Answers
Answer:
[tex]{ \sf{( \sec \theta - \csc \theta)(1 + \tan \theta + \cot \theta) }} \\ = { \sf{( \sec \theta + \tan \theta \sec \theta + \cot \theta \sec \theta) - ( \csc \theta - \csc \theta \tan \theta - \csc \theta \cot \theta)}} \\ = { \sf{( \sec \theta + \sec \theta \tan \theta + \csc \theta) - ( \csc \theta - \sec \theta - \csc \theta \cot \theta)}} \\ = { \sf{ \sec \theta \tan \theta + \csc \theta \cot \theta }} \\ { \bf{hence \: proved}}[/tex]
Related Questions
find the values of x and y.
Answers
Answer:
x=15.75 y=59
Step-by-step explanation:
In total there is 360 degrees. We know y is 59 so we will replace it with that.
59+59=118. 360-118=242. 242/2=121. 29+29=58. So we can subtract that to equal 63. Now 63=4x. We can divide so 2x=31.5. x=15.75.
Therefore, 15.75=x and 59=y
I hope this helped ^^.
a) 7°
c) 26°
b) 64°
d) 83°
Answers
Answer:
x = 26
Step-by-step explanation:
sin x =4/9
Take the inverse sin of each side
sin ^-1 (sin x) = sin^-1(4/9)
x=26.38779
To the nearest degree
x = 26
what is the smallest number by which 6400 must be multiplied to make a perfect cube?
Answers
Answer:
10
Step-by-step explanation:
i looked it up to be sure but if wrong very sorry.
[15 points]The distance from the earth to the moon is approximately 380592 km. Assuming the moon has a circular orbit around the earth, find the distance the moon travels in orbiting the earth through an angle of 2.62 radians.
Answers
Answer:
634806 km travelled by the Moon as it orbits 2.62 radians about the Earth.
Step-by-step explanation:
convert to pi.
SOMEONE HELP ME PLEASE
Answers
For the given question,
Total number of outcomes
= 6 (i.e. 1, 2, 3, 4, 5 and 6)
Number of favourable outcomes
= 4 (i.e. 3, 4, 5, 6)
So,
[tex]P = \frac{Number \: of \: favourable \: outcomes}{Total \: number \: of \: outcomes} \\ = > P= \frac{4}{6} \\ = > P = \frac{2}{3} \\ = > P = 0.6666......[/tex]
3x + ky = 8
X – 2ky = 5
are simultaneous equations where k is a constant.
b) Given that y = 1/2 determine the value of k.
Answers
Answer:
(a): x is 3 and ky is -1
(b): k is -2
Step-by-step explanation:
Let: 3x + ky = 8 be equation (a)
x - 2 ky = 5 be equation (b)
Then multiply equation (a) by 2:
→ 6x + 2ky = 16, let it be equation (c)
Then equation (c) + equation (b):
[tex] { \sf{(6 + 1)x + (2 - 2)ky = (16 + 5)}} \\ { \sf{7x = 21}} \\ { \sf{x = 3}}[/tex]
Then ky :
[tex]{ \sf{2ky = 3 - 5}} \\ { \sf{ky = - 1}}[/tex]
[tex]{ \bf{y = \frac{1}{2} }} \\ { \sf{ky = - 1}} \\ { \sf{k = - 2}}[/tex]
Simultaneous equations are used to represent a system of related equations.
