Answer:
Step-by-step explanation
-6(3i)(-2i)=-6(3i*-2i)=-6*-6i²=36i²
2(3-i)(-2+4i)=(6-2i)(-2+4i)=-12+24i+4i-8i²=-8i²+28i-12
Answer:
1. -36
2. -4+28i
3. 10+8i
Step-by-step explanation:
EDGE2022
Find a potential function for the vector field
(a) We want to find a scalar function [tex]f(x,y,z)[/tex] such that [tex]\mathbf F = \nabla f[/tex]. This means
[tex]\dfrac{\partial f}{\partial x} = 2xy + 24[/tex]
[tex]\dfrac{\partial f}{\partial y} = x^2 + 16[/tex]
Looking at the first equation, integrating both sides with respect to [tex]x[/tex] gives
[tex]f(x,y) = x^2y + 24x + g(y)[/tex]
Differentiating both sides of this with respect to [tex]y[/tex] gives
[tex]\dfrac{\partial f}{\partial y} = x^2 + 16 = x^2 + \dfrac{dg}{dy} \implies \dfrac{dg}{dy} = 16 \implies g(y) = 16y + C[/tex]
Then the potential function is
[tex]f(x,y) = \boxed{x^2y + 24x + 16y + C}[/tex]
(b) By the FTCoLI, we have
[tex]\displaystyle \int_{(1,1)}^{(-1,2)} \mathbf F \cdot d\mathbf r = f(-1,2) - f(1,1) = 10-41 = \boxed{-31}[/tex]
[tex]\displaystyle \int_{(-1,2)}^{(0,4)} \mathbf F \cdot d\mathbf r = f(0,4) - f(-1,2) = 64 - 41 = \boxed{23}[/tex]
[tex]\displaystyle \int_{(0,4)}^{(2,3)} \mathbf F \cdot d\mathbf r = f(2,3) - f(0,4) = 108 - 64 = \boxed{44}[/tex]
_A straight line L has equation 3y=5x-6. Find the gradient of L
Answer:
gradient = [tex]\frac{5}{3}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope/gradient and c the y- intercept )
given
3y = 5x - 6 ( divide through by 3 )
y = [tex]\frac{5}{3}[/tex] x - 2 ← in slope- intercept form
with gradient = [tex]\frac{5}{3}[/tex]
A recursive rule for an arithmetic sequence is a1=4;an=an−1−3.
What is the explicit rule for this sequence?
Enter the simplified answer in the box.
an=
I NEED HELP ASAP
The explicit rule for this sequence is [tex]a_{n} =7-3n[/tex].
What is the arithmetic sequence?"Arithmetic means" refers to repeatedly adding a fixed number to produce a series. Let n be "the number." Because the numbers in the sequence are becoming progressively negative, we might conclude that n is negative.We can locate a particular term in an arithmetic series using the method for locating the nth term. An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d. Therefore, enter the values a = 2 and d = 3 into the formula to determine the nth term.The Arithmetic Mean or Mean of the Group is the sum of all the numbers in a group divided by the total number of items in the list. For instance, since 5 + 7 + 9 = 21 and 21 divided by 3 [there are three numbers] is 7, the mean of the digits 5, 7, and 9 is 4.The difference between each succeeding pair of terms in an arithmetic series is always the same. The following is the explicit guideline for formulating any arithmetic sequence: a = a1 + d (n - 1)The explicit rule for this sequence:
The obvious rule for an arithmetic sequence is given as follows:
[tex]a_{n}=a_{1} +(n-1)d[/tex]
The first term = [tex]a_{1}[/tex].
The number of terms = n.
The common difference for two consecutive terms = d.
A recursive rule for an arithmetic sequence: [tex]a_{1} =4[/tex].
[tex]a_{n} =a_{n-1}-3[/tex]
The arithmetic sequence is given by:
[tex]a_{n} =a_{n-1}+d[/tex]
We get: d = -3
Substitute the given values:
[tex]a_{n} =4+(n-1)(-3)[/tex]
[tex]a_{n} =4-3n+3[/tex]
=7-3n
The explicit rule for this sequence is [tex]a_{n} =7-3n[/tex].
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The explicit rule for the given arithmetic sequence is [tex]a_n=7-3n[/tex].
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This difference is known as the common difference of the arithmetic sequence.For example, [tex]2,5,8,11,...[/tex] is an arithmetic sequence with the first term [tex]a=2[/tex] and the common difference [tex]d=3[/tex].The formula for the nth term [tex]a_n[/tex] of an arithmetic sequence whose first term is [tex]a[/tex] and the common difference is [tex]d[/tex] can be given by [tex]a_n=a+(n-1)d[/tex].Given the recursive formula for an arithmetic sequence: [tex]a_1=4, a_n=a_{n-1}-3[/tex].
Thus, the first term of the arithmetic sequence is [tex]a=a_1=4[/tex]. using the recursive formula, we can get the 2nd term by putting [tex]n=2[/tex], [tex]a_2=a_1-3=4-3=1[/tex].
So, the common difference of the given arithmetic sequence is [tex]d=a_2-a_1=1-4=-3[/tex].
Thus, the nth term of the arithmetic sequence is given by [tex]a_n=a+(n-1)d\\\Longrightarrow a_n=4+(n-1)\times(-3)\\\Longrightarrow a_n=7-3n[/tex]
Therefore, the explicit rule for the given arithmetic sequence is [tex]a_n=7-3n[/tex].
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Find the number if 11% of it is 55
Answer:
Step-by-step explanation:
.11x = 55
11x = 5500
x = 500
A box contains 13 green marbles and 13 white marbles. If the first marble chosen was a white marble, what is the probability of choosing, without replacement, another white marble? Express your answer as a fraction or a decimal number rounded to four decimal places.
[tex]\textbf{Answer:\ \ \large\boxed{\frac{12}{25} }\ or\ 0.4800}[/tex]
Step-by-step explanation:
[tex]\large\boxed{13\ green\ marbles\ and\ 13\ white\ marbles}[/tex]
After a white marble is chosen:
[tex]\large\boxed{13\ green\ marbles\ and\ 12\ white\ marbles}[/tex]
Now there are 25 (13 + 12) total marbles.
Without replacing the white marble we chose already, what is the probability of choosing another white marble?
Well, now there are 12 white marbles to choose from, out of a total of 25 marbles. This means our probability is:
[tex]\large\boxed{\frac{12}{25} }[/tex]
This in decimal form is:
0.4800
HOW MANY AUTOMOBILE LICENSE PLATES CAN BE MADE IF EACH PLATE
CONTAINS 3 DIFFERENT DIGITS FOLLOWED BY 3 DIFFERENT LETTERS?
The number of license plates is 11232000
How to determine the number of license plates?The given parameters are:
Characters = 6 i.e. 3 letters and 3 digits
Letters = 3 different letters
Digits = 3 different digits
There are 10 different digits and 26 different letters.
Since each character is different from the other, then we have:
Digits = 10, 9 and 8
Characters = 26, 25 and 24
The number of license plates is then calculated as:
n = 10 * 9 * 8 * 26 * 25 * 24
Evaluate the product
n = 11232000
Hence, the number of license plates is 11232000
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Prove the following relations.
Cos²A + cos²A.cot²A=cot²A
(1-sin²A)(1+cot²A)=cot²A
Step-by-step explanation:
Let's solve for the first one,
[tex]R.H.S. = Cos²A + cos²A.cot²A[/tex]
Step 1- Take Cos²A common,
[tex] = Cos²A( 1+ cot²A)[/tex]
[tex] \small \sf \: Now \: we \: know \: that \\ \small (1 + Cot^{2} \theta = Cosec^{2} \theta)[/tex]
Step 2 - Substituting above value in step 1,
[tex] = Cos^{2} A(Cosec^2A)[/tex]
[tex] \small \sf \: We \: know \: that \: Cosec \theta= \frac{1}{Sin \theta} [/tex]
Step 3 - Substitute Cosec²A with 1/Sin²A
[tex] = \frac{Cos^2A}{Sin^2A} [/tex]
[tex] \small \sf \: Now \: the \: basic \: trigonometric \: function \: is \\ \small \frac{Cos\theta}{Sin \theta} = Cot\theta[/tex]
Step 4 - Replacing the product of step 3 with above function,
[tex] = {Cot}^{2} A[/tex]
Hence proved,
[tex]R.H.S = L.H.S[/tex]
﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
Now let's prove the second relation,
[tex](1-sin²A)(1+cot²A)=cot²A[/tex]
Let's solve for R.H.S.,
[tex]R.H.S.= (1-sin^{2} A)(1+cot^{2} A)[/tex]
As I told above,
[tex]\small(1+cot^{2} \theta) = cosec^{2} \theta[/tex]
Another important relation is,
[tex] \small sin^2\theta + cos^2\theta= 1 \: or \: \\ \small cos^2\theta = 1 - sin^2\theta[/tex]
Replacing both the above brackets with this relation we get,
[tex] = Cos^2A \cdot Cosec^2A [/tex]
Now follow the step 3 and step 4 of first question and you will get,
[tex]R.H.S. = L.H.S.[/tex]
﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
Some important trigonometric relations that you must learn,
[tex]Sin^2\theta + Cos^2\theta = 1 \\ 1 + Cot^2\theta = Cosec^2\theta \\ 1+Tan^2\theta = Sec^2\theta[/tex]
[tex] \small\sf \: Thanks \: for \: joining \: brainly \: community! [/tex]
Consider the quadratic equation x2 + 2x - 35 = 0. Solve by factoring and using the zero-product property.
