The second tree is 56.4 ft tall.
Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are identical, their respective sides are equal in number and their corresponding angles are congruent.
Let the length of the tall tree be x. Thus by similarity of triangles we get,
Length of small tree/ Shadow Length of small tree =
Length of Tall tree/ Shadow Length of tall tree
Substituting the values we get,
5.6/4.2 = x/42.3
x = 56.4
Thus the second tree is 56.4 ft tall.
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Show that the curve x = 7 cos(t), y = 4 sin(t) cos(t) has two tangents at (0, 0) and find their equations
The equations with tangents at (0,0) are [tex]y = \frac{4}{7} x[/tex] and
[tex]y = -\frac{4}{7} x[/tex].
In this question,
The curves are x = 7 cos(t), y = 4 sin(t) cos(t)
Two tangents at (0, 0)
In this case, the parametric derivative of x and y are expressed in terms of t.
The first derivative dy/dx can be expressed as
[tex]\frac{dy}{dx}=\frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]
Now, dy/dt is obtained by differentiate y with respect to t,
[tex]\frac{dy}{dt}= 4[cos(t)(cos(t))+sin(t)(-sin(t))][/tex]
⇒ [tex]\frac{dy}{dt}= 4[cos^{2} (t)-sin^{2} (t)][/tex]
Now, dx/dt is obtained by differentiate x with respect to t,
[tex]\frac{dx}{dt} =7(-sin(t))[/tex]
⇒ [tex]\frac{dx}{dt} =-7sin(t)[/tex]
Thus, [tex]\frac{dy}{dx}=\frac{4[cos^{2}(t)-sin^{2}(t ) ]}{-7sin(t)}[/tex]
At (0,0) x = 0 and y = 0, Then
0 = 7 cos(t)
0 = 4 sin(t) cos(t)
and
cos(t) = 0
sin(t) cos(t) = 0
There are two values between -π and π which satisfy these equations simultaneously are
t = π/2
t = -π/2
The equation of a straight line given a point and its slope is
y-y₀ = m(x-x₀)
The two tangents lies at (0,0), so the equation becomes
y = mx
Then the two straight lines will be
y = m₁x and
y = m₂x
For t = π/2,
[tex]m_1=\frac{dy}{dx}=\frac{4[cos^{2}(\frac{\pi }{2} )-sin^{2}(\frac{\pi }{2} ) ]}{-7sin(\frac{\pi }{2} )}[/tex]
⇒ [tex]m_1=-\frac{4[0-1]}{7(1)}[/tex]
⇒ [tex]m_1=\frac{4}{7}[/tex]
For t = -π/2,
[tex]m_2=\frac{dy}{dx}=\frac{4[cos^{2}(-\frac{\pi }{2} )-sin^{2}(-\frac{\pi }{2} ) ]}{-7sin(-\frac{\pi }{2} )}[/tex]
⇒ [tex]m_2=-\frac{4[0-1]}{-7(1)}[/tex]
⇒ [tex]m_2=-\frac{4}{7}[/tex]
Thus the equations with tangents at (0,0) are [tex]y = \frac{4}{7} x[/tex] and
[tex]y = -\frac{4}{7} x[/tex].
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Kelley writes the expression n 2 to model the phrase "xander studied two more hours than nandini." which best explains the accuracy of kelley’s expression? it is accurate. in the phrase "two more hours than nandini," "two" is "2," "more" is " ," and nandini’s study time is unknown or "n," so 2 n or n 2 are correct translations. it is inaccurate. in the phrase "two more hours than nandini," "two" is "2," "more" is " ," and nandini’s study time is unknown or "n," so 2 n is the correct translation. it is inaccurate. in the phrase "two more hours than nandini," "two" is "2," "more than" is ">," and nandini’s study time is unknown or "n," so 2 greater-than n is the correct translation. it is inaccurate. in the phrase "two more hours than nandini," "two" is "2," "more than" is "<," and nandini’s study time is unknown or "n," so 2 less-than n is the correct translation.
It is accurate. In the phrase “two more hours than Nandini,” n + 2 are correct translations. Then the correct option is A.
What is Algebra?Algebra is used to analyze mathematical symbols, and logic is used to manipulate those symbols.