The value of k when [tex]y = \frac 12[/tex] is -2
Given that:
[tex]3x + ky = 8[/tex]
[tex]x - 2ky = 5[/tex]
[tex]y = \frac 12[/tex]
Substitute [tex]y = \frac 12[/tex] in both equations
[tex]3x + ky = 8[/tex]
[tex]3x + k \times \frac 12 = 8[/tex]
[tex]3x + \frac k2 = 8[/tex]
[tex]x - 2ky = 5[/tex]
[tex]x - 2k \times \frac 12 = 5[/tex]
[tex]x - k = 5[/tex]
Make x the subject in [tex]x - k = 5[/tex]
[tex]x = 5 + k[/tex]
Substitute [tex]x = 5 + k[/tex] in [tex]3x + \frac k2 = 8[/tex]
[tex]3(5 + k) + \frac k2 = 8[/tex]
Open bracket
[tex]15 + 3k + \frac k2 = 8[/tex]
Multiply through by 2
[tex]30 + 6k + k = 16[/tex]
[tex]30 + 7k = 16[/tex]
Collect like terms
[tex]7k = 16 - 30[/tex]
[tex]7k = - 14[/tex]
Divide both sides by 7
[tex]k = -2[/tex]
Hence, the value of constant k is -2.
Read more about simultaneous equations at:
https://brainly.com/question/16763389
The base of the rectangle is 7 inches, and the height is 6 inches. The area of one triangle is square inches.
Answers
Answer:
21
Step-by-step explanation:
area of triangle = 1/2 * base * height
assuming the triangle is made by cutting the rectangle into half,
1/2 * 7 * 6 = 21
Answer:
the answer is 21
Step-by-step explanation:
To avoid the problem of having access to tables of the F distribution with values for the lower tail when a one-tailed test is required, let the _____ variance be the numerator of the test statistic. a. sample variance from the population with the larger hypothesized b. larger sample c. sample variance from the population with the smaller hypothesized d. smaller sample
Answers
Answer:
The answer is "Option b".
Step-by-step explanation:
The significant variance shows that the numbers in the set are far from the mean and far from each other as well. Alternatively, a little variation implies the reverse. The variance value of 0, on either hand, shows that all values inside a set of numbers are the same. If you need yet another test, use a greater sample variance as the numerator of the test statistic to avoid having to reference tables of the F distribution that primary device from of the lower tail.
WHERE ARE THE EXPERTS AND ACE!!!!!!! I NEED HELP PLS SHARE YO SMARTNESS!!!!! WILL GIVE BRAINLIEST AND RATE AND VOTE!!!
Answers
Answer:
A and c
Step-by-step explanation:
1) Length arc = r*theta
5.11=1*theta. Theta is 5.11 rads
2) Law of cosines is the correct answer
Problem Apply the distributive property to create an equivalent expression. (m-3+4n)\cdot (-8) =(m−3+4n)⋅(−8)=
Answers
Given:
The expression is:
[tex](m-3+4n)\cdot (-8)[/tex]
To find:
The equivalent expression by using the distributive property.
Solution:
Distributive property:
[tex]a(b+c)=ab+ac[/tex]
We have,
[tex](m-3+4n)\cdot (-8)[/tex]
Using the distributive property, we get
[tex](m-3+4n)\cdot (-8)=(m)\cdot (-8)+(-3)\cdot (-8)+(4n)\cdot (-8)[/tex]
[tex](m-3+4n)\cdot (-8)=-8m+24-32n[/tex]
Therefore, the equivalent expression is [tex]-8m+24-32n[/tex].
Use the product of powers property to simplify the expression -2x^3y4x^2y^3
Answers
Answer:
= -8x^5 y^4
Step-by-step explanation:
Multiply the numbers: -2 . 4 = -8
-2x^3 yx^2 y^3
Simplify x^3 x^2 : x^5
= -8x^5yy^3
Simplify yy^3 : y^4
= -8x^5 y^4
An explanation for the results is that those over the age of 55 grew up exposed to media that was displayed in black and white. Can these results be used to verify that explanation? A. No. The results speak to a possible difference between the proportions of people over 55 and under 25 who dream in black and white, but the results cannot be used to verify the cause of such a difference. B. Yes. The results can be used to verify the given explanation because the difference in proportions is statistically significant. C. Yes. The results can be used to verify the given explanation because the difference in proportions is practically significant. D. No. The results speak to a possible difference between the proportions of people over 55 and under 25 who dream in black and white, but the results are not statistically significant enough to verify the cause of such a difference.
