Prove the trigonometric identity!
Please help!! 50 Points!
Answer:
:)
Step-by-step explanation:
For simplicity I will substitue [tex]x[/tex] for β.
[tex]1-sin(2x)=(cosx-sinx)^2\\1-2sin(x)cos(x)=cos^2x-2sin(x)cos(x)+sin^2x\\1=cos^2(x)+sin^2(x)\\1=1[/tex]
In the first step I used the identity
[tex]sin(2x)=2sin(x)cos(x)[/tex]
And I factored out [tex](cosx-sinx)^2[/tex]
Then it's just simple algebra to cancel till the 3rd step where we used another identity derived from the Pythagorean Theorem.
[tex]cos^2(x)+sin^2(x)=1[/tex]
That's it!
please Hurryyy
Triangle HIJ has side lengths h=12, i = 17, j = 7. What is the measure of angle J?
35.4°
16.0⁰
124.8*
19.8°
The measure of angle J is 19.8°, and the correct option is D.
What is the formula of cosine?The law of cosine or cosine rule in trigonometry is a relation between the side and the angles of a triangle. Suppose a triangle with sides a, b, c and with angles cosC.
The following formula is used to find the angle j is;
[tex]\rm j^2 = h^2 + i^2 -2hicosC[/tex]
Triangle HIJ has side lengths h=12, i = 17, j = 7.
Substitute all the values in the formula;
[tex]\rm j^2 = h^2 + i^2 -2hicosJ\\\\(7)^2=(12)^2+(17)^2-2 \times 12 \times 17 cosJ\\\\49=144+289-408cosJ\\\\144+289 -49 =408cosJ\\\\384 =408cosJ\\\\cosJ=\dfrac{384}{408}\\\\cosj = 0.94\\\\J =cos^{-1}(0.94)\\\\J=19.8[/tex]
Hence, the measure of angle J is 19.8°, and the correct option is D.
Learn more about law cosine here;
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How many edges are there in a cube
Answer:
12
Step-by-step explanation:
Cindy has $25 saved and earns $12 per week for walking dogs. Mindy has $55 saved and earns $7 per week for watering plants. Cindy and
Mindy save all of the money they earn and do not spend any of their savings. After how many weeks will they have the same amount saved?
How much money will they have saved?
Answer:
c : they will have both saved 97
Step-by-step explanation:
7*6 = 42 + 55(base) = 97
12*6 = 71 = 25(base) =97
A regular hexagon is dilated by a scale factor of 4/3 to create a new hexagon. How does the perimeter of the new hexagon compare with the original perimeter?
oPTIONS:
The perimeter of the new hexagon is 4/3 the perimeter of the original hexagon.
The perimeter of the new hexagon is 12/3 the perimeter of the original hexagon.
The perimeter of the new hexagon is 16/3 the perimeter of the original hexagon.
The perimeter of the new hexagon is 16/9 the perimeter of the original hexagon.
Answer:
When a figure is dilated by a scale factor of a/b, then the new perimeter is a/b of the original perimeter and the new area is a 2 b 2 of the original area. Therefore, if the hexagon is dilated by a scale factor of , then the new perimeter is of the original perimeter.
A building contractor is to dig a foundation 12 feet long, 9 feet wide, and 6 feet deep for a toll booth. The contractor pays $180 per load for trucks to remove the dirt. Each truck holds 6 cubic yards. What is the cost to the contractor to have all the dirt hauled away?
The cost for the contractor to have all the dirt hauled away for a foundation of 12 feet long, 9 feet wide and 6 feet deep is $720
Volume of rectangular prism
volume of a rectangular prism = lwh
where
l = lengthw = widthh = heightTherefore,
l = 12 ft
w = 9 ft
h = 6 ft
volume of the foundation = 12 × 9 × 6
volume of the foundation = 648 ft³
Therefore, the contractor pays $180 per load for the trucks remove the dirt.
648 cubic feet = 24 cubic yard
6 cubic yards = 1 truck load
24 cubic yard =
cross multiply
number of truck load = 24 / 6 = 4 truck loads
Hence,
1 truck load = $180
4 truck load =?
cross multiply
cost = 4 × 180 = $720
learn more on volume here: https://brainly.com/question/3008257
How can I solve that problem
What do we know so far:
[tex]2\frac{2}{3}laps[/tex] in [tex]\frac{4}{15}hour[/tex] ⇒ [tex]\frac{8}{3}laps[/tex] in [tex]\frac{4}{15}hour[/tex]*we converted the number of laps into improper fractions
[tex]2\frac{2}{3} = \frac{8}{3}[/tex]
We want to know the number of laps in an hour
⇒ so we must find the rate which ⇒ lap/hour
[tex]lap/hour =\frac{8/3laps}{4/15hours} =\frac{8}{3}*\frac{15}{4} =\frac{8}{4} *\frac{15}{3} =2*5=10laps/hour[/tex]
So William can run ⇒ 10 laps in one hour
Hope that helps!
