Answer:
To simplify the expression |2(11-3)/2|^2, we follow the order of operations (parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right).
First, simplify the expression inside the absolute value:
2(11-3)/2 = 2(8)/2 = 16/2 = 8
Now, simplify the absolute value of 8, which is simply the magnitude of 8:
|8| = 8
Finally, square the result:
8^2 = 8 * 8 = 64
Therefore, the simplified value of |2(11-3)/2|^2 is 64.
Step-by-step explanation:
What function represents the same relationship
H(x)=-4+7
H(x) =-22x+1.75
H(x)=4x+1.75
H(x)=1.75x-4
The linear function that is modeled by the given table is:
y = -4x + 7
How to find the linear function represented by the table?A general linear function is written as:
y = ax + b
Where a is the slope and b is the y-intercept.
If we know two points on the line (x₁, y₁) and (x₂, y₂) then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
Here we can use the first two points on the table:
(-11, 51) and (-5.5, 29)
Then the slope is:
a = (29 - 51)/(-5.5 + 11)
a = -4
Then the linear function is:
y = -4x + b
We know that when x = -5.5, the value of y is 29
29 = -4*-5.5 + b
29 = 22 = b
29 - 22 = b
7 = b
The linear function is:
y = -4x + 7
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Jenny wanted to study how the area of a rectangle changes with the length if its width is fixed. She computed the areas of several rectangles that have the same width and different lengths. She then plotted the results and connected them with a line, as shown below. The graph shows the area (in ) versus the length (in ).
Find the range and the domain of the function shown.
Area
()
y12345678910x1234567890
Length ()
Write your answers as inequalities, using or as appropriate.
Or, you may instead click on "Empty set" or "All reals" as the answer.
look at picture
The domain and range of a function for the area of a rectangle indicates;
(a) Range; 0 ≤ y < ∞
(b) Domain; 0 ≤ x < ∞
What is a function?A function is a definition or rule that maps the values of an input unto the values of the output variables.
The area of a rectangle, A = Length, L × Width, W
Therefore;
The area of a rectangle is directly proportional to the width of a rectangle
A ∝ W
The graph of the area to the length of the width of the rectangle indicates that we get;
(a) The domain is the set of the possible x-values of the function
The proportional relationship between the area and the width of a rectangle indicates;
The domain is; 0 ≤ x < ∞
(b) The range is the set of the possible output values of the graph, which is the set of the y-values
The proportional relationship between the area, y and the width, x , the range is; 0 ≤ y < ∞
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expand using the Binomial Theorem: (2x+5y)^3
The Binomial coefficients, we get:
(2x+5y)^3 = 8x^3 + 60x^2y + 150xy^2 + 125y^3
Therefore, (2x+5y)^3 expands to 8x^3 + 60x^2y + 150xy^2 + 125y^3.
To expand (2x+5y)^3, we can use the Binomial Theorem, which states that:
(a + b)^n = nC0a^n + nC1a^(n-1)b + nC2a^(n-2)b^2 + ... + nCn-1ab^(n-1) + nCn b^n
where nCk represents the binomial coefficient, which is the number of ways to choose k items from a set of n items.
In this case, we have:
a = 2x
b = 5y
n = 3
So, we can apply the Binomial Theorem as follows:
(2x+5y)^3 = 3C0 (2x)^3 + 3C1 (2x)^2(5y) + 3C2 (2x)(5y)^2 + 3C3 (5y)^3
Simplifying each term using the binomial coefficients, we get:
(2x+5y)^3 = 8x^3 + 60x^2y + 150xy^2 + 125y^3
Therefore, (2x+5y)^3 expands to 8x^3 + 60x^2y + 150xy^2 + 125y^3.
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Mark was suspicious that his wife was unfaithful to him. He obtained blood samples from all family members. When the results came back, it turned out that Mark has blood type AB. His wife has blood type O. They have three children. One child has blood type A. One child has blood type B. One child has blood type O. “You cheated!” Mark yells accusingly. Is he right to make such a statement or does he owe his wife an apology? Show your work with Punnett Squares or with a written explanation
Mark's accusation is incorrect. Based on the blood type combinations, it is possible for the children to have the observed blood types without any infidelity. Mark owes his wife an apology for the false accusation.