What are solutions to quadratic equations called? Show your work.
Answer:
x = -7
x = 5
Step-by-step explanation:
The standard form of quadratic equations is
Ax^2 + Bx + C = 0
The factors need to multiply together to be C and add together to be B.
The two numbers that will multiply together to be -35 and add together to be 2 are -5 & 7.
The factor pairs are (x+7)(x-5). Zero product property means we set each of those factor pairs = 0 and solve.
x + 7 = 0
-7 -7 Subtract 7 from each side to solve
x = -7
x - 5 = 0
+5 +5 Add 5 to each side to solve
x = 5
To solve the equation, factor x²+2x−35 use the formula x² +(a + b) x + ab = (x + a)(x + b). To find a and b, set up a system to be solved.
a + b = 2
ab = −35
Since ab is negative, a and b have opposite signs. Since a+b is positive, the positive number has a greater absolute value than the negative. Show all pairs of integers whose product is −35.
−1.35−5.7Calculate the sum of each pair.
−1 + 35 = 34−5 + 7 = 2The solution is the pair that gives sum 2.
a = −5b = 7Rewrite the factored expression (x + a)(x + b) with the values obtained.
(x − 5)(x + 7)To find solutions to equations, solve x−5=0 and x+7=0.
x = 5x = −7What are the solutions of quadratic equations called?The "solutions" of a Quadratic Equation are the values where the equation equals zero. They are also called "roots", or even "zeros".
ヘ( ^o^)ノ＼(^_^ )If you want to learn more about mathematics, I share this link to complement your learning:
https://brainly.com/question/16413695For a class project student in health class ask every tenth student entering school if they eat breakfast in the morning
Please answer all 4 I really need help
The types of study that we have hereare the
surveyexperimentobservational survey1. The statistical question that has to be answered would beHow many students in this school ate breakfast?The type of study is the survey2. The question here would be
Does music help in the recalling of knowledge?The type of study that is going to be conducted would be the experiment.3. The answer that would be answered here would be
Does regular exercise affect the rate of heart beat of an individual?The observation of the study participants and their behavior would be used to determine this.4. The question would be
Is there a relationship between the physical activity of children and their energy levelThe type of study is the surveyRead more on research study here:
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Given: m space measured angle space B equals 18 degree, b = 9, and c = 20. Find m space measured angle space C degree to nearest whole number.
Given the measure of angle B, side b and side, the measure of angle C to the nearest whole number is 43 degrees.
What is the measure of angle space C?
From the Rule of Sine;
sinA/a = sinB/b = sinC/c
Where A,B and C are the angles of the triangle and a, b and c are the corresponding opposing sides.
Given that;
Angle B = 18°side b = 9side c = 20Angle C = ?Using the rule of sine.
sinB/b = sinC/c
We substitute the given values into the equation
sin( 18° )/9 = sinC/20
We solve for C.
sin( 18° ) × 20 = sinC × 9
0.309016994 × 20 = sinC × 9
6.18033988 = sinC × 9
Divide both sides by 9
6.18033988/9 = (sinC × 9)/9
sinC = 0.686704431
C = sin⁻¹( 0.686704431 )
C = 43.3697°
C = 43°
Given the measure of angle B, side b and side, the measure of angle C to the nearest whole number is 43 degrees.
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Use a calculator to explore the pattern. Write a conjecture based on what you observe. i did the whole calculator bit, but I just am clueless about the conjecture bit. Could someone please explain this to me?
