Answer:
I'm assuming where you wrote x2, you meant 2x.
Anyway, if csc (x) = 2, since csc(x) = 1/sin(x), we know that 1/sin x = 2, so sin (x) = 1/2. Since sin2x + cos2x = 1, cos2x = 1 - sin2x, so cos x = √1 - sin2x. In this case, cos x = √ 1 - (1/2)2 = √(3/4) = (√3)/2. Finally, since sin x = opp / hyp , cos = adj/ hyp: sin x / cos x = (opp/hyp)/(adj/hyp) = opp/adj = tan x. So this means that tan x = sin x / cos x = 1/2 / √ 3 / 2 = 1/√3 = √3 / 3
At this point, all that is necessary is to use the double angle formulas for sin, cos, and tan.
sin (2x) = 2 sin x cos x = 2 (1/2) (√3/2) = √3 / 2
cos (2x) = cos2x - sin2x = (√3/2)2 - (1/2)2 = 3/4 - 1/4 = 1/2
tan (2x) = 2 tan x / (1 - tan2x) = 2 (√3 / 3) / ( 1 - (√3/3)2) = 2/√3 / (1 - 1/3) = 2/√3 / (2/3) = 3/√3 = √3
To sum up, sin (2x) = √4 / 2, cos (2x) = 1/2, and tan(2x) = ✓3.
Step-by-step explanation:
BRAIN LY FAST
MARK A BRAINLESS
[tex]\sin\left(\frac{x}{2}\right) = \pm\frac{\sqrt{4 + \sqrt{15}}}{\sqrt{8}}\\\cos\left(\frac{x}{2}\right) = \pm\frac{\sqrt{4 - \sqrt{15}}}{\sqrt{8}}\\\tan\left(\frac{x}{2}\right) = \pm\frac{\sqrt{4 + \sqrt{15}}}{\sqrt{4 - \sqrt{15}}}\\[/tex]
To find sin(x/2), cos(x/2), and tan(x/2), we need to use the half-angle identities for trigonometric functions.
Given: csc(x) = 4 for 90° < x < 180°
Step 1: Find sin(x). Since csc(x) is the reciprocal of sin(x), we have:
csc(x) = 1/sin(x) = 4
Now, find sin(x):
sin(x) = 1/csc(x) = 1/4
Step 2: Find cos(x). To do this, use the Pythagorean identity:
[tex]sin^2(x) + cos^2(x) = 1\\cos^2(x) = 1 - sin^2(x) \\= 1 - (1/4)^2 \\= 1 - 1/16 \\= 15/16[/tex]
Now, find cos(x):
[tex]\cos(x) = \pm \sqrt{\frac{15}{16}}[/tex]
Since x is in the second quadrant (90° < x < 180°), cos(x) is negative. So,
[tex]\cos(x) = - \sqrt{\frac{15}{16}}[/tex]
[tex]= -\sqrt{15} / 4[/tex]
Step 3: Find tan(x). To do this, use the identity:
[tex]\tan(x) = \frac{\sin(x)}{\cos(x)}\\\tan(x) = \frac{\frac{1}{4}}{-\frac{\sqrt{15}}{4}}\\\tan(x) = -\frac{1}{\sqrt{15}}[/tex]
Now, let's find sin(x/2), cos(x/2), and tan(x/2) using the half-angle identities:
Half-angle identities:
[tex]\sin \left ( \frac{x}{2} \right ) = \pm \sqrt{\frac{1 - \cos x}{2}}\\\cos \left ( \frac{x}{2} \right ) = \pm \sqrt{\frac{1 + \cos x}{2}}\\\tan \left ( \frac{x}{2} \right ) = \frac{\sin \left ( \frac{x}{2} \right )}{\cos \left ( \frac{x}{2} \right )}[/tex]
Step 4: Find sin(x/2):
[tex]\sin \left( \frac{x}{2} \right) = \pm \sqrt{\frac{1 - \cos x}{2}}\\\sin \left( \frac{x}{2} \right) = \pm \sqrt{\frac{1 + \frac{\sqrt{15}}{4}}{2}}\\\sin \left( \frac{x}{2} \right) = \pm \sqrt{\frac{4 + \sqrt{15}}{8}}\\\sin \left( \frac{x}{2} \right) = \pm \frac{\sqrt{4 + \sqrt{15}}}{\sqrt{8}}\\\sin \left( \frac{x}{2} \right) = \pm \frac{\sqrt{4 + \sqrt{15}}}{2}[/tex]
Step 5: Find cos(x/2):
[tex]\cos\left(\frac{x}{2}\right) = \pm\sqrt{\frac{1 + \cos(x)}{2}}\\\cos\left(\frac{x}{2}\right) = \pm\sqrt{\frac{1 + \left(-\frac{\sqrt{15}}{4}\right)}{2}}\\\cos\left(\frac{x}{2}\right) = \pm\sqrt{\frac{1 - \frac{\sqrt{15}}{4}}{2}}\\\cos\left(\frac{x}{2}\right) = \pm\sqrt{\frac{4 - \sqrt{15}}{8}}\\\cos\left(\frac{x}{2}\right) = \pm\frac{\sqrt{4 - \sqrt{15}}}{\sqrt{8}}\cos\left(\frac{x}{2}\right) = \pm\left(\frac{\sqrt{4 - \sqrt{15}}}{\sqrt{8}}\right)[/tex]