As an example, Kelley models the sentence "Xander studied two more hours than Nandini" using the equation n + 2.
Consequently, the following will describe Kelley's expression's accuracy the best:
It is precise. Since "two" is translated as "2," "more" as "+," and "Nandini's study time is unknown or "n," 2 + n or n + 2 are the appropriate translations for the sentence "two more hours than Nandini."
So, option A is the best choice.
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I understand that the question you are looking for is :
Kelley writes the expression n + 2 to model the phrase “Xander studied two more hours than Nandini.” Which best explains the accuracy of Kelley’s expression?
It is accurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more” is “+,” and Nandini’s study time is unknown or “n,” so 2 + n or n + 2 are correct translations.
It is inaccurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more” is “+,” and Nandini’s study time is unknown or “n,” so 2 + n is the correct translation.
It is inaccurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more than” is “>,” and Nandini’s study time is unknown or “n,” so 2 greater-than n is the correct translation.
It is inaccurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more than” is “<,” and Nandini’s study time is unknown or “n,” so 2 less-than n is the correct translation.
The functions f(x) and g(x) are graphed.
f(x)
324
2
-6-5-4-3-2-1₁.
297 49
-2+
-3
-4
g(x)
1 2 3 4 5 6 x
Which represents where f(x) = g(x)?
Of(0) = g(0) and f(2)= g(2)
Of(2)= g(0) and f(0) = g(4)
Of(2)= g(0) and f(4) = g(2)
Of(2)= g(4) and f(1) = g(1)
Answer: Option 1
Step-by-step explanation:
The graphs intersect at x=0 and x=2.
The answer that represents the point where f(x) = g(x) is; A: f(2) = g(2) and f(0) = g(0)
What are functions?A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math.
Given is a graph we need to find the point of intersection where f(x) = g(x)
How to find the coordinates of Intersection :-
From the attached graph, we see that is represents the relationship between the functions f(x) and g(x).
Now, the coordinates of the points where f(x) = g(x) will be the coordinates of the points where both graphs intersect.
The first point of intersection, we see that;
f(0) = g(0) = 4
Second point shows;
f(2) = g(2) = 0
Thus, we can conclude that;
f(2) = g(2) and f(0) = g(0)
Hence, the answer that represents the point where f(x) = g(x) is; A: f(2) = g(2) and f(0) = g(0)
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Please help me on this one I got it wrong
Answer: E. 10,000,000 cubic millimeters
Step-by-step explanation: To find out any result from cubic centimeters to cubic millimeters, you multiply the cubic centimeters' value by 1000 to get the cubic millimeters' value.
10,000 * 1,000 = 10,000,000 cubic millimeters.
Hope this helped!
Step-by-step explanation:
The correct answer is E 10,000,00
Given the following coordinates complete the reflection transformation.
A(1,−5)
B(2,−2)
C(5,−2)
Transformation: Complete the double reflection over the lines y=−1 followed by y=1.
The double reflection generates the following three points: A''(x, y) = (1, - 1), B''(x, y) = (2, 2) and C''(x, y) = (5, 2).
How to generate a set of point by rigid transformations
In this problem we must apply two rigid transformations to find three points. The formula for reflection over an axis parallel to the y-axis is defined below:
P'(x, y) = (x', k) - [P(x, y) - (x', k)] (1)
Where:
x' - x-coordinate of the point P(x, y).P(x, y) - Original pointP'(x, y) - Resulting pointIf we know that A(x, y) = (1, - 5), k = - 1 and k' = 1, then the resulting points are:
Point A
A'(x, y) = (1, - 1) - [(1, - 5) - (1, - 1)]
A'(x, y) = (1, - 1) - (0, - 4)
A'(x, y) = (1, 3)
A''(x, y) = (1, 1) - [(1, 3) - (1, 1)]
A''(x, y) = (1, 1) - (0, 2)
A''(x, y) = (1, - 1)
Point B
B'(x, y) = (2, - 1) - [(2, - 2) - (2, - 1)]
B'(x, y) = (2, - 1) - (0, - 1)
B'(x, y) = (2, 0)
B''(x, y) = (2, 1) - [(2, 0) - (2, 1)]
B''(x, y) = (2, 1) - (0, - 1)
B''(x, y) = (2, 2)
Point C
C'(x, y) = (5, - 1) - [(5, - 2) - (5, - 1)]
C'(x, y) = (5, - 1) - (0, - 1)
C'(x, y) = (5, 0)
C''(x, y) = (5, 1) - [(5, 0) - (5, 1)]
C''(x, y) = (5, 1) - (0, - 1)
C''(x, y) = (5, 2)
The double reflection generates the following three points: A''(x, y) = (1, - 1), B''(x, y) = (2, 2) and C''(x, y) = (5, 2).