Answers
Answer:
No. The results speak to a possible difference between the proportions of people over 55 and under 25 who dream in black and white, but the results cannot be used to verify the cause of such a difference.
Hence the correct option is option A.
Looking at the top of tower A and base of tower B from points C and D, we find that ∠ACD = 60°, ∠ADC = 75° and ∠ADB = 30°. Let the distance between points C and D be 100. Find the height AB of the tower.
Picture attached for the problem. Please show your work too. Thanks!
Answers
Answer:
[tex]\text{Exact: }AB=25\sqrt{6},\\\text{Rounded: }AB\approx 61.24[/tex]
Step-by-step explanation:
We can use the Law of Sines to find segment AD, which happens to be a leg of [tex]\triangle ACD[/tex] and the hypotenuse of [tex]\triangle ADB[/tex].
The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:
[tex]\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}=\frac{c}{\sin \gamma}[/tex]
Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is [tex]\angle CAD[/tex]. The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:
[tex]\angle CAD+\angle ACD+\angle CDA=180^{\circ},\\\angle CAD+60^{\circ}+75^{\circ}=180^{\circ},\\\angle CAD=180^{\circ}-75^{\circ}-60^{\circ},\\\angle CAD=45^{\circ}[/tex]
Now use this value in the Law of Sines to find AD:
[tex]\frac{AD}{\sin 60^{\circ}}=\frac{100}{\sin 45^{\circ}},\\\\AD=\sin 60^{\circ}\cdot \frac{100}{\sin 45^{\circ}}[/tex]
Recall that [tex]\sin 45^{\circ}=\frac{\sqrt{2}}{2}[/tex] and [tex]\sin 60^{\circ}=\frac{\sqrt{3}}{2}[/tex]:
[tex]AD=\frac{\frac{\sqrt{3}}{2}\cdot 100}{\frac{\sqrt{2}}{2}},\\\\AD=\frac{50\sqrt{3}}{\frac{\sqrt{2}}{2}},\\\\AD=50\sqrt{3}\cdot \frac{2}{\sqrt{2}},\\\\AD=\frac{100\sqrt{3}}{\sqrt{2}}\cdot\frac{ \sqrt{2}}{\sqrt{2}}=\frac{100\sqrt{6}}{2}={50\sqrt{6}}[/tex]
Now that we have the length of AD, we can find the length of AB. The right triangle [tex]\triangle ADB[/tex] is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]x[/tex] is the side opposite to the 30 degree angle and [tex]2x[/tex] is the length of the hypotenuse.
Since AD is the hypotenuse, it must represent [tex]2x[/tex] in this ratio and since AB is the side opposite to the 30 degree angle, it must represent [tex]x[/tex] in this ratio (Derive from basic trig for a right triangle and [tex]\sin 30^{\circ}=\frac{1}{2}[/tex]).
Therefore, AB must be exactly half of AD:
[tex]AB=\frac{1}{2}AD,\\AB=\frac{1}{2}\cdot 50\sqrt{6},\\AB=\frac{50\sqrt{6}}{2}=\boxed{25\sqrt{6}}\approx 61.24[/tex]
Answer:
[tex] \displaystyle 25 \sqrt{6} [/tex]
Step-by-step explanation:
the triangle ∆ABD is a special right angle triangle of which we want to figure out length of its shorter leg (AB).
