Answer:
Step-by-step explanation:
A: V = πr²h
B: V = 1/3π(2r)²(2h) = 1/3π(4r²)(2h) = 1/3π8r²h = 8/3πr²h
C: V = π(2r)²(2h) = π(4r²)(2h) = π8r²h = 8πr²h
D: V = 1/3πr²(2h) = 2/3πr²h
If GE = 42 and DH = 16, find GF
Based on the above. (see image attached), The value of GF in the rhombus is option A: 26.4
What is the value of the rhombus?A four-sided shape with equal side lengths is known as a rhombus. Equally sided four-sided figure is also referred to as an equilateral quadrilateral, because equilateral denotes that its sides have the same length.
Note that the properties of a rhombus are :
All the sides are equalOpposite angles are equaladjacent angles are supplementaryDiagonals are perpendicular bisector of each otherSo, note that:
DH = HF = 16
GH = HE = 21
Therefore, by Using Pythagoras theorem we can look for GF by:
GF = √21² + 16²
= √441 + 256
= √697
= 26.4007575649
= 26.4
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Given the values of the linear functions f(x) and g(x) in the tables, what is (f – g)(-1)?
The domain of the composite function (f - g)(-1) is derived to be 12 which makes c the correct option.
What is composite function?A function is composite when the co- domain of the first mapping is the domain of the second mapping
We shall evaluate the domains of the function (f - g)(-1) as follows:
Observing from the table of values, at the point x = -1 we have;
f(x) = 5 and g(x) = -7
So;
(f - g)(-1) = 5 - (-7)
(f - g)(-1) = 5 + 7
(f - g)(-1) = 12
Therefore, the value for domain of the composite function (f - g)(-1) is derived to be 12.
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Name the acute angle in the shape
Answer:
∠ADB
Step-by-step explanation:
Acute angles measure less than 90°.
So, here ∠ADB is acute angle,
PLEASE PLEASE HELP WILL MARK BRAINLIST!!!!!!!!!!!!
Answer:
y ≤ - [tex]\frac{2}{7}[/tex] x
Step-by-step explanation:
the blue region indicates where the solutions lie
that is below the given line
the equation of the line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 7, 2) ← 2 points on the line
m = [tex]\frac{2-0}{-7-0}[/tex] = [tex]\frac{2}{-7}[/tex] = - [tex]\frac{2}{7}[/tex]
the line crosses the y- axis at (0, 0 ) ⇒ c = 0
y = - [tex]\frac{2}{7}[/tex] x ← equation of line
the line is solid thus the region below is denoted by y ≤ , that is
y ≤ - [tex]\frac{2}{7}[/tex] x
In recent years, Sheffield Transportation purchased three used buses.
This acquisition of used buses reflects Sheffield Transportation's commitment to providing reliable and cost-effective transportation options for their customers.
In recent years, Sheffield Transportation has acquired three used buses for their transportation fleet. The decision to purchase these buses was likely made to meet the growing demand for transportation services in the area, while also keeping costs down by opting for used vehicles instead of new ones.
It is important to note that when purchasing used buses, Sheffield Transportation would have had to ensure that the vehicles were in good condition and met safety standards before putting them into service. Overall, this acquisition of used buses reflects Sheffield Transportation's commitment to providing reliable and cost-effective transportation options for their customers.
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Another right triangular prism has the same base as the prism in the example. The height of his prism is 8 m. What is the volume of the prism? Show your work
The first triangular prism has a height of 4
The length was x which was found out to be 10
And the width was 12
Here is the work shows for the first triangular prism
V=bh
240=(1/2)(x)(4)(12)
240=24x
10=x
Please help I give 25 brainly
The volume of the second right triangular prism is 7488.96 cubic meters.
For the second right triangular prism, we have:
Base: A right triangle with base 10 m and height 12 m
Height: 8 m
To find the volume, we can use the same formula as before:
Volume = (1/2) x base x height x altitude
Using the Pythagorean theorem, we can find that the altitude is:
altitude = √(10² + 12²) = √(244) ≈ 15.62
Now we can substitute the given values into the volume formula:
Volume = (1/2) x 10 x 12 x 8 x 15.62
Volume ≈ 7488.96 m^3
Therefore, the volume of the second right triangular prism is 7488.96 cubic meters.
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(Worth 100 Brainly points) After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the
rainbow is the shape of a parabola.
