Answers
Answer:
[tex]\tan 2 x = \dfrac{24}7[/tex]
Step by step explanation:
[tex]\textbf{2)}\\\\\text{Given that,} \\\\~~~~~\cos x = -\dfrac 45\\\\\implies \cos^2 x = \dfrac{16}{25}~~~~~~~~~~;[\text{Square both sides}]\\\\\implies 1- \sin^2 x= \dfrac{16}{25}\\\\\implies \sin^2 x = 1- \dfrac{16}{25}\\\\\implies \sin^2 x = \dfrac{9}{25}\\\\\implies \sin x =\pm\sqrt{\dfrac{9}{25}}\\\\\implies \sin x = \pm \dfrac 35\\\\[/tex]
[tex]\text{Since,}~ \pi \leq x \leq \dfrac{3\pi}{2}, ~ \text{the angle lies in the 3rd quadrant, where}~ \sin x ~ \text{is negative.}\\\\\text{So,}~ \sin x = -\dfrac 35[/tex]
[tex]\text{Now,}~\\\\\tan x = \dfrac{\sin x }{\cos x} = \dfrac{-\tfrac 35}{-\tfrac 45} = \dfrac 35 \times \dfrac 54 = \dfrac 34\\\\\\\tan 2x =\dfrac{2 \tan x }{ 1- \tan^2 x}\\\\\\~~~~~~~~~=\dfrac{2 \left( \tfrac 34 \right)}{1- \left( \tfrac 34 \right)^2}\\\\~~~~~~~~~=\dfrac{\tfrac 64}{1-\tfrac {9}{16}}\\\\\\~~~~~~~~~=\dfrac{\tfrac 32 }{\tfrac 7{16}}\\\\\\~~~~~~~~~=\dfrac 32 \times \dfrac{16}7\\\\\\~~~~~~~~~=\dfrac{24}7[/tex]
Related Questions
Points a and b lie on a circle centered at point o. if oa = 5 and what is the area of sector aob? use the value π = 3.14, and choose the closest answer. a. 19.6 square units b. 39.3 square units c. 7.85 square units d. 15.7 square units
Answers
The area of sector AOB whose radius OA 5 units is 19.6 sq. units.
What is the Sector?A sector is a portion of a circle which is enclosed between its two radii and the arc adjoining them. The most common sector of a circle is a semi-circle which represents half of a circle.
Here, Radius of Circle = 5 units
length of arc AB / circumference = 1/4
So, Area of Sector AOB = one fourth of area of circle
= 1/4 X π X r²
= 0.25 X 3.14 X 5²
= 0.25 X 3.14 X 25
= 19.625 sq. units
Thus, the area of sector AOB whose radius OA 5 units is 19.6 sq. units.
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Answer:
19.6
Step-by-step explanation:
What is the phenotypic ratio of the offspring? 1:1:1:1:2:2:2:2:4 1:3:3:9 1:4 4:12
Answers
The phenotypic ratio of the offspring as shown in the given Punnett square is: 1:3:3:9.
What is Phenotypic Ratio?Phenotypic ratio is quantitative relation of the number of offspring of a cross that manifest a certain combination of traits or characteristic.
From the Punnett square given, there are:
9 round and yellow individuals3 round and green individuals3 wrinkled and yellow individuals1 wrinkled and green individualsTherefore, the phenotypic ratio would be: 1:3:3:9.
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Answer:
B it the answer 1:3:3:9
Step-by-step explanation:
The volume of air in a balloon is represented by the function v(r)=4/3 pi ^3, where r is the radius of the balloon, in
inches. The radius of the balloon increases with time, in seconds, by the function r(t) = 1².
Write a composite function that can be used to determine the volume of the balloon after t seconds. Then, select the
two true statements.
Answers
find the altitude of a kite where 120 feet of string makes a 64 degree angle to the ground
Answers
Answer:
107.86 to 2 d.p.
Step-by-step explanation:
makes a triangle. 120 feet is the hypotenuse.
we want to find the opposite so we will use sine.
sin(x) = opp/hyp which means opp = sin(x)hyp.
opp = sin(64)120
opp = 107.86 to 2d.p.
Factorise completely 12 x³y - 18 xy²
Answers
Answer:
6xy(2x²-3y)
Step-by-step explanation:
factorized completely
If a baseball player hits 10 home runs in the first 45 game, at the same rate how many home runs can he expect to hit during the 162 game season
Answers
Using proportions, it is found that he can be expected to hit 36 home runs during the 162 game season.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, the player hits 10 home runs in 45 games, hence the proportion is:
p = 10/45.
