The trigonometric substitution x = 2secθ simplifies the expression x^2 - 4x to (-4sin^2θ)/cosθ.
To make the indicated trigonometric substitution in the given algebraic expression and simplify, we can use the substitution x = 2secθ, where secθ = 1/cosθ.
First, we need to solve for x in terms of θ:
x = 2secθ
x = 2/(cosθ)
Now, we can substitute this expression for x in the original expression:
x^2 - 4x = (2/(cosθ))^2 - 4(2/(cosθ))
Simplifying, we get:
x^2 - 4x = 4/cos^2θ - 8/cosθ
To further simplify, we can use the identity cos^2θ = 1 - sin^2θ:
x^2 - 4x = 4/(1-sin^2θ) - 8/cosθ
We can then combine the two fractions by finding a common denominator:
x^2 - 4x = (4cosθ - 8(1-sin^2θ))/((1-sin^2θ)cosθ)
Simplifying further, we get:
x^2 - 4x = (-4sin^2θ)/cosθ
Therefore, the trigonometric substitution x = 2secθ simplifies the expression x^2 - 4x to (-4sin^2θ)/cosθ.
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The regular price of The Mario Kart 8 Deluxe video game is $59.99. On Amazon, the discount is $10.05. What is the percent discount on this video game?
Answer:
It was a 16.7% discount
Step-by-step explanation:
You have to get the discount and divide it by the original price and it would be 0.16753 and so the percent becomes 16.7%
Answer: About 6 percent off.
Step-by-step explanation:
hope this helps :)
Your sister goes to a restaurant with her friends. The total for the food is $50.43. How much TAX will you pay if the percentage rate is 6%?
Answer:
3.0258
Step-by-step explanation:
50.43*6%=3.0258
2. The lengths of the sides of a triangle are 4cm, 5cm and 6cm. Find, in degrees to one decimal
place, the size of the largest angle of the triangle.
Answer:
82.8 degrees.
Step-by-step explanation:
The largest angle is opposite the longest side.
So we find the angle opposite the 6cm line using The Cosine Rule:
6^2 = 4^2 + 5^2 - 2.4.5 cos A
cos A = (6^2 - 4^2 - 5^2) / (-2*4*5)
= -5/ -40
= 0.125.
So m angle A = 82.819 degrees.
The table shows the total cost to use Mark's Moving Company.
Hours
Total
Cost
1
$190
2
$280
3
$370
4
$460
Using f(x) to represent the total cost, and x to represent the number of hours, which function models this situation?
A. f(x) = 190x + 90
B. f(x) = 100x + 90
C. f(x) = 90x + 190
D. f(x) = 90x + 100
Answer:
The answer would be C can I get brainliest?
Step-by-step explanation:
Did this kind of math before. Hope this helps you.
Combine like terms
(3x^2−10x+4)+(10x^2−5x+8)
I will give brainliest
Answer:
13x^2-15x+12
Step-by-step explanation:
Evaluate 8(a +b) when a = 5 and b = 11
Answer:
Hi there
your answer is 128
Step-by-step explanation:
8(5+11)
Answer:
128
Step-by-step explanation:
8(5+11)= 128
The length of the minute hand on a clock is 10in what's the diameter
Answer:
20
Step-by-step explanation:
1. Janna works at a lab with a huge circular particle accelerator. It has a radius of 4 kilometers. What is the accelerator's diameter?
2. KC wants to know the area of the portion with a lot of cheese. The radius of the pizza is 9 inches and the intercepted arc of the pizza with lot of cheese measures 140°. What will be the area of the shaded sector?
3. From the main entrance of the park, there are two pathways where visitors can walk along going to the circular garden. The pathways are both tangent to the garden whose center is 40m away from the main entrance. If the area of the garden is about 706.5 m2, how long is each pathway?
pakisagot po ty!!
Answer:
1. diameter=8 kilometres
2. area=98.96 inches
3. 37m
Step-by-step explanation:
1. diameter= 2*radius
2. area of sector=θ out of 360*π[tex]r^{2}[/tex] where θ is the angle
3. area of garden=π[tex]r^{2}[/tex]
706.5=π[tex]r^{2}[/tex]
[tex]r^{2}[/tex]=706.5/π
= 225(nearest whole)
r=[tex]\sqrt{225}[/tex]=15m
we now use Pythagoras theorem to find length of each pathway
[tex]40^{2} =15^{2} +x^{2}[/tex]
1600=225+[tex]x^{2}[/tex]
[tex]x^{2}[/tex]=1600-225=1375
x=[tex]\sqrt{1375}[/tex]=37 m (to nearest whole)
The tangent pathways from the entrance form right triangles from which
the length of the pathway which are the sides of the triangle, can be found.
