96 points here, having to ask same question again - please help a brother out.
Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation. Show your work.
1. cot x sec^4 x = cot x + 2 tan x + tan^3 x
2. (sin x)(tan x cos x - cot x cos x) = 1 - 2 cos^2 x
3. 1 + sec^2 x sin^2 x = sec^2 x
4. ((sin x)/(1-cos x)) + ((sin x)/(1+cos x))=2csc x
5. - tan^2 x + sec^2x = 1
Answers
the equation is - tan2 x + sec2 x = 1.
Left hand side identity : - tan2 x + sec2 x.
Trigonometric function : tan x = sin x / cos x,
Reciprocal identity : sec x = 1/cos x.
- tan2 x + sec2 x = - (sin x/cos x)2 + (1/cos x)2
= - sin2 x/cos2 x + 1/cos2 x
= (1 - sin2 x)/cos2 x
Pythagorean identity : sin2 x + cos2 x = 1 .
= cos2 x / cos2 x
= 1
Related Questions
Write an equation of the line through (5,5)and parallel to the line 4x+3y=-2
Please help
Answers
4x + 3y = -2
Subtract 4x from both sides.
3y = -4x - 2
Divide all terms by 3.
y = -4/3x - 2/3
The slope in this equation is -4/3 (4 down, 3 to the right).
Using that slope, input the coordinates (5, 5) into the equation of a line:
y - y1 = m(x - x1)
y - 5 = -4/3(x - 5)
y - 5 = -4/3x + 20/3
y = -4/3x + 35/3
The equation of the line is y = -4/3x + 35/3.
Which is an equation of the line with x-intercept 2 and y-intercept 12?
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Find the diameter of a cone that has a volume of 56.52 cubic inches and a height of 6 inches. use 3.14 for pi. (1 point) 3 inches 6 inches 9 inches 12 inches
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To find the answer, set the volume of the cone (56.52) equal to the formula for the volume of the cone (3.14(r)squared times height) Plug in the height and solve for the radius. When you have the radius (3) multiply it by 2 to get the diameter (6).
Answer:
Diameter= 6 inches
Step-by-step explanation:
Find the next two terms of the sequence. 2, 6, 10, 14, ... (1 point)
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Noticing this sequence, we will find that the sequence increases by 4 each time. This means that:
The next number = the current number + 4
In other words:
2
2+4 = 6
6+4 = 10
10+4 = 14
14+4 = 18
Therefore, the next number in the sequence would be 18
Answer:
C. 18,22
Step-by-step explanation:
A card is drawn from a deck of 52 cards. find the probability of drawing a king or a red card
Answers
drawing a red car:26/52
drawing a red king: 2/52
4/52 +26/52 -2/52=28/52
change to decimal if required: 0.5385
$40 is discounted into $32 what is the percent decrease
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Please Help With This. What is the equation of the line shown in this graph? Answer your answer in the box.
Points are:
(-2,-3) (3,-3)
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[tex]\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-3)=0[x-(-2)] \\\\\\ y+3=0\implies y=-3[/tex]
What is the next term in the sequence 1/2 1/6 1/18 1/54
Answers
2*3=6
6*3=18
18*3=54
54*3=162
A girl starts to walk to her school, which is 20 miles away, at 6:50 and at a rate of 3 miles per hour. After a while, her dad picks her up and drives her through the remainder of the way at 30 miles per hour. If they arrived at school at 9:00, how far did she walk?
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Answer:
She walked 5 mi
tell weather the side lengths can form a trangle
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Triangles XYZ and PQR are drawn on a square grid. What fraction of the area of triangle XYZ is the area of trianglePQR?
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From the given figure: The base of the bigger triangle is 6 units and the height is 3 units.
The base of the smaller triangle is 3 units and the height is 2 units.
The area of the big triangle is [tex] \frac{1}{2} \times6\times3=9\, square\, units[/tex]
The area of the small triangle is [tex] \frac{1}{2} \times3\times2=3\, square\, units[/tex]
The required fraction is [tex] \frac{3}{9} = \frac{1}{3} [/tex]
To determine the fraction of area of triangle XYZ that is occupied by triangle PQR on a square grid, we can compare their linear dimensions and use the fact that area is proportional to the square of these dimensions, or we can approximate the area through summation of small rectangular areas on the grid. Alternatively, vector methods such as the cross product can provide precise area calculations for triangles with known vertices.
Finding the Area of Triangles on a Square Grid
To find what fraction of the area of triangle XYZ is the area of triangle PQR, we follow several steps. First, we can draw both triangles on a square grid and establish their respective areas. If we assume that XYZ is the larger triangle and PQR is the smaller one, we can use the fact that area scales in proportion to the square of the linear dimensions. This means, if the linear dimensions of PQR are half that of XYZ, the area of PQR would be one-fourth that of XYZ. In mathematical terms, if the side length of XYZ is scaled by a factor of 's', the area is scaled by s².
Another method to approximate the area of irregular shapes like these triangles, as mentioned in a reference, is by dividing the shape into smaller, manageable rectangular areas whose sum approximates the total area. Counting the smallest square units within the grid and making rough estimates of the fractional squares can yield the area as well.
To demonstrate the calculation of the area of a triangle through vector methods, one can use the cross product of two vectors defined by the triangle's vertices. Given vertices A(1,2,3), B(2,4,5), and C(1,-8,0), their position vectors can be used to compute the cross product, and the magnitude of this cross product gives twice the area of the triangle ABC. This is a more advanced method and offers a precise way to calculate the area without relying on the grid.
Give the first four nonzero terms of the series about x=8 representing the function x^(1/3)
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The population of bees has been decreasing at a rate of 10% per year in 2012 there were 6000 bees in particular hive how many bees were there in 2014
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10% of 6000 is 60
so 6000 - 60 = 5940
2013 = 5940 bees
10% of 5940 = 59.4
so 5940 - 59.4 = 5880.6
so in 2014 you 5881 because you cant have a 0.6 of a bee
QUICKK EXPERTS/ACE OR ANYONE WHO WANTS TO HELP!!
Answers
bottom left,
since the lines are parallel with each other there is no solution
Maybelle looked at a hotel. She waited a week before she decided to book nights at that hotel, and now the prices have increased. The original price was $1195. The price for the same room and the same number of nights is now $2075. What is the percent increase? Round to the nearest whole percent. Explain and Show your work.
-20 points. Better yet, 30 points!! Please help!
Diff in price = %
_________ _________ thats the formula i think...
original price 100
Answers
Plug in to get (2075-1195)/1195*100
880/1195*100
.7364*100
73.64% rounding we get
74%
Is the square root of 37 rational or irrational
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Hope this helps!
If you know how to do this, can you show the work, please?
Thanks
Answers
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Let x be the original side length of the square. The original area is therefore going to be x*x = x^2. For now we don't know the area but once we figure out x, we can compute the area.
The original side length x is increased by 7 ft to jump up to (x+7) ft
At the same time, the other dimension is reduced to (x-2) ft, which is a decrease of 2 ft
The old square is x ft by x ft with area x*x = x^2
The new rectangle is (x+7) ft by (x-2) ft
Let's find the area of this rectangle
Have a look at the image attachment to see how to multiply out (x+7)*(x-2) using the box method
The terms in red are x^2, 7x, -2x and -14 which are found by multiplying the headers
x times x = x^2
x times 7 = 7x
-2 times x = -2x
-2 times 7 = -14
The like terms are 7x and -2x which combine to 5x
Overall the result of multiplying out (x+7)*(x-2) is x^2+5x-14
Note: we can get the same result if we use the FOIL or distribution rule. The box method is a handy way to visually keep track of all the terms.
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The area of the rectangle, in terms of x, is x^2+5x-14
We are told that the area is 90 square feet
So equate the two expressions and solve for x
x^2+5x-14 = 90
x^2+5x-14-90 = 90-90
x^2+5x-104 = 0
(x-8)(x+13) = 0 ... see note below
x-8 = 0 or x+13 = 0
x = 8 or x = -13
note: find two numbers that multiply to -104 and add to 5. Those numbers are -8 and 13 which helps us factor
We ignore x = -13 as a negative side length makes no sense
The only practical root is x = 8
The side length of the original square is 8 feet
The area is
x*x = 8*8 = 64 square feet
We can check the answer by adding 7 to 8 to get 15, and subtracting 2 from 8 to get 6. The 8 by 8 square turns into a 15 by 6 rectangle. Since 15*6 = 90, we have confirmed the right answer.
root of 108 is between______ and ______
Determine what two whole numbers the square root is between without using a calculator or table. Then use a calculator or table to check.
Answers
How I found the answer:
I know 10 * 10 = 100
I know 11 * 11 = 121
So the root of 100 = 10 and the root of 121 = 11 so that means the root of 108 is somewhere between 10 and 11, which the root of 108 = 10.3923
Brock is a plumber. He charges a flat rate of $40 to visit a house to inspect it's plumbing. He charges an additional $20 for every hour he spends inspecting or making repairs.
Which graph below correctly shows the price of using Brock's plumbing service vs time?
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W is correct. the red line starts at 40 which is the initial fee
then it crosses 60 and 1.0 and 80 at 2.0 which is 20 dollars for 1 hour
LANDSCAPING The equation 3x+7y =105 represents the number of bags of sand x and bags of multch y that can be bought with $105. If no bags of sand are bought, how many bags of mulch can be bought with $105 ?
Answers
To find the answer, plug in 0 for x since you aren't buying any bags of sand and then you have 7y=105 and divide by 7 to find y which is 15.
When no bags of sand are bought, you can buy 15 bags of mulch with $105.
Explanation:To find the number of bags of mulch that can be bought with $105 when no bags of sand are bought, we need to substitute x = 0 into the equation 3x+7y = 105. This will allow us to solve for y.
Since x = 0, the equation becomes:
3(0) + 7y = 105
0 + 7y = 105
7y = 105
Dividing both sides by 7, we get:
y = 15
Therefore, when no bags of sand are bought, you can buy 15 bags of mulch with $105.
The solution to f - (-4) = 12 is f = 8.
True or False
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PLAESE HELP ME FAST THIS IS WORTH 20 POINTS
Answers
When the function f(x) is divided by x-2 the quotient is 3x^2+8x-4 and the remainder is 9 find the function f(x) and write the result in standard form?
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∴ dividend = divisor(quotient) + remainder ... there is a reason why I am not multiplying the remainder by the divisor in this case... your remainder is not represent as a fraction with the divisor as the denominator..
[tex]f(x)=(x-2)(3x^2+8x-4)+9=3x^3+8 x^{2} -4x-6 x^{2} -16x+8+9[/tex]
[tex]f(x)=3x^3+2x^2-20x+17[/tex]
The expression for the function f(x) in standard form is f(x) = 3x³ + 2x² - 20x + 17 if the function f(x) is divided by x-2.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
When the function f(x) is divided by (x - 2) the quotient is 3x² + 8x - 4 and the remainder is 9
By using the division algorithm:
f(x) = (x - 2)(3x² + 8x - 4) + 9
After simplification:
f(x) = 3x³ + 8x² - 4x - 6x² - 16x + 8 + 9
f(x) = 3x³ + 2x² - 20x + 17
Thus, the expression for the function f(x) in standard form is f(x) = 3x³ + 2x² - 20x + 17 if the function f(x) is divided by x-2.
Learn more about the function here:
brainly.com/question/5245372
#SPJ5
Fatema loves to run marathons. The last one she participated in took her 2 hours to complete. The year before (2016) , she completed the same marathon in 8/11 of the time and the year before that (2015) she completed it in 9/12 of the time. What year did Fatema run the fastest? JUSTIFY YOUR ANSWER PLEASE I NEED HELP ASAP!
Answers
2016 = 8/11 x 120 mins = 87.27 mins
2015 = 9/12 x 120 mins = 90 mins
Therefore, Fatema ran the fastest in 2016.
Given 11 is conguent to 3, which lines, if any, must be parallel based on the given information? Justify your conclusion
A. a || b, Converse of the Alternate Exterior Angles Theorem
B. c || d, Converse of the Same-Side Interior Angles Theorem
C. a || b, Converse of the Corresponding Angles Theorem
D. not enough information to make a conclusion
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the average cost for a company to produce x items is x^2-10x+43 dollars. how many items should the company produce to minimize the average cost per item?
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[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{llll} y = &{{ 1}}x^2&{{ -10}}x&{{ +43}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \left( -\cfrac{(-10)}{2(1)}~~,~~43-\cfrac{(-10)^2}{4(1)} \right)\implies (\stackrel{\textit{items to produce}}{5}~~,~~\stackrel{\textit{production cost}}{18})[/tex]
Kevin has $4.85 in nickels and dimes. If he has 34 fewer dimes than nickels, how many coins (nickels and dimes) does he have altogether?
A.) 74 coins
B.) 75 coins
C.) 76 coins
D.) 77 coins
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Answer:
The answer would be (D) 77 coins :)
Step-by-step explanation:
is (3,4) a solution of y=-x+5
Answers
4=y
4=-3+5
So no it’s not.
What is 120 degrees in radians?
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Answer:
[tex]\frac 23 \pi [/tex]
Step-by-step explanation:
120 degrees is one third of the whole circle, or [tex] \frac 13 2\pi [/tex]
Answer:
the answer is 2pi/3
What number is diviscible by 2?