Answer:
(i) [tex]64+192 x^2+240 x^4+160x^6[/tex]
(ii) 1072
Step-by-step explanation:
Part (i)
Using Binomial series formula:
[tex](2+x^2)^6=2^6+6C1 \cdot 2^{6-1}\cdot x^2+6C2 \cdot 2^{6-2}\cdot(x^2)^2+6C3 \cdot 2^{6-3}\cdot(x^2)^3[/tex]
[tex]=64+6 \cdot 32\cdot x^2+15 \cdot 16\cdot x^4+20 \cdot 8 \cdot x^6[/tex]
[tex]=64+192 x^2+240 x^4+160x^6[/tex]
Part (ii)
[tex](1-\frac{3}{x^2})^2=(1-\frac{3}{x^2})(1-\frac{3}{x^2})[/tex]
[tex]=1-\dfrac{6}{x^2}+\dfrac{9}{x^4}[/tex]
[tex](2+x^2)^6(1-\frac{3}{x^2})^2=(64+192 x^2+240 x^4+160x^6)\left(1-\dfrac{6}{x^2}+\dfrac{9}{x^4} \right)[/tex]
[tex]=64-\dfrac{384}{x^2}+\dfrac{576}{x^4}+192x^2-1152+\dfrac{1728}{x^2}+240x^4-1440x^2+2160+...[/tex]
There is no need to keep expanding since the remaining will include the variable.
Therefore, the term independent of x = 64 - 1152 + 2160 = 1072
A Goodyear Blimp is positioned at a height of 1,500 feet over the M&T
Bank Stadium to broadcast the Baltimore Ravens game. The blimp is
observed by a car of fans as they look upward at an angle of 22º.
Another car closer to the stadium can see the blimp if they look
upward at an angle of 65º.
DEOOV
כשע
Figure not
drawn to scale
1500 ft
65
22
x ft.
Determine x, the distance between the two cars.
The distance between two cars comes to be 4412.06 feet.
Find the attached diagram to visualize it better.
From the attached diagram
The Distance between two cars is x+y
The angle of elevation for the first car = 22 degrees
The angle of elevation for the second car = 65 degrees.
Height of the Goodyear blimp = 1500 feet
What is the tangent of an angle?The tangent of an angle is the ratio of the opposite side to the adjacent side of that angle.
So, tan 22° = 1500/x
So, x= 1500/tan 22°
x = 3712.63 feet
tan 65° = 1500/y
So, y = 1500/tan 65°
y = 699.46 feet
x+y = 4412.06 feet
So, the distance between two cars = 4412.06 feet
Therefore, the distance between two cars comes to be 4412.06 feet.
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Write the value of (2 +√ 2) (2 -√3)
[tex]\left(2 + \sqrt 2 \right)\left(2-\sqrt 3 \right)\\\\=4- 2\sqrt 3 + 2 \sqrt 2 - \sqrt 6\\\\=0.91484.....[/tex]
Two of the interior angles of a triangle are 84.0° and 30.0. Find the measure of the
third interior angle in degrees to one decimal place.
Answer:
66.0°
Step-by-step explanation:
The sum of the measures of the interior angles in a triangle is 180°.
Let "x" represent the measure of the third interior angle. We can use this to set up an equation:
84.0° + 30.0° + x = 180°
Add like terms:
114.0° + x = 180°
Subtract 114.0° from both sides:
x = 66°
The question asks for the answer to be in degrees to one decimal place, therefore:
x=66.0°
on
Find the distance between -1/2 and 1 2/3
on
a number line.
units
Answer:
Step-by-step explanation:
1 2/3 -(-1/2)
=5/3+1/2
[tex]=\frac{10+1}{6} \\=\frac{11}{6} \\=1\frac{5}{6}[/tex]
Let y=6 and z=2. Translate “z less than y” into an algebraic expression and solve it
Answer:
y - z; 6 - 2; 4
Step-by-step explanation:
z less than y means subtract z from y
y - z
Substitute the given values.
6 - 2
4
if f(-3)=14 what would be the equation for f(x)
Answer:
Step-by-step explanation:
if quadratic
(-3)²+5=9+5=14
so f(x)=x²+5
or
if linear
(-3)+17=14
f(x)=x+17
if cubic
(-3)³-2(-3)²-3(-3)+14=14
f(x)=x³-2x²-3x+14
so on.
Felix is dividing 322 by 12. He says the answer is going to be smaller than 322.
Do you agree with him and why?
Answer: Because dividing means to split into smaller groups
Solve For X.
6x + 9 - 4x = -3
Answer:
x = -6
Step-by-step explanation:
6x + 9 - 4x = -3
2x +9 = -3
2x = -12
x = -6
If line segment AB is 400%, what is the length of a line segment that is 100%?
the length of the line would be 1 inch
CAN SOMEBODY HELP ME PLEASE
Answer:
(A) P(t) = 220t - 435 390
(B) predicted moose population = 6370
Step-by-step explanation:
the longer working shows the explanation and working for part A while the shorter working is for part B
the ratio of the corresponding edge lengths of two similar solids is 4;9 what is the ratio of their volume ?