1. The diameter is 8 kilometers2. The area of the shaded sector is 98.96 square inches3. The length of each pathway from the entrance is approximately 37.1 metersReasons:
1. The radius of the particle accelerator = 4 kilometers
The diameter of the particle accelerator = 2 × The radius
Therefore;
The diameter = 2 × 4 km = 8 km
The accelerator's diameter is 8 kilometers
2. The area of a sector of a circle is A = [tex]\displaystyle \frac{\theta}{360^{\circ}} \times \pi \cdot r^2[/tex]
The angle subtended by the sector, θ = 140°
The radius of the sector, r = 9 inches
Therefore;
[tex]\displaystyle A = \frac{140^{\circ}}{360^{\circ}} \times \pi \times 9^2 = \mathbf{ 31.5 \cdot \pi}[/tex]
The area of the shaded sector, A = 31.5·π in.² ≈ 98.96 in.²
3. The distance from the center to the main entrance, d = 40 m
Area of the circular garden, A = 706.5 m²
Solution:
The radius of the garden, r = √(A ÷ (π))
Therefore;
r = √(706.5 ÷ (π)) ≈ 15
The tangent pathways are perpendicular to the radius of the circular garden.
Therefore, the pathway from the entrance, the 40 m. distance from the center to the entrance and the radius form a right triangle.
Where;
The 40 m. distance = The hypotenuse side
By Pythagorean theorem, we have;
40² = r² + (Length of the pathway)²
Which gives;
40² = 15² + (Length of the pathway)²
Length of the pathway ≈ √(40² - 15²) ≈ 37.1
The length of each pathway is approximately 37.1 m.
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Find the explicit formula for the given sequence.
-4, 12, -36, 108,...
a
a_n=-4·(-3)^{n-1}
b
a_n=4·3^{n-1}
c
a_n=15·3^{n-1}
d
a_n=5·3^{n-1}
Answer:
Option a.) an = -4(-3)^(n-1)
Simplify.
Rewrite the expression in the form 6^n. 6^-6/6^-5=
Answer:
cacacc
Step-by-step explanation:
sorr
Answer:
the answer is 0.1666667
what is (9m)4 without exponents
Answer:
The answer is 36m
Step-by-step explanation:
Multiply 9m by 4, and you'll get (9x4)m, which is (36)m, which can be simplified into 36m.
Please help me out thank you.
its A
Step-by-step explanation:
Answer:
_____________
The table below shows the monthly balances a person had on their credit card over a five-month period.
Month Balance
January -$50
February $25
March -$70
April -$45
May $25
What was the average monthly balance over the five-month period? Enter your answers and your explanations or work in the space provided.
Answer:
43 dollars
Step-by-step explanation:
to take the average we have to add up all the numbers and divide by 5 which is
215/5=43
if my answer helps please mark as brainliest.
7. The cost of 2 notebooks and 4 folders is
$2.50. The cost of 1 notebook and 6
folders is $2.25. Which statement is true?
A The cost of a notebook is $1.00, and
the cost of a folder is $0.25.
B The cost of a notebook is $0.75, and
the cost of a folder is $0.25.
C The cost of a notebook is $0.25, and
the cost of a folder is $0.75.
Answer: B (The cost of a notebook is $0.75, and the cost of a folder is $0.25.)
Step-by-step explanation:
No need for explanation. i know i’m right!!
Find the product.
3(x+4)(x-5)
A. 3x2 − 11x − 20
B. 3x2 − 20x
C. 3x2 − 3x − 60
D. 3x2 − x − 20
Step-by-step explanation:
la respuesta es la letra C
Answer:
First distribute the 3
(3x + 12)(x - 5)
Multiply
3x - 3x - 60
Step-by-step explanation:
Convert the following quadratic equation to vertex form. 2) 3x2 - 12x - 5
Answer:
2*12x-5
Step-by-step explanation:
In geometry, a vertex form is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices. For example, a square has four corners, each is called a vertex.
14.3 times 6.2
[NEED ANSWER ASAP]
Answer:
88.66
Step-by-step explanation:
used calculator
the scale of a model is 0.5in : 6 ft. find the length of the model for an actual length of 204 ft
Answer:
17 in
Step-by-step explanation:
.5 in : 6 ft
204/6 x .5 = 17
Factor-
2x^2+5x+3
Answer choices:
1. (2x+1)(x+3)
2. (2x+5)(x+1)
3. (2x+3)(x+1)
4. The Polynomial Is Prime
Factor-
3x^2+10x+4
Answers
1. (3x-4)(x-1)
2. (3x-2)(x-2)
3. (3x-4)(x+1)
4. The Polynomial Is Prime
Factor -
8x^2+10x-3
Answers
1. (2x-1)(4x+3)
2. (2x+3)(4x-1)
3. (8x+1)(x-3)
4. The Polynomial Is Prime
Factor-
6x^2-7x-4
Answers
1. (2x+2)(3x-2)
2. (6x+2)(x-2)
3. (6x-4)(x+1)
4. The Polynomial Is Prime
Factor Completely
2x^2+x-28
Answers
1. (2x+1)(x-28)
2. (2x-7)(x+4)
3. (2x+7)(x-4)
4. (2x-7)(2x+8)
Step-by-step explanation:
(2x+3)(x+1)prime(2x+3)(4x-1)The Polynomial Is Prime (2x-7)(x+4)find the number of terms and the degree of this polynomial.
[tex] - 9 {r}^{9} [/tex]
Step-by-step explanation:
there is 1 term
9th degree or degree =9
Solve x, show work. what equation would i need to use
Answer:
x=6
Step-by-step explanation:
You can find the answers using similar triangles.
The leftmost side of the small triangle we shall call y. The leftmost side of the big triangle is twice this: 2y.
This tells us that the the side lengths in the big triangle are twice that of the small:
19x-28=2(6x+7)
19x-28=12x+14
7x=42
x=6
X-y=3
6x-7y=11
what is the answer to this HELP plz
simplify: 5(3x-4)-6(2x+3)
Step-by-step explanation:
I am doing the same math and I have no idea one nobody is helping me :/ there just looking at my problem and saying the wrong number :((
Step-by-step explanation:
Given
5(3x-4)-6(2x+3)
= 15x - 20 - 12x - 18
= 3x - 38
Which graph represents the function f(x)=2x-2/x-2
Answer:
graph in attachment.
Step-by-step explanation:
A department controls 3 accounts. Account A started at $1,750 and increased annually by 8% for 3 years. Account B started at $3,000 and increased annually by 6% for two years and then decreased by 2.5% for one year. Account C started at $3,250 and decreased in value by 11% for the first year and then increased in value annually by 7% for two years. What is the total value of all three accounts after these three years?
Answer:
$8802.65
Step-by-step explanation:
$2204.50
$3286.53
$3311.62
2−4(5p+1) Simplify to create an equivalent expression.
Answer:
2-20p-4 = -20p-2
Step-by-step explanation:
Answer:
- 20p - 2
Step-by-step explanation:
Given
2 - 4(5p + 1) ← distribute parenthesis
= 2 - 20p - 4 ← collect like terms
= - 20p - 2
Linear pairs are supplementary
True or false
Plss answerr
True
If two angles form a linear pair, the angles are supplementary. A linear pair types a straight angle which contains 180º, so you have 2 angles whose measures add to 180, which skill they are supplementary.
Find the slope of the line that passes through these two points: (4, 19) and (-15, 7) -19/12 19/12 12/19 -12/19
Answer:
12/19
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(7-19)/(-15-4)
m=-12/-19
m=12/19
Help please.........
MATTHEW WENT INTO THE STORE WITH $750.00. HE WANTS TO BUY NEW CLOTHES FOR THE FIRST WEEK
OF SCHOOL. EVERYTHING IN THE STORE IS ON SALE FOR 35%. HOW MUCH MONEY WILL HE HAVE LEFT?
Answer:
the money left is $487.50
Step-by-step explanation:
The computation of the money left is shown below:
= Total money - spent money
= $750 - $750 × 35%
= $750 - $262.50
= $487.50
Hence, the money left is $487.50
We simply deduct the spent money from the total money