to do so we need to find the length of AD (the hypotenuse). With the help of ∆ADC it can be done. so recall law of sin
[tex] \boxed{ \displaystyle \frac{ \alpha }{ \sin( \alpha ) } = \frac{ \beta }{ \sin( \beta ) } = \frac{ c}{ \sin( \gamma ) } }[/tex]
we'll ignore B/sinB as our work will be done using the first two
step-1: assign variables:
[tex] \sin( \gamma ) = \sin( {60}^{ \circ} ) [/tex][tex]c=AD[/tex][tex] \rm \sin( \alpha ) = \sin( {180}^{ \circ} - ({60}^{ \circ} + {75}^{ \circ} )) = \sin( {45}^{ \circ} ) [/tex][tex]a=100[/tex]step-2: substitute
[tex] \displaystyle \frac{100}{ \sin( {45}^{ \circ} )} = \frac{AD }{ \sin( {60}^{ \circ} )} [/tex]
recall unit circle therefore:
[tex] \displaystyle \frac{100}{ \dfrac{ \sqrt{2} }{2} } = \frac{AD }{ \dfrac{ \sqrt{3} }{2} } [/tex]
simplify:
[tex]AD = 50 \sqrt{6} [/tex]
since ∆ABD is a 30-60-90 right angle triangle of which the hypotenuse is twice as much as the shorter leg thus:
[tex] \displaystyle AB = \frac{50 \sqrt{6} }{2}[/tex]
simplify division:
[tex] \displaystyle AB = \boxed{25 \sqrt{6} }[/tex]
and we're done!
This is a scale drawing of a house where 1 centimeter represents 0.6 meters. What is the height of the house at its highest point? Round to one decimal point, if necessary.
Answers
Answer:
Height of the house = 3 meter (Approx.)
Step-by-step explanation:
Given:
Scale model;
1 centimeter = 0.6 meter
According to graph
Height of cube = 5 cube = 5 centimeter
Find:
Height of the house
Computation:
Height of the house = height of the house in scale model x Scale model
Height of the house = 5 x 0.6
Height of the house = 3
Height of the house = 3 meter (Approx.)
please ans this question pleaseee
Answers
Answer:
[tex]{ \tt{ \tan {}^{4} \theta + { \sec }^{2} \theta }} \\ { \tt{ = ({ \tan }^{2} \theta ){}^{2} + { \sec }^{2} \theta }} \\ = { \tt{ {-(1 - { \sec }^{2} \theta) }^{2} + { \sec }^{2} \theta }} \\ { \tt{ = -(1 - 2 { \sec }^{2} \theta + { \sec }^{4} \theta) + { \sec}^{2} \theta}} \\ { \tt{ = -(1 - { \sec }^{2} \theta) + { \sec }^{4} \theta}} \\ { \tt{ = -{ \tan}^{2} \theta + { \sec }^{4} \theta }} \\ = { \tt{ { \sec}^{4} \theta - { \tan }^{2} \theta}} \\ { \bf{hence \: proved}}[/tex]
20 laborers can complete the construction of building in 24 days .In how many days
would 16 laborers complete the construction?
7. In a survey of 468 tourists who visited Nepal during visit Nepal 2020 it was found that
275 visited Rara ,300 visited Bardiya and 56 tourist do not visit both the place .
(i) How many tourists were there who visited Rara as well as Bardiya ?
(ii) Represent the above information in venn diagram.
8. Two numbers are in the ratio 7:5 .When 10 is subtracted from each term their ratio
becomes 3:2.Find the numbers.
Answers
Answer:
20=24
8. =? Cross multply
Identify the perimeter and area of an equilateral triangle with height 12 cm. Give your answer in simplest radical form.
Answers
Answer:
perimeter is 36 cm
Step-by-step explanation:
IF a and bare roots of 3x² - 6x + 2=0 ,then find. a, a-b
Answers
Answer:
a is 1.58 and b is 0.42
Step-by-step explanation:
[tex]{ \sf{3 {x}^{2} - 6x + 2 = 0 }} \\ { \sf{x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} }} \\ \\ { \sf{x = \frac{ - ( - 6)± \sqrt{ {( - 6)}^{2} - (4 \times 3 \times 2) } }{(2 \times 3)} }} \\ \\ { \sf{x = \frac{6± \sqrt{12} }{6} }} \\ \\ { \sf{x = 1.58 \: and \: 0.42}}[/tex]
Amanda teaches the art of quilling to 4 students. These students each teach the art of quilling to 4 other students. This process continues through 3 more generations.