Mark has blood type AB, which means he has one A allele and one B allele.
Mark's wife has blood type O, which means she has two O alleles.
One child has blood type A, indicating they have inherited one A allele.
One child has blood type B, indicating they have inherited one B allele.
One child has blood type O, indicating they have inherited two O alleles.
Child 1:
Mark's allele: A
Wife's allele: O
Possible combinations: AO
Child 2:
Mark's allele: B
Wife's allele: O
Possible combinations: BO
Child 3:
Mark's allele: A or B (since Mark has AB blood type)
Wife's allele: O
Possible combinations: AO or BO
From the possible combinations, we can see that it is possible for the children to have blood types A, B, and O without any issues.
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Show all work and/or explain your reasoning. Please help:)
To make both triangles equal, their corresponding angles must be equal and when x = 106 degrees, the second angle in triangle 2 is equal to the third angle in triangle 1, which refutes Terry's claims.
What value of x will refute Terry's claims? Show all workTo determine the value of x that refutes Terry's claims, we need to examine the angles of the triangles and find a valid configuration where triangle 1 is similar to triangle 2.
In triangle 1, the given angles are 18 degrees and 96 degrees. The third angle can be found using the property that the sum of the angles in a triangle is always 180 degrees:
Third angle in triangle 1 = 180 - (18 + 96) = 180 - 114 = 66 degrees.
let's find the value of x that will make both triangles similar to one another or their corresponding angles to be equal.
Since we already know one angle in triangle 2 is 8 degrees, we can find the second angle as follows:
Second angle in triangle 2 = 180 - (8 + x) = 180 - 8 - x = 172 - x degrees.
To refute Terry's claims, we need to find a value of x such that the second angle in triangle 2 (172 - x degrees) is equal to the third angle in triangle 1 (66 degrees).
Setting up the equation:
172 - x = 66
Solving for x:
172 - 66 = x
106 = x
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The probability of randomly drawing a light blue crayon from a box of crayons is 1/24.
What are the odds against drawing a light blue crayon?
The answer is 23/24
there are 23 out of the 24 crayons that arent light blue and that gives you the odds against the light blue crayon
Please help as soon as possible
The exact values are:
sin(α + β) = (-6√5 - 8)/25
cos(α + β) = (4√5 - 6)/25
sin(α - β) = (-6√5 + 8)/25
tan(α - β) = (-9√5 + 45)/4
We have,
Recall the trigonometric identities:
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
sin(a - b) = sin(a)cos(b) - cos(a)sin(b)
cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
tan(a - b) = (tan(a) - tan(b))/(1 + tan(a)tan(b))
Using these identities, we can find the exact values of the expressions given.
(a) Sin (α + β)
sin(α + β) = sin(α)cos(β) + cos(α)sin(β)
= (√5/5)(-3/5) + (2/5)(-4/5) (using the values given for sin and cos)
= -6√5/25 - 8/25
= (-6√5 - 8)/25
(b) Cos (α + β)
cos(α + β) = cos(α)cos(β) - sin(α)sin(β)
= (2/5)(-3/5) - (√5/5)(-4/5) (using the values given for sin and cos)
= -6/25 + 4√5/25
= (4√5 - 6)/25
(c) Sin (α - β)
sin(α - β) = sin(α)cos(β) - cos(α)sin(β)
= (√5/5)(-3/5) - (2/5)(-4/5) (using the values given for sin and cos)
= -6√5/25 + 8/25
= (-6√5 + 8)/25
(d) tan (α - β)
tan(α - β) = (tan(α) - tan(β))/(1 + tan(α)tan(β))
= ((√5/5) - (-4/5))/(1 + (√5/5)(-4/5)) (using the values given for sin and cos)
= (9√5/5)/(1 - 4/5√5)
= (-9√5 + 45)/4
Therefore,
The exact values are:
sin(α + β) = (-6√5 - 8)/25
cos(α + β) = (4√5 - 6)/25
sin(α - β) = (-6√5 + 8)/25
tan(α - β) = (-9√5 + 45)/4
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6) Stacy ran 8 miles. She
recorded how long it took her to run each mile in minutes. How many total minutes did it take Stacy to run the 8 miles?