Then, in 162 games, the amount is:
HR = 10/45 x 162 = 36.
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A cylindrical container is packaged inside a prism-shaped box. the box has a volume of 96 cubic units. if the container has a diameter of 4 units and a height of 6 units, what is the volume of the empty space between the cylinder and the box? round the answer to two decimal places. a. 20.60 cubic units b. 37.77 cubic units c. 51.27 cubic units d. 75.40 cubic units
Answers
Volume is a three-dimensional scalar quantity. The volume of the empty space is 20.602 units³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
Given the volume of the prism, the box is 96 units³ and the diameter of the cylindrical container is 4 units(Radius=2 units), while the height of the cylinder is 6 units. Therefore, The volume of the empty space is,
The volume of the empty space
= Volume of prism - Volume of the cylindrical container
= 96 units³ - (π×2²×6) units³
= 96 units³ - 75.398 units³
= 20.602 units³
Hence, the volume of the empty space is 20.602 units³.
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what is the distance from (7,0)- (-5,5)
Answers
Answer:
[tex]\frac{5}{-12}[/tex]
Step-by-step explanation:
If you use the formula [tex]m = \frac{y2 - y1} {x2 - x1}[/tex] with x1 being 7, y1 being 0, -5 being x2 and 5 being y2, then you can subtract. 5(y2) minus 0(y1) is 5, and -5(x2) minus 7(x1) is -12. The formula would look like this: [tex]m = \frac{5 - 0}{-5 - 7} \frac{5}{-12}[/tex].
(tip: you need to do rise over run, aka y over x, shown as [tex]\frac{y}{x}[/tex] or [tex]\frac{rise}{run}[/tex])
I hope I helped you answer your question, and helped better understand it as well
how can i find area of abd triangle. .............
Answers
Answer:
6 square units
Step-by-step explanation:
The attachment shows the figure redrawn to scale, along with helpful semicircle O with diameter EB. Trig relations can be used to find the area of triangle ADB. The relation between an inscribed angle and its corresponding central angle is also helpful.
__
anglesAny right triangle can be inscribed in a semicircle whose diameter is the hypotenuse. Accordingly, we have constructed semicircle O whose center is the midpoint of EB. Hence its radius is EB/2 = 4/2 = 2.
Then angle EBD is an inscribed angle, hence half the measure of central angle EOD. Since ∠EOD is double the measure of ∠EBD, it is congruent to ∠EBC, which is also double the measure of ∠EBD. We have called the measure of this double angle θ. Its complement is the angle marked β.
segmentsThe fact that angles EOD and EBC are congruent means that segments OD and BC are parallel. Segment BC is the altitude of ΔADB with respect to base AD.
The tangent ratio is ...
Tan = Opposite/Adjacent
Applying that to angle β, we have
tan(β) = OD/AD [eqn 1]
tan(β) = BC/AC [eqn 2]
These two relations can be solved for the measures of AD and BC, which we need in order to find the area of ΔADB.
areaEquation [eqn 1] tells us ...
AD = OD/tan(β)
Equation [eqn 2] tells us ...
BC = AC·tan(β)
The area of ΔADB is ...
Area = 1/2bh
Area = 1/2(AD)(BC) = 1/2(OD/tan(β))·(AC·tan(β))
Area = 1/2(OD)(AC) . . . . . . factors tan(β) cancel
The length of AC is given as 6, and we know OD = 2, so the area is ...
Area = 1/2(2)(6) = 6
The area of triangle ADB is 6 square units.
Choose the expression that represents a linear expression.
6x + 6
O-6x² +8x-9
O8x3 + 9x² - 10x + 11
07x4-8x³+9x² - 10x + 11
Question 3(Multiple Choice Worth 1 points)
(06.01 LC)
Answers
Answer:
6x+6
Step-by-step explanation:
a linear expression has no power attached to the x (the unknown)
An mp3 player was reduced from $229.99 to $129.99. find the percent reduction in price. round the answer to the nearest tenth of a percent, if necessary.
Answers
Answer:
43.4%
Step-by-step explanation:
229.99 - 129.99
= 100
The percent reduction is:
100/229.99 * 100
=43.4%
In a statistics activity, students are asked to determine the proportion of times that a spinning penny will land with tails up. the students are instructed to spin the penny 10 times and record the number of times the penny lands tails up. for one student, it lands tails side up six times. the student will construct a 90% confidence interval for the true proportion of tails up. are the conditions for inference met?
Answers
Using the Central Limit Theorem, it is found that the conditions for inference are not met, as there are less than 10 successes and less than 10 failures.
What does the Central Limit Theorem state?It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].
