PLZ HELP WILL GIVE 50 POINTS - QUADRATIC APPLICATIONS
find how far away (ground distance) from the catapult will white bird be at its highest. (round to the nearest 2 decimal points)
h= -0.114x^2+2.29x+3.5
Answers
Answer:
The bird will be at a ground distance of 10.04 units away.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
Equation for the height:
The height of the bird after x seconds is given by:
[tex]h(x) = -0.114x^2 + 2.29x + 3.5[/tex]
Which is a quadratic equation with [tex]a = -0.114, b = 2.29, c = 3.5[/tex].
When the bird is at its highest?
Quadratic equation with [tex]a < 0[/tex], and thus, at the vertex. The ground distance is the x-value of the vertex. Thus
[tex]x_{v} = -\frac{b}{2a} = -\frac{2.29}{2(-0.114)} = 10.04[/tex]
The bird will be at a ground distance of 10.04 units away.
Related Questions
In January I saved £10 then double the amount each month. How much would I save in April?
Answers
Answer:
$80Step-by-step explanation:
Jan >> Feb >> Mar >> Apr
x2 x2 x2
$10 >> $20 >> $40 >> $80
In a large population of adult rabbits, the mean ear length is 4.5 inches with standard deviation 1.25 inches. Suppose 16 rabbits from this population are randomly selected for an experiment. The approximate distribution of the sample mean ear length is:
Answers
Answer:
(4.5, 0.3125)
Step-by-step explanation:
given that
The mean is 4.5 inches
the standard deviation is 1.25 inches
and, the sample of 16 rabbits is selected
we need to find out the approximate distribution
so,
= (4.5, 1.25 ÷√16)
= (4.5, 0.3125)
hence, the same is to be considered
In parallelogram ABCD shown, point E and F are located on diagonal BD and point G is located on side AB such that GE and CF are perpendicular to BD. Prove: trainge BEG is similar to traingle DFC
Answers
Answer:
Match the Statement number with the Reason number.
Step-by-step explanation:
Statements:
1.GE is perpendicular to BD
CF is perpendicular to BD
2. Angle GED equal 90
Angle DFC equal 90
3. Angle GED is congruent to Angle DFC
4. Angle GBE is congruent to Angle FDC
5. Triangle BEG is similar to DFC
Reasons:
1.Given
2. Definition of perpendicular lines
3. Transitive property
4. Alternate Interior Angles
5. AA Similarity
By satisfying essential conditions for two triangles to be similar, we can say that triangle BEG is similar to triangle DFC.
What is a parallelogram?A quadrilateral in which opposites sides are equal and parallel. Also, opposite angles are equal to each other.
As we know that AB║ DC
so,∠GBE = ∠CDF (alternate angles)
∠GEB= ∠DFC = 90°
so triangle BEG≈DFC
Therefore, we can say that triangle BEG is similar to triangle DFC
to get more about parallelograms visit:
https://brainly.com/question/12167853
What are the equation and slope of the line shown on the grid ?
F y = 6; slope is zero
G x = 6; slope is zero
H y = 6; slope is 6
J x = 6; slope is undefined
Answers
Answer:
The answer is J x= 6; slope is undefined
Step-by-step explanation:
iTS undefined because it's a line
The answer is J
The reason the line is unidentified is because it is going straight up and the slope is unable to be determined.
please helpppppppppppppp
Answers
Answer=A
Area=Length ×Breath
Length=2cm
Breath=5cm +4cm=9cm
area = 2cm ×9cm=18cm square
(5,-10) and (15,-20). find the equation of this line.
Answers
Answer:
y = -x-5
Step-by-step explanation:
slope of the line is =(-20+10) / (15-5) = -10/10 = -1
Now equation of line is y+10=(-1)(x-5)
i.e. y+10= -x +5
i.e y = -x-5
Answer:
y = -x - 5.
Step-by-step explanation:
The slope of the line is (-20-(-10) /(15-5)
= -10/10 = -1.
Now use the point slope form of a straight line:
y - y1 = m(x - x1) where m = the slope and (x1, y1) is a point on the line.
So we have:
y - (-10) = -1(x - 5)
y + 10 = -x + 5
y = -x + 5 - 10
y = -x - 5.
What is the volume of the cone below?
O A. 396pie units 3
O B. 132 units 3
O C. 792pie units3
O D. 264pie units 3
Answers
Answer:
D. 264π units³
Step-by-step explanation:
1/3(πr²h)
1/3(π•6²•22)
1/3(π•36•22)
1/3(π•792)
264π
27
Sara is considering purchasing a certain stock. After doing her research, she determins that there is a 68%
chance of making $3,500 and a 32% of losing $1,800. Find the expected value of this purchase.