Answer Options
36 1/2
72 1/2
81
54 1/4
Answer:
72 1/2
Step-by-step explanation:
so, she ran 2 miles in 8 3/4 minutes each.
3 miles in 9 minutes each.
2 miles in 9 1/4 minutes each.
1 mile in 9 1/2 = 9 2/4 minutes.
in total that means
2×(8 3/4) + 3×9 + 2×(9 1/4) + 9 2/4 =
= 16 6/4 + 27 + 18 2/4 + 9 2/4 =
= 16 + 27 + 18 + 9 + 6/4 + 2/4 + 2/4 =
= 70 + 10/4 = 70 + 2 + 2/4 = 72 2/4 = 72 1/2 minutes
Give your answer in degrees (°).
35°
44°
x
Find X
The value of x is 53.
We have,
From the figure,
There are two parallel lines.
This means,
44 and angle M are corresponding angles.
And,
We can consider a triangle as:
M + P + P = 180
Where P is the angle opposite to the equal sides.
So,
44 + P + P = 180
44 + 2P = 180
2P = 180 - 44
2P = 36
P = 18
Now,
x is the exterior angle.
This means,
x = 35 + P
x = 35 + 18
x = 53
Thus,
The value of x is 53.
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100 points asap step by step What is the value of x in the equation x/-3 = 2?
Answer:
-6
Step-by-step explanation:
[tex]\frac{x}{-3} = 2\\x = 2 * (-3)\\x = -6[/tex]
The answer is x equals negative 6
What is the square root of 35*35*35?
Answer:
Step-by-step explanation:
7247.1977343
The square root of (35 x 35 x 35) is approximately 207.57.
The square root of (35 x 35 x 35) can be found by simplifying the expression under the radical sign:
√(35 x 35 x 35) = √(35³)
On simplifying 35³ to get:
√(35³) = √(42,875) ≈ 207.57
Therefore, the square root of (35 x 35 x 35) is approximately 207.57.
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What is the probability?
The true statements regarding the probability are:
It is likely that the bag has a black marbleIt is not unlikely that the bag has at least one pink marble (equivalently, it is likely that the bag has at least one pink marble)How to explain the probabilityBased on the given information, it is likely that the bag has at least one black marble (with a probability of 0.1). It is not certain or impossible, as the probability is not 0 or 1.
It is not certain or unlikely that the bag has at least one pink marble, as the probability is not 0 or 1. However, the probability of the bag having at least one pink marble is relatively high (0.79), so it is more likely than not that the bag has a pink marble.
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Solid Geometry
HSG-GMD
1. Examine the 2 cylinders below and explain why the volume to the two
cylinders are the same or explain why the volume of the two cylinder are
different.
Is Sue correct? Explain why.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
2. Two stacks of 23 quarters each are shown below. One stack forms a
cylinder but the other stack does not form a cylinder.
Use Cavelieri’s principle to explain why the volumes of these two stacks of
quarters are equal.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
Solid Geometry
HSG-GMD
The diagram below shows two figures. Figure A is a right triangular prism and
figure B is an oblique triangular prism.
Use Cavalieri's Principle to explain why the volumes of these two triangular prisms
are equal.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
1. The two cylinders have the same height and the same cross-sectional area at every point along that height, so they have the same volume. Sue is correct.
2. The two stacks of quarters have the same height and the same cross-sectional area at every point along that height, so they have the same volume.
3. The two triangular prisms have the same height and the same cross-sectional area at every point along that height, so they have the same volume. This can also be explained using Cavalieri's principle.
How to explain the informationThe two stacks of quarters have the same height and the same cross-sectional area at every point along that height, so they have the same volume.
This can be explained using Cavalieri's principle, which states that two solids have the same volume if they have the same height and the same cross-sectional area at every point along that height.
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Adam wants to plant flowers in a triangular plot. He has three lengths of plastic edging that measures 8 feet, 15 feet, and 17 feet. Determine whether these pieces fit for a right triangle. Explain.