This morning, Christines car had 22.13 gallons of fuel. Now, 1.9 gallons are left. How much fuel did Christine use?
Answer:
21.4 I think, I might be wrong though
Please help me i litterally can not figure this out way to many numbers.
Answer:
A,C and E
Step-by-step explanation:
For every 3ml of vinegar we have 8ml of oil
This implies that
For case (A):
80ml of oil with 30ml of vinegar
dividing the amount of vinegar by 3 and multiplying the result by 8 gives 80 I.e
[tex]8ml (oil)\alpha 3ml(vinegar) \\ \frac{30ml(vinegar)}{2} = 10 \\ multiplying \: by \: 8 \: gives \: 80ml(oil)[/tex]
hence that's it
What would be your first step in solving -3x > 0?
A. multiply both sides by -3 and flip your sign
B. divide both sides by -3 and flip your sign
C. multiply both sides by 3 and flip your sign
D. divide both sides by 3 and flip your sign
Answer:
I would divide both sides by -3 then flip your sign since it is a multiplication equation in -3x which means you have to isolate it to find x.
Answer:
D
Step-by-step explanation:
You divide both sides by 3 and then you flip the sign.
Saul has 8 bags. He records the weight of each bag on the line plot.
What is the total weight of the three heaviest bags?
Answer:
24
Step-by-step explanation:
just MultiplMultiply 8 times 3 and 24
help me with this plssss
answer choices 3/5, 9/16, 8/15 3/4
Find the mean 3,4,4,2,5,7,2
If an order is for 500mg from a dosage strength of 250 mg/mL, is to be administered in 20 cc D5 1/2NS, how many mL of drug is used and how many mL of D5 1/2NS is used?
Answer:
Dosage strength
250mg = 1.5mL
expression represents the product of b and 34?
Answer:
b*34
Step-by-step explanation:
an expression does not include an equal sign but an equation does
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
(49,-56)
Step-by-step explanation:
I not sure but scale factor show the magnitude therefore you multiply by the scale factor to get the image.
What percentage of times are between 6 and 22 hours?
16%
68%
95%
99.7%
Answer:
16 percent of times are between 6 and 22
Answer: c I think. Sorry I'm wrong. Might be a.
Step-by-step explanation:
2. What is the value of the expression?
2.4 +3.5 x 1.7
A 7.99
B 8.35
С
9.42
D
10.03
Show your work
Answer Choice:
Answer:
B. 8.35
Step-by-step explanation:
3.5 x 1.7 = 5.95
5.95 + 2.4 = 8.35
You multiply first because of PEMDAS.
P=parenthesis
E=exponents
M=multiply
D=divide
A=add
S=subtract
The clock shows when the soccer game ended what time was it The hour hand is on the 10 and the mini hands on the five
Answer:
10:25
Step-by-step explanation:
Please help i have an assignment due TODAY i need to get this done
rules:
NO LINKS! im not getting myself a virus
Answer:
i think it is diameter
Step-by-step explanation:
if you are in England
Answer:
CHORD
Step-by-step explanation:
A chord of a circle is any line segment joining two points on the circumference of the circle
(Diameter is the longest chord of a circle which passes through the center of the circle)
Since this line does not pass through the center,this is a chord
The sides of an isosceles triangle are28 ,28 ,10 and long. What is the area of the triangle?
Answer: Approximately 137.74977 square units
===================================================
Explanation:
We can use Heron's formula to find the area of a triangle when given all three sides.
First we need the semiperimeter
s = semiperimeter
s = (perimeter)/2
s = (a+b+c)/2
s = (28+28+10)/2
s = 33
Now we can compute the area of the triangle.
[tex]A = \sqrt{s(s-a)(s-b)(s-c)}\\\\A = \sqrt{33(33-28)(33-28)(33-10)}\\\\A = \sqrt{18975}\\\\A \approx 137.74977\\\\[/tex]
A particle moves along a hyperbola
xy = 12.