1
$2,158
$2,956
$1,804
$3,071
Answers
PLEASE HELP!!! CALCULUS ASSIGNMENT
Answers
Answer:
(d) [tex]\displaystyle 12x^3 - 15x^2 + 2[/tex]
General Formulas and Concepts:
Algebra I
FunctionsFunction NotationCalculus
Derivatives
Derivative Notation
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = 3x^4 - 5x^3 + 2x - 1[/tex]
Step 2: Differentiate
Basic Power Rule: [tex]\displaystyle y' = 4(3x^{4 - 1}) - 3(5x^{3 - 1}) + 2x^{1 - 1} - 0[/tex]Simplify: [tex]\displaystyle y' = 4(3x^3) - 3(5x^2) + 2[/tex]Multiply: [tex]\displaystyle y' = 12x^3 - 15x^2 + 2[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
Answer:
( d ) 12x³ - 15x² + 2
Step-by-step explanation:
y = 3x⁴ - 5x³ + 2x - 1
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of axⁿ is nax^{n-1}.[tex] \small \sf \: y = 4\times 3x^{4-1}+3\left(-5\right)x^{3-1}+2x^{1-1} [/tex]
multiply 4 × 3.[tex] \small \sf \: y = 12x^{4-1}+3\left(-5\right)x^{3-1}+2x^{1-1} [/tex]
Multiply 3 × -5[tex] \small \sf \: y = 12x^{3}-15x^{3-1}+2x^{1-1} [/tex]
subtract the exponentsy = 12x³ - 15x² + 2⁰
For any term t except 0, t⁰ = 1.y = 12x³ - 15x² + 2 × 1
y = 12x³ - 15x² + 2
Hence, option ( d ) is the correct answer.
The sales tax rate is 10%. If Kamal buys a gold ring priced at $391, how much tax will he
pay?
Round your answer to the nearest dollar: $
Answers
Answer: $39
Step-by-step explanation: Actual answer is $39.1 but I rounded down
Michele correctly solved a quadratic equation using the quadratic formula as shown below.
Which could be the equation Michele solved?
A.
B.
C.
D.
Answers
Can someone explain why the ans is X=6? Its (x-6)
Answers
Answer:
because either x-6=0 or x+1=0
x-6=0
x=0+6
x=6 OR,
x+1=0
x=0-1
x=-1
Step-by-step explanation:
At a concession stand, seven hot dog(s) and four hamburger(s) cost $15.00; four hot dog(s) and seven hamburger(s) cost $18.00. Find the cost of one hot dog and the cost of one hamburger.
Answers
Answer:
hotdog $1, and hamburger $2
Step-by-step explanation:
D-is hot dogs, H-hamburgers
7D +4H = 15
4D +7H = 18
we got 2 equations with 2 unknown so we can solve
7D +4H = 15 multiply by 7
4D +7H = 18 multiply by -4
49D +28H = 105
-16D -28H = -72 add the two equations
33D= 33 so D=$1
go back to the first equation:
7*1 +4H =15 gives us 4H = 15-7; 4H = 8 so H= $2
What does 7 x 1/3 equal to
Answers
[tex]7 \times \frac{1}{3} \\ \\ = \frac{7 }{3} [/tex]
I need help on this question
Answers
Answer:
A
Step-by-step explanation:
The area of a parallelogram is 120 cm ^ 2 and the height is 30 cm . Find the corresponding base
Answers
Answer:
4 cm
Step-by-step explanation:
The Area of a parallelogram is given by :
Area = base * height
Area = 120 cm² ; height = 30
Area = base * height
120 = base * 30
Base = 120 / 30
Base of parallelogram = 4 cm
Answer this please Help
Answers
Answer:
x=10.75 in
Step-by-step explanation:
A = 390 = x(3x+4)
3x²+4x-390 =0
ax²+bx+c=0
x= (-b±√b²-4ac)/2a
x= (-4±√(16+4680))/6 = (-4±2√1174)/6 = (-2±√1174)/3
We will consider only the x that gives us a positive answer because the dimensions cannot be negative.
x= (-2+√1174)/3 = 10.75456113≈ 10.75
X=10.75
tessa burned 357 calories in 42 minutes on the elliptical. ashley only spent 0 minutes on the elliptical and burned 267 calories. who burned calories at a faster rate
Answers
Answer:
ashley
Step-by-step explanation:
because she didnt spend any time
Determine the area of the figure. Note that each unit is one unit in length.
Answers
Answer:
nao sei ispoosksjjdkdddks
Answer:
54
Step-by-step explanation:
Split into 2 rectangles and 2 triangles and calculate area
Pete can type 80 words in the same time that Ralph can type 50 words. If they type at those rates
for an extended period of time, when Ralph has typed 4000 words, how many words has Pete
typed?