Using the Pythagorean triple formula the numbers 8, 15 and 17 are Pythagorean triple and as such will form a right-angle triangle.
What is Pythagorean triple?Pythagorean triples are x² = y² + z² where x, y and z are the three positive integers. These triples are represented as (x, y, z). Here, y is the perpendicular, z is the base and x is the hypotenuse of the right-angled triangle.
In this problem, to determine if the given numbers will form a right-angle triangle, we have to check if the numbers are Pythagorean triple.
In doing so, we would use the previous formula given as;
x² = y² + z²
In a Pythagorean triple, the largest side is the hypothenuse.
17² = 8² + 15²
289 = 64 + 225
289 = 289
The numbers are equal and they're Pythagorean triple.
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can you help me solve this
The division of the polynomial 3x³ - 2x² + x - 4 by x + 3 is:
Quotient: 3x² + 11x + 34
Remainder: -106/(x + 3)
What is synthetic division?When dividing a polynomial by a linear binomial of the form (x - c) or (x + c), where "c" is a constant, the process is known as synthetic division. This streamlined method of polynomial long division offers a faster and clearer method for dividing polynomials by linear factors.
The process of synthetic division involves arranging the coefficients of the polynomial in descending order and performing a sequence of simple arithmetic operations.
The result of the synthetic division is:
[tex]Quotient: 3x^2 + 11x + 34[/tex]
Remainder: -106/(x + 3)
Kindly find the step by step analysis below.
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please solve to the nearest 10th
The value of the sides are;
c = 35. 5, y = 32. 2, <H = 65 degrees
Option D
How to determine the valueWe have that the ratios of the trigonometric identities are;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the information given, we have that;
Using sine identity
sin 25 = 15/c
cross multiply the values, we get;
c = 35. 5
Then, using tan identity;
tan 25 = 15/y
cross multiply
y = 32. 2
Sum of angles in a triangle is equal to 180 degrees.
Then, we have that;
90 + 25 + <H = 180
collect the terms
<H = 65 degrees
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How many faces dose a dodecahedron have
Answer:12 faces and 20 vertices
Step-by-step explanation:
Dodecahedron:- The three-dimensional geometric geometry of a dodecahedron comprises 20 vertices, 30 edges, and 12 flat faces.
Each face is a regular pentagon, with five equal-length sides and five equal-sized angles. One of the five Platonic solids, regular, convex polyhedrons with identical regular polygon faces and equal angles between them, the dodecahedron is one of these regular, convex polyhedrons. The dodecahedron is frequently utilised in architecture, design, and the arts because of its great degree of symmetry.
A dodecahedron has 12 faces.
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Which value of h makes the inequality 4h + 3 < 10 true? A: h = -2 B: h =2 C: h = 4 D: h = 7
Answer: A h = - 2
Step-by-step explanation:
Substitute -2 for h
4(-2) + 3 < 10
-8 + 3 < 10
-5 < 10 true
If the piece of paper is 60 inches long and 80 inches wide, how long is the diagonal cut that Zack made?
Answer:
100
Step-by-step explanation:
square root(L^2 + W^2)
Which of the following sets of ordered pairs represents a function? {(−5, −4), (−3, −2), (−1, 0), (0, −1), (0, 3)} {(−4, −4), (−4, −3), (−4, −2), (−4, −1), (−4, 0)} {(−3, −4), (−3, 0), (−2, −3), (0, −2), (2, −1)} {(−5, −2), (−3, −2), (−2, −2), (−1, −2), (0, 0)}
The required set of ordered pairs that represent a function is {(−5, −4), (−3, −2), (−1, 0), (0, −1), (0, 3)}. Option A is correct.
Given functions,
A= {(−5, −4), (−3, −2), (−1, 0), (0, −1), (0, 3)}
B= {(−4, −4), (−4, −3), (−4, −2), (−4, −1), (−4, 0)}
C = {(−3, −4), (−3, 0), (−2, −3), (0, −2), (2, −1)}
D = {(−5, −2), (−3, −2), (−2, −2), (−1, −2), (0, 0)}
The other sets have repeated x-values with different y-values, which violates the definition of a function where each x-value can only have one corresponding y-value.
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Answer: The awnser is D
Step-by-step explanation: Hope this helps
A bag has 2 red marbles and 2 blue marbles. Jade randomly selects two marbles
from the bag, one at a time. What is the probability that both marbles are the
same color? Show your work.
The probability that both marbles are the same color is 1/3.
How to solve for the probabilityP(R₂ | R₁) = 1/3
The probability of both events happening together (drawing two red marbles) is the product of the probabilities of each event:
P(R₁ and R₂) = P(R₁) * P(R₂ | R₁)
= (1/2) * (1/3)
= 1/6
P(B₁) = 2/4 = 1/2
P(B₂ | B₁) = 1/3
Probability of B₁ and B₂
P(B₁ and B₂)
= P(B₁) * P(B₂ | B₁)
= (1/2) * (1/3)
= 1/6
P(Same color)
= P(R₁ and R₂) + P(B₁and B₂)
= 1/6 + 1/6 = 2/6
= 1/3
So, the probability that both marbles are the same color is 1/3.
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1. What properties of quadratic functions cause this "death ray" effect?
2. Using the diagram below, what is the point called where the sun's rays are concentrated? Will the "death ray" always hit the same spot? Why?
2. Could this property of quadratic functions be helpful in a different situation? Explain
The properties of quadratic functions cause this "death ray" effect is discussed below.
The "death ray" effect refers to the phenomenon where a quadratic function appears to have a sharp point or vertex that shoots off to infinity in a graph. This effect is caused by the properties of quadratic functions, specifically:
The degree of the quadratic function: Quadratic functions have a degree of 2, which means they have a leading term that is a squared variable (x²). This leads to a graph that is a parabola.
The coefficient of the squared term: The coefficient of the squared term in the quadratic function determines the shape of the parabola. If the coefficient is positive, the parabola opens upward, and if the coefficient is negative, the parabola opens downward.
However, when the coefficient of the squared term is negative (a < 0), the graph of the quadratic function opens downward, and the vertex represents the maximum point of the parabola.
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Find the measure of Zb.
←
Zb=
Blank 1:
76 a
104/b
∠b and 76° are alternate angles. They are equal.
So, m∠b = 76
That's it :)
Find the unlabeled side length. If necessary, round your answer to the nearest
hundredth (two decimal places).
5
12
The unlabeled side length for this problem has the measure given as follows:
13.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side, is equals to the sum of the squares of the lengths of the other two sides.
Hence the equation for the theorem is given as follows:
c² = a² + b².
In which:
c > a and c > b is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The sides for this problem are given as follows:
5 and 12.
Hence the measure of the hypotenuse is obtained as follows:
h² = 5² + 12²
h² = 169
h = 13.
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What is the value of x?
Use the rules of special right triangles to find x.
The value of the length x is 1.5
How to determine the valueUsing the sine trigonometric identity, we have that;
sin 45 = y/6√2
cross multiply the values, we have that;
y = 1/√2 × 6/√2
Multiply the values, we get;
y = 6/2
Divide the values
y = 3
Then, using the cosine identity, we get;
cos 60 = x/3
Find the cosine value and cross multiply, we get;
x = 0.5(3)
Now, multiply the values, we get;
x = 1.5
Hence, the value of the length is 1.5
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What is the value of S?
The value of s in the circle is 11.
We have,
When two chords in a circle have the same arc length intercepted by the chords, it means that the distances from each endpoint of the chords to the center of the circle are equal.
Now,
The arc length XY and WZ are the same.
This means,
Chord XY and Chord WZ are equal.
Now,
2s = s + 11
Solve for s.
2s - s = 11
s = 11
Thus,
The value of s in the circle is 11.
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May someone please help me find the domain and range thank you for the help
The domain and the range of the table of values are Domain = {-15, 0, 9, 33, 44, 45} and Range = {21, 33, 57, 15, 97, 46}
Calculating the domain and range of the table of values?From the question, we have the following parameters that can be used in our computation:
The table of values
The above table of values can be represented as a list of ordered pairs
The rule of a table of values is that
The domain is the x valuesThe range is the f(x) valuesusing the above as a guide, we have the following:
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Write the answer to Kiran's question using mathematical notation. (the money kiran)
-12x stands for the amount Kiran takes out each month.
B. any value of x that is less than or equal to 6.25 will work for Kiran.
c. One can use x ≤ 6.25 to show all the values that would work for Kiran.
d. The answer to Kiran's question can be written using mathematical notation as:
Kiran can be able to take out a maximum of $6.25 every month to make sure that he has at least $25 in the account a year from that time now.
What is the statement about?Since the inequality is -12x + 100 ≥ 25, the term -12x stands for the amount Kiran takes out each month. It is seen as a negative value because it stands for the monthly withdrawals from the said account.
b. To find values of x that would work for Kiran, it can be done by:
-12x + 100 ≥ 25.
-12x + 100 ≥ 25
So, subtract 100 from both sides:
-12x ≥ 25 - 100
-12x ≥ -75
Then divide both sides by -12 ( dividing by a negative number changes the inequality sign) Hence it will be:
x ≤ (-75) / (-12)
x ≤ 6.25
So, any value of x that is less than or equal to 6.25.
c. One can use x ≤ 6.25 to show all the values that would work for Kiran. based on the fact that:
Kiran requires to have at least $25 in the account a year from now, he cannot withdraw more than $6.25 per month. If he withdrew more than that, he would not have more money left in the account after a single year.
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See text below
Kiran has $100 saved in a bank account. (The account doesn’t earn interest.) He asked Clare to help him figure out how much he could take out each month if he needs to have at least $25 in the account a year from now.
a. Clare wrote the inequality -12x + 100 ≥ 25, where x represents the amount Kiran takes out each month. What does -12x represent?
b. Find some values of x that would work for Kiran.
c. We could express all the values that would work using either x ≤ _ or x ≥ _. Which one should we use?
d. Write the answer to Kiran’s question using mathematical notation.
Find the value of x. If necessary, round to the nearest tenth.
5
6
x
The value of x in the circle using the intersecting secants and tangents equation is 4
How to find the value of x in the circleFrom the question, we have the following parameters that can be used in our computation:
The circle
The value of x in the circle can be calculated using the intersecting secants and tangents equation
So, we have
6² = x * (x + 5)
When expanded, we have
x² + 5x - 36 = 0
When factored, we have
(x + 9)(x - 4) = 0
Using the zero product property , we have
x = -9 or x = 4
The valiue of x cannot be negative
So, we have
x = 4
Hence, the value of x in the circle is 4
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A photographer has been commissioned to take a series of photographs of a rocket being launched from the Kennedy Space Center in Florida. They have positioned their camera at (B) and the launching pad of rocket (A) is 300 meters. The camera must keep the rocket in sight and therefore its angle of elevation t must change with the height x of the rocket.
Find angle t as a function of the height x.
Find angle t in degrees when x is equal to 150, 300, and 600 meters. (approximate your answer to 1 decimal place).
Graph t as a function of x.
Explain the steps you took to arrive at your answer with at least 3 complete sentences.
After considering the given data we conclude that angle t as a function of the height x is θ = tan⁻¹ (x/300), and angle t in degrees when x is equal to 150, 300, and 600 meters is 63.4°, the graph represent a curve when drawn.
The angle of elevation of the camera can be evaluated by
θ=tan⁻¹(x/2000)
Here, x = height of the rocket.
Hence, the angle t as a function of the height x is given by:
θ = tan⁻¹ (x/300)
To evaluate the angle t in degrees when x is equal to 150, 300, and 600 meters, we stage these values into the equation above:
θ = tan⁻¹ (150/300) = 26.6° (approximate to 1 decimal place)
θ = tan⁻¹ (300/300) = 45° (approximate to 1 decimal place)
θ = tan⁻¹ (600/300) = 63.4° (approximate to 1 decimal place)
To graph t as a function of x, we can plot the values of θ for different values of x. The graph will be a curve that starts at 0° when x=0 and increases as x increases.
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