Answer:
Do the math
Step-by-step explanation:
If you do the math you get answer
Find all the factors of 12.
A) 2, 3, 4, 6
B) 2, 3, 4, 6, 12
C) 1, 2, 3, 4, 6, 12
Answer:
1, 2, 3, 4, 6, and 12, because each of those divides 12 without leaving a remainder (or each of those is a counting number that can be multiplied by another counting number to make 12).
Step-by-step explanation:
hope this helps.
What is the mean (average) of
a, a, b, b, b,c
Answer:
Ans might be a+b+c
Step-by-step explanation:
Hope the picture will help
What does Opie create with simple geometric shapes and lines?
A. Facial features
B. Eyes and ears
C. The portrait's hair
D. The shape of the bust
Opie created facial features with simple geometric shapes and lines. Option A
Who is Julian Opie?
Julian Opie is a known as a renowned British artist known for his distinctive depictions of figures, portraits, and landscapes.
His earliest works was the painted steel sculptures, domestic appliances, architectural structures and geometrical shapes showing the relationship between visual and spatial observation
He created distinct facial shapes and forms on a flat surface by means of lines, colors and shadings.
Thus, Opie created facial features with simple geometric shapes and lines. Option A
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Can Someone Assist Me Please? It would be much appreciated
Ya sure.... What's your doubt?
how many part time and full time employees does the company have?
Answer:
there are 36 part time employees and there are 144 full time employees
Step-by-step explanation: multiply 45 by 4
then multiply 180 by 0.2 to get 36 and 180 by 0.8 and get 144
Hey ! Can anyone help me solve these problems please. Thank you !
[tex] \qquad\begin{gathered} \begin{array}{ ||c|| c} \hline \\ \textsf { \huge{ \underline{lets\: \: solve}}} \\ \\ \: \: \sf6. \: \underline{ find \: measure \: of \: angle \: TSR}\: \: \\ \\ \textsf {As we know, diameter subtends 90° } \\ \textsf{ at an arc of same circle.} \\ \textsf{ hence we can conclude that :} \\ \\ \rm{ \therefore\angle \:TSR = 90 \degree } \\ \\ \\ \sf7. \: \underline{ find \: measure \: of \: angle \: subtended }\\ \: \underline{ \sf by \: arc \: ST \: at \: the \: centre \: of \: circle}\: \\ \\ \\ \textsf{Angle subtended by an arc at centre} \\ \textsf{ of the circle is double the angle} \\ \textsf{ subtended by the same arc on other } \\ \textsf{ part of circle, hence we can} \\ \textsf{conclude that :} \\ \\ \sf\angle SOT =2 \angle SRT \\ \\ \angle \sf SOT =2 \times 41\degree \\ \\ \sf \therefore\angle SOT = 82 \degree \\ \\ \\ \\ \hline \end{array} \end{gathered}[/tex]
b^2 – 4ac if a = 2, b = 9, and c = 4
Answer:
49
Step-by-step explanation:
[tex](b)^{2} - 4(a)(c) \\(9)^{2} - 4(2)(4) \\81 - 4(2)(4) \\81 - 32 \\49[/tex]
[tex] \rm \int_{0}^2 \left( \sqrt[3]{ {x}^{2} + 2x} + \sqrt{1 + {x}^3 } \right )dx \\ [/tex]
If f(x) has an inverse on [a, b], then integrating by parts (take u = f(x) and dv = dx), we can show
[tex]\displaystyle \int_a^b f(x) \, dx = b f(b) - a f(a) - \int_{f(a)}^{f(b)} f^{-1}(x) \, dx[/tex]
Let [tex]f(x) = \sqrt{1 + x^3}[/tex]. Compute the inverse:
[tex]f\left(f^{-1}(x)\right) = \sqrt{1 + f^{-1}(x)^3} = x \implies f^{-1}(x) = \sqrt[3]{x^2-1}[/tex]
and we immediately notice that [tex]f^{-1}(x+1)=\sqrt[3]{x^2+2x}[/tex].
So, we can write the given integral as
[tex]\displaystyle \int_0^2 f^{-1}(x+1) + f(x) \, dx[/tex]
Splitting up terms and replacing [tex]x \to x-1[/tex] in the first integral, we get
[tex]\displaystyle \int_1^3 f^{-1}(x) \, dx + \int_0^2 f(x) \, dx = 2 f(2) - 0 f(0) = 2\times3+0\times1=\boxed{6}[/tex]
hi i need help thank u so much
WORTH 5o points
Answer:
it will be 8 answer letter A
Answer:
A. 8
Step-by-step explanation:
From pythagoras theorem
10^2=6^2+x^2
100-36=x^2
sqrt 64=x
x=8
Diego is flying from Philadelphia to Barcelona. On the trip to Barcelona, the plane flies at a constant cruising
speed of 550 mph.
reaches its cruising speed, which is
On the trip home, Diego makes a chart of the plane's progress once
constant
Which is faster the cruising speed on the flight from Philadelphia to Barcelona, or the cruising speed on the flight home?