Answers
4x4=16 16x3=48 so I think the answer is 48
The length of a rectangle is six times its width. If the area of the rectangle is 384^2, find its perimeter.
Answers
Answer:
Perimeter, P = 112 meters
Step-by-step explanation:
Let the length of the rectangle be L.Let the width of the rectangle be W.Translating the word problem into an algebraic expression, we have;
L = 6W ...... equation 1
Given the following data;
Area of rectangle = 384 m²To find the perimeter of the rectangle;
First of all, we would determine the dimensions of the rectangle using its area.
Mathematically, the area of a rectangle is given by the formula;
Area of rectangle = LW ..... equation 2
Substituting eqn 1 into eqn 2, we have;
384 = 6W(W)
384 = 6W²
Dividing both sides by 6, we have;
W² = 384/6
W² = 64
Taking the square root of both sides, we have;
W = √64
Width, W = 8 meters
Next, we would find the length;
L = 6W
L = 6 * 8
Length, L = 48 meters
Lastly, we would determine the perimeter of the rectangle using the above dimensions;
Mathematically, the perimeter of a rectangle is given by the formula;
Perimeter = 2(L + W)
Substituting the values into the formula, we have;
Perimeter, P = 2(48 + 8)
Perimeter, P = 2(56)
Perimeter, P = 112 meters
Please hurry I will mark you brainliest
What is the equation of the line that passes through (3,-1) and is parallel to the line y=3x+2?
Answers
Answer:
y = 3x-10
Step-by-step explanation:
When lines are parallel, they have the same slope
y = 3x+2 is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is 3
y = 3x+b
We have a point on the line
-1 = 3(3)+b
-1 = 9+b
-10 = b
y = 3x-10
Please help me find which expression is correct
Answers
Answer:
IN MY OPINION D NO IS THE CORRECT ANSWER OF YOUR QUESTION.
Answer:
in my opinion d is the correct answer of your questions.
Step-by-step explanation:
Because subtract subtract sign is always add.
hope this will help you
thanks
a car can complete journey of 300 km with the average speed of 60 km per hour how long does it take to complete the journey what is the speed of the car if it covers only 200 km in the same interval of the time
please I need help urgent
Answers
Answer:
a. 5 hours
b. 40 kph
Step-by-step explanation:
300 km ÷ 60 km = 5 hours
200 km ÷ 5 hours = 40 kilometers per hour
To wash a window that is 4 meters off the ground, Rafi leans a 5-meter ladder against the side of the building. To reach the window, how far away from the building should Rafi place the base of the ladder?
Answers
Answer:
Base of the ladder is 3 meters away from the building.
Step-by-step explanation:
Let's use Pythagoras theorem to solve.
Pythagoras theorem says,
[tex]a^{2} +b^{2} =c^{2}[/tex]
Here let horizontal distance is "a''
Vertical distance of window is 4 m
So, b=4
The Rafi leans 5 m ladder against the wall. So, c=5.
[tex]a^{2} +4^{2} =5^{2}[/tex]
Simplify it
[tex]a^{2} +16=25[/tex]
Subtract both sides 16
[tex]a^{2} =9[/tex]
Take square root on both sides
a=±3
So, base of the ladder is 3 meters away from the building.
Rearranging formulae. Can anyone help me with this question and show how you did it please? Will mark brainliest!
Answers
A. -5x+4y=-20
B. -5x-4y=-20
C. -5x+4y=0
D. 5x+4y=-20
Answers
So the first step is to change the equation into that.