Check the picture below.
now hmmm let's observe, hmmmm 11 has two digits, and low and behold, the 2 is right in the middle, then 1 and 1 on flanking it.
let's check 111 hmmmm has three digits and has a 3 right in the middle as well, and low and behold, is flanked by a regressing count, namely an "outwards" count.
let's check 1111 and 11111, same happens, one has a digit of 4 in the middle and the other 5, and yes, the "outwards" count on each, outwards count towards 1 each time btw.
so, if we were to take that pattern, we can say that eight 1's, namely 11111111 x 11111111, will have an 8 in the middle, and will look like 1234567 8 7654321.
Jon rented a car a company that charged a daily rental fee and a mileage charge. He rented the car for 6 days and drove 400 miles and was charged $210. His friend Amanda later rented the same car for 7 days and drove 360 miles and was charged $229. What was the daily rental charge? How much did the company charge per mile?
If the r-value, or correlation coefficient, of a data set is 0.854, what is the
coefficient of determination to three decimal places?
A. 0.829
• B. 0.754
• C. 0.729
D. 0.854
Which of the following demonstrates the correct calculation for simple interest?
The statement that demonstrates the correct calculation for simple interest is " A principal balance of $10,000 at 5% interest earns $500 each year as interest.
What is a simple interest?Simple interest is based on the principal amount of a loan or the first deposit in a savings account.
Simple interest does not compound interest on an interval basis. For instance quarterly, semi annually, annually etc. This are carried out in the case of compound interest.
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.
Hence base don the explanation above, the statement that demonstrates the correct calculation for simple interest is " A principal balance of $10,000 at 5% interest earns $500 each year as interest.
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if im taking a 32 hour course and ive completed 73% of it how much time do i have left
Answer:
8.64 hours, so
8 hours, 38 mins, 24 seconds
Just find that 27% you have left, then find how much that 27% is in terms of time.
It might be wrong so double check it please.
Answer:
8.64 hours
which is 8hrs 38mins and 24secs
Step-by-step explanation:
If you've completed 73% then you have 27% left to go still. (100-73 = 27)
27% of 32
= .27×32
= 8.64 hours left
That is 8hrs and .64 of an hour .64×60=38.4 mins
which is 38 mins and .4 of a minute.
.4×60 = 24secs
Probably you will just round this answer.
10. Lin and Andre biked home from school at a steady pace. Lin biked 1.5 km and it took her 5 minutes. Andre biked 2 km and it took him 8 minutes. a) Draw a graph with two lines that represent the bike rides of Lin and Andre. b) For each line, highlight the point with coordinates (1, k) and find k. c) Who was biking faster?
According to the data, it can be inferred that Lin is faster than Andre because she is going at 0.3 km/min speed while he is going at 0.25 km/min speed.
How to calculate who goes faster?To calculate who goes faster we must divide the time into the distance traveled by each character as shown below:
1.5km ÷ 5min = 0.3km/min2km ÷ 8min = 0.25km/minWhat is the K point for each character?According to the above, the point K of each would be equal to the distance that each of them travels in one minute. As shown in the graph, after 5min (Lin) and 8min (Andre), each one reaches their respective destination located 1.5km and 2km away, respectively, taking the point (0,0) as the starting point.
Lin: (1,0.3)Andrew: (1,0.25)The graph is attached.
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A COUPLE PLAN TO HAVE SIX CHILDREN. HOW MANY POSSIBLE OUTCOMES ARE IN
THE SAMPLE SPACE?
Express (x + 3)² as a trinomial in standard
Answer:
x² + 6x + 9
Step-by-step explanation:
(x + 3)²
= (x + 3)(x + 3)
each term in the second factor is multiplied by each term in the first factor , that is
x(x + 3) + 3(x + 3) ← distribute parenthesis
= x² + 3x + 3x + 9 ← collect like terms
= x² + 6x + 9 ← in standard form
What is the perimeter of a triangle whose three sides are 5x+1, 6x+4, and 2x
which line segment has the same measure as TQ
The line segment that has the same measure as TQ is TR
How to determine the line segment that has the same measure as TQ?The figure that completes the question is added as an attachment
From the figure, we have the following properties:
Lines TQ and TR are congruentLines QS and RS are congruentThe above implies that the line segment that has the same measure as TQ is TR
Hence, the line segment that has the same measure as TQ is TR
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Answer:
It's TR
Step-by-step explanation:
did it on edgenuidy
veronica and marty ride their hikes 46 miles every saturday. veronica rides at an average speed of 9.2 miles per hour
Answer:
5
Step-by-step explanation:
46/9.2 = 5
Please answer asap! If 2 or more people answer I will give brainliest
Answer:
the answer will be 6 centimeter
Kayla created the graph below to represent the solution to the inequality Negative 8 less-than x.
A number line going from negative 11 to negative 1. A closed circle is at negative 8. Everything to the left of the circle is shaded.
What errors did she make? Select two options.
She should have used an open circle at the end of the ray.
She should have pointed the arrow to the right.
She should have used a circle at –7 as the end of the ray.
She should have used a circle at –9 as the end of the ray.
Kayla made two errors which are as follows :-
She should have used an open circle at the end of the rayShe should have pointed the arrow to the right.How to Graph a Linear Inequality
First, graph the "equals" line, then shade in the correct area.
There are three steps:
Rearrange the equation so "y" is on the left and everything else on the right. Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)Shade above the line for a "greater than" (y> or y≥)
or below the line for a "less than" (y< or y≤).
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A survey was done with 205 women. Each women was asked how many children she had. The results showed that 28% of the women had 3 or more children. How many surveyed women had less than 3 children?
Identify what a, b, and c would equal in standard form.
Do not simplify the equation.
-14y= 28-10x
a=
b=
C=
Answer:
below
Step-by-step explanation:
-14y = 28 - 10x
10x - 14y - 28 = 0.
a = 10
b = -14
c = -28
Answer:
a = 10
b = -14
c = 28
Step-by-step explanation:
Goal form: Standard form
ax + by = c
Given form: linear form (not fully simplified)
-14y = 28 - 10x
Add 10x on both sides (to move the x-value to the left-hand side of the equation)
-14y + 10x = 28 - 10x + 10x
-14y + 10x = 28
10x - 14y = 28
Determine [ a ], [ b ], [ c ]
ax + by = c
10x - 14y = 28
[tex]\Large\boxed{a=10}[/tex]
[tex]\Large\boxed{b=-14}[/tex]
[tex]\Large\boxed{c=28}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Evaluate the expression if a=2,b=-3,C=-1, and D=4
-2(b^2-5c)
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Equivalent value = -28[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex] \qquad❖ \: \sf \: - 2( {b}^{2} - 5c)[/tex]
( put the values )
[tex] \qquad❖ \: \sf \: - 2 \{( - 3) {}^{2} - 5( - 1) \}[/tex]
[tex] \qquad❖ \: \sf \: - 2(9 - (- 5))[/tex]
[tex] \qquad❖ \: \sf \: - 2(9 + 5)[/tex]
[tex] \qquad❖ \: \sf \: - 2 \times 14[/tex]
[tex] \qquad❖ \: \sf \: - 28[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
-2(b² - 5c) = -28A van traveled 216 km in 4 hours. Find its average speed in km/h.
Answer:
86.9 km/h
Step-by-step explanation:
54 mph = 86.9046
Full number: 86.9046 km/h
Someone help me with this question !,
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
The side opposite to the largest angle is the longest side of a triangle.
[tex] \qquad \large \sf {Conclusion} : [/tex]
hence, we can conclude that longest side is e
( since it's opposite angle is the largest, i.e 86° )
The baseball coach is 70 inches tall. How tall is the child?
There is a picture that has the child's head slightly below the coach's shoulder.
The child is 59.4 inches tall, assuming the length from the coach's shoulder to his head cap is approximately 10 inches.
What is Heigth?Height refers to the vertical distance between the top and bottom of something.
Height measures the length of some objects or persons vertically to determine whether it is high or low, according to some ascertained criteria.
Data and Calculations:Baseball coach's height = 70 inches
Coach's shoulder to head = 10.6 inches
Height of the child standing slightly below the coach's shoulder = 59.4 inches (70 - 10.6)
Thus, the child standing slightly below the coach's shoulder is 59.4 inches tall.
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Question Completion:Assume that the height of the coach from his shoulder to the head is 10.6 inches.
7. A coin is tossed and a day of the week is selected. What is the probability that you get tails and a day that begins with "S"?
Answer:
1/7
Step-by-step explanation:
Lets start with the probability of flipping tails, 1/2.
Then the probability of the day starting with the letter s, 2/7.
Calculate the final probability by multiplying the two together.
[tex]\frac{1}{2}*\frac{2}{7}=\frac{2}{14}[/tex]
You can simplify 2/14 down to 1/7