Use the suggested substitution to write the expression as a trigonometric expression. Simplify your answer as much as possible. Assume 0≤θ≤π2.
[tex]\sqrt{9x^2+36[/tex] , x/2=cot(∅)
Answer:
[tex]\sqrt{9x^2+36} = 6 \csc(\theta)[/tex]
Step-by-step explanation:
Given
[tex]\frac{x}{2}=\cot(\theta)[/tex]
Required
Express [tex]\sqrt{9x^2+36}[/tex] as trigonometry expression
[tex]\sqrt{9x^2+36}[/tex]
Factorize
[tex]\sqrt{9x^2+36} = \sqrt{9(x^2+4)}[/tex]
Split
[tex]\sqrt{9x^2+36} = \sqrt{9} * \sqrt{(x^2+4)}[/tex]
[tex]\sqrt{9x^2+36} = 3 * \sqrt{(x^2+4)}[/tex]
[tex]\sqrt{9x^2+36} = 3\sqrt{(x^2+4)}[/tex]
We have:
[tex]\frac{x}{2}=\cot(\theta)[/tex]
Make x the subject
[tex]x = 2 \cot(\theta)[/tex]
So:
[tex]\sqrt{9x^2+36} = 3\sqrt{(x^2+4)}[/tex]
[tex]\sqrt{9x^2+36} = 3\sqrt{((2 \cot(\theta))^2+4)}[/tex]
Evaluate all squares
[tex]\sqrt{9x^2+36} = 3\sqrt{4\cot^2(\theta)+4}[/tex]
Factorize
[tex]\sqrt{9x^2+36} = 3\sqrt{4(\cot^2(\theta)+1)}[/tex]
Split
[tex]\sqrt{9x^2+36} = 3\sqrt{4} * \sqrt{\cot^2(\theta)+1}[/tex]
[tex]\sqrt{9x^2+36} = 3*2 * \sqrt{\cot^2(\theta)+1}[/tex]
[tex]\sqrt{9x^2+36} = 6 * \sqrt{\cot^2(\theta)+1}[/tex]
In trigonometry
[tex]\cot^2(\theta)+1 = \csc^2(\theta)[/tex]
So, we have:
[tex]\sqrt{9x^2+36} = 6 * \sqrt{\csc^2(\theta)}[/tex]
Evaluate the square root
[tex]\sqrt{9x^2+36} = 6 * \csc(\theta)[/tex]
[tex]\sqrt{9x^2+36} = 6 \csc(\theta)[/tex]
⚠️URGENT PLS HELP
LINKS WILL BE REPORTED
Answer:
e and c
Step-by-step explanation:
Factoring out the GCF of the polynomial 2x^6+2x^5 will give
if P = 5, 4 find the image of P under the following rotation
Answer:
(-4,5)
Step-by-step explanation:
90 degree rotation = (-y,x)
Share up 184 snail between a salamander how many snail does each salamander get
Answer:
How many salamanders are there
or does it say that there are "a salamanders"
If so, it's 184/a
Gillian has completed 25% of a bicycle race. If the length of the race is 32 km, how many has she traveled so far?
800
80
8
8000
Answer:8
Step-by-step explanation:
24+z/10 = 31 solve for Z
0.782 ___ 0.784
I Need HElP NOW!
Answer:
0.783, just look at the pattern.
If you're comparing, this is the answer:
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Find the value of x. Round to the nearest tenth.
Can somebody plz help me with 16 and 19
Answer:
BRAINLIESTTTTYSYDEUJEJE JJ3JEHSSNAAKWhat is the vertex of the graph of
y = 2(x + 6)^2 – 2?
O A. (2.6)
O B. (-6,2)
O C. (-6, -2)
O D. (6,-2)
Please help
The formula for the Volume...
Answer:
cones
Step-by-step explanation:
Volume of a cone:
V = (1/3)πr2h
A 12-kg bag of mangoes costs $9.00
Answer:
I think it would be around $1.33 for each kg
Step-by-step explanation:
You would divide 12 by 9. Once you do that, you get 1.33
What is the area of the shaded segment ?
9514 1404 393
Answer:
5.1 cm²
Step-by-step explanation:
The area of a segment is given by the formula ...
A = 1/2r²(α -sin(α)) . . . . . where α is the central angle in radians
For this segment, its area is ...
A = 1/2(6 cm)²(7π/18 -sin(70°)) ≈ 5.077 cm²
The area of the segment is about 5.1 square centimeters.
_____
The angle is converted to radians by multiplying by π/180°. Then a 70° angle is π(70°/180°) = 7π/18 radians.
Perform the following subtraction - 1/2 - (- 7/10)
Answer:
1.2
I t is the answer
I need your help guys help me differentiate this question
Answer:
[tex]6((4 {x}^{3} - 5x + 1) ^{ - 4} + 4 {x}^{10} + 4) ^{5} \times (- 4(4x ^{3} - 5x + 1)^{ - 5} \times 12 {x}^{2} - 5 ) + 40 {x}^{9} [/tex]
The minute hand on a clock has an angular
velocity of 2 radians/hour, while the hour hand has an angular velocity of radians/hour. At 12:00, the hour and second hands both point straight up. The two
hands will next come back together sometime after 1:00. At what exact time will this
happen? (Hint: You want to find the next time when the angle of rotation made by
the hour hand is coterminal with the angle made by the minute hand after it has first
completed one full revolution.)