Step 6: Find tan(x/2):
[tex]\tan \left ( \frac{x}{2} \right ) = \frac{\sin \left ( \frac{x}{2} \right )}{\cos \left ( \frac{x}{2} \right )} = \pm \frac{\sqrt{4 + \sqrt{15}}}{\sqrt{4 - \sqrt{15}}}[/tex]
So, the values are:
[tex]\sin\left(\frac{x}{2}\right) = \pm\frac{\sqrt{4 + \sqrt{15}}}{\sqrt{8}}\\\cos\left(\frac{x}{2}\right) = \pm\frac{\sqrt{4 - \sqrt{15}}}{\sqrt{8}}\\\tan\left(\frac{x}{2}\right) = \pm\frac{\sqrt{4 + \sqrt{15}}}{\sqrt{4 - \sqrt{15}}}\\[/tex]
Note: The ± symbol indicates that there are two possible solutions due to the quadrant restrictions.
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Complete Question is:
If csc ( x ) = 4, for 90 ∘ < x < 180, then sin ( x /2 ) = ? cos ( x /2 ) = ? tan ( x /2 ) = ?
Question is in image please help
I will give Brainliest :)
Answer:
D;the last answer
Step-by-step explanation:
The more negative a fraction or decimal, the lower that actual value.
Therefore since -1 1/5 is the lowest it should go first, and D is the only answer like this! Hope this helps ^^
Answer: -1 [tex]\frac{1}{5}[/tex], -1, 0.25, [tex]\frac{1}{2}[/tex] , 0.75
Step-by-step explanation:
I will turn all of these numbers into numbers that are not fractions since most of the numbers are already this way.
0.75 -> 0.75
-1 -> -1
[tex]\frac{1}{2}[/tex] -> 0.5
-1 [tex]\frac{1}{5}[/tex] -> -1.2
0.25 -> 0.25
First of all, the negative numbers are smaller than the positive numbers. Then, we can order them least to greatest by number.
-1.2, -1, 0.25, 0.5, 0.75
Putting the numbers into what they were originally given as gives us this:
-1 [tex]\frac{1}{5}[/tex], -1, 0.25, [tex]\frac{1}{2}[/tex] , 0.75
The answer is the last option, -1 [tex]\frac{1}{5}[/tex], -1, 0.25, [tex]\frac{1}{2}[/tex] , 0.75.
Bashir bought snacks for his team's practice. He bought a bag of apples for $2.91 and a 6-pack of juice bottles. The total cost before tax was $15.69. Write and solve an equation which can be used to determine j j, how much each bottle of juice costs.
An equation that can be used to determine j j, each bottle of juice costs 15.69 = 6j + 2.91
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Bashir bought snacks for his team's practice. He bought a bag of apples for $2.91 and a 6-pack of juice bottles.
The total cost before tax was $15.69.
An equation that can be used to determine j j, is how much each bottle of juice costs.
15.69 = 6j + 2.91
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Nancy found that x=1 is one solution to the quadratic equation (x+2)2=a. What is the value of a?
-9
-3
3
9
Answer:
the answer is a
Step-by-step explanation:
i literaly just tookthetest on edginuity
Answer:
a = 9
Step-by-step explanation:
First we substitute 1 into the quadratic equation :
(x+2)² = a
(1+2)² = a
(3)² = a
3×3 = a
a = 9
Hope you understood, hope this helped and brainliest please.
WRITE Mask Explain how you can prove that 3 weeks is
less than 24 days.
Answer:
7x3 = 21
Step-by-step explanation:
It's simple math. One week is 7 days. So just multiply 7x3 and then that's equaled to 21.
NO LINKS! Please help me with this problem.
#1
[tex]\\ \rm\Rrightarrow \dfrac{WX}{UV}=\dfrac{HI}{FE}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{WX}{16}=\dfrac{10}{8}[/tex]
[tex]\\ \rm\Rrightarrow WX/2=10[/tex]
[tex]\\ \rm\Rrightarrow WX=20[/tex]
Again
#2
[tex]\\ \rm\Rrightarrow \dfrac{WX}{UT}=\dfrac{HI}{FG}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{20}{20}=\dfrac{10}{FG}[/tex]
[tex]\\ \rm\Rrightarrow FG=10[/tex]
Answer:
WX = 20
FG = 10
Step-by-step explanation:
If EFGHI ~ VUTXW
then:
EF~VUFG~UTGH~TXHI~XWIE~WVThe only pair of sides that both have measures is EF and VU
EF = 8
VU = 16
VU/EF = 16/8 = 2
Therefore, VUTXW is enlargement of EFGHI by a scale factor of 2.
As HI = 10
⇒ WX = 10 × 2 = 20
As UT = 20
⇒ FG = 20 ÷ 2 = 10
Let f(t) ANSWER: 1+ = t² - 1 t+3 Find f'(1)
Answer:
f(1) = 3
Step-by-step explanation:
f(t) = t² - 1t + 3
we want to find f(1)
all we have to do is replace the t's with 1 and evaluate
f(1) = (1)² - 1(1) + 3
evaluate exponent 1² = 1
f(1) = 1 - 1(1) + 3
multiply
f(1) = 1 - 1 + 3
subtract
f(1) = 3
The perimeter of an equilateral triangle is 1/8 unit. What is the length, in units, of each side of the triangle
Answer:
[tex] {\longrightarrow \pmb{\sf {\qquad \frac{1}{24} }}} \\ \\[/tex]
[tex] \: [/tex]
Step-by-step explanation:
It is given that the perimeter of an equilateral triangle is 1/8 unit and we have to find the length of each side of the triangle.
So, we know that,
[tex] \\ {\longrightarrow \pmb{\sf {\qquad 3a = Perimeter_{(Equilateral triangle) }}}} \\ \\[/tex]
Now, substituting the given values in the formula :
[tex]\\ {\longrightarrow \pmb{\sf {\qquad 3a = \frac{1}{8} }}} \\ \\[/tex]
By doing cross multiplication we get :
[tex]{\longrightarrow \pmb{\sf {\qquad 3a(8) = 1(1) }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad 24a = 1 }}} \\ \\[/tex]
Dividing both sides by 24 we get :
[tex] \\ {\longrightarrow \pmb{\sf {\qquad \frac{24a}{24} = \frac{1}{24} }}} \\ \\[/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad a = \frac{1}{24} }}} \\ \\[/tex]
Therefore,
The length of each side of the triangle is 1/24 unitsHow many days are in 19 lunar calendar new years with an extra month added in seven times?
There are 6939.56 days in 19 lunar calendar new years with an extra month added in seven times.
What is lunar year?"A lunar year is 12 lunar months, so 19 of these would be 228 lunar months. With the 7 extra months, the total period would be 235 lunar months of 29.530589 days each and is 6939.69 days.
We will notice that this is almost the same as 19 solar years of 365.24 days, which is 6939.56 days.
Now, you are referring to the Hebrew Calendar, a 19-year period that consists of 12 years of 12 months plus 7 years of 13 months,
Therefore, 19 years is the period after which the Hebrew and solar calendar dates will match up."
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How do you explain a math equation?
What is the following sum?
3 b squared (RootIndex 3 StartRoot 54 a EndRoot) + 3 (RootIndex 3 StartRoot 2 a b Superscript 6 Baseline EndRoot)
6 b squared (RootIndex 3 StartRoot 2 a EndRoot)
12 b squared (RootIndex 3 StartRoot 2 a EndRoot
6 b squared (RootIndex 6 StartRoot 2 a EndRoot)
12 b squared (RootIndex 6 StartRoot 2 a EndRoot)
[tex]12b^2\sqrt[3]{2a}[/tex]
In word form, this is 12 b squared (RootIndex 3 StartRoot 2 a EndRoot
Or you could say 12b^2 times the cube root of 2a
========================================================
Work Shown:
[tex]3b^2\sqrt[3]{54a}+3\sqrt[3]{2ab^6}\\\\3b^2\sqrt[3]{27*2a}+3\sqrt[3]{b^6*2a}\\\\3b^2\sqrt[3]{(3)^3*2a}+3\sqrt[3]{(b^2)^3*2a}\\\\3b^2\sqrt[3]{(3)^3}*\sqrt[3]{2a}+3\sqrt[3]{(b^2)^3}*\sqrt[3]{2a}\\\\3b^2*3*\sqrt[3]{2a}+3*b^2*\sqrt[3]{2a}\\\\9b^2\sqrt[3]{2a}+3b^2\sqrt[3]{2a}\\\\(9b^2+3b^2)\sqrt[3]{2a}\\\\\boldsymbol{12b^2\sqrt[3]{2a}}\\\\[/tex]
The idea here is that we break the cube roots into smaller pieces, so we pull out perfect cubes when factoring.