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Geometry: fill in the blanks, ASAP! It’s urgent
Answer:
3. 125
4. 115
5. m<1 = 70, m<2 = 55, m<3 = 55
6. m<2 = 50, m<3 = 50, m<4 = 80, m<6 = 130
Find the coordinates of the vertices of the figure after the given transformation: T<−5,−2>
The vertices of the figure after the transformation: T<−5, −2>; 5 units left and 2 units down is X'(-3, -3), V'(-4, 0), E'(-1, -1), K'(0, -5)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Rigid transformations are transformation that preserve the shape and size of a figure such are reflection, rotation and translation.
The vertices of the figure after the transformation: T<−5, −2>; 5 units left and 2 units down is X'(-3, -3), V'(-4, 0), E'(-1, -1), K'(0, -5)
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After a rotation of 90° about the origin, the coordinates of the vertices of the image of a triangle are A'(5, 3), B'(–2, 1), and C'(1, 7). What are the coordinates of the vertices of the pre-image?
A -
B -
C -
The coordinates of the vertices of the preimages are A ( 3, 5) , B ( 1, 2) and C ( 7, -1)
How to determine the coordinatesIt is important to note the following about the 90 degrees rotation about the origin
A( x ,y ) becomes A' ( -y, x ) switch x and y and make y negativeNote that
A ( x, y) is the coordinates of the preimage
A' ( -y , x) is the coordinates after the said rotation about the origin
Converting the transformed coordinates to the preimage coordinates
For vertex A
A' ( 5, 3)
Compare with A' ( -y, x)
x = 3
y = -5
Substitute the values
A ( 3, 5 )
For vertex B
B' ( -2, 1)
Compare with B' ( -y, x)
x = 1
y = 2
Substitute the values
B ( 1, 2)
For vertex C
C' ( 1, 7)
Compare with C' ( -y, x)
x = 7
y = -1
Substitute the values
C ( 7, -1)
Thus, the coordinates of the vertices of the preimages are A ( 3, 5) , B ( 1, 2) and C ( 7, -1)
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Arlana graphed the system of equations that can be used to solve x cubed minus 5 x squared 2 = negative x cubed 17 x.
The roots of the resulting polynomial equation are [tex](x_{1} ,y_{1} ) = (-2 , -26), (x_{2} ,y_{2} ) = ( 0.11 , 1.94 )[/tex] and [tex]( x_{3} , y_{3} ) = ( 4.39, - -9.81)[/tex] , respectively.
What is a polynomial easy definition?
A mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power (such as a + bx + cx2).
Ariana must graph two polynomic expressions:
[tex]f(x) = x^{3} -5 . x^{2} + 2[/tex] and [tex]g(x) = -x^{3} + 17 . x[/tex]
The roots of the resulting polynomial equation are found by means of this formula-
f(x) - g(x) = 0.........................1
Then, we must look for every point so that f(x) = g(x)
The roots of the resulting polynomial equation are [tex](x_{1} , y_{1} ) = ( -2,-26) , (x_{2} ,y_{2} ) = ( 0.114 , 1.937 )[/tex] and [tex](x_{3},y_{3} ) = ( 4. 386 , -9. 812)[/tex] respectively.
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Answer:
D
Step-by-step explanation:
.
y = x2 + 3
y = x + 5
can you guys help me please or you can just explain how to solve it thanks
The composition of transformation that maps ABCD to EHGF is "(x, y) → (x', -y') → (x' + 6, y' + 3)".
What are the transformation rules?The basic transformation rules are:
Translation: (x, y) → (x + a, y + b);Reflection: (x, y) → (x, -y) over x-axis; (x, y) → (-x, y) over y-axis;Dilation: (x, y) → (kx, ky)Rotation 90° counter-clockwise: (x, y) → (-y, x)Rotation 180°: (x, y) → (-x, -y)Calculation:The given quadrilateral ABCD has vertices,
A(-5, 2), B(-3, 4), C(-2, 4), and D(-1, 2)
The transformed quadrilateral EHGF has vertices,
E(1, 1), H(3, -1), G(4, -1), and F(5, 1)
In the map ABCD to EHGF, the transformations that took place are:
1) Reflection over x-axis
2) Translation by (x + a, y + b)
Step 1: Reflection over x-axis; (x, y) → (x, -y)
A(-5, 2) → A'(-5, (-2)) = A'(-5, -2)
B(-3, 4) → B'(-3, (-4)) = B'(-3, -4)
C(-2, 4) → C'(-2, (-4)) = C'(-2, -4)
D(-1, 2) → D'(-1, (-2)) = D'(-1, -2)
So, the reflected quadrilateral is A'B'C'D'
Step 2: Translation by (x, y) → (x + a, y + b);
The reflected quadrilateral A'B'C'D' is now translated by
A'B'C'D' → EHGF
So, (for A'(-5, -2) and E(1, 1))
x + a = 1
⇒ -5 + a = 1
⇒ a = 1 + 5
∴ a = 6
and
y + b = 1
⇒ -2 + b = 1
⇒ b = 1 + 2
∴ b = 3
Thus, the translation is (x + 6, y + 3).
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A rope that is 245cm long is cut into three pieces. The ratio of the lengths of the first piece to the second piece is 2/3, and the ratio of the lenghts of the second piece to the third piece is 4/5. What is the length of the longest of the the three pieces?
The length of the longest piece of the cut rope is; 105 cm
How to work with ratios?We are given that;
Length of rope = 245 cm
We need to make the ratio of second piece equal in both the ratio to find the ratio of all three pieces.
2:3
4:5
Multiply 1st ratio by 4 and 2nd ratio by 3:
Now, the ratio becomes: 8:12 and 12:15
And the ratio of three pieces can be represented as:
8: 12: 15, this ratio is the first piece: second piece: third piece
Thus;
8x + 12x + 15x = 245
35x = 245
x = 245/35
So, the pieces lengths will be;
First piece = 8 * 7 = 56 cm
Second piece = 12 * 7 = 84 cm
Third piece = 15 * 7 = 105 cm
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25. Jen ran x miles last week and 18 miles
this week. Write an expression to represent
the total number of miles Jen ran over the
last two weeks.
Solve: If she ran 34 miles over the last two
weeks, how many did she run last week?
Answer:
Step-by-step explanation:
If Jen ran 34 miles over the last 2 weeks and only 18 miles the second week, she would've had to have run 16 miles the first week.
34= 18+x
I hope this helps!
Show your work and hurry please
Answer:
15
Step-by-step explanation:
Note: Take note , absolute value will give the magnitude of the value. (Which means ignoring the + / - signs.)
Eg. | - 19 | = 19
Therefore,
[tex] \frac{12(30 - (9 + {4}^{2})) }{10 - | - 6| } \\ = \frac{12(30 - (9 + 16))}{10 - 6} \\ = \frac{12(30 - 25)}{4} \\ = \frac{12(5)}{4} \\ = \frac{60}{4} \\ = 15[/tex]
find unknown angles, value of 'x' and unknown sides:
a=3. b=2
5ab+4b+10a
help please?
Answer:
68
Step By Step Explanation:
Evaluate for a=3,b=2
(5)(3)(2)+(4)(2)+(10)(3)
(5)(3)(2)+(4)(2)+(10)(3)
=68
Answer:
The solution is 68
Step-by-step explanation:
a = 3 and b = 2
5ab+4b+10a
= 5(3)(2)+4(2)+10(3)
= 5(6)+8+30
= 30+8+30
= 38+30
= 68
At time t, the position of a body moving along the s-axis is s=t^3 -18t^2+60t m. Find the displacement of the body from t=0 to t=3.
a. 56 m
b. 67 m
c. 105 m
d. 45 m
The displacement between t = 0 and t = 3 is 45 meters, so the correct option is d.
How to find the displacement?The displacement is defined as the difference between the final position and the initial position.
The initial position is what we get when we evaluate in t = 0.
s = 0^3 -18*0^2+60*0 = 0
The initial position is 0 meters.
The initial position is what we get when we evaluate in t = 3.
s = 3^3 -18*3^2+60*3 = 45
The final position is 45 meters.
Then the displacement is:
D = 45m - 0m = 45m
The correct option is d.
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A team plays 93 games in a season. The team won 15
more than twice as many games as they lost.
How many wins and losses did the team have?
PLS HELPPPP THE WORDING IS CONFUSING
Answer:67 wins, 26 losses
Step-by-step explanation: They played 93 games. Let L = their losses and w = their wins. They won 15 more than twice as many games they lost so w = 2L + 15. So, 93 = 3L + 15. 93 - 15 = 78. 78 divided by 3 is 26 so they lost 26 games and won the rest of them or 93-26 = 67 wins and 26 losses.
HELP!!! MATH!!! 100 PTS !!!
Suppose f is a one-to-one, differentiable function and its inverse function f−1 is also differentiable. One can show, using implicit differentiation (do it!), that
(f^−1)′(x)=1/(f′(f^−1(x)))
Find (f^−1)′(6) if f(−1)=6 and f′(−1)=3/7.
Answer:
(f^−1)′(6)=1/(f'(f^-1(6)))
(f^−1)′(6)=1/(f'(f^-6)))
I hope this helps.
How many ways are there to put five beads on a necklace if there are eight distinct beads to choose from, and rotations and reflections of the necklace are considered the same
Answer:
3,360
Step-by-step explanation:
so, to start with, there are 8 over 5 permutations (the sequence of the picked beads matters, but no repetitions of beads are possible) to pick 5 items out of 8 available ones.
that is
8! / ((8-5)!) = 8! / 3! = 8×7×6×5×4 = 6,720
rotations and reflections are the same thing here for a 1- dimensional sequence.
1 2 3 4 5 rotated around the middle (3) is
5 4 3 2 1
a reflection is again
5 4 3 2 1
so, we need to consider that instead of 8 beads for the first choice we have only 4 beads to choose from to leave the other 4 beads as choices for the last position.
once we have this established, it is sure that the first and the last position cannot have mirrored beads in any permutation. and therefore rotational or reflectional permutations are impossible.
in other words, half of the possible permutations would be rotations/reflections, and we need to eliminate them.
so, the calculation is
4×7×6×5×4 = 8×7×6×5×4/2 = 6,720/2 = 3,360
Select the correct answer from each drop-down menu.
-60
8-
6-
4
2-
-4-2 O
-2-
-4-
-6-
-8-
-N
4
2
-6
Quadrilateral 1 and quadrilateral 2 are polygons that can be mapped onto each other using similarity transformations. The
transformation that maps quadrilateral 1 onto quadrilateral 2 is a
followed by a dilation with a scale factor of
Reset
Nexts
The transformation that maps quadrilateral 1 onto quadrilateral 2 is a translation followed by a dilation with a scale factor of 2.
What is a transformation?A transformation can be defined as the movement of a point on a cartesian coordinate from its original (initial) position to a new location.
The types of transformation.In Geometry, there are different types of transformation and these include the following:
DilationReflectionRotationTranslationBased on similarity transformation of both quadrilateral 1 and quadrilateral 2, we can infer and logically deduce that the transformation which directly maps quadrilateral 1 onto quadrilateral 2 is a translation followed by a dilation with a scale factor of 2, as shown in the image attached below.
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need help finding the measurement of s
Answer:
∠S = 66°
Step-by-step explanation:
A parallelogram's 4 angles always add up to 360°, and opposite angles are the same. (∠S = ∠U; ∠T = ∠V)
So, ∠S + ∠T = 180°.
180° = (2x + 4x + 12 + 6)°
180° = (6x + 18)°
162° = (6x)°
27° = x°
(2x + 12)° = ∠S
(2(27) + 12)° = ∠S
(54 + 12)° = ∠S
66° = ∠S
Find the midpoint of the line segment joining (–4, –2) and (2, 8).
y=4x−5 y=2x+3 Is (4,11)(4,11)left parenthesis, 4, comma, 11, right parenthesis a solution of the system?
The solution to the systems if equation y = 4x - 5, y = 2x + 3 is (x, y) = (4, 11)
Equationy = 4x - 5
y = 2x + 3
Equation both equations4x - 5 = 2x + 3
collect like terms4x - 2x = 3 + 5
2x = 8
divide both sides by 2x = 8/2
x = 4
Substitute x = 4 intoy = 4x - 5
= 4(4) - 5
= 16 - 5
y = 11
Therefore, the solution to the system of be equation is x = 4 and y = 11
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x =
30°
xo
90°
Report a pro
Answer:
here is the answer
hope it helps u
happy to help
stay safe and healthy
step by step explanation :x=90(being adjacent angle)
now ,
x+30=180(being alternate angle)
x=180-30
x=150#
i think my answer ia wrong sorry -_-
Answer:
x=90
Step-by-step explanation:
x is on a straight line with 90 degrees (given angle measure angle)
you should do 180-90=90 to find that angle x is 90 degrees.
Solve the equation by first using a sum-to-product formula. (enter your answers as a comma-separated list. let k be any integer. round terms to three
Solutions of the equation are 22.5°, 30°.
The given equation is sin(5θ) - sin(3θ) = cos(4θ)
We take left side of the equation
sin(5θ) - sin(3θ) = 2cos ((5θ+3θ)/2) (sin(5θ-3θ)/2)
=2cos4θsinθ [From sum-product identity]
Now we can write the equation as
2cos(4θ)sin(θ) = cos(4θ)
2cos(4θ)sinθ - cos(4θ) = 0
cos(4θ)[2sinθ - 1] = 0
cos(4θ) = 0
4θ = 90°
θ = 90/4
θ = 22.5°
and (2sinθ - 1) = 0
sinθ = 1/2
θ = 30°
Therefore, solutions of the equation are 22.5°, 30°
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X
-3
-1
1
3
f(x) = -x + 7
f(x)
8
2323
20
6
Determine the input that would give an output value of
W/N!
2
X=
=-3x+7
Answer: 19
Step-by-step explanation:
Multiplying both sides of the equation by [tex]-3[/tex] gives that [tex]x=19[/tex].
A vector in the xy plane has a magnitude of 25 and an x component of 12. The angle it makes with the positive x axis is?
The angle it makes with the positive x axis in the xy plane is 61.3145 degrees.
In this question,
A normal vector to the plane is any vector that starts at a point in the plane and has a direction that is orthogonal (perpendicular) to the surface of the xy plane .
The magnitude of the xy plane, hypotenuse = 25 units
The x component of the xy plane, base = 12 units
Let θ be an angle, then the angle it makes with the positive x axis is
[tex]\theta = cos^{-1}(\frac{base}{hypotenuse} )[/tex]
⇒ [tex]\theta = cos^{-1}(\frac{12}{25} )[/tex]
⇒ [tex]\theta = cos^{-1}(0.48)[/tex]
⇒ [tex]\theta = 61.3145[/tex]
Hence we can conclude that the angle it makes with the positive x axis in the xy plane is 61.3145 degrees.
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Which of the following fractions has the largest value 11/20 10/21 9/19 8/17 or 6/13
Answer:
11/20
Step-by-step explanation:
You could turn them all into equivalent fractions, but the common denominator would be 1,763,580. Yuck.
Look at the relationship for the numerators to the denominators. The only numerator that is more than half of its denominator is 11/20. Half of 20 would be 10 and 11 has a larger value than 10, so as a decimal, it would be more than .5. All of the other numerators are less than half, so that they have to less than .5.
If you changed all of the numbers to decimals, you would see that 11/20 has the largest value.
product of squre of x and cube of y
Answer:
x²y³
Step-by-step explanation:
(x²) (y³) = x²y³
Hope it helps!
Have a nice day:)
❄ Hi there,
let us find the product of the square of x and the cube of y.
[tex]\sf{The \ square \ of \ x: \ x^2}\\\sf{The \ cube \ of \ y: y^3}\\\sf{The \ product \ of \ the \ two: x^2y^3}[/tex]
The square of x means: x times x, or, as I said earlier, x².
The cube of y means: y times y times y, or, as I said earlier, [tex]\sf{y^3}[/tex].
The product means: you multiply x² times y³.
❄