In this problem, we have that np = 6 < 10, n(1-p) = 4 < 10, hence the conditions for inference are not met.
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A coffee table is on sale for 20% off the original price of $115. If there is 7.5% sales tax, what is the final price of the coffee table?
Answers
Answer:
The final price for the coffee table is $98.9.
Step-by-step explanation:
1. First, is to convert the percentage to decimal form
We can do this by changing 7.5% to decimal number by dividing 7.5 by 100, we get:
\frac{7.5}{100}
100
7.5
= 0.0750.075
2. Then multiply 0.075 to the original price of $115
0.075(115) = 8.625
Then, add 8.625 to the original price of $115, we get:
115 + 8.625 = $123.625
3. After this, we subtract the 20% discount to $123.625
We can do this by converting 20% to decimal form, we get:
\frac{20}{100}
100
20
= 0.20.2
Then, multiply $123.625 by 0.2, we get:
123.625(0.2) = $24.725
4. Then subtract 24.725 from $123.625, we get:
123.625 -123.625−24.725 = $98.9
Final price of the table coffee which is on sale by 20% with a sales tax of 7.5% is $98.9.
A rectangle is 21 meters long and 11 meters wide. what is the perimeter of this rectangle?
Answers
Step-by-step explanation:
the perimeter is simply the distance you would have to walk when going around the whole object once.
so, you would go a length, a width, another length and another width, until you are finally arriving back at the starting point.
so, the perimeter of a rectangle is
2×length + 2×width = 2×21 × 2×11 = 42 + 22 = 64 m
Please help me thank you :3
Answers
Quadrilaterals are angles that has 4 sides and angles. The measure of the angle m<SPQ is 110 degrees
Angles in a quadrilateralQuadrilaterals are angles that has 4 sides and angles. The given quadrilateral is a rhombus with equal opposite sides.
Given the following angles
m<SPR = 2x + 15
m<QPR = 3x - 5
From the figure
m<SPR = m<QPR
Substitute
2x+ 15 = 3x - 5
2x - 3x = -5 - 15
x = 20
Determine the measure of <SPQ
m<SPQ = 3x - 5 +2x +15
m<SPQ = 5x + 10
m<SPQ =5(20) + 10
m<SPQ = 110 degrees
Hence the measure of the angle m<SPQ is 110 degrees
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I need to know how to solve this
Answers
Answer:
K=-6/11
Step-by-step explanation:
3(k/3+4-2k)=3(-9k)
K+12-6k=-27k
12-5k=-27k
12=-22k
K=-6/11
A number cube is rolled 15 times how many times would you expect a number less than 3 to be rolled
Answers
Answer:
45
Step-by-step explanation:
how many number you rolled 3 times how many times its rolled 15 x 3 +45
Therefore,the answer would be 45
The diagram shows a regular polygon.
x
What is the value of x?
Write your answer as an integer or as a decimal rounded to the nearest tenth.
Answers
Answer:
To find the value of x, use the formula
(n-2) x 180, where n is the number of sides.
In this case, we have a TRIangle, which has THREE sides.
So, n=3
(3-2) x 180
1 x 180
180
If the total sum of the angles is 180, then the measure of one angle would be 180 divided by 3, which is 60.
Let me know if this helps, or if you got any more questions
The slope of a line is 7/8 The y-intercept of the same line is 4
Complete the slope-intercept form equation
Answers
Answer:
y = -7/8x + 4
Step-by-step explanation:
Slope-intercept form :
y = mx + b
m = slopeb = y-interceptHence, the equation formed is :
y = -7/8x + 4Which is true about the functional relationship shown in the graph?
Answers
represent the sum of 3/4 and -5/8 is ???
Answers
3/4 + -5/8
---Find a common denominator
6/8 + -5/8
---Simplify
1/8
Hope this helps!
Answer:
3/4 + -5/8 = 1/8
Step-by-step explanation:
When adding fractions, you always need to find a common denominator. 4 and 8 share a common denominator of 8.
You multiply 3/4 by 2/2 and get 6/8.
When adding negative numbers, it is the same as subtracting.
6/8 + (-5/8) =
6/8 - 5/8 = 1/8
So 1/8 is the answer.
I hope this helps!
What is the value of f(x) when x=3?
Answers
Slope of (-9,-2) and (-9,-6)
Answers
Answer:
Slope is undefined.
Step-by-step explanation:
The troupe’s account balance first reached $500 on Day 4. The last day the account balance was $500 was
Day 8.
(a) Determine C(5), C(6), and C(7). Explain how you determined these amounts.
(b) Estimate C(1), C(2), and C(3). Explain how you determined these amounts.