The sum of the expression is 12 b squared (Root Index 6 Start Root 2 a End Root) or 12b²∛(2a).
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.
We have the expression,
3 b squared (Root Index 3 Start Root 54 a End Root) + 3 (Root Index 3 Start Root 2 a b Superscript 6 Baseline End Root).
In numerical form,
3b²∛(54a) + 3∛(2ab⁶)
To find the sum of the above expression:
we simplify the expression,
3b²∛(54a) + 3∛(2ab⁶)
= 3b²∛3³(2a) + 3∛(2a)(b²)³
= 9b²∛(2a) + 3b²∛(2a)
= 12b²∛(2a)
Therefore, the sum is 12b²∛(2a).
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The website for Company A receives 8×10 6 visitors per year. The website for Company B receives 4×10 3 visitors per year. Determine how many times more visitors per year the website for Company A receives than the website for Company B.
Answer:
2000 times
Step-by-step explanation:
I'm assuming you mean 4*10^3 and 8*10^6.
8*10^6/(4*10^3)
=(8/4)*(10^6/10^3)
=2*(10^3)
=2*1000
=2000 times
Henry is researching the elephant exhibit at his town's zoo.
Which of the following is a statistical question Henry could ask?
A.
When was the zoo opened?
B.
What was the name of the first elephant in the exhibit?
C.
What is the average weight of the adult elephants in the exhibit?
D.
How many elephants are in the exhibit?
What is the average weight of the adult elephants in the exhibit? This is the correct statistical question.
What is the statistical questions?Statistical question is that type of question which have more than one possible answers.
The answer of statistical question is the collection of various points of data.
The answer of statistical question depends on variety and situations.
The answer of statistical question may be range . Answer of statistical question are more than one.
What is the average weight of the adult elephants in the exhibit?
This is the correct statistical question.
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A college graduate invests $3,000 into an account that earns 6% annual interest compounded monthly. What is the value (in dollars) of
the investment after 5 years? (Round your answer to the nearest cent.)
Answer:
$4,014.68
Step-by-step explanation:
A = $4,014.68
A = P + I where
P (principal) = $3,000.00
I (interest) = $1,014.68
First, convert R as a percent to r as a decimal
r = R/100
r = 6/100
r = 0.06 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 3,000.00(1 + 0.06/1)^(1)(5)
A = 3,000.00(1 + 0.06)^(5)
A = $4,014.68
What is the sum?
3 5/
x²-9x+3
Answer:
9x3 + 3x2 + 35
x2
Step-by-step explanation:
I hope this helped u
Which graph corresponds to the
equation y = –2x + 3?
A.
B.
C.
D.
[tex]\frac{2}{1}[/tex]Answer: A.
Step-by-step explanation:
The first graph has a slope of -2/1 (down 2 and over 1). It also has a y-intercept of 3, meaning it crosses the y-axis or vertical axis at 3.
How many cubes with side length of 4cm can be packed into a wooden box measuring 32cm by 16cm by 8cm
PLEASE HELP Me!!
Answer:
64 cubes
Step-by-step explanation:
The volume of wooden box,
→ x = l × b × h
→ x = 32 × 16 × 8
→ [x = 4096 cm³]
The volume of a cube,
→ y = side³
→ y = 4 × 4 × 4
→ [ y = 64 cm³]
Now we have to,
find how many cubes can be packed inside the wooden box.
→ x ÷ y
→ 4096 ÷ 64
→ 64 cubes
Hence, the solution is 64 cubes.
(PLEASE HURRY)
Milan borrowed money from a credit union for 6 years and was charged simple interest at an annual rate of 7%. The total interest that he paid was $3780. How much money did he borrow?
