Answer:
18.25 feetStep-by-step explanation:
The given function is quadratic.
The maximum of the quadratic function is its vertex.
The x-coordinate is determined by x = - b/(2a)
x = - 20/(-16*2) = 5/8Apply the x-value and find the value of f:
f(x) = - 16(5/8)² + 20(5/8) + 12 = 18.25 feetAnswer:
18.25
Step-by-step explanation:
we are given a quadratic function
[tex] f(x) = - 16 {x}^{2} + 20x + 12[/tex]
where:
f(x) represents the heightx represents the timeTo find the maximum value of f(x) in other words, the maximum height, in feet, reached by the arrow.
Differentiate both sides:
[tex] f'(x) = \dfrac{d}{dx}( - 16 {x}^{2} + 20x + 12)[/tex]
with sum differentiation rule, we acquire:
[tex] \displaystyle f'(x) = \frac{d}{dx}( - 16 {x}^{2} )+ \frac{d}{dx} 20x + \frac{d}{dx} 12[/tex]
recall that,
differentiation of a constant is equal to 0[tex] \dfrac{d}{dx} {x}^{n} = n {x}^{n - 1} [/tex]utilizing the rules we acquire:
[tex] \displaystyle f'(x) = - 32 {x}^{} + 20 [/tex]
now equate f'(x) to 0:
[tex] \displaystyle - 32 {x}^{} + 20 = 0[/tex]
solving the equation for x yields:
[tex]x _{max}= \dfrac{5}{8} [/tex]
plug in the maximum value of x into the quadratic function:
[tex]f(x )_{max}= - 16 {( \frac{5}{8} )}^{2} + 20( \frac{5}{8} ) + 12[/tex]
simplify:
[tex]f(x )_{max} = 18.25[/tex]
hence,
The maximum height reached by the arrow is 18.25 feet
find the 39th term for the aritmethic sequence, 10,15,20
The 39th term of the sequence is 200.
What is Arithmetic Sequence?Arithmetic sequence or arithmetic progression is the set of numbers for which the difference of any two consecutive numbers in that set will be a constant.
The constant term which is the difference of the two consecutive numbers is called the common difference and is usually denoted by 'd'.
Arithmetic sequence is usually represented as
a, a + d, a + 2d, ........, a + (n - 1)d
The nth term of an arithmetic sequence, aₙ is given by the formula,
aₙ = a + (n - 1) d
where, a is the first term and d is the common difference.
The given sequence is 10, 15, 20, ......
a = 10
d = 15 - 10 = 5
Here, we have to find the 39th term of the sequence.
a₃₉ = 10 + (39 - 1) 5
= 10 + (38 × 5)
= 10 + 190
= 200
Hence, the 39th term of the progression 10, 15, 20,..... is 200.
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pls help me in this math problem
Answer:
cUse the following equation
Step-by-step explanation:
Because of the way these angles are positioned, they must be equal to 180 together
(2x + 5) + (0.5x + 150) = 180
2.5x + 155 = 180
- 155 - 155
2.5x = 25
2.5x/2.5 = 25/2.5
x = 10
Put x into the original equations and solve
Find a function for the graph below.
a. f(t) = 3 cos 41
b. ft) = 8 sin 3t
fit) = 3 sin 41
d. (t) = 3 cos 6
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
The given function has Amplitude of 3, and by seeing it we can conclude that it's a sine function.
Therefore, we can conclude that the required Answer is ~
[tex]\qquad \sf \dashrightarrow \:c. \: f(t) = 3 \sin(4t) [/tex]
The sinusoidal function is represented as y = 3 sin 4t. Then the correct option is C.
What is a sinusoidal Function?It is a function that repeats itself in a particular time interval.
The sine function is given as
y = A sin (wt + Ф)
where A is the amplitude, w frequency, and Ф is the phase difference.
From the graph, the value of the amplitude will be 3, the frequency will be 4, and the phase difference will be 0. Then the equation will be
y = 3 sin4t
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The area of'a rectangular piece of cardboard is 108 em and its length is 18em. Find the width of the cardboard
Answer:
I think you meant cm, not em. So the answer is 6 cm.
Step-by-step explanation:
18cm x 6cm = 108 cm
How much would $400 be worth after 6 years if it was invested at 2% interest compounded annually
450.46497
Step-by-step explanation:Based on the given condition:[tex]We\ know\ that:[/tex]
[tex]\left\{\begin{matrix}P=400\\r=2\%\\n=1\\t=6\\\end{matrix}\right.[/tex]
________________________________________________
Formulate and substitute:[tex]Substitute[/tex] [tex]\left\{\begin{matrix}P=400\\r=2\%\\n=1\\t=6\\\end{matrix}\right.[/tex][tex]into\ formula[/tex]
[tex]F=P*(1+r/n)^n^t\\ F=400\bullet(1+2\bullet\frac{1}{100})^6[/tex]
_________________________________________________
Evaluate[tex]Evaluate\ the\ equation/expression:\\ 450.46497[/tex]
I hope this helps you
:)
A scale model of a ramp is a right triangular prism as given in this figure. In the actual ramp, the triangular base has a height of 0.5 yards.
