act for a concert charges a $700.00 flat fee as well as 16% of all ticket profits from ticket sales. if the band earned $1,200, how much was made in total ticket sales for the show?
Answers
1. Subtract the flat fee 1,200-700 =500
2. 500 is what just the band made. Divide that by .16 (16%) to get the total ticket amount... 500 divided by .16 = 3,125
The total ticket amount was $3,125.