Hour
1
2
3
A
Miles
530
1060
1590
US
Choose 1 answer:
Со
The cruising speed on the flight from Philadelphia to Barcelona
The cruising speed on the flight home
Pro
Pro
© The two cruising speeds are the same.
The faster speed is the cruising speed on the flight from Philadelphia to Barcelona.
Which speed is faster?
Average speed is the total distance travelled per time. It is used to determine how fast an object is moving with respect to time.
Average speed = total distance / total time
Average speed on the flight back home = 530 / 1 = 530 mph
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The points plotted below are on the graph of a polynomial. In what range of x- a values must the polynomial have a root? Check all that apply. A. -2 to -1 B. -1 to 0 C. -3 to-2 D. 1 to 2 E. -4 to -3 F. O to 1
which functions graph is the widest parabola A. y=1/8x^ B.y=3x^ C. y=1/3x^ D. y=8x^
[tex] \frac{1}{8} = 0.125[/tex]
[tex]3 = 3[/tex]
[tex] \frac{1}{3} = 0.333[/tex]
[tex]8 = 8[/tex]
Answer:y=1/8 x²Answer:
A. y=1/8x^
Step-by-step explanation:
Becket needs to solve the system of equations using elimination.
-2x+4y=-2
(6x-y=28)
Which correctly describes the first step Becket should take?
A. Multiply each term in the 1st equation by -3
B. Multiply each term int he 1st equation by 3
C. Multiply each term in the 2nd equation by -4
D. Both B and C would work
Answer:
B. Multiply each term in the 1st equation by 3
Step-by-step explanation:
A is incorrect because multiplying the entire 1st equation by -3 will give you 6x - 12y = 6. This does not cancel with either x or y term in the second equation.B is correct because by multiplying the entire 1st equation by 3 will give you -6x + 12y = -6. The -6x term will cancel (or eliminate) the 6x term in the second equation.C is incorrect because multiplying the entire 2nd equation by -4 will give you -24x + 4y = -112. This does not cancel with either x or y term in the 1st equation.D is incorrect because C was proven to be incorrect.Step-by-step explanation:
step 1
Multiply each term in the second equation with 4
step 2
Add equation 1 to equation 2
step 3
make x subject of formula and obtain value of X
step 4
substitute value of X in equation 1 and find Y
Roberto's science grade is calculated using a weighted average. Quizzes are worth 25%, homework is worth 10%, unit tests are worth 30%, and labs are worth 35%.
Roberto earned an average of 94% on his quizzes, 99% on his homework, 92% on his unit tests, and 94% on his labs.
What is Roberto's final science grade?
93.3%
93.9%
94.8%
95.3%
Answer: the answer is 93.9
I hope this helps
Step-by-step explanation:
i know it its on k12
Answer:
93.9
Step-by-step explanation: I took the k12 test
Triangle ABC is isoceles and has a perimeter of 20cm.Sides AB and AC are each twice as long as BC. Calculate the length of the side BC
Answer:
length of the side BC=4
Step-by-step explanation:
length of the side BC = x
length of the side AB = 2x
length of the side AC = 2x
x + 2x + 2x = 20
5x=20
x=4
BC = 4
AB=8
AC=8
8+8+4=20
simplify the following 42÷7+14-4×5
Answer:
1
Step-by-step explanation:
42/7 + 14 - 4 × 5
7 + 14 - 4 × 5
7 +14 - 20
20 - 20
0
Answer:0
because 42 divided by 7 is 6 and 6 + 14 is 20 and 4 times 5 is 20 som then 20 -20 = 0
Plsss help mee I’m not sure what the answer is
Answer:
D. would be the correct answer
Drew and Beau each brought cylindrical water bottle to football practice. Drew's water bottle has a diameter of 3 inches and a height
of 7 inches. Beau's water bottle has a radius of 2 inches and a height of 9 inches. Whose water bottle holds more water and how much more does it hold? Round to the nearest hundredth.
The bottle that holds more water has the larger volume
Beau's water bottle holds more water
How to determine the bottle with more water?The given parameters are:
Drew
Diameter = 3 inchesHeight = 7 inchesBeau
Radius = 2 inchesHeight = 9 inchesThe volumes of their bottles is calculated using:
V = πr^2h
So, we have:
Drew = 3.14 * (3/2)^2 * 7
Drew = 49.46
Beau = 3.14 * (2)^2 * 9
Beau = 113.04
By comparison, 113.04 is greater than 49.46
Hence, Beau's water bottle holds more water
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PLEASE ANSWER FAST WILL MARK BRAINLIEST
[tex]\sf y=50\left(1.8\right)^{x}[/tex]
=================================
the first term : 50
crosses point : (0, 50), (1, 90)
solve for y,
[tex]\sf y=50\left(1.8\right)^{1}[/tex]
[tex]\sf y=90[/tex]
Thus D is correct option.Graph: