Answers
Answer: 47°
Step-by-step explanation:
Related Questions
Line segment Z E is the angle bisector of AngleYEX and the perpendicular bisector of Line segment G F. Line segment G X is the angle bisector of AngleYGZ and the perpendicular bisector of Line segment E F. Line segment F Y is the angle bisector of AngleZFX and the perpendicular bisector of Line segment E G. Point A is the intersection of Line segment E Z, Line segment G X, and Line segment F Y.
Triangle G E F has angles with different measures. Point A is at the center. Lines are drawn from the points of the triangle to point A. Lines are drawn from point A to the sides of the triangle to form right angles and line segments A X, A Z, and A Y.
Which must be true?
Point A is the center of the circle that passes through points E, F, and G but is not the center of the circle that passes through points X, Y, and Z.
Point A is the center of the circle that passes through points X, Y, and Z but is not the center of the circle that passes through points E, F, and G.
Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.
Point A is not necessarily the center of the circle that passes through points E, F, and G or the center of the circle that passes through points X, Y, and Z
Answers
The correct option that depicts the centroid of the triangle is; C. Point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
How to interpret the segments formed from Triangle Centroid?The center of inscribed circle into the triangle is the point where the angle bisectors of the triangle meet.
The center of the circumscribed circle over the triangle is the point where the perpendicular bisectors of the sides meet.
Line segments ZE, FY and GX are both angle bisectors and perpendicular bisectors of the sides. Thus, the point of intersection of line segments ZE, FY and GX is the center of inscribed circle into the triangle and the center of the circumscribed circle over the triangle.
Inscribed circle passes through the points X, Y and Z. Circumscribed circle passes through the points E, F and G. So, point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
Thus, the correct option is option C. Point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
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The diagonals of a rectangle measure x+5 feet and 2x+1 feet what is the value of x?
Answers
The value of x is 4.
Given that diagonals of a rectangle measure x+5 feet and 2x+1 feet as shown in the attached figure.
The diagonal of a rectangle is a line or straight line that connects the opposite corners or vertices of the rectangle.
In the given figure ABCD is a rectangle.
OA=2x+1 and OD=x+5 [Given]
AC and BD are diagonals of a rectangle.
As we know that the diagonals of a rectangle are always equal.
So, AC = BD
We can also write it as,
2×OA=2×OD
2×(2x+1) =2×(x+5)
Apply the distributive property a(b+c)=ab+ac, we get
4x+2=2x+10
Subtract 2x from both sides, we get
4x+2-2x=2x+10-2x
2x+2=10
Subtract 2 from both sides, we get
2x+2-2=10-2
2x=8
Divide both sides by 2, we get
2x/x=8/2
x=4
Hence, the value of x=4 when diagonals of a rectangle measure x+5 feet and 2x+1 feet.
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The official height to width ratio of the United States flag is 1:1.9 If a United States flag is 6 feet high, how wide is it?
Answers
Answer:
11.4 feet
Step-by-step explanation:
1/1.9 = h/w (h= height, w=width)
Solving for w, gives you the formula
w = (1.9)h
This means the width is 1.9 times the height.
Use the formula to find the width where the height is 6 feet.
h = 6
w = (1.9)(6) = 11.4
The width is 11.4 feet.
What is the total probability of rolling a single die twice, and having it land on 3 the
first roll, and a number greater than 3 the second roll?
er:
Answers
Answer:
0,5*0,5=0,25
Step-by-step explanation:
assuming a die of 6 faces
25
0,5 for < 4; 0,5 for < 3
Determine the slope of the line
Answers
Answer:1+1
Step-by-step explanation:
Can you construct an example of a discrete random variable which does not have a finite expectation?
Answers
Throwing a coin until it lands tails is an example of a discrete random variable which does not have a finite expectation.
For the given question,
A discrete random variable is a type of variable whose value depends upon the numerical outcomes of a certain random phenomenon. Discrete random variables are always whole numbers, which are easily countable.
It is a variable that can take on a finite number of distinct values and takes numerous values. It is also known as a stochastic variable. When you consider probabilistic experiments with infinite outcomes, it is easy to find random variables with an infinite expected value.
Let X be a random variable that is equal to 2ⁿ with probability 2⁻ⁿ (for positive integer n). Then,
[tex]E(X)=\sum_{n:1}^{\infty} |2^{-n}2^{n}|[/tex]
⇒ [tex]E(X)=\sum_{n:1}^{\infty} (1)[/tex]
⇒ [tex]E(X)=\infty[/tex]
Consider the following example,
You throw a coin until it lands tails.
Let n be the number of heads
Then number of heads can be found by, 2ⁿ
Now, the expected value function is
[tex]E(X)=\frac{1}{2}(2^{0} )+ \frac{1}{4}(2^{1} )+....[/tex]
⇒ [tex]E(X)=\sum_{n:1}^{\infty} |2^{-n}2^{n-1}|[/tex]
⇒ [tex]E(X)=\sum_{n:1}^{\infty} \frac{1}{2}[/tex]
⇒ [tex]E(X)=\infty[/tex]
Since the number of outcomes is infinite. The probability of each outcome decreases exponentially.
Hence we can conclude that throwing a coin until it lands tails is an example of a discrete random variable which does not have a finite expectation.
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Consider the function f(x) = one-third(6)x. what is the value of the growth factor of the function?
Answers
6 is the growth factor in the function f(x) = (1/3)(6ˣ).
The rate at which a quantity multiplies itself over the independent factor, to increase the value of the function exponentially is known as its growth factor.
In the question, we are given a function f(x) = (1/3)(6ˣ) and are asked to identify the growth factor of the function.
We know that the rate at which a quantity multiplies itself over the independent factor, to increase the value of the function exponentially is known as its growth factor.
In the given function, f(x) = (1/3)(6ˣ), (1/3) remains unaffected with the change in the independent factor x, but 6 is exponentially increasing with x.
Thus, 6 is the growth factor in the function f(x) = (1/3)(6ˣ).
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The lifetime of a certain type of battery is normally distributed with mean value 13 hours and standard deviation 1 hour. There are nine batteries in a package. What lifetime value (in hours) is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages
Answers
The lifetime of the batteries in a package is 14.31 hours which exceeds that value for only 5% of all packages.
Give sample mean of 13 hours and standard deviation of 1 hour and sample size is 9.
We have to apply t test in this because the value of n which is sample size is less than 30.
We have been given the p value of the required mean so we have to find the t value for this with degree of freedom (9-1)=8
t value=2.306.
We know that
t=X bar-μ/s/[tex]\sqrt{n}[/tex]
s/[tex]\sqrt{n}[/tex]=1/[tex]\sqrt{3}[/tex]=0.57
Put all the values in the above formula to calculate required mean.
2.306=X bar-13/0.57
X bar=1.31442+13
=14.31442
after rounding off we get
X bar=14.31
Hence the lifetime of the batteries is 14.31 for which the percentage exceeds 5%.
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can someone help me with answer C? its the last one i need
Answers
Using the monthly payment formula, it is found that her down payment should be of $1,419.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.For this problem, the parameters are:
A = 250, r = 0.072, n = 72.
Hence:
r/12 = 0.072/12 = 0.006.
We solve for P to find the total amount of the monthly payments, hence:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]P\frac{0.006(1.006)^{72}}{(1.006)^{72}-1} = 250[/tex]
0.0171452057P = 250
P = 250/0.0171452057
P = $14,581.
The total payment is of $16,000, hence her down payment should be of:
16000 - 14581 = $1,419.
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Type the correct answer in each box. Use numerals instead of words.
Simplify the following polynomial expression.
(5x² + 13x4) (17x² + 7x - 19) + (5x-7)(3x + 1)
-
x +
Answers
The simplification of the polynomial expression will give 3x² - 20x + 8.
How to illustrate the polynomial?The polynomial expression is given as:
(5x² + 13x4) (17x² + 7x - 19) + (5x-7)(3x + 1)
= 5x² + 13x - 4 - 17x² - 7x + 19 + 15x² + 5x - 21x - 7
Then collect like terms
= 5x² + 15x² - 17x² + (13x - 7x + 5x - 21x) - 4 - 7 + 19
= 3x² - 20x + 8.
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=
Triangle R S T is shown. Angle T R S is a right angle. The length of R T is 5, the length of R S is 12, and the length of hypotenuse S T is 13.
Given right triangle RST, what is the value of sin(S)?
Five-thirteenths
Five-twelfths
Twelve-thirteenths
Thirteen-twelfths
Answers
Answer:
Step-by-step explanation:
I would use the law of sins.
13/sin90 = 5/sin s
sin s = (5 sin 90)/13
sin s = .3846.
Now put in your calculator sin-1 .3846 and you will get the angle of 22.6 degrees rounded to the tenths place.
Answer:
22.6 = 113/5
Step-by-step explanation:
I need help with these questions because I don't understand it.
Answers
Evaluating the given expressions and inequalities, we have;
[tex]11) \: \frac{x}{4} \cdot \left(2 + y - x \right) = 4[/tex]
12) (8•a - 5•b) - 2•(a + b) = 4
[tex] 13) \: \frac{p \cdot (p + {a}^{2} )}{6} = 55 [/tex]
[tex] 14) \: 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = 12 [/tex]
[tex] 16) \: x \geq 11\frac{2}{3} [/tex]
17) k > 9
18) v > 9
20) m ≤ 16
Which method can be used to evaluate the expressions and inequalities?The given expressions are;
[tex]11) \: \frac{x}{4} \cdot \left(2 + y - x \right)[/tex]
Where x = 4, and y = 6, we have;
[tex]\frac{x}{4} \cdot \left(2 + y - x \right) = \frac{4}{4} \cdot \left(2 + 6 - 4 \right) = 4[/tex]
Therefore;
[tex]\frac{x}{4} \cdot \left(2 + y - x \right) = 4[/tex]
12) (8•a - 5•b) - 2•(a + b)
Where a = 3 and b = 2, we have;
(8•a - 5•b) - 2•(a + b) = (8×3 - 5×2) - 2•(3 + 2) = 4
Therefore;
(8•a - 5•b) - 2•(a + b) = 4[tex]13) \: \mathbf{\frac{p \cdot (p + {a}^{2} )}{6}} [/tex]
Where a = 7, and p = 6, we have;
[tex] \frac{p \cdot (p + {a}^{2} )}{6} = \mathbf{ \frac{6 \times (6 + {7}^{2} )}{6}} = 55 [/tex]
Therefore;
[tex] \frac{p \cdot (p + {a}^{2} )}{6} = 55 [/tex]
[tex]14) \: \mathbf{3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} } [/tex]
Where m = 5, and n = 6, we have;
[tex] 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = \mathbf{3\times 5 - \frac{2\times 5}{2} +\frac{6}{3} }= 12 [/tex]
Therefore;
[tex] 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = 12 [/tex]
[tex]16) \: \mathbf{1 \frac{1}{6} }\leq \frac{x}{10} [/tex]
Which gives;
[tex] \frac{7}{6} \times 10 \leq x [/tex]
[tex] \mathbf{ \frac{35}{3} }\leq x [/tex]
[tex] x \geq 11\frac{2}{3} [/tex]
17) 20 < k + 11
Therefore;
k > 20 - 11 = 9
k > 918) 6•v > 54
v > 54 ÷ 6 = 9
Therefore;
v > 9[tex]20) \: 8 \geq \mathbf{ \frac{m}{2}} [/tex]
Therefore;
2 × 8 = 16 ≥ m
Which gives;
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The Bay announced it would open a 9000-plus square metre freestanding store in the new West Grand Promenade. This would be the largest store on the promenade, with other smaller stores selling food, tires, and shoes. How else can this particular Bay store be described
Answers
This Bay store can also be described as a big box retailer store.
Big Box Retailer
A big box retailer is a physically enormous retail store that is typically a component of a chain of stores (also known as a hyper store, supercenter, superstore, or megastore). By extension, the phrase, big box retailer can also refer to the business that runs the store.
The Bay Store as a Big Box
There are numerous retail chains that only operate in Canada, aside from the large American big box retailer stores like Walmart Canada and the formerly-existent Target Canada. These include places like Hudson's Bay by Home Outfitters, Loblaws by Real Canadian Superstore, Rona, Winners by HomeSense, Canadian Tire by Mark's & Sport Chek, Shoppers Drug Mart, Chapters by Indigo Books and Music, Sobeys, and several others.
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What is the perimeter of a regular heptagon with a side length of 8 units? 48 units 56 units 72 units 32 units
Answers
Answer:
The answer to your question is P=56
Step-by-step explanation:
P=7a=7·8=56
I hope this helps and have a good day!
PLEASE HELPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
x intercepts: (1,0), (-3,0)
the roots are 1 and -3
Step-by-step explanation:
Using the Quadratic Formula:
x=−b±sqrt(b2−4ac)/2a
Substitute:
x= -8±sqrt(8^2-4(4)(-12))/2(4)
x=-8±sqrt((64- -192))/8
x=-8±sqrt(256)/8
Solve two equations (±)
x=-8±16/8
x=8/8 and x=-24/8
x=1 and x=-3
Answer:
x = -3
x = 1
Step-by-step explanation:
Hello!
We can solve the quadratic by Factoring the Equation and using the Zero Product Property.
Factor[tex]y = 4x^2 + 8x - 12[/tex][tex]y = 4(x^2 + 2x - 3)[/tex]
We want to find two numbers that multiply out to -3, but add up to 2. The numbers that work are -1 and 3. We can expand 2x to -x and 3x and factor by grouping.
[tex]y = 4(x^2 -x + 3x - 3)[/tex][tex]y = 4(x(x - 1) + 3(x - 1))[/tex][tex]y = 4(x + 3)(x - 1)[/tex]Solve for x
Set each factor to 0 and solve for x in both.
[tex]0 = 4(x + 3)(x - 1)[/tex][tex]0 = (x + 3), x = -3[/tex][tex]0 = (x - 1), x = 1[/tex]Therefore, the x-interecpts are -3 and 1.
Find the equation of the line through point (−1,4) and parallel to 5x+y=4. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 12).
Answers
The equation of the parallel line is y = -5x - 1
How to determine the line equation?The equation is given as:
5x + y = 4
Make y the subject
y = -5x + 4
The slope of the above equation is
m = -5
Parallel lines have equal slope.
This means that the slope of the new line is 5
The equation is then calculated as:
y = m(x - x1) + y1
So, we have:
y = -5(x + 1) + 4
Expand
y = -5x - 5 + 4
Evaluate
y = -5x - 1
Hence, the equation of the parallel line is y = -5x - 1
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Function the graphic below:
Answers
The graph is a decreasing exponential graph.
How to illustrate the information?Part A: The given graph is decreasing the exponential graph since the graph is decreasing rapidly as the value of x is increasing and the value of y is decreasing rapidly.
Part B: The graph shown here is maybe the case of any electric appliance which is of cheap quality. The time when it is brought then its performance and its life is awesome after that its life is decreasing rapidly.
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Complete question:
Describe a relationship that can be modeled by the function represented by the graph, and explain how the function models the relationship. Identify and interpret the key features of the function in the context of the situation you described in part A.
Select all that apply.
Which functions have a range of {y ∈ all real numbers | -∞ < y < ∞}?
f(x) = -(x + 1)^2 - 4
f(x) = -4x + 11
f(x) = 2/3x - 8
f(x) = 2^x+3
f(x) = x^2 + 7x - 9
Answers
The functions f(x) = -4x + 11 and f(x) = 2/3x - 8 are having the range of {y ∈ R | -∞ < y < ∞}.
What are the domain and range of a function?The domain is the set of all the possible values of x that are taken as inputs for the function.The range is the set of all the values(output) that are obtained for the domain of x.So, domain = {input values(x)} and range = {output values(y)}Calculation:Step 1: Finding the range for the function f(x) = -(x + 1)² - 4
The given function is quadratic in the form of a(x - h)² + k,
So, the range of the function is y ≤ k if a < 0 or y ≥ k if a > 0
For the given function, a = -1 so, a < 0. thus, the range of the given function is y ≤ k, where k = -4
∴ Range of f(x) = -(x + 1)² - 4 is: (-∞ -4], {y | y ≤ -4}
Step 2: Finding the range for the function f(x) = -4x + 11
This is a linear function. So, the range is R.
∴ Range of f(x) = -4x + 11: (-∞, ∞), { y | y ∈ R}
Step 3: Finding the range for the function f(x) = 2/3x - 8
This is also a linear function. So, the range is R.
∴ Range of f(x) = 2/3x - 8: (-∞, ∞), { y | y ∈ R}
Step 4: Finding the range for the function f(x) = 2^x + 3
This is an exponential function. So, the range is y > k
Here k = 3.
∴ Range of f(x) = 2^x+3: (3, ∞), {y | y > 3}
Step 5: Finding the range for the function f(x) = x² + 7x - 9
This is a quadratic function.
we can write it as,
f(x) = x² + 2 × x × (7/2) + (7/2)² - (7/2)² - 9
= (x + 7/2)² - 85/4
This is in the form of a(x - h)² - k. where a = 1 > 0 and k = -85/4
Since a > 0, the range of the function is y ≥ -85/4
∴ Range of f(x) = x² + 7x - 9: [-85/4, ∞), {y | y ≥ -85/4}
Therefore, the functions f(x) = -4x + 11 and f(x) = 2/3x - 8 are having the given range {y ∈ R, -∞ < y < ∞}
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PLEASE ANSWER QUICKLY
Answers
By applying the definition of product between two square matrices, we find that [tex]\vec A \,\cdot \,\vec A = \left[\begin{array}{cc}1&2\\3&6\end{array}\right] \cdot \left[\begin{array}{cc}1&2\\3&6\end{array}\right][/tex] is equal to the matrix [tex]\vec A \,\cdot \,\vec A = \left[\begin{array}{cc}7&14\\21&42\end{array}\right][/tex]. (Correct choice: D)
What is the product of two square matrices
In this question we must use the definition of product between two square matrices to determine the resulting construction:
[tex]\vec A \,\cdot \,\vec A = \left[\begin{array}{cc}1&2\\3&6\end{array}\right] \cdot \left[\begin{array}{cc}1&2\\3&6\end{array}\right][/tex]
[tex]\vec A \,\cdot \,\vec A = \left[\begin{array}{cc}7&14\\21&42\end{array}\right][/tex]
By applying the definition of product between two square matrices, we find that [tex]\vec A \,\cdot \,\vec A = \left[\begin{array}{cc}1&2\\3&6\end{array}\right] \cdot \left[\begin{array}{cc}1&2\\3&6\end{array}\right][/tex] is equal to the matrix [tex]\vec A \,\cdot \,\vec A = \left[\begin{array}{cc}7&14\\21&42\end{array}\right][/tex].
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Type SSS, SAS, ASA, SAA, or HL to
justify why the two larger triangles are
congruent.
A
B
F
D
C
E AC = BC
ZAZB
Answers
Answer:
ASA
Step-by-step explanation:
I WILL GIVE BRAINLIEST!!!!
2 step equation:
4x + 3 = 19
2 step equation w/ fractions:
(4/3)x + 5 = 17
Distributive Property:
4x(6 - 2) - 10 = 20
Decimals:
4.3x + 0.7 = 5
Real world equation:
Sharon's restaurant is bringing in money from customers, and she needs to know how much she needs to pay off the bill for the electricity to run the place. To turn the electricity on, she has to pay $25. For every hour that the electricity is on for, she has to pay $4. How many hours can she have the electricity on for if she makes $49 profit?
i really need some help solving these
Answers
The answers to the questions are:
1. x = 4
2. x = 1.5
3. x = 1.875
4. x = 1
2 step equation:1. 4x + 3 = 19
4x = 19 - 3
4x = 16
divide by 4
x = 4
2 step equation w/ fractions:(4/3)x + 5 = 17
= 1.33x + 5 = 7
Take like terms
1.33x = 7-5
1.33x = 2
divide through by 1.33x to get 2
x = 2/1.33
x = 1.5
3. Distributive Property:4x(6 - 2) - 10 = 20
Multiply and open the bracket
24x - 8x - 10 = 20
Take like terms
16x = 20+10
16x = 30
x = 30/16
= 1.875
4. Decimals:4.3x + 0.7 = 5
4.3x = 5 - 0.7
4.3x = 4.3
x = 1
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Chanda is planning to visit universities over the summer to help decide where she wants to attend college. The first two universities on her proposed route are 6 inches apart on Claudias map. In real life, this distance is 30 miles. What scale does the map use? 1 in = _____ miles.
Answers
The map scale to use would be: 1 in. = 5 miles.
What is Map Scale?The scale of a map relates the actual distance of two places to the distance on paper on a scale drawing. It is a ratio between length on the map and distance in real life.
Given that, 6 inches would equal actual distance of 30 miles, let x be the actual distance on ground. We would have:
6/30 = 1/x
Solve for x
x = (30 × 1)/6
x = 5.
Therefore, the scale of the map is: 1 in = 5 miles.
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5.
MATHEMATICS Year'
A square is folded into half to form a rectangle as shown below. The perimeter of the rectangle is 36 cm.
Calculate the area of the square.
Answers
Answer: 144 [tex]cm^{2}[/tex]
Step-by-step explanation:
The rectangle's length is twice as long as it's width as the square is folded in half. Let's say that the width's length is x, we get the equation
x + 2x + x + 2x = 36
6x = 36
x = 6 cm
The length of the rectangle is the length of the square which is 2x = 2 * 6 = 12 cm
So the area of the square is 12 * 12 = 144 [tex]cm^{2}[/tex]
Can someone please help me on this?
Answers
Answer:
[tex]\frac{9\pi }{4}[/tex] inches
Step-by-step explanation:
I suppose they are asking you for the length of the red part.
18[tex]\pi \\[/tex] * [tex]\frac{45}{360}[/tex] = [tex]\frac{9\pi }{4}[/tex] inches
Answer:
L = 7.07 in
Step-by-step explanation:
L = arc lenght
[tex]L=\frac{\pi (45)(9)}{180} =2.25\pi =7.07in.[/tex]
Hope this helps
question 12 please, i cannot find the central angle.
Answers
Answer:
Below.
Step-by-step explanation:
12. That is a semicircle
The central angle is 180 degrees.
Find the equation of the line with slope = 6 and passing through (2,20). write your equation in the form y = mx + b.
Answers
Answer:
y = 6x + 8
Step-by-step explanation:
y = mx + b
20 = 6(2) + b
b = 8
y = 6x + 8
Given that SQ⎯⎯⎯⎯⎯ bisects ∠PSR and PS⎯⎯⎯⎯⎯≅SR⎯⎯⎯⎯⎯, which of the following triangle congruence statements can be used to prove that ∠P≅∠R?
The figure shows two triangles P S Q and R S Q with a common side S Q.
Answers
The congruency proof that can be used to show that ∠P≅∠R is as given in the steps below.
How to prove Triangle Congruence?
From the figure as seen online, we can see that;
The figure shows the same triangles PQS and RQS as in the beginning of the task. Angles SPQ and SRQ are highlighted in red.