We know m = the slope and b = the y-intercept
So,
m = y1-y2/x1-x2 ( I decided to use the intercepts)
The rest is on the paper, and sorry I wasn't neat with my working
Consider this linear function y=1/2x+1 plot all ordered pairs for the values in the domain D:{-8,-4,0,2,6}
Answers
Answer:
Following are the calculated points to the given question:
Step-by-step explanation:
[tex]When\ x=-8\\\\y=\frac{1}{2}(-8)+1=-3\\\\[/tex]
so,
[tex]Point \ A(-8,-3)[/tex]
[tex]When\ x=-4\\\\y=\frac{1}{2}(-4)+1=-1\\\\[/tex]
so,
[tex]Point \ B(-4,-1)[/tex]
[tex]When\ x=0\\\\y=\frac{1}{2}(0)+1=1\\\\[/tex]
so,
[tex]Point \ C(0,1)[/tex]
[tex]When\ x=2\\\\y=\frac{1}{2}(2)+1=2\\\\[/tex]
so,
[tex]Point \ D(2,2)[/tex]
[tex]When\ x=6\\\\y=\frac{1}{2}(6)+1=4\\\\[/tex]
so,
[tex]Point \ E(6,4)[/tex]
find cosØ if sinØ=-12/13 and tanØ>0.
A) -5/12
B) -5/13
C) 12/5
D) -13/12
Answers
Answer:
-5/13
Step-by-step explanation:
sin theta = opp / hyp
sin theta = -12 /13
we can find the adj side by using the pythagorean theorem
adj^2 + opp ^2 = hyp^2
adj^2 +(-12)^2 = 13^2
adj^2 +144 =169
adj^2 = 169-144
adj^2 = 25
Taking the square root of each side
adj = ±5
We know that it has to be negative since it is in the third quad
adj = -5
cos theta = adj / hyp
cos theta = -5/13
Answer:
B) -5/13
Step-by-step explanation:
i hope it will help
plzz mark as brainliest if you want
Samantha’s hockey team is fundraising for a trip to Europe! They are aerating lawns to raise money. Aerating lawns is a great service for homeowners because it helps the grass grow new roots and absorb water producing healthier lawns! The team has decided to charge $35/lawn for city sized lots. The rental cost for two aerating machines is $215. Samantha’s team has planned a Saturday to aerate!
Write an equation to relate the fund raised, R, in dollars to the number of lawns, l, aerated during the day.
Samantha’s team was able to aerate 26 lawns in one day! How much money did they raise?
How much money would the team lose if they were unable to aerate due to weather conditions? Is there any possible way they could avoid this potential loss?
Answers
Answer:
R = 35l-215
Step-by-step explanation:
total amount they earn = 35l
however, to account for the money used to rent the machines, we have to deduct 215 from the total cost.
hence,
R= 35l-215
total amount they raised = 35(26)-215 = $695
they would lose $215 if they were unable to aerate due to weather conditions
they could avoid this potential loss by checking the weather report before renting the machines
A department store is ordering the fall line of shoes. Which of the following statistical measurements would they use to determine what sizes they should order the most? A. range B. median C. mean D. mode
Answers
Answer:
Mode
Step-by-step explanation:
If I'm not mistaken the mode is the value that appears most which in this case would mean the size that is bout the most.So he should use the mode which basically shows what size is bought the most and buy that size
The statistical measurements they would use to determine what sizes they should order the most is mode option (D) is correct.
What is the mode?It is defined as the highest frequency of data and how many times the element is repeated in the data set, known as the mode value.
We have:
A department store is ordering the fall line of shoes.
As we know, Statistics is a mathematical tool defined as the study of collecting data, analysis, understanding, representation, and organization. Statistics is described as the procedure of collecting data, classifying it, displaying that in a way that makes it easy to understand, and analyzing it even further.
The mean value for the given set of data or the closed value for each entry given in the set of data.
Thus, the statistical measurements they would use to determine what sizes they should order the most is mode option (D) is correct.
Learn more about the mode here:
brainly.com/question/300591
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