Answer:
$54000
Step-by-step explanation: 3780 divided by the number of years he paid interest for, (6) gives you 630. If he pays 7% interest, you calculate what number 630 is 7% of (9000.) Therefore he takes out 9000 dollars a year. Meaning that in total, he borrowed 54,000 dollars. (9000 x 6)
What is the circumference of a circle with a radius of 11 cm? (Use = 3.14.)
A.
103.62 cm
B.
69.08 cm
C.
34.54 cm
D.
379.94 cm
First, we need to follow the circumference of a circle formula, which is [tex]C = 2 \pi r[/tex]. Since we know the radius, we can plug 11 for the radius and 3.14 for pi.
The equation should now look like this: [tex]C = 2 * 3.14 *11[/tex]. Then, we multiply. After solving, the circumference of the circle is 69.08 centimeters.
The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced to a mass of 1 mg. What was the initial mass (in mg) of the sample?
If D denotes the number of degree and G denotes the number of grades Prove D/9=G/10
Answer:because each answers eachother
Step-by-step explanation:
BRAINLIEST + STARSS!!!
What is the volume of this cone? Use 3.14 for pi and round your answer to the nearest tenth.
In your answer, give the volume of the cone rounded to the nearest tenth, and then explain how u calculated it
Answer:
33.5 in^3
Step-by-step explanation:
The formula for a cone is (pi)(r^2)(h/3)
Since we need to use 3.14 for pi, we will plug in 3.14 for pi. It should look like this: (3.14)(r^2)(h/3)
The radius is 2 and the height is 8. Plug in the numbers:
(3.14)(2^2)(8/3)
Simplify:
(3.14)(4)(2.66...)
Multiply:
(12.56)(2.66...) -> 39.4933...
Finally, 39.4933... is rounded to the tenths place:
39.5
Hope this helps :)
if z 2 square equal 49 what are the solutions
z = 7, z = -7
Calculations ↓z² = 49
Take the square root of both sides to find what z equals
z = 7
Is that the only solution? Is 7 the only number that can be multiplied by itself and have a result of 49? No, there's another number. This number is -7.
So the solutions are ↓7, -7
hope helpful ~
Brainly needs 20 characters I can’t even get 2
Answer:
B. the spring has a length of 1 inch when no force is applied
Step-by-step explanation:
Answer:
the last guy who answered is correct
Step-by-step explanation:
sorry I needed to answer for more answers I can get
The chart below describes the speed of four runners. Which runner is the fastest?
Runner A ran 1 mile in 8 minutes
Runner B ran 2 miles in 10 minutes
Runner C ran 3 miles in 20 minutes
Runner D ran 5 miles in 30 minutes
Answer:
Runner B
Step-by-step explanation:
speed = distance ÷ time
Runner A: 1 ÷ 8 = 0.125m/ms
Runner B: 2 ÷ 10 = 0.2m/ms
Runner C: 3 ÷ 20 = 0.15m/ms
Runner D: 5 ÷ 30 = 0.17m/ms
Runner B has the highest speed so he is the fastest runner.
Find the area of the figure.
129m^2
A= bxh/2
Since I have 2 triangle I'll x 2 to get rid of the ÷ by 2
A= 13x5
= 65
A= bxh
= 8x8
=64
64 + 65= 129
Hope this helps!
Your friend Jenny wants to use a robo-adviser to manage her portfolio. What does this mean?
Use 3.14 as pie to find the circumference
Factorise 14e-16
Please explain
The expression 14e - 16 is an algebraic expression, and the factored expression is 2(7e - 8)
How to factor the expression 14e - 16?The expression is given as:
14e - 16
Express both terms as a product of 2
14e - 16 = 2 * 7e - 2 * 8
Factor out 2 in the expression
14e - 16 = 2 * (7e - 8)
Remove the product sign
14e - 16 = 2(7e - 8)
Hence, the factored expression of 14e - 16 is 2(7e - 8)
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A loan has an APR of 8%. The maximum that Steve can pay back monthly on a loan is $129.60. He wants the loan for 1 year.
Answer:
$1,679.62
Step-by-step explanation:
129.60*12=$1,555.20
You then do 1,555.2*.08, and get:124.416
You then add the 2 together to find the amount needed to be paid back.
-5 + 20m + 3 < 18m + 12
Answer:
m<7
m is greater than 7, i hope that helps
Answer:
m<7
Step-by-step explanation:
-5+20m+3<18m+12
Group like terms
20m-18m<12+5-3
2m<17-3
2m<14
2m÷2<14÷2
m<7
hope this helps *_*
pls brainliest