As it reaches the point (4, 3), the y-coordinate is decreasing at a rate of 3 cm/s. How fast is the x-coordinate of the point changing at that instant?
first off, let's notice that "x" and "y" are encapsulating a function in terms of time or namely "t", and that dy/dt is decreasing at a rate of 3 cm/s, since the rate is decreasing, that makes the rate negative, thus is changing at -3 cm/s.
[tex]xy=12\implies \stackrel{product~rule}{\cfrac{dx}{dt}y~~ + ~~ x\cfrac{dy}{dt}}~~ = ~~0\implies \cfrac{dx}{dt}y~~ + ~~x(-3)~~ = ~~0 \\\\\\ \cfrac{dx}{dt}y=3x\implies \left. \cfrac{dx}{dt}=\cfrac{3x}{y} \right|_{(\stackrel{x}{4},\stackrel{y}{3})}\implies \cfrac{3(4)}{3}\implies 4[/tex]
Complete the frequency table for the following set of data. You may optionally click a
number to shade it out.
12, 4, 11, 3, 4, 0, 13, 13,
2, 6, 11, 0, 10, 11, 3, 4,
0, 10, 13, 2, 11, 9
12=1
4=3
11=4
3=2
0=3
13=3
2=2
6=1
10=2
9=1
Describe how the graph of the function is related to the graph of its parent function.
y=-2X+1
O A Reflected across the y-axis and shifted up 1 unit
shirjeno
OB. Reflected across the x-axis and shifted up 1 unit
O C. Reflected across the y-axis and shifted to the right 1 unit
O D. Reflected across the x-axis and shifted to the right 1 unit
Answer:
B
Step-by-step explanation:
The -2 reflects across the x -axis
The + 1 shifts it up one unit
The number of wins in the American Baseball League, Central Division, for a recent year is given in the table. Find the mean number of wins. Round your answer to one decimal place.
The mean number of wins for the five teams is ______wins?
Answer:
81
Step-by-step explanation:
Average | x = 81
Count | n = 5
Sum | Sum = 405
Solution:
The average (mean) is equal to the sum of all the data values divided by the count of values in the data set.
Average = Sum / Count
= 405 / 5
= 81
Question 5. Bob Orleans invested $3,000 and borrowed $3,000 to purchase shares in Verizon Communications. At the time of his investment, Verizon was selling for $47 a share.
o If Bob paid a $30 commission, how many shares could he buy if he used only his own money and did not use margin?
o If Bob paid a $60 commission, how many shares could he buy if he used his $3,000 and borrowed $3,000 on margin to buy Verizon stock?
o Assume Bob did use margin and paid a $60 total commission to buy his Verizon stock. Also, assume he paid another $60 to sell his stock and sold the stock for $54 a share. How much profit did he make on his Verizon stock investment?
The number of shares could he buy is 63.19 and 126.38. Then the profit gained by Bob is $764.68.
What is the profit gained by Bob?
Bob Orleans invested $3,000 and borrowed $3,000 to purchase shares in Verizon Communications.
At the time of his investment, Verizon was selling for $47 a share.
If Bob paid a $30 commission, then the number of shares could he buy if he used only his own money and did not use margin.
[tex]\rightarrow \dfrac{3000- 30}{47}\\\\\rightarrow \dfrac{2970}{47}\\\\\rightarrow 63.19[/tex]
If Bob paid a $60 commission, then the number of shares could he buy if he used his $3,000 and borrowed $3,000 on margin to buy Verizon stock will be
[tex]\rightarrow \dfrac{6000 - 60 }{47}\\\\\rightarrow \dfrac{5940}{47}\\\\\rightarrow 126.38[/tex]
Assume Bob did use margin and paid a $60 total commission to buy his Verizon stock. Also, assume he paid another $60 to sell his stock and sold the stock for $54 a share. Then the profit will be
[tex]\rightarrow (126.38 \times 54 - 60) - (6000)\\\\\rightarrow (6824.68 - 60) - 6000\\\\\rightarrow 6764.68 - 6000\\\\\rightarrow \$764.68[/tex]
More about the profit link is given below.
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Anyone know how to round 2.5678 round to the nearest half
Answer:
2.5678 to the nearest half is 13,000
Answer: I think it would be 5 1/2 or 5.5 Fraction and decimal
Step-by-step explanation: Hope this helps! :)
The length of a rectangle is 4 meters less than
wice its width. The area of the rectangle is 70.
Find the
of the rectangle.
dimensions
What is the volume of a square pyramid with a 10 x 10 foot base and an altitude of 6 feet?
Answer:
I believe the answer is 200 feet squared
Step-by-step explanation: