To rewrite 12sinxcosx using the double angle formula, multiply by (1/2) and use the formula for sin(2x) to obtain the answer of 12sin(2x).
Explanation:To rewrite 12sin(x)cos(x) using the double angle formula, we need to know the formula for sin(2x) and cos(2x). The double angle formula for sine is sin(2x) = 2sin(x)cos(x), and for cosine it is cos(2x) = cos^2(x) - sin^2(x). Let's use these formulas to rewrite the expression:
12sin(x)cos(x) = 12 * (1/2) * 2sin(x)cos(x), since 1/2 is the value of cos^2(x) - sin^2(x).12 * (1/2) * 2sin(x)cos(x) = 6 * 2sin(x)cos(x).6 * 2sin(x)cos(x) = 12sin(2x). This is our final answer, using the double angle formula to rewrite the original expression.Learn more about double angle formula here:https://brainly.com/question/34830073
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Final answer:
The expression 12sinxcosx can be rewritten as 6sin(2x) by using the double angle formula for sine.
Explanation:
The expression 12sinxcosx can be rewritten using the double angle formula for sine, which is sin(2a) = 2sina ⋅ cosa. By comparing this to the given expression, we can see that it is in the form of the right-hand side of the double angle formula, where a is equivalent to x. Therefore, the expression can be rewritten as 6sin(2x). Such double angle formulae are available for other trigonometric ratios as well.
A new medical test provides a false positive result for hepatitis 2% of the time that is a perfectly healthy subject being tested for hepatitis will test as being infected 2% of the time. And research, the test is given to 30 healthy (not having hepatitis) subjects. Let X be the number of subjects who test positive for the disease
A. What is the probability that all 30 subjects will appropriately test as not being infected?
B. What are the mean and standard deviation of X?
C. To what extent do you think this is a viable test to use in the field of medicine?
The dot product of u with itself is 12. what is the magnitude of u?
Answer: The magnitude of the vector u is √12 units.
Step-by-step explanation: Given that the dot product of a vector u with itself is 12.
We are to find the magnitude of the vector u.
Let <a, b> represents the vector u.
That is, u = <a, b>
Then, according to the given information, we have
[tex]u.u=12\\\\\Rightarrow <a, b>.<a, b>=12\\\\\Rightarrow a^2+b^2=12\\\\\Rightarrow \sqrt{a^2+b^2}=\sqrt{12}\\\\\Rightarrow |u|=\sqrt{12}.[/tex]
Thus, the magnitude of the vector u is √12 units.
Which represents a quadratic functionWhich represents a quadratic function? f(x) = 2x3 + 2x2 – 4 f(x) = –7x2 – x + 2 f(x) = –3x + 2 f(x) = 0x2 + 3x – 3
Answer:
[tex]f(x) = -7x^2 -x +2[/tex] represents a quadratic function.
Step-by-step explanation:
A polynomial of degree two is called quadratic function,
Also, degree of polynomial is the highest power of its monomial ( individual term with non zero coefficient ),
Since, [tex]f(x) = 2x^3 + 2x^2 -4[/tex] has degree 3,
⇒ [tex]f(x) = 2x^3 + 2x^2 -4[/tex] is not a quadratic function,
[tex]f(x) = -7x^2 -x +2[/tex] has degree 2,
⇒ [tex]f(x) = -7x^2 -x +2[/tex] is a quadratic function,
[tex]f(x) = -3x+2[/tex] has degree 1,
⇒ [tex]f(x) = -3x+2[/tex] is not a quadratic function,
[tex]f(x) = 0x^2 + 3x -3[/tex] has degree 1,
⇒ [tex]f(x) = 0x^2 + 3x -3[/tex] is not a quadratic function,
n circle A shown below, m Arc BC is 61° and m Arc EF is 76°: Points B, C, E, F lie on Circle A. Lines BE and CF pass through point D creating angle EDF. Measure of arc BC is 61 degrees and What is m∠FDE?
Answer:
The correct answer is 68.5°
The calculated result of the angle FDE is 68.5°. Whenever two chords cut across a circle, the resulting angle is equivalent to half of the sum of the measurements of the arc the angle intersects and that which the angle vertical to the first angle intercepts.
m<FDE = 1/2( Arc BC + Arc 76)
m<FDE = 1/2 (61° + 76°)
m<FDE = 137/2 = 68.5°
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Wai recorded the length of each wire needed for a science project. What is the total length of wire needed?
Answer:
14 5/8
Step-by-step explanation:
multiply each number by it's frequency the product is the total value .
If BY = 4, YC = 7, XC = 10. Which of the following proportions could be used to solve for AC?
4/7 = 10/AC
7/4 = 10/AC
4/11 = 10/AC
7/11 = 10/AC
Answer:
The correct option is 4.
Step-by-step explanation:
In triangle ABC and XYC,
[tex]\angle BAC=\angle YXC=60^{\circ}[/tex] (Given)
[tex]\angle BCA=\angle YCX[/tex] (Reflexive Property)
By AA rule of similarity,
[tex]\triangle ABC\sim \triangle XYC[/tex]
The corresponding sides of similar triangles are proportional.
Since triangle ABC and XYC, therefore
[tex]\frac{XC}{AC}=\frac{YC}{BC}[/tex]
[tex]\frac{XC}{AC}=\frac{YC}{BY+YC}[/tex]
[tex]\frac{10}{AC}=\frac{7}{4+7}[/tex]
[tex]\frac{10}{AC}=\frac{7}{11}[/tex]
Therefore option 4 is correct.
An item that originally cost $100 is decreased by 8%. The reduced price is then increased by 8%.
The resulting price is _____.
Answer:
The resulting price is $99.36.
Step-by-step explanation:
Original cost of the item = $100
The decrease percentage is 8% or 0.08
So, the reduced price becomes :
[tex]100-(0.08\times100)=92[/tex] dollars
Now again the reduced price is increased by 8%.
So, multiplying the reduced price by 8% and adding it again we get;
[tex]92+(0.08\times92)[/tex] =$99.36
So, the resulting price is $99.36.
Haley measured the distances between her house and two of her friends' houses. ellen's house is 1.41 miles away from haley's, and dirk's house is 6,547 feet away from haley's. whose house is farther away from haley's, and how many feet farther away is it, to the nearest whole foot?
Answer: Ellen's house is farther away by 898 feet.
Step-by-step explanation:
Given: The distance between Haley's house and Ellen's house = 1.41 miles
We know that 1 mile = 5,280 feet
Then, [tex]1.41\text{ miles}=1.41\times5,280\text{ feet}=7,444.8\text{ feet}[/tex]
The distance between Haley's house and Dirk's house = 6,547 feet
Clearly, 6,547<7,444.8
And [tex]7444.8-6547= 897.8\approx898[/tex]
Therefore, Ellen's house is farther away by 898 feet.
Q: what is the complete factorization of the polynomial below x^3+4x^2-x-4?
A. (x+1)(x-1)(x+4)
B. (x-1)(x-1)(x-4)
C. (x+1)(x-1)(x-4)
D. (x-1)(x-1)(x+4)
The solution is Option A.
The factorized form of the polynomial equation A = x³ + 4x² - x - 4 is given by B = ( x + 1 ) ( x - 1 ) ( x + 4 )
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the factorized equation be represented as = B
Now , let the equation be A
The value of A is given by A = x³ + 4x² - x - 4
On simplifying the equation , we get
A = x³ + 4x² - x - 4
Taking x² as the common term in the first two terms of the equation ,
A = x² ( x + 4 ) - x - 4
The equation can be further simplified as
A = x² ( x + 4 ) - ( x + 4 )
Taking ( x + 4 ) as the common term in the first two terms of the equation ,
A = ( x² - 1 ) ( x + 4 )
Now , ( x² - 1 ) can be simplified as ( x + 1 ) ( x - 1 )
So , the value of B is
B = ( x + 1 ) ( x - 1 ) ( x + 4 )
Therefore , the value of B is ( x + 1 ) ( x - 1 ) ( x + 4 )
Hence , the factorized equation is ( x + 1 ) ( x - 1 ) ( x + 4 )
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The figure below is the two-dimensional net of a rectangular prism. What is the surface area of the prism it can be folded to form? Show your work.
8 square units
20 square units
24 square units
28 square units
Answer:
the answer is d:)
Step-by-step explanation:
i took the quiz on edge and got 100:D
The base of a triangle is 15 centimeters and its height is 6 centimeters. What is the area of the triangle?
a.21 cm2
b.45 cm2
c.90 cm2
d.180 cm2 Submit
What is the measure of the angle?
Evaluate the series 4 – 2 + 1 – 0.5 + 0.25 to S10. Round to the nearest hundredth.
New York City gift shop sells miniature Statue of Liberty sculptures that are 7.8 inches tall. the scale of the model to the actual statue is 1:232. what is the height of the actual statue to the nearest foot?