What is the surface area of the actual ramp, including the underside?
Enter your answer as a decimal in the box.
yd²
Right triangular prism. Each base is a triangle whose legs are 13 in, 13 in, and 24 in. The height of the triangles is 5 in. The prism is oriented so that the side labeled 24 in is on the bottom. The distance between the bases is labeled 12 in.
Answer:
The answer is 7.2
The surface area of the actual ramp, including the underside is 16.8 ft²
H1 = 1.2 feet (height of the actual ramp)
and, H2 = 6 cm (height of the model)
The scale factor (k) is:
k = 1.2 feet / 6 cm
k = 0.2 ft/cm
The actual measurements would be:
16cm = 16 cm x 0.2 ft/cm = 3.2 ft
and, 9 cm = 9 cm x 0.2 ft/cm = 1.8 ft,
and, 10 cm = 10 cm x 0.2 ft/cm = 2 ft,
So, the surface area is
Area = 2(0.5 x 3.2 ft x 1.2 ft) + 2(2 ft x 1.8 ft) + (1.8 ft x 3.2 ft)
Area = 16.8 ft²
Hence, the surface area of the actual ramp is 16.8 ft²
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If HI = IJ = 14 and GH = 12, what is HJ?
Answer:
24 unitsStep-by-step explanation:
Missing drawing but assumed that:
HI and IJ are equal sides of the isosceles triangle HIJIG is the perpendicular bisector of same triangleSince G is the midpoint of HJ, we have:
GH = GJ = 12So
HJ = 2*GH = 2*12 = 24Answer:
24 units
Step-by-step explanation:
IJ = 14 and GH = 12
Gh=gj=12
Hj=2gh
2*12=24
The longest worm is blank times as long as the shortest worm
An artist has completed 1/4
of a penting in 2 weeks. At what rate is she working?
Answer:
1/8
Step-by-step explanation:
1/4 ÷ 2 = 0.125
0.125 as a decimal is 1/8
Y varies inversely as x: y=13, when x=3
Answer:
I'm not to sure of this answer
In your own words describe how to find the perimeter of a shape with fractional sides used the rectangle below to example
Answer:
U add both side of the shape to get the fractional
Step-by-step explanation:
I just did this not to long ago
what is the effect on the graph of y=-2x+7 if the slope changes to 2
The data set below represents the different costs of a refrigerator at a local home improvement store.
$777, $498, $619, $379, $895, $1,256, $1,052
a. What is the median of the first half of the data? (first quartile)
The price of the refrigerators that is the median for the first half of the data is $498.
What is the median of the first half of the data?Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order
The prices arranged in ascending order is: $379, $498, $619, $777, $895, $1052, $1256
The first half of the prices are $379, $498, $619,
Median = $498
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How can I find the value of X?
Answer:
D
Step-by-step explanation:
Remark
The first thing you must do is notice that <D = <BEA. Mark it that way on your diagram.
The Second thing you need to notice is that <BEA and <A are equal because <A and <D are marked as equal.
So both the large triangle and the small one are isosceles. because 2 of the 3 angles are equal.
Now are you ready for this? That means that BA = 10 because BA is opposite one of the 2 equal angles in the small triangle. So now you are ready to set up a proportion.
Proportion
AB / AC = AE/AD
Givens
AB = 10
AC = 18
AE = 8
AD = x + 8
Solution
Substitute the Givens into the Proportion.
10/18 = 8/(x + 8) Cross multiply
10(x + 8) = 8 * 18 Simplify both sides
10x + 80 = 144 Subtract 80 from both sides
10x + 80 - 80 = 144 - 80
10x = 64 Divide by 10
10x/10 = 64/10
Answer: x = 6.4
how do I not know 4th grade math I really am 0iq
Answer:
C) 8 sheets of red and 13 sheets of yellow felt
Step-by-step explanation:
Red felt
Red felt needed for 1 toy = 3/8 sheet
⇒ Red felt needed for 20 toys = 20 × 3/8 sheets
[tex]\sf \implies 20 \times \dfrac38=\dfrac{20}{1}\times \dfrac38=\dfrac{20 \times 3}{1 \times 8}=\dfrac{60}{8}=7\frac12[/tex]
Therefore, 8 complete sheets of red felt are needed.