The equation for this parabola is y=-x² + 36
1.Create a table of atleast 4 values of the function that includes two points of intersection between the airplane and the rainbow
2.What is the domain and range of the rainbow? Explain what the domain and range represent.Do all of the values make sense in the situation. Why or why not.
3.what are the x and y intercepts of the rainbow. Explain what each intercept represents.
The table of at least 4 values of the function is
x 0 -6 6 3
y 36 0 0 27
The domain is All set of real values and the range: y ≤ 36
The x and y intercepts of the rainbow are x = (-6, 0) and (6, 0) y = (0, 36)
Creating a table of at least 4 values of the functionGiven that we have
y = -x² + 36
From the graph, we have the following values
x y
0 36
-6 0
6 0
Set x = 3
So, we have
y = -3² + 36
Evaluate
y = 27
So, we have
x y
0 36
-6 0
6 0
3 27
The domain and the rangeFrom the graph, we have
Domain: All set of real valuesRange: y ≤ 36These values mean that;
Domain: The time of the dayRange: The height of the sunFor the x and y intercepts of the rainbow, we have
x = (-6, 0) and (6, 0)
y = (0, 36)
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help please answer the number 1 only thanyou
i will give brainliest
Answer:
[tex]\sin\theta=\dfrac{\sqrt{5}}{5}[/tex]
[tex]\cos\theta=\dfrac{2\sqrt{5}}{5}[/tex]
[tex]\tan\theta=\dfrac{1}{2}[/tex]
[tex]\csc\theta=\sqrt{5}[/tex]
[tex]\sec\theta=\dfrac{\sqrt{5}}{2}[/tex]
Step-by-step explanation:
The cotangent ratio is the reciprocal of the tangent ratio.
[tex]\cot \theta = \dfrac{1}{\tan \theta}[/tex]
Therefore, if cot θ = 2 then:
[tex]\dfrac{1}{\tan \theta}=2[/tex]
[tex]\tan \theta=\dfrac{1}{2}[/tex]
The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle:
[tex]\tan\theta = \sf \dfrac{opposite}{adjacent}[/tex]
Therefore, the length of the side opposite angle θ is 1 and the length of the side adjacent angle θ is 2.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
We can use Pythagoras Theorem to calculate the length of the hypotenuse, H:
[tex]1^2+2^2=H^2[/tex]
[tex]1+4=H^2[/tex]
[tex]H^2=5[/tex]
[tex]H=\sqrt{5}[/tex]
Therefore, the length of the hypotenuse is √5.
Now we have the lengths of the three sides of the right triangle, we can find the other trigonometric function of angle θ.
[tex]\boxed{\begin{minipage}{8cm}\underline{Trigonometric functions}\\\\$\sf \sin\theta=\dfrac{O}{H}\quad\cos\theta=\dfrac{A}{H}\quad\tan\theta=\dfrac{O}{A}$\\\\\\$\sf\csc\theta=\dfrac{H}{O}\quad\sec\theta=\dfrac{H}{A}\quad\cot\theta=\dfrac{A}{O}$\\\\\\where:\\\phantom{ww}$\bullet$ $\theta$ is the angle.\\\phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle.\\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse.\\\end{minipage}}[/tex]
Given values:
O = 1A = 2H = √5Substitute these values into the six trigonometric functions:
[tex]\sin\theta=\dfrac{O}{H}=\dfrac{1}{\sqrt{5}}=\dfrac{\sqrt{5}}{5}[/tex]
[tex]\cos\theta=\dfrac{A}{H}=\dfrac{2}{\sqrt{5}}=\dfrac{2\sqrt{5}}{5}[/tex]
[tex]\tan\theta=\dfrac{O}{A}=\dfrac{1}{2}[/tex]
[tex]\csc\theta=\dfrac{H}{O}=\dfrac{\sqrt{5}}{1}=\sqrt{5}[/tex]
[tex]\sec\theta=\dfrac{H}{A}=\dfrac{\sqrt{5}}{2}[/tex]
[tex]\cot\theta=\dfrac{A}{O}=\dfrac{2}{1}=2[/tex]
Help which one is correct
the base of the triangle below is b. bc.
I will give the BRAINIEST!!
It is 12pm and Maria and Nemzet are about to try and complete a jigsaw puzzle together before they have to get ready for a party that starts at Spes. If attempting this puzzle alone, it would take Maria 7
hours to complete it and it would take Nemzet 5 hours
Use the information above to choose all sentences which are true. Select all that apply
It will take them approximately 2.9 hours to finish the puzzle together. Therefore, options B, C are the correct answers.
Given that, Maria and Nemzet are about to try and complete a jigsaw puzzle.
Together attempting this puzzle alone, it would take Maria 7 hours to complete it and it would take Nemzet 5 hours
Here, 1/7 + 1/5 = 1/t
(5+7)/35 = 1/t
12/35 = 1/t
t=35/12
t=2.91
t=2.9 hours
Therefore, options B, C are the correct answers.
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Strontium-90 has a half-life of 28.1 years. How many years will it take for a sample of Strontium-90 to decay to 25% of its initial quantity?
Answer:
B
Step-by-step explanation:
One half life there will be 50 %
another half life and there will be 25 %
so TWO half lives * 28.1 yrs/ half life = 56.2 yrs
7. A card is randomly selected from a standard deck of cards. Write the theoretical
probability of each event as a fraction, decimal, and percent. [K:18)
a. A spade
b. A face card (jack, queen or king)
c. Not a face card
d. A black jack
e. A red or black card
f. A red face card
Answer:
a. The theoretical probability of drawing a spade from a standard deck of cards is 13/52, which reduces to 1/4, or 0.25, or 25%.
b. The theoretical probability of drawing a face card (jack, queen, or king) from a standard deck of cards is 12/52, which reduces to 3/13, or approximately 0.231, or 23.1%.
c. The theoretical probability of drawing a non-face card from a standard deck of cards is 40/52, which reduces to 10/13, or approximately 0.769, or 76.9%.
d. The theoretical probability of drawing a black jack from a standard deck of cards is 2/52, which reduces to 1/26, or approximately 0.038, or 3.8%.
e. The theoretical probability of drawing a red or black card from a standard deck of cards is 52/52, which reduces to 1/1, or 100%.
f. The theoretical probability of drawing a red face card from a standard deck of cards is 6/52, which reduces to 3/26, or approximately 0.115, or 11.5%.
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
The three true statements about the function and its graph are The graph of the function is a parabola, The graph does not open down (it opens upwards). and None of the given points, (20, -8) or (0, 0), lie on the graph.
Based on the quadratic function f(x) = x^2 – 5x + 12:
The value of f(-10) = 82 is not true.
To find the value of f(-10), substitute x = -10 into the function: f(-10) = (-10)^2 - 5(-10) + 12 = 100 + 50 + 12 = 162.
The graph of the function is a parabola.
This statement is true. The quadratic function has a degree of 2, which means its graph will be a parabola.
The graph of the function opens down.
This statement is not true. The coefficient of the x^2 term in the quadratic function is positive (1), so the parabola opens upwards.
The graph contains the point (20, -8).
This statement is not true. To verify if the point (20, -8) is on the graph, substitute x = 20 into the function: f(20) = (20)^2 - 5(20) + 12 = 400 - 100 + 12 = 312. Therefore, the point (20, -8) does not lie on the graph.
The graph contains the point (0, 0).
This statement is not true. To verify if the point (0, 0) is on the graph, substitute x = 0 into the function: f(0) = (0)^2 - 5(0) + 12 = 0 - 0 + 12 = 12. Therefore, the point (0, 0) does not lie on the graph.
Therefore, the three true statements about the function and its graph are:
The graph of the function is a parabola.
The graph does not open down (it opens upwards).
None of the given points, (20, -8) or (0, 0), lie on the graph.
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HELP ASAPPPPPP
Given: line AB with endpoints A2,5and B−4,−2.
Identify the coordinates of the midpoint.
Answer:
(-1, 1.5).
Step-by-step explanation:
To find the midpoint of line segment AB with endpoints A(2, 5) and B(-4, -2), you can use the midpoint formula. The midpoint formula states that the midpoint (M) of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by:
M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
Let's calculate the midpoint using this formula:
x-coordinate of midpoint:
x = (2 + (-4)) / 2 = -2 / 2 = -1
y-coordinate of midpoint:
y = (5 + (-2)) / 2 = 3 / 2 = 1.5
Therefore, the midpoint of line AB is M(-1, 1.5).
Which point is represented by 6 times the quantity cosine 11 pi over 6 plus i times sine 11 pi over 6 end quantity question mark
[tex]6\left[\cos\left( \frac{11\pi }{6} \right) +i\sin\left( \frac{11\pi }{6} \right) \right] \\\\\\ 6\left[\cfrac{\sqrt{3}}{2}~~,~-\cfrac{1}{2}i \right]\implies (3\sqrt{3}~~,~-3i) ~~ \approx ~~ \stackrel{ \textit{\LARGE S} }{(5.2~~,~-3i)}[/tex]
The values listed are waiting times (in minutes) of customers at two different banks...
(a) The 99% confidence interval for the population standard deviation at Bank A is 1.33 to 2.16.
(b) The 99% confidence interval for the population standard deviation at Bank B is 1.41 to 2.29.
How to calculate the confidence interval?To find the confidence interval for the population standard deviation, we can use the chi-square distribution. The formula for the chi-square distribution is:
(X²) / (n-1) = s²
where X² is the chi-square value, n is the sample size, and s is the sample standard deviation.
For Bank A:
n = 20
s = 1.252
Using the chi-square distribution table with a degree of freedom of n-1 = 19 and a 99% confidence level, we find the critical values to be 8.907 and 32.852. Substituting these values into the formula above, we get:
(19 x 1.252²) / 32.852 < o² < (19 x 1.252²) / 8.907
1.78 < o² < 4.67
1.33 < o < 2.16
Therefore, the 99% confidence interval for the population standard deviation at Bank A is 1.33 to 2.16.
For Bank B:
n = 20
s = 1.397
Using the chi-square distribution table with a degree of freedom of n-1 = 19 and a 99% confidence level, we find the critical values to be 8.907 and 32.852. Substituting these values into the formula above, we get:
(19 x 1.397²) / 32.852 < o² < (19 x 1.397²) / 8.907
2.00 < o² < 5.24
1.41 < o < 2.29
Therefore, the 99% confidence interval for the population standard deviation at Bank B is 1.41 to 2.29.
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12,15,20,25,30,20,30,15,12,12
Answer:
The mode of this set of numbers is 12. If that is what you are looking for.
Please help asap
Find the indicated measure for circle P.
26. The length FE in the circle is 6 units
27. The arc AE has a measure of 64 degrees
26. Calculating the length FEFrom the question, we have the following parameters that can be used in our computation:
The circle
Given that the lengths from the center to either chords are equal
This means that
FE = 6 units
27. Calculating the measure of arc AEFor the other circle, we have
BC = 58 degrees
AB = ED
The arc AE is calculated as
AE = 180 - BC - ED
Where
AB = ED = BC = 58 degrees
So, we have
AE = 180 - 58 - 58
Evaluate
AE = 64
Hence, the arc AE is 64 degrees
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Select the slope that would be parallel to y= 12.50x + 5
12.50
Step-by-step explanation:Parallel lines are lines that will never intersect.
Parallel Lines
Parallel lines run opposite of each other without intersecting. For lines to be parallel, they must have the same slope. The equation given to us is written in slope-intercept form. The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. So, the slope from the equation is 12.50.
Finding Parallel Lines
In order to find other lines that are parallel to the line given, all we need to do is write another equation with the same slope. However, 2 lines that are the same are not considered to be parallel. This means that for 2 lines to be parallel they must have the same slope but different y-intercepts. For example, a parallel line could be y = 12.50x + 6.
Solve for the missing side length. Round to 2 decimal places
23°
6
X
The value of missing side is,
⇒ x = 2.54
We have to given that;
A triangle is shown.
And, To find the missing side of triangle.
Now, By using trigonometry formula, we get;
⇒ tan 23° = Opposite / Base
⇒ tan 23° = x / 6
⇒ 0.424 = x / 6
⇒ x = 0.424 × 6
⇒ x = 2.54
Thus, The value of missing side is,
⇒ x = 2.54
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10. In this figure, a line through points X and Y will
A line through points X and Y will be perpendicular bisector of AB.
By examining the figure, it is evident that the compass created arcs as follows:
An arc was drawn with A as the center and a radius greater than half the length of AB.
and, another arc was drawn with B as the center using the same radius.
The points where these arcs intersect are labeled as X and Y.
This construction clearly represents the creation of a perpendicular bisector for the line segment AB.
Therefore, if we draw a line segment passing through points XY, it will serve as the perpendicular bisector of AB.
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Which is equivalent to 49 2*
92x
0 gx
0 /g*
0 §g*
The expression that is equivalent to [tex]49^{\frac{3}{2}}[/tex] is given as follows:
D. 343.
What is the power of a power rule?The power of a power rule is used when a single base is elevated to multiple exponents.
Then the simplified expression is obtained keeping the base, while the exponents are multiplied.
The expression for this problem is given as follows:
[tex]49^{\frac{3}{2}}[/tex]
49 is the square of 7, hence:
49 = 7².
Then the expression can be simplified as follows:
[tex]7^2^{\frac{3}{2}}[/tex]
The multiplication of the exponents is of:
2 x 3/2 = 3.
(when we apply the power of power rule, we keep the base and multiply the exponents)
Hence:
7³ = 343.
Missing InformationThe problem is given by the image presented at the end of the answer.
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2. Find the least number by which each of the given numbers should be multiplied so as to get a perfect square. Also, find the square root of the resulting number. a) 845 b) 1008
The least number by which each of the given numbers should be multiplied so as to get a perfect square are 5 and 7.
Here, we have,
we have
a) 845 =5×13×13
The smallest whole number is 5, by which 845 should be multiplied so as to get a perfect square.
Now , we get,
845 ×5=5×13×13×5
4225=5×13×13×5
√4225=65
b) 1008=2×2××2×3×3×3
The smallest whole number is 7, by which 1008 should be multiplied so as to get a perfect square.
Now , we get,
1008×7=2×2×2×2×3×3×7×7
7056=2×2×3×7
=84
Answer : 5 and 7
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please help with this
Answer:
F(- 3) = - 2 , F(0) = 0
Step-by-step explanation:
(a)
F(- 3) with x = - 3 is in the interval x < 0 , then
F(- 3) = 3x = x + 1 = - 3 + 1 = - 2
(b)
F(0) with x = 0 is in the interval x ≥ 0 , then
F(0) = 3x = 3 × 0 = 0
Which function is represented by this graph?
-10 -8 -6 -4 -2
-10
-2
-6
-8
-10
2
4
6
8
10
The standard absolute value graph has been shifted 7 units to the right and 3 units down to get this graph.
That means we have answer B: f(x) = | x - 7 | - 3
Remember that the left-right shifts are opposite from what they would appear to be in the equation.
| x - 7 | shifts it right 7 units.
| x + 7 | shifts it left 7 units.
Help please I have to answer these questions using the graph.
The answers to all parts is shown below.
a. According to the graph, the concentration after 8 hours is approximately 22 mg/L.
b. The concentration increases from 0 to approximately 30 mg/L over the first 4 hours, and then decreases from approximately 30 mg/L to 16 mg/L between 4 and 20 hours.
c. The drug is at its maximum concentration after approximately 4 hours, with a maximum concentration of approximately 30 mg/L.
d. According to the graph, it takes approximately 12 hours for the concentration to decrease from the maximum concentration of approximately 30 mg/L to 16 mg/L.
e. After 1 week, the graph predicts that the concentration will be very close to 0 mg/L. After 1 month, the concentration is predicted to be essentially 0 mg/L.
f. During the first 4 hours, the concentration increases from 0 to approximately 30 mg/L.
Between 4 and 8 hours, the concentration decreases slightly from approximately 30 mg/L to 28 mg/L.
Between 8 and 12 hours, the concentration decreases more rapidly from 28 mg/L to approximately 22 mg/L.
Between 12 and 20 hours, the concentration decreases gradually from 22 mg/L to 16 mg/L.
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Help please answer the number 3 only thanyou
i will give brainliest
Answer:If cos(\theta) = \sqrt(3)/2, then we can use the Pythagorean identity sin^2(\theta) + cos^2(\theta) = 1 to find sin(\theta):
sin^2(\theta) + (\sqrt(3)/2)^2 = 1
sin^2(\theta) + 3/4 = 1
sin^2(\theta) = 1 - 3/4
sin^2(\theta) = 1/4
sin(\theta) = +/- 1/2
Since \theta is an acute angle, sin(\theta) must be positive. Therefore, sin(\theta) = 1/2.