Thus, the 2 column proof to show that ∠P≅∠R is;
Statement 1; ∠SPQ≅∠SRQ
Reason 1; Given
Statement 2; SQ bisects ∠PSR
Reason 2; Given
Statement 3; ∠PSQ≅∠QSR
Reason 3; Definition of angle bisector
Statement 4; SQ ≅ SQ
Reason 4; Reflexive Property of Congruence
Statement 5; △PQS≅△RQS
Reason 5; Angle - Angle Side (AAS) Congruency Postulate
Statement 6; PS ≅ SR
Reason 6; CPCTC (Corresponding parts of congruent triangles are congruent)
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Answer the question please!!!!!!
[tex]Simplify \: \: \\ ( \: a \: ) \: 287 \: \times \: 90 \\ ( \: b \: ) \: 105 \: \times 95[/tex]
Answers
Answer:
a) 25830
b)9975
Step-by-step explanation:
a) 287
x 90
25830
b) 105
x 95
9975
If sint=18 , and t is in quadrant i, find the exact value of sin(2t) , cos(2t) , and tan(2t) algebraically without solving for t
Answers
The value of Sin2t is 1/4 and cos2t is (15/16)^1/2 and tan2t is 1/(15)^1/2.
According to the statement
we have given that the sint=1/8 then we have to find the exact value of
sin(2t) , cos(2t) , and tan(2t).
Here the value of Sint = 18
then sin2t becomes
sin2t = 2*1/8 then
sin2t = 1/4.
And
(Cos2t)^2 = 1 - (Sin2t)^2
(Cos2t)^2 = 1 - 1/16
(Cos2t)^2 = (16 - 1)/16
(Cos2t)^2 = 15/16
(Cos2t) = (15/16)^1/2
then
tan2t = sin2t/cos2t
tan2t = (1/4)/(15)^1/2 / 4
tan2t = 1/(15)^1/2
these are the values of given terms.
So, The value of Sin2t is 1/4 and cos2t is (15/16)^1/2 and tan2t is 1/(15)^1/2.
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The sequence$$1,2,1,2,2,1,2,2,2,1,2,2,2,2,1,2,2,2,2,2,1,2,\dots$$consists of $1$'s separated by blocks of $2$'s with $n$ $2$'s in the $n^{\rm{th}}$ block. What is the sum of the first $1234$ terms of this sequence
Answers
Consider the lengths of consecutive 1-2 blocks.
block 1 - 1, 2 - length 2
block 2 - 1, 2, 2 - length 3
block 3 - 1, 2, 2, 2 - length 4
block 4 - 1, 2, 2, 2, 2 - length 5
and so on.
Recall the formula for the sum of consecutive positive integers,
[tex]\displaystyle \sum_{i=1}^j i = 1 + 2 + 3 + \cdots + j = \frac{j(j+1)}2 \implies \sum_{i=2}^j = \frac{j(j+1) - 2}2[/tex]
Now,
[tex]1234 = \dfrac{j(j+1)-2}2 \implies 2470 = j(j+1) \implies j\approx49.2016[/tex]
which means that the 1234th term in the sequence occurs somewhere about 1/5 of the way through the 49th 1-2 block.
In the first 48 blocks, the sequence contains 48 copies of 1 and 1 + 2 + 3 + ... + 47 copies of 2, hence they make up a total of
[tex]\displaystyle \sum_{i=1}^48 1 + \sum_{i=1}^{48} i = 48+\frac{48(48+1)}2 = 1224[/tex]
numbers, and their sum is
[tex]\displaystyle \sum_{i=1}^{48} 1 + \sum_{i=1}^{48} 2i = 48 + 48(48+1) = 48\times50 = 2400[/tex]
This leaves us with the contribution of the first 10 terms in the 49th block, which consist of one 1 and nine 2s with a sum of [tex]1+9\times2=19[/tex].
So, the sum of the first 1234 terms in the sequence is 2419.