Yellow felt
Yellow felt needed for 1 toy = 5/8 sheet
⇒ Yellow felt needed for 20 toys = 20 × 5/8 sheets
[tex]\sf \implies 20 \times \dfrac58=\dfrac{20}{1}\times \dfrac58=\dfrac{20 \times 5}{1 \times 8}=\dfrac{100}{8}=12\frac12[/tex]
Therefore, 13 complete sheets of yellow felt are needed.
A company interviewed 21 applicants for a recent opening. Of these applicants, 7 wore blue and 6 wore white, while 5 applicants wore both blue and white. What is the number of applicants who wore neither blue nor white?
A.1
B.6
C.12
D.13
Answer: D
Step-by-step explanation:
21=7+6+neither-5
7+6=13-5=8
21-8=13
→ 12 cm.
3,5cm.
16cm.
>3.5cm.
Find the total
Volume.
Can someone please help me
Answer:
Step-by-step explanation:
CONE:
height of cone = h = 12 cm
r =3.5 cm
[tex]Volume \ of \ cone =\dfrac{1}{3}\pi r^{2}h[/tex]
[tex]=\dfrac{1}{3}*\dfrac{22}{7}*3.5*3.5*12\\\\\\=22*0.5*3.5*4\\\\= 154 \ cm^{3}[/tex]
Cylinder:
h = 16 cm
r = 3.5 cm
[tex]Volume \ of \ cylinder = \pi r^{2}h\\[/tex]
[tex]= \dfrac{22}{7}*3.5*3.5*16\\\\\\= 22*0.5*3.5*16\\\\= 616 \ cm^{3}[/tex]
Total volume = 154 + 616
= 770 cm³
Please help! Consider the given circle with the shaded sector xy and central angle 225. The circumference is 30 units
[tex]\textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=30\pi \end{cases}\implies 30\pi =2\pi r\implies \cfrac{30\pi }{2\pi }=r\implies \boxed{15=r} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=15\\ \theta =225 \end{cases}\implies \widehat{XY}=\cfrac{(225)\pi (15)}{180}\implies \boxed{\widehat{XY}\approx 58.90} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad \qquad A=\pi (15)^2\implies A=225\pi \implies \boxed{A\approx 706.86}[/tex]
Jeremiah answered 20 out of 25 questions correctly on the math test. What percent of the questions did Jeremiah answer correctly?
Answer, explain and setup problem.
estimate the product 8.1 times 4.2
Answer:
Approximately 32
Step-by-step explanation:
8.1 is closest to 8
4.2 is closest to 4
Thus, you can estimate the product to be 8*4=32
The actual product is 8.1*4.2=34.02, so it's about 2 greater than the estimated product
100+200x300=what is the answer
Answer:
100+200×300 = 60100
Step-by-step explanation:
According to the BODMAS, the order to solve any question is as follows
B - Brackets
O - Order
D - Division
M - Multiplication
A - Addition
S - Subtraction.
in the above expression Addition and multiplication two different operations are functioning. According to BODMAS the multiplication expression will be solved first, that outputs.
200×300 = 60000
after calculating correctly we have to operate second function i.e. addition and add 100 to the above result,
60000+100 = 60100
[tex]{Answer = 60100}[/tex]
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The collection of all equally likely outcomes is known as the
Answer:
The Sample space
Step-by-step explanation:
The collection of all equally likely outcomes is known as the- the sample space.
I need help with this question
Answer:
Length: 20, Width=34
Step-by-step explanation:
Say the length of the width is w, and the length of the length is l. Then, we can establish an equation of W=2L-6. Since the area of a rectangle is W*L, we can substitute W with 2L-6. If we multiply 2L-6 and L, we get [tex]2L^{2} -6L[/tex]=680. We can simplify this equation by dividing everything by 2. We then get [tex]L^{2}-3L=340[/tex]. If we solve for L, we get 20. Now, we plug 20 into the equation, W=2L-6. Since W=2(20)-6, which simplifies to W=40-6 which is 34, we get a width of 34.
Hope this helps
Help help help help ASAP apa
Answer:
A=49.12
Step-by-step explanation:
The area of the figure=
Area of the triangle + area of the semicircle.
Area of the triangle=
½×the base × the height=
½×6×8=
24ft.
Area of the semicircle=
½πr²=½×3.14×4²=
25.12ft.
Area of the figure=
24+25.12=
49.12ft
The function h(x) is a transformation of the square root parent function,
f(x) = V. What function is h(x)?