(c) The stage manager said that the amount of money taken out of the account each day between Day 8
and Day 11 was the same amount of money put into the account each day between Day 0 and Day 4.
Recall that Day 11 is when the balance first reached $0. Without doing any calculations, how could
you show the stage manager was incorrect?
Answers
Answer:
The answer is c, hope this helps
Step-by-step explanation:
I will choose brainlyist and 20 POINTS
Answers
Answer:
They are all non triangles, but I'm not in your math class, so I don't know.
Step-by-step explanation:
Quadrilateral ABCD has the following coordinates: A(-6,3) B(-4,5) C(-1,6) and D(-3,2) and
maps onto A"B"C"D". It will undergo transformations that will consist of a reflection over
the y-axis followed by a translation. Point D" is shown plotted in the plane after the
transformation.
A) Write the translation rule that maps point D' to point D".
B) Write the coordinates of point A"
Answers
The translation rule that maps point D' to D" is (x + 3, y) and the coordinate of point A" is (9,3)
How to determine the translation rule?The coordinates are given as:
A(-6,3) B(-4,5) C(-1,6) and D(-3,2)
When reflected across the y-axis, the transformation rule is:
(x,y) -> (-x,y)
So, we have:
A' = (6,3)
D' = (3,2)
Point D" on the grid is (6,2).
This means that the translation rule that maps both point is (x + 3, y)
The coordinates of point AIn (a), we have:
A' = (6,3)
Using the translation rule (x + 3, y), we have:
A" = (6 + 3,3)
A" = (9,3)
Hence, the coordinate of point A" is (9,3)
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Kelly made fruit punch to serve at a party for her chess team. She mixed 1
2/5
liters of cranberry juice and 1
3/5
liters of pineapple juice together. Then, she split the fruit punch evenly among 9 glasses. How much fruit punch did Kelly pour into each glass?
Answers
Answer:
1/3 liters. or 33.33333 ml
Step-by-step explanation:
1 2/5 + 1 3/5 = 3
3 liters of juice is there.
3 liters of juice/9 glasses.
1/3 liters of juice is in every glass
Help!! Also the questions says “Which of the following shows JUST a variable?”
Answers
Variables are letters that represent unknown numbers
It can be any letter if the alphabet (a,b,c,d…..)
The others are what we call an (expression )which is basically when we put variables with other numbers
Which point is one fourth of the way between point A and point B on the line segment AB shown on the coordinate plane below?
Answers
The coordinate of the point between point A and point B on the line segment AB is [tex](\frac 92, -\frac{19}4)[/tex]
How to determine the point?The points are given as:
A = (4,-5)
B = (6,-4)
m : n = 1 : 3
The coordinate of the point is then calculated using:
[tex]P = \frac{1}{m + n}(mx_2 + nx_1,my_2 + ny_1)[/tex]
So, we have:
[tex]P = \frac{1}{1 + 3}(1 * 6 + 3 * 4, 1 * -4 + 3 * -5)[/tex]
Evaluate the sum of product
[tex]P = \frac{1}{4}(18, -19)[/tex]
Evaluate the product
[tex]P = (\frac 92, -\frac{19}4)[/tex]
Hence, the coordinate of the point is [tex](\frac 92, -\frac{19}4)[/tex]
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the diagram shows a sector of a circle radius 10cm
calculate the perimeter of the sector
give answer to 1 decimal place
Answers
Answer:
[tex]\text{Perimeter of sector = 43.6 (Rounded to the nearest tenth.)}[/tex]
Step-by-step explanation:
[tex]\text{Perimeter of the sector = Radius + arc length + radius}[/tex]
[tex]\text{Radius = 10 cm}[/tex]
[tex]\text{Perimeter of the sector = 10 + arc length + 10 }[/tex]
[tex]\text{Perimeter of the sector = 20 + arc length }[/tex]
[tex]\text{arc length = (sector angle/ 360 ) * perimeter of the circle}[/tex]
[tex]\text{Perimeter of a circle }=2\pi r[/tex]
[tex]\text{sector angle} = 135[/tex]
[tex]\text{arc length} = (135/ 360 ) * 2\pi (10)[/tex]
[tex]= (3/8) 20\pi[/tex]
[tex]= 15\pi /2[/tex]
[tex]\text{Using }\pi =3.14[/tex]
[tex]= 15 * 3.14 /2[/tex]
[tex]= 23.55[/tex]
[tex]\text{Perimeter of the sector = 20 + 23.55}[/tex]
[tex]= 43.55[/tex]
[tex]= 43.6 cm[/tex]
[tex]\text{perimeter of the sector = 43.6 cm }[/tex]