We can then use the identity tan(\theta) = sin(\theta)/cos(\theta) to find tan(\theta):
tan(\theta) = sin(\theta)/cos(\theta)
tan(\theta) = (1/2)/(\sqrt(3)/2)
tan(\theta) = 1/\sqrt(3)
Finally, we can use the reciprocal and quotient identities to find the values of sec(\theta) and csc(\theta):
sec(\theta) = 1/cos(\theta)
sec(\theta) = 2/\sqrt(3)
csc(\theta) = 1/sin(\theta)
csc(\theta) = 2
Step-by-step explanation:
Answer:
[tex]\sin\theta=\dfrac{1}{2}[/tex]
[tex]\tan\theta=\dfrac{\sqrt{3}}{3}[/tex]
[tex]\csc\theta=2[/tex]
[tex]\sec\theta=\dfrac{2\sqrt{3}}{3}[/tex]
[tex]\cot\theta=\sqrt{3}[/tex]
Step-by-step explanation:
The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse of a right triangle:
[tex]\cos\theta= \sf \dfrac{adjacent}{hypotenuse}=\dfrac{\sqrt{3}}{2}[/tex]
Therefore, the length of the side adjacent angle θ is √3 and the length of the hypotenuse is 2.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
We can use Pythagoras Theorem to calculate the length of the side opposite angle θ:
[tex](\sqrt{3})^2+O^2=2^2[/tex]
[tex]3+O^2=4[/tex]
[tex]O^2=1[/tex]
[tex]O=1[/tex]
Therefore, the length of the side opposite angle θ is 1.
Now we have the lengths of the three sides of the right triangle, we can find the other trigonometric function of angle θ.
[tex]\boxed{\begin{minipage}{8cm}\underline{Trigonometric functions}\\\\$\sf \sin\theta=\dfrac{O}{H}\quad\cos\theta=\dfrac{A}{H}\quad\tan\theta=\dfrac{O}{A}$\\\\\\$\sf\csc\theta=\dfrac{H}{O}\quad\sec\theta=\dfrac{H}{A}\quad\cot\theta=\dfrac{A}{O}$\\\\\\where:\\\phantom{ww}$\bullet$ $\theta$ is the angle.\\\phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle.\\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse.\\\end{minipage}}[/tex]
Given values:
O = 1A = √3H = 2Substitute these values into the six trigonometric functions:
[tex]\sin\theta=\dfrac{O}{H}=\dfrac{1}{2}[/tex]
[tex]\cos\theta=\dfrac{A}{H}=\dfrac{\sqrt{3}}{2}[/tex]
[tex]\tan\theta=\dfrac{O}{A}=\dfrac{1}{\sqrt{3}}=\dfrac{\sqrt{3}}{3}[/tex]
[tex]\csc\theta=\dfrac{H}{O}=\dfrac{2}{1}=2[/tex]
[tex]\sec\theta=\dfrac{H}{A}=\dfrac{2}{\sqrt{3}}=\dfrac{2\sqrt{3}}{3}[/tex]
[tex]\cot\theta=\dfrac{A}{O}=\dfrac{\sqrt{3}}{1}=\sqrt{3}[/tex]
Find the missing information:
In the figure below, mZPSR = 106°. Find m PTR.
The arc angle in the circle is as follows:
mPTR = 63 degrees.
How to find measure of an arc angle?The tangent intersection theorem states that If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one-half the measure of its intercepted arc.
Therefore,
m∠PSR = 1 /2 (mPTR - mPR)
mPTR = ?
mPR = 149 degrees
m∠PSR = 106
Therefore,
106 = 1 / 2 (x - 149)
106 = 0.5x - 74.5
106 - 74.5 = 0.5x
31.5 = 0.5x
divide both sides by 0.5
x = 31.5 / 0.5
x = 63 degrees
Therefore,
mPTR = 63 degrees
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What is the volume of the prism? 3ft. 1 1/2 ft. 6ft. Use the formula V=Bh to calculate the volume of the prism.
Answer:
18 ft.
Step-by-step explanation:
if a car left Lagos for portharcourt with the average speed of 60 km per hour, how long will it take for the car to arrive portharcourt?
Answer:
8 hours and 20 minutes
Step-by-step explanation:
Let's assume the distance between Lagos and Port Harcourt is approximately 500 kilometers. With an average speed of 60 km per hour, we can use the formula:
Time = Distance / Speed
Substituting the values, we get:
Time = 500 km / 60 km/h ≈ 8.33 hours
Therefore, it would take approximately 8 hours and 20 minutes for the car to travel from Lagos to Port Harcourt, assuming the distance is around 500 kilometers and the average speed is 60 km per hour. Please note that this is just an example calculation, and the actual time may vary depending on the distance and road conditions.