Answer:
Step-by-step explanation:
I gotcha my dude.......
x-5 and 2x+3
This pattern follows the rule add 14. What other features do you observe?
13, 27, 41, 55
please help meeeeee
The above pattern follows an arithmetic sequence with a common difference of 14 and first term of 13
How to solve a pattern?The pattern can be represented as follows:
13, 27, 41, 55
The first term of the sequence is 13 and the common difference is 14.
The above pattern is an arithmetic sequence.
Therefore, the following can be used to find the nth term.
nth term = a + (n - 1)d
where
n = number of termd = common differencea = first termTherefore,
a = 13
d = 27 - 13 = 14
Let's find the next term
5th term = 13 + (5 - 1)14
5th term = 13 +(4)14
5th term = 13 + 56
5th term = 69
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Express 60 as a product of its prime factors
Answer:
The actual prime factors of 60 are 2, 3, and 5.
Step-by-step explanation:
Greetings !
Use a factor tree to express 60 as a product of prime factors. So the prime factorization of 60 is 2 × 2 × 3 × 5, which can be written as 2² × 3 × 5.
A football is kicked toward the goal. the height of the ball is modeled by the function h(t) = −16t2 64t, where t equals the time in seconds and h(t) represents the height of the ball at time t seconds. what is the axis of symmetry, and how does it relate to the time the ball is in the air? t = 2; it takes the ball 2 seconds to reach the maximum height and 2 more seconds to fall back to the ground. t = 2; it takes the ball 2 seconds to reach the maximum height and 4 more seconds to fall back to the ground. t = 4; it takes the ball 4 seconds to reach the maximum height and 4 more seconds to fall back to the ground. t = 4; it takes the ball 4 seconds to reach the maximum height and 8 more seconds to fall back to the ground.
The function [tex]H(t) = -16t^2 + 64t[/tex] exists in a parabola.
The axis of symmetry of a parabola exists at the midpoint between the two real roots.
The roots exist the solutions of H(t) = 0
To estimate the roots equation exists [tex]-16t^2 + 64t = 0[/tex]
Factor t(-16t + 64) = 0
t = 0 and -16t + 64 =0
-16t + 64 = 0
t = 64 / 16 = 4
t = 4
Then the two roots are t = 0 and t = 4, and the axis of symmetry exists
t = (0+4)/2 = 4/2 = 2
How to estimate the axis of symmetry?The axis of symmetry exists at t = 2.
It represents the time at which the ball is at the higher point, the maximum height.
You can find the maximum height replacing t = 2 in the function H(t)
[tex]H(t) = -16(2^2) + 64(2)[/tex]
= 64 feet.
And you can also deduce that the second part of the flight will take 2 seconds, for a total flight time of 4 seconds.
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Answer:
answer is a
Step-by-step explanation:
it takes 2 seconds for the ball to reach maximum height and 2 seconds to fall on the ground.
t = 2; it takes the ball 2 seconds to reach the maximum height and 2 more seconds to fall back to the ground
Took the FLVS test!
Use the given transformation x=4u, y=3v to evaluate the integral. ∬r4x2 da, where r is the region bounded by the ellipse x216 y29=1
The Jacobian for this transformation is
[tex]J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} 4 & 0 \\ 0 & 3 \end{bmatrix}[/tex]
with determinant [tex]|J| = 12[/tex], hence the area element becomes
[tex]dA = dx\,dy = 12 \, du\,dv[/tex]
Then the integral becomes
[tex]\displaystyle \iint_{R'} 4x^2 \, dA = 768 \iint_R u^2 \, du \, dv[/tex]
where [tex]R'[/tex] is the unit circle,
[tex]\dfrac{x^2}{16} + \dfrac{y^2}9 = \dfrac{(4u^2)}{16} + \dfrac{(3v)^2}9 = u^2 + v^2 = 1[/tex]
so that
[tex]\displaystyle 768 \iint_R u^2 \, du \, dv = 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2 \, du \, dv[/tex]
Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.
[tex]\begin{cases} u = r\cos(\theta) \\ v = r\sin(\theta) \\ u^2+v^2 = r^2\\ du\,dv = r\,dr\,d\theta\end{cases}[/tex]
Then
[tex]\displaystyle 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2\,du\,dv = 768 \int_0^{2\pi} \int_0^1 (r\cos(\theta))^2 r\,dr\,d\theta \\\\ ~~~~~~~~~~~~ = 768 \left(\int_0^{2\pi} \cos^2(\theta)\,d\theta\right) \left(\int_0^1 r^3\,dr\right) = \boxed{192\pi}[/tex]
A group of 65 baseball players were surveyed about which hand they favor for batting. The data from the survey are shown in the Venn diagram.
Determine the value for each variable in the two-way table.
The value of each variable in the two-way table is:
a = 7
b = 31
c = 28
d = 13
e = 65
What are the value of the variables?A Venn diagram uses circles that overlap each other to show the relationship between two or more sets of items. A two-way table represents the frequency of dataset by arranging the dataset into a table made up of rows and columns.
a = females that favor the left. Looking at the Venn diagram, this number is 7.
b = total number of females : 24 + 7 = 31
c = males that favor the right = total number of males - males that favor the left34 - 6 = 28
d = Total number of people who favor the left = 7 + 6 = 13
Total number of baseball players = 65
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Given the functions f(x) = –4ˣ + 5 and g(x) = x³ + x² – 4x + 5, what type of functions are f(x) and g(x)? Justify your answer. What key feature(s) do f(x) and g(x) have in common? (Consider domain, range, x-intercepts, and y-intercepts.)
Answer:
f(x) is an exponential functiong(x) is a polynomial function of degree 3Key common features: same domain, both have one x-intercept and one y-intercept.Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=-4^x+5\\g(x)=x^3+x^2-4x+5 \end{cases}[/tex]
Function f(x)This is an exponential function.
An exponential function includes a real number with an exponent containing a variable.
x-intercept (when y = 0):
[tex]\begin{aligned}f(x) & = 0\\\implies -4^x+5 & =0\\ 4^x &=5\\\ln 4^x &= \ln 5\\x \ln 4 &= \ln 5\\x&=\dfrac{ \ln 5}{\ln 4}\\x&=1.16\:\: \sf(2\:d.p.)\end{aligned}[/tex]
Therefore, the x-intercept of f(x) is (1.16, 0).
y-intercept (when x = 0):
[tex]\begin{aligned}f(0) & = -4^{0}+5\\& = 1+5\\& = 6\end{aligned}[/tex]
Therefore, the y-intercept of f(x) is (0, 6).
End behavior
[tex]\textsf{As }x \rightarrow \infty, \: f(x) \rightarrow \infty[/tex]
[tex]\textsf{As }x \rightarrow -\infty, \: f(x) \rightarrow 5[/tex]
Therefore, there is a horizontal asymptote at y = 5 which means the curve gets close to y = 5 but never touches it. Therefore:
Domain: (-∞, ∞)Range: (-∞, 5)Function g(x)This is a polynomial function of degree 3 (since the greatest exponent of the function is 3).
A polynomial function is made up of variables, constants and exponents that are combined using mathematical operations.
x-intercept (when y = 0):
There is only one x-intercept of function g(x). It can be found algebraically using the Newton Raphson numerical method, or by using a calculator.
From a calculator, the x-intercept of g(x) is (-2.94, 0) to 2 decimal places.
y-intercept (when x = 0):
[tex]\begin{aligned}g(0) & = (0)^3+(0)^2-4(0)+5\\& = 0+0+0+5\\& = 5 \end{aligned}[/tex]
Therefore, the y-intercept of g(x) is (0, 5).
End behavior
[tex]\textsf{As }x \rightarrow \infty, \: f(x) \rightarrow \infty[/tex]
[tex]\textsf{As }x \rightarrow -\infty, \: f(x) \rightarrow - \infty[/tex]
Therefore:
Domain: (-∞, ∞)Range: (-∞, ∞)Conclusion
Key features both functions have in common:
One x-intercept (though not the same)One y-intercept (though not the same)Same unrestricted domain: (-∞, ∞)The graph below shows the speed of a car that is driven through a town and then on a major highway. During which of the following time intervals was the car stopped at a traffic light?
Considering the graph of the velocity of the car, it is found that the interval in which it was stopped at a traffic light was:
Between 3 and 4 minutes.
When is a car stopped at a traffic light?When a car is stopped at a traffic light, the car is not moving, that is, it's velocity is of zero.
In this problem, the graph gives the velocity as a function of time, and it is at zero between 3 and 4 minutes, hence the interval in which it was stopped at a traffic light was:
Between 3 and 4 minutes.
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Select the correct answer. what is the completely factored form of this expression? 3x2 − 17x − 28 a. (3x 4)(x 7) b. (3x 4)(x − 7) c. 3x2 − 17x − 28 d. (3x2 4)(x − 7)
Answer:
A. (3x + 4)(x-7)
Step-by-step explanation:
3x times x = 3x^2
3x times -7 = -21x
4 times x = 4x
4 times -7 = -28
-21x + 4x = -17x
3x^2 - 17x - 28
How many times do you need to divide by ten to get from 0.747 to 0.0747?
Answer:
Step-by-step explanation:
Quick Answer 1
Solution
x = 0.747 / 0.0747
When you do the division, you get 10. That means that you need to divide 0.747 by just 1 ten to get 0.0747
Answer:
Once
Step-by-step explanation:
You have to divide once because if you divide a decimal by 10, you add a zero before the decimal point
A hydrogen atom has one positively charged proton and one negatively charged electron.
Write an addition equation to represent how their charges combine to make the overall charge of the atom.
The addition equation to represent how their charges combine to make the overall charge of the atom is + 1 + - 1 = 0
How to write equation to represent charges of atom?A hydrogen atom has one positively charged proton and one negatively charged electron.
An atom of every elements has an electron(negatively charged) and positively charge(proton) part.
An atom as a whole is electrically neutral if the number of proton and electron are equal. They will cancel each other to make the atom neutral.
Therefore, the addition equation to represent how their charges combine to make the overall charge of the atom is as follows;
+ 1 + - 1 = 0
1 positively charged proton plus single negatively charged electron = zero(neutral)
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Find the number of integral solutions of x+y +z = 12, where −3 ≤ x ≤ 4, 2 ≤ y ≤ 11, and
z ≥ 3.
There are 59 integer solutions
Such questions are best solved by writing cases and calculating the total number of cases. So beginning with
1) x = -3. The possible combinations are as follows:-
-3 2 13
-3 3 12
-3 4 11
-3 5 10
-3 6 9
-3 7 8
-3 8 7
-3 9 6
-3 10 5
-3 11 4
10 combinations
2) x = -2
-2 2 12
through
-2 11 3
10 combinations
3) x = -1
-1 2 11
through
-1 10 3
9 combinations
4) x = 0
0 2 10
through
0 9 3
8 combinations
as we can see from the pattern at x =1 we get 7 combinations, at x =2 we get 6 combinations, at x=3 we get 5 combinations and at x =4 we get 5 combinations.
Thus total number of combinations 4+5+6+7+8+9+10+10 = 59 integer solution.
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Let f(x) = 8x3 + 18x2 − 10 and g(x) = 4x + 1. Find f of x over g of x.
The value of function f(x) over g(x) is [tex]2x^{2} +4x-1-\frac{9}{4x+1}[/tex]
Given functions are:
f(x)=8[tex]x^{3}[/tex]+18[tex]x^{2}[/tex]-10
g(x)=4x+1
In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). Functions exist everywhere, and they are crucial for constructing physical links in the sciences.
In mathematics, a function is represented as a rule that produces a distinct result for each input x. A function is indicated by a mapping or transformation. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
[tex]\frac{f(x)}{g(x)}=\frac{8x^{3}+18x^{2} -10 }{4x+1}[/tex]
= [tex]2x^{2} +4x-1-\frac{9}{4x+1}[/tex]
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define ratio (maths short definition)
Answer:
division
Step-by-step explanation:
ratio compares 2 numbers by dividing them
example
2 out of 3 dentists like gum
2 ÷ 3 = .67 = 67%
so you can say
67% of dentists like gum
A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one. For example, if the number of marks scored in a test is 7 out of 10, then the ratio of marks obtained to the total number of marks is written as 7:10.
At the beginning of the summer, sarah has $250. she takes a summer job and saves $150 per week. felicia has $1,650 at the beginning of the summer. she travels during the summer and spends $200 per week. at the end of which week do sarah and felicia have the same amount of money?
Answer:
Week 4
Step-by-step explanation:
Victoria has $250 and saves $150 each week, hence have increments $150 each week
250+150 (first week)
= 400
second week = 400 + 150 = 550
third week = 550 + 150 = 700
fourth week = 700 + 150 = $850
Felicia on the other hand has $1,650 and spends $200 each week, hence has decrements of $200 each week.
1650+200 (first week)
= 1450
second week = 1450 - 200 = 1250
third week = 1250 - 200 = 1050
fourth week = 1050 + 200 = $850
what time 2 equals 25
Answer:
the answer to "2 times what equals 25?" is 12.5.
I need some help with this
Answer:
5.09 years
Step-by-step explanation:
The formula for the future value of an investment can be filled with the given values and solved for time.
FormulaThe future value of a one-time investment P earning interest at annual rate r compounded n times per year for t years is ...
FV = P(1 +r/n)^(nt)
ApplicationUsing this formula with the given values, we have an expression for t:
7300 = 5000(1 +0.075/4)^(4t)
Dividing by 5000, we have ...
1.46 = 1.01875^(4t)
Taking logarithms gives the linear equation ...
log(1.46) = 4t·log(1.01875)
Dividing by the coefficient of t, we find ...
t = log(1.46)/(4·log(1.01875)) ≈ 5.0929
The time required for the value to reach $7300 is about 5.09 years.
__
Additional comment
The attachments show different calculator solutions. They give the same value for t.
The TVM Solver uses P/Y = 1 so the value of N is in years.
The graphical solution recasts the problem to f(x) = 0. It finds the value of t that makes the difference between the investment value and $7300 be zero.
Algebra 3, in the excercise size the graphs to determine the functions domain and range, x and y intercepts if any, and the functions values indicated below the graphs
Answer:
Read Explanation
Step-by-step explanation:
The domain is a list of all possible x-values, this graph starts at 0 and proceeds to positive infinity, making the domain:
[0,∞)
The range is a list of all possible y-values, this graph starts at -1 and proceeds to positive infinity, making the range:
[-1,∞)
x-intercepts Are where the line crosses the x-axis, in this graph the line only crosses the x-axis at x of 2. Making its only x-intercept 2.
y-intercepts Are where the line crosses the y-axis, in this graph the line only crosses the y-axis at y of -1. Therefore its y-intercept is -1.
In function notation when a question asks for f(x) its asking for the y values at the given x-values. At x of 3 the y value equals 1.
Urgent!!!!!!!!!!!!!!!!!!
18. A tennis player uses up 800 calories every hour. In 1 hour and 15 minutes, how many calories does this player use? (A) 900 (B) 1000 (C) 1100 (D) 1200
A basketball is shot into the air. its height is represented by the polynomial equation h(t) = –16t2 35t 5, where h is the height of the basketball at t seconds. what is the height of the basketball at 0.5 seconds?
The height of the basketball at 0.5 seconds will be = 26.5
What is a polynomial equation?A polynomial equation is an equation where a polynomial is set equal to zero. i.e., it is an equation formed with variables, non-negative integer exponents, and coefficients together with operations and an equal sign. It has different exponents. The highest one gives the degree of the equation.
Example of a polynomial equation is: 2x2 + 3x + 1 = 0, where 2x2 + 3x + 1 is basically a polynomial expression which has been set equal to zero, to form a polynomial equation.
According to the given equation if we put value in it we will follow the following steps -
[tex]h(t) = - 16t^{2} + 35t+ 5\\ h(0.5) = -16(0.5)^{2} + 35(0.5) + 5\\h(0.5) = -16(0.25) + 17.5 + 5\\h(0.5) = 4 + 17.5 + 5\\h(0.5) = 26.5\\[/tex]
Therefore, the height of the basketball at 0.5 s will be 26.5
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Answer:
Is the question supposed to be (1.5), if so then the answer would be 21.5
Step-by-step explanation:
ht=-16t^2+35t+5
h(1.5)=-16(1.5)^2+35(1.5)+5
=21.5
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
[tex]m = m \\ \frac{97 - 68}{2 - 1} = \frac{134 - 97}{3 - 2} \\ 29 = 37 \\ this \: function \: is \: non \: linear[/tex]
Since the only two other options are quadratic and given that it must satisfy one of them i will assume the following general form of the function.[tex]f(1) = 68 \: \: \: f(2) = 97 \: \: \: \: f(3) = 134 \\ f(x) = ax {}^{2} + bx + c[/tex]
Substitute in the first function any point.[tex]f(1) = 68 \\ 7.8(1) {}^{2} - 2.9(1) + 67.1 = 68 \\ 7.8 - 2.9 + 67.1 = 68 \\ 72 = 68 \\ this \: is \: false[/tex]
I'm pretty sure something is wrong with the givenConsider the function . find the vertical asymptote(s) of f(x). x = 0, –9 x = –9 x = 0, 9 x = 9
The vertical asymptote of f(x) is (A) x = 0, –9.
What is a function?A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.To find the vertical asymptote of f(x):
The vertical asymptotes of a function are the zeroes of the denominator of a rational function
The function is given as: [tex]f(x) = \frac{(x-9)}{(x^{3} -81x)}[/tex]
Set the denominator to 0:
[tex]x^{3} -81x=0[/tex]Factor out x:
[tex]x(x^{2} -81)=0[/tex]Express 81 as 9^2:
[tex]x(x^{2} -9^{2} )=0[/tex]Express the difference between the two squares:
[tex]x(x-9)(x+9)[/tex]Split, [tex]x=0[/tex] or [tex]x=-9[/tex] or [tex]x+9=0[/tex].
Solve for x:
[tex]x=0\\[/tex] or [tex]x=-9[/tex] or [tex]x+9=0[/tex].Therefore, the vertical asymptote of f(x) is (A) x = 0, –9.
(See attachment for the graph of f(x))
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The complete question is given below:
Consider the function f(x)=(x-9)/(x^3-81x) . find the vertical asymptote(s) of f(x).
A) x = 0, –9
B) x = –9
C) x = 0, 9
D) x = 9
how many terms are there in the series 7+21+15+19+.....+79?
anybody can answer these .
Answer:
7+21+15+19+.....+79
Here 21 be replaced by 11.
Now., common diffrence btw terms , d = 11-7 = 4
first term , a = 7
Last term , l = 79
number of terms = ( a + l ) ÷ d
=( 7 + 79 ) ÷ 4 = 86 ÷ 4 = 21.5 { It cannot be in decimal }
There's some mistake in the terms you provided please check your question again...
Use a calculator to find the mean of the data. {211, 226, 186, 221, 181, 228, 207, 215, 203, 203, 204, 196, 226, 212, 212, 201, 219, 191, 191, 185, 193, 231}
The mean of the given data is 206.5.
What is a mean?A dataset's mean (also known as the arithmetic mean, as opposed to the geometric mean) is the sum of all values divided by the total number of values. It is the most widely used measure of central tendency and is frequently referred to as the "average."It is the total (sum) of all the values in a set of data, such as numbers or measurements, divided by the number of values in the list. Add up all of the values in the set to find the mean. Then divide the total by the number of possible values.To find the mean of the given data:
Sum of values = 211 + 226 + 186 + 221 + 181 + 228 + 207 + 215 + 203 + 203 + 204 + 196 + 226 + 212 + 212 + 201 + 219 + 191 + 191 + 185 + 193 + 231 = 4,542
Number of values = 22
Mean = 4,542 ÷ 22 = 206.5
Therefore, the mean of the given data is 206.5.
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Answer:
Step-by-step explanation:
1. How do you prove congruence through transformations?
2. How do you prove triangle congruence using congruency postulates? Give a general explanation of what the S and A stand for. Please name each of the postulates and what the letters stand for.
One can prove congruence through transformation if they have the same shape and size.
The congruency postulates include:
SSS - Side-Side-SideSAS - Side-Angle-SideASA- Angle-Side-AngleAAS - Angle-Angle-SideRHS - Right angle-Hypotenuse-SideWhat is congruence?In geometry, it should be noted that two figures are congruent if they have the same shape and size.
In this case, if two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.
One can prove triangle congruence using congruency postulates by using the SSS theorem( side side side theorem).
It should be noted that the congruence postulate is used to illustrate that the triangles are equal.
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Haley and tyler are on the cross country team. tyler can run 1 mile (ata constant speed) in 8 minutes and 20 seconds. haley's distances and times for a training run are given by the equation y=8x where x represent distanse and times in miles and y represents time in minutes. who ran farther in 10 minutes how much farther
Haler ran farther than Tyler in 10 minutes. She covered an extra 0.05 miles compared to Tyler.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
Tyler can run 1 mile in 8 minutes and 20 seconds.
Time taken = 8 mins + 20 sec (0.33 min) = 8.33 minutes
Speed = distance / time = 1 mile / 8.33 = 0.12 mile per min
In 10 minutes, distance = 0.12 mile per min * 10 min = 1.2 mile
Haler is given by:
y = 8x; where y is time and x is distance.
In 10 minutes, distance = y/8 = 10/8 = 1.25 miles
Haler ran farther than Tyler in 10 minutes. She covered an extra 0.05 miles compared to Tyler.
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Find the results of the given vector subtractions for u = <-8, 4> and v = <2, 7>.
The resultant of subtractions of u = <-8, 4> and v = <2, 7> are
-u-v = <6, -11>,
u-v = <-10, -3>,
and v-u= <10,3>.
What is a vector in simple definition?
A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity. Examples of vectors in nature are velocity, momentum, force, electromagnetic fields, and weight.The resultant of subtractions of u = <-8, 4> and v = <2, 7> are
-u-v = <6, -11>,
u-v = <-10, -3>,
and v-u= <10,3>.
Given that,
The results of the given vector subtractions for u = <-8, 4> and v = <2, 7>.
We have to determine,
The value of -u-v, u-v, and v-u.
According to the question,
The results of the given vector subtractions for u = <-8, 4> and v = <2, 7>.
The value of -u-v is,
-u -v = - < -8 ,4 > - <2,7>
-u -v = <8, -4> - < 2, 7 >
-u - v = < 8 - 2 , -4 - 7 >
-u -v = < 6 , - 11 >
The value of u-v is,
u -v = < -8 ,4 > - < 2,7 >
u - v = < - 8 - 2, 4 - 7 >
u - v = < 10 ,3>
The value of v - u is,
v - u = < 2 , 7> - < - 8,4 >
v - u = < 2 + 8 , 7 - 4 >
v - 4 = < 10 , 3 >
Hence, The resultant of subtractions of u = <-8, 4> and v = <2, 7> are
-u-v = <6, -11>,
u-v = <-10, -3>,
and v-u= <10,3>.
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Given u=2i-9j and v=-5i+7j, what is u•v?
The value of the vector will be -53. The correct option is C.
What are vectors?In mathematics and physics, the term "vector" is used informally to describe certain quantities that cannot be described by a single number or by a set of vector space elements.
The dot product, also known as the scalar product, is an algebraic operation that takes two sequences of integers of equal length and outputs a single number.
The given vectors are u=2i-9j and v=-5i+7j, the dot product of the vectors will be calculated as below:-
u.v = ( 2i-9j ).( -5i+7j)
u.v = -10i² + 17 (i.j) -45(i.j) -63j²
Substitute i² = 1, j² = 1 and (i.j) = 0 in the above equation.
u.v = -10 + 63
u.v = 53
Therefore, the value of the vector will be -53. The correct option is C.
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Prove this please
Optional Math
Cos2A =
[tex] \frac{( \cot\alpha - \tan\alpha ) }{( \cot\alpha + \tan\alpha ) } [/tex]
Step-by-step explanation:
proof from r.h.s to l.h.s
(cot(a)-tan(a))(cot(a)+tan(a))
cot(a)=cos(a)/sin(a)
tan(a)=sin(a)/cos(a)
(cot(a)-tan(a))=cos(a)/sin(a) - sin(a)/cos(a)
=cos²(a)-sin²(a)/sin(a)cos(a)
from trigonometry identity cos²(a)-sin²(a)=cos2(a)
so we have cos2(a)/sin(a)cos(a)
(cot(a)+tan(a))=cos(a)/sin(a) +sin(a)/cos(a)
=cos²(a)+sin²(a)/cos(a)sin(a)
from trigonometry identity cos²(a)+sin²(a)=so we have 1/cos(a)sin(a)
(cot(a)-tan(a)) ÷(cot(a)+tan(a))
=cos2(a)/cos(a)sin(a) ÷ 1/cos(a)sin(a)
=cos2(a)/cos(a)sin(a) * cos(a)sin(a)
=cos2(a)
proved
Samuel is arranging books in shelves at their library. He has 80 books to arrange he needs to put the same number of books on each shelf, and he needs to use all of the books. Between 9, 10 and 11 shelves, which is his best choice for the number of shelves that he can use?
(Show the solution and do not use Division (optional) and use the Divisibility rules of numbers)
Answer:
10 shelves
Step-by-step explanation:
out of the other choices, 10 is most suitable to divide with 80