I am first going to try finding the tangent line at this point:
Take the derivative:
dy/dx = (3x^2 - e^x)/2y
Solve using (0, 1)
dy/dx = (0 - 1)/6 = -1/6
I believe that -1/6 is the slope of the tangent line, so the slope of the normal line should be +6, right?
what is the following product 3 sqrt 2(5 sqrt 6-7 sqrt 3)
Answer:
[tex](30\sqrt{3}-21\sqrt{6})[/tex]
Step-by-step explanation:
We have to find the product of the expressions.
[tex]3\sqrt{2}(5\sqrt{6}-7\sqrt{3})\\[/tex]
= [tex]3\sqrt{2}\times 5\sqrt{6}-7\sqrt{3}\times 3\sqrt{2}[/tex] ( By distributive rule)
= [tex]3\times 5(\sqrt{2})(\sqrt{6})-7\times 3(\sqrt{3})(\sqrt{2})[/tex]
= [tex]15\sqrt{12}-21\sqrt{6}[/tex]
= [tex]15\sqrt{4\times 3}-21\sqrt{6}[/tex]
= [tex]30\sqrt{3}-21\sqrt{6}[/tex]
= [tex](30\sqrt{3}-21\sqrt{6})[/tex]
A bag contains 5 5 green marbles, 10 10 yellow marbles, 4 4 red marbles. two marbles are drawn without replacement which means that once the first marble is selected it is not put bag into the bag. it is not replaced. what is the probability of drawing a green marble then a red marble?
A museum charges a school $200 to hold a trip + $2 entrance fee per person. The students must share the total cost of the trip equally include the entrance feee for 8 teachers. What is the function Y(x) that gives that gives the cost per X person attending the trip?
What is the area of a regular hexagon with a side length of 12 cm
What are the factors of x^2-64
The factors of x^2 - 64 are (x - 8) and (x + 8), derived by recognizing the expression as a difference of squares and applying the formula a^2 - b^2 = (a - b)(a + b).
Explanation:The question asks about the factors of x^2-64. This expression is a difference of squares, which can be factored using the formula a^2 - b^2 = (a - b)(a + b). In this case, x^2 is a^2, and 64 is b^2, with b being 8 since 82 = 64. Applying the formula, we get:
x^2 - 64 = (x - 8)(x + 8)
This shows that the factors of x^2-64 are (x - 8) and (x + 8). This process of factoring by recognizing patterns, especially the difference of squares, is a useful algebraic skill when simplifying expressions or solving equations.
(need help!) A dart is thrown at the board shown. It hits the board at a random point. Find the probability that it will land in the unshaded region. Round to the nearest percent.
20%
33%
17%
25%
[tex] |\Omega|=360\\
|A|=120\\\\
P(A)=\dfrac{120}{360}=\dfrac{1}{3}\approx33\% [/tex]
Quick need the answer!
jen is thinking of a number. the product of this number and 3.4 is 176.8. find jens number.
Find the area of the rectangle below (3x-2) (4x-7)
Am I correct in thinking that the answer to this derivative problem is B?
dy/dx = y/x^2
dy/y = dx/x^2
ln y * ln c = -1/x
cy = e^(-1/x)
y = ce^(-1/x)
Find the surface area of each right regular pyramid. a pentagonal pyramid with base sides 1.5 meters, base area 3.9 m2, and slant height 4 meters
Techechtium-99m has a half-life of 6 hours. If 1000mg is in use, in how many hours will 62.5mg remain?
Techechtium-99m has a half-life of 6 hours. It will take 96 hours for 62.5 mg of Techechtium-99m to remain from an initial amount of 1000mg.
Explanation:To determine how many hours it will take for 62.5 mg of Techechtium-99m to remain from an initial amount of 1000mg, we can use the concept of half-life.
Techechtium-99m has a half-life of 6 hours, which means that after every 6 hours, half of the initial amount will decay.
So, to find the number of half-lives required to reach 62.5 mg, we can divide the initial amount by the remaining amount:
1000mg / 62.5mg = 16.
Since each half-life is 6 hours, we can multiply the number of half-lives by 6 to find the total number of hours:
16 x 6 = 96.
Therefore, it will take 96 hours for 62.5 mg of Techechtium-99m to remain from an initial amount of 1000mg.
a garden patio is covered with grey slabs and yellow slabs. 1/5 is grey. 1/4 is yellow. there’s 55 slabs in total. what is the number of yellow slabs
Answer:
44
Step-by-step explanation:
1:4
4+1=5
55/5=11
11*4=44
the answer is 44
Suppose that there were a strong correlation between the variables n and p. Which of these is a true statement?
A. n may cause p.
B. p must cause n.
C. n must cause p.
D. n must not cause p.
please help asap 50 pts
Your answer should be C.
[tex]The\; vertex\; is\; at\; 19,361\; so\; your\; answer\;is\;c![/tex]