Answer:
Step-by-step explanation:A. h(x) = √(x-2)
Step-by-step explanation:
To translate a function right by p units and up by q units, the function becomes ...
g(x) = f(x -p) +q
Here, there is no translation upward, but there is a translation of 2 units to the right. The transformed function's name is given as h (not g), so you have ...
(p, q) = (2, 0)
h(x) = f(x -2) +0
h(x) = √(x -2)
The function h(x) , a transformation of the parent function f(x) = √x is √(x+1). Option A is correct option.
What is transformation of a function?The transformation of the function is a function that curves a graph formed by the moving the original graph to left / right / up / down or by expansion or compression.
The transformation is of type horizontal shift when the curve moves to left or right. For y = f(x) , when this curve moves left or right the transformation is given by y = f(x +c), c > 0 moves y=f(x) to the left by c units
and if c < 0 , moves y =f(x) to the right by c units
Given that the graph of the f(x) = √x by dotted line and the graph of its transformation h(x) given by solid line.
h(x) is clearly formed by moving f(x) one units to the left as it is moved to left by 1 on origin
Then transformation of y =f(x) moving one unit to left will be given by
y = f(x+1) =√(x+1)
Therefore , transformation h(x) of f(x) is h(x) =√(x+1) and option A is correct option.
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Which statements are true about the figure? Check all that apply.
A net has 3 rectangular faces and 2 triangular faces.
The figure is a triangular prism.
The figure is a rectangular pyramid.
The figure has 6 vertices.
The figure has 6 faces.
The figure has 9 edges.
Answer:
Step-by-step explanation:
The figure is a triangular prism.
The figure has 6 vertices.
The figure had 9 edges.
Vertex: The meeting point of two edges is called vertex
Edge: The meeting point of two faces is called an edge.
Please Help.........
What is the equation of the given line in the point-slope form?
A.
= - + 1
B.
+ = 1
C.
+ + 1 = 0
D.
4 = 3 + 1
E.
– 4 = 1( – 3)
[tex]============================[/tex]
First, let's use the Slope Formula to find the slope:
[tex]\pmb{\displaystyle\frac{y2-y1}{x2-x1} }[/tex]
[tex]\pmb{\displaystyle\frac{4-1}{3-0} }[/tex]
[tex]\pmb{\displaystyle\frac{3}{3}}[/tex]
Which simplifies to
[tex]\pmb{1}[/tex]
So the slope is 1.
Now, here's a point that the line passes through:
(0, 1)
Write the equation in point-slope form:
[tex]\pmb{y-y1=m(x-x1)}[/tex]
y-1=1(x-0)
================================================
note:-Hope everything is clear; if you need any more clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)
6/5 + ? = 27/10? Help me pls
[tex]\cfrac{6}{5}~~ + ~~\boxed{?}~~ = ~~\cfrac{27}{10}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{10}}{10\left( \cfrac{6}{5}~~ + ~~\boxed{?} \right)~~ = ~~10\left( \cfrac{27}{10} \right)}\implies 12+10\boxed{?}=27 \\\\\\ 10\boxed{?}=15\implies \boxed{?}=\cfrac{15}{10}\implies \boxed{?}=\cfrac{3}{2}[/tex]
Use the digital text feature to complete the explanation: The 24th Amendment states that citizens of the United States will not be stopped from voting if
they are sick or elderly
Othey are guilty of a crime
Othey are in a political office
Othey do not pay their taxes
D or A not sure
The Twenty-fourth Amendment (Amendment XXIV) of the United States Constitution prohibits both Congress and the states from conditioning the right to vote in federal elections on payment of a poll tax or other types of tax.
Answer:
(D) they do not pay their taxes
Step-by-step explanation:
I got it correct on an exam I did.
find the second derivative of 2x^3-3y^2=8
Answer:
[tex]\frac{d^2y}{dx^2}=\frac{x(2y-x^3)}{y^3}[/tex]
Step-by-step explanation:
Find the first implicit derivative using implicit differentiation
[tex]2x^3-3y^2=8\\\\6x^2-6y\frac{dy}{dx}=0\\ \\-6y\frac{dy}{dx}=-6x^2\\ \\\frac{dy}{dx}=\frac{x^2}{y}[/tex]
Use the substitution of dy/dx to find the second derivative (d²y/dx²)
[tex]\frac{d^2y}{dx^2}=\frac{(y)(2x)-(x^2)(\frac{dy}{dx})}{y^2}\\ \\\frac{d^2y}{dx^2}=\frac{2xy-(x^2)(\frac{x^2}{y})}{y^2}\\\\\frac{d^2y}{dx^2}=\frac{2xy-\frac{x^4}{y}}{y^2}\\\\\frac{d^2y}{dx^2}=\frac{x(2y-x^3)}{y^3}[/tex]