Answer:
12
Step-by-step explanation:
Find KL.
K
X-1
L
12
M
Answer:
KL = 9
Step-by-step explanation:
(7 + x - 1)(x - 1) = 12²
(x + 6)(x - 1) = 144
x² -x + 6x - 6 = 144
reduce:
x² + 5x -150 = 0
(x + 15)(x - 10) = 0
x = -15, x = 10
KL = 10 - 1 = 9
You spin the spinner and flip a coin. Find the probability of the compound event.
The probability of spinning a 6 and flipping tails is
You spin the spinner and flip a coin. Find the probability of the compound event.
The probability of spinning a number less than 3 and flipping tails is
.
You spin the spinner and flip a coin. Find the probability of the compound event.
The probability of spinning a number less than 3 and flipping tails is
.
.
Answer:
0
Step-by-step explanation:
there is no 6 option on the spinner
PLEASE HELP ME PLEASEE
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: A= 1 b= -8 c= -20
Explanation:
I hope this helped!
<!> Brainliest is appreciated! <!>
- Zack Slocum
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer:
a = 1
b = -8
c = -20
Step-by-step explanation:
Jan’s family has 3/4 of a cake left. How many members of her family can get 1/4 of what is left?
Answer:
3
Step-by-step explanation:
3/4 divided by 1/4 equals 3
Answer:
3
Step-by-step explanation:
3/4 is currently left
Subtract 1/4 by 3/4 until nothing is left
The number you get is 3 therefore the answer is 3
Solve the right triangle. Round decimal answers to the nearest tenth. E D 8 14 1 F DE ~ ,mZE ~ MZD
Answer:
DE≈16.1
m<E≈60.3
m<D≈29.7
Step-by-step explanation:
HELP MEEEEEEE PLEASE
Answer:
C
Step-by-step explanation:
The last part is -8, which means 8 fewer.
A group of students is painting the background of a set for a school play what is the area of the part that is painted in gray
Question 11. What is the product of 1.6 x 10- and 3.2 x 10' A. 5.12 x 10-4 B. 5.12 x 10 C.5.12 x 10 D. 5.12 x 104 please help will mark as brallinat
Answer:
A- [tex]5.12*10^{-4}[/tex]
Step-by-step explanation:
1.6* 3.2
add the exponents so 10 to the -4
find the missing length
20 POINTS!! PLEASE HELP!! GIVING BRAINLIEST:)
Answer:
d
Step-by-step explanation:
Solve for x over the real numbers:
x^2 + 5 x + 6 = 0
The left hand side factors into a product with two terms:
(x + 2) (x + 3) = 0
Split into two equations:
x + 2 = 0 or x + 3 = 0
Subtract 2 from both sides:
x = -2 or x + 3 = 0
Subtract 3 from both sides:
Answer: |
| x = -2 or x = -3
A farmer bought a number of pigs for $160. However, 8 of them died before he could sell the rest at a profit of 6 per pig. His total profit was $8. How many pigs did he originally buy?
Answer:
The farmer bought 36 pigs in all.
Step-by-step explanation:
Given that a farmer bought a number of pigs for $ 160, but, however, 8 of them died before he could sell the rest at a profit of 6 per pig, and his total profit was $ 8, to determine how many pigs did he originally buy the following calculation must be performed:
160 + 8 = 168
168/6 = 28
28 + 8 = 36
Thus, the farmer bought 36 pigs in all.
At the city museum, child admission is $5.30 and adult admission is $9.20. On Monday, 121 tickets were sold for a total sales of $836.30.
How many adult tickets were sold that day?
Answer:
50 adult tickets were sold that day.
Step-by-step explanation:
Child ticket is $5.30Adult ticket is $9.20Total amount of ticket sold is 121, for $836.30We will use "c" to represent child ticket and "a" to represent adult ticket
Using these info, we can make a system of equations:
[tex]\left \{ {{9.2a + 5.3c = 836.3} \atop {a + c = 121}} \right.[/tex]
Solve the system of equations using substitution.
a + c = 121
c = 121 - a
9.2a + 5.3 (121 -a) = 836.3
9.2a + 641.3 - 5.3a = 836.3
3.9a = 195
a = 50
50 adult tickets were sold that day.
George Washington looks kinda different here ngl
Answer:
Yeah you know something might be a little off
Answer: yeah ur right but I’m confused if he’s really George Washington. I’m not sure I don’t think George Washington
Step-by-step explanation:
Consider the function f(x) = x3 + 34 over the interval [–3, 4]. According to the extreme value theorem, the function has a minimum value of
and a maximum value of
.
The answer for this question is:
7, 98
The minimum value of the function is 7 and the maximum value of the function will be 98.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The function is given below.
f(x) = x³ + 34
The function is defined for the interval of [–3, 4].
The minimum value of the function at x = –3 will be
f(–3) = (–3)³ + 34
f(–3) = –27 + 34
f(–3) = 7
The maximum value of the function at x = 4 will be
f(4) = (4)³ + 34
f(4) = 64 + 34
f(4) = 98
Thus, the minimum value of the function is 7 and the maximum value of the function will be 98.
The graph is given below.
More about the function link is given below.
https://brainly.com/question/5245372
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