Answers
Answer:
After the extended period of time, Pete would have typed 6400 words.
Step-by-step explanation:
Given the data in the question;
In the same time;
number typed word of Pete = 80
type word of Ralph = 50
After a period time;
number of typed word of Pete = ?
number of typed word of Ralph = 4000
so, let x represent the number of typed word by Pete after an extended period.
so
80 words = 50 words
x words = 4000 words
we cross multiply
x × 50 = 4000 × 80
x = ( 4000 × 80 ) / 50
x = 320000 / 80
x = 6400
Therefore, After the extended period of time, Pete would have typed 6400 words.
The mean life expectancy of a certain type of light bulb is 945 hours with a standard deviation of 21 hours. What is the approximate standard deviation of the sampling distribution of the mean for all samples with n
Answers
Answer:
The approximate standard deviation of the sampling distribution of the mean for all samples of size n is [tex]s = \frac{\sigma}{\sqrt{n}} = \frac{21}{\sqrt{n}}[/tex]
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The mean life expectancy of a certain type of light bulb is 945 hours with a standard deviation of 21 hours
This means that [tex]\mu = 945, \sigma = 21[/tex].
What is the approximate standard deviation of the sampling distribution of the mean for all samples of size n?
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{21}{\sqrt{n}}[/tex]
The approximate standard deviation of the sampling distribution of the mean for all samples of size n is [tex]s = \frac{\sigma}{\sqrt{n}} = \frac{21}{\sqrt{n}}[/tex]
Is this correct. Please let me know thank you
Answers
Answer:
Yes it is correct, the amount of flour is 1.5 times larger than eggs needed
Step-by-step explanation:
Which point is located at (2, -5)?
Answers
Answer:
J
Step-by-step explanation:
Go to the right 2 units from the origin (0,0) and then down 5 units
The point at that location is J
6. Two linear equations are shown in the graph.
*(0.6)
(6,5),
COD).
(6.0)
dat
35344
tett
What are the coordinates of the point where the two lines intersect?
A. (-2, 3)
B. (3, 0)
C.(-3.3)
D. (3, 3)
Mark for review (Will be highlighted on the review page)
Alaviation
Answers
Answer:
(3,3)
Step-by-step explanation:
Linear equations of lines are given in the form:
y = mx + b;
where m is the slope of the line, b is the y intercept and x, y are variables.
From the graph, we can see that line 1 passes through (0,6) and (6,0) while line 2 passes through (0, 1) and (6, 5).
The equation of line 1 is given as:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-6=\frac{0-6}{6-0} (x-0)\\\\y=-x + 6\ \ \ (1)[/tex]
The equation of line 2 is given as:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-1=\frac{5-1}{6-0} (x-0)\\\\y=\frac{2}{3}x + 1\ \ \ (2)[/tex]
Solving equation 1 and 2 simultaneously by subtracting equation 1 from 2 gives:
(5/3)x - 5 = 0
(5/3)x = 5
x = 3
Put x = 3 in equation 1:
y = -3 + 6 = 3
Therefore the two lines meet at (3, 3).
Witch property is NOT true of all rhobuses
Answers
Answer:
Hide Explanation. All sides of the rhombus are equal. The opposite sides of a rhombus are parallel. Opposite angles of a rhombus are equal.
0.199999 a fraccion porfavor
Answers
Answer:
199999/1000000
Step-by-step explanation:
50 PTS AND BRAINLIEST FOR CORRECT ANSWER
Answers
Answer: I asked my teacher, she said it is c
Step-by-step explanation:
Answer:
yes it's c
have a great day
10 POINTS
Which statement best describes the expression 2 + 3 ÷ y?
a. The sum of 2 and the quotient of 3 and y
b. The sum of 2 and the quotient of y and 3
c. The quotient of y and the sum of 2 and 3
d. The quotient of the sum of 2 and 3, and y
Answers
Answer:
a. The sum of 2 and the quotient of 3 and y
Step-by-step explanation:
a. The sum of 2 and the quotient of 3 and y
Find the sum of the first four terms of the geometric series 2 + 1 +....
Answers
Answer:
15/4
Step-by-step explanation:
This is a geometric sequence with a common ratio of 1/2. Therefore, the sum of the first four terms of the geometric sequence is 2 + 1 + 1/2 + 1/4 = 15/4.
What is the value of X equal?
Answers
Answer:
113º
Step-by-step explanation:
(x + 14) + (180 - 83) + x + 90 + x = 540
3x + 201 = 540
3x = 339
x = 113