The direction of the net magnetic field is [tex]$167.36^{\circ}$[/tex]
How to find the magnitude?[tex]q_1=-4 \mathrm{nC} \text { at }(0.6,0.8)[/tex]
[tex]$q_2=6 \mathrm{nC}$[/tex] at (0.6,0)
[tex]$r_1=$[/tex]Distance of [tex]$q_1$[/tex] from origin[tex]$=\sqrt{0.6^2+0.8^2}$[/tex]
[tex]$r_2=$[/tex] Distance of [tex]$q_2$[/tex] from origin [tex]$=0.6$[/tex]
[tex]$\mathrm{k}=$[/tex] Coulomb constant[tex]$=9[/tex]times [tex]10^9 \mathrm{Nm}^2 / \mathrm{C}^2$[/tex]
Electric field is given by
[tex]&E_1=\frac{k q_1}{r_1^2} \\[/tex]
[tex]&\Rightarrow E_1=\frac{9 \times 10^9 \times 4 \times 10^{-9}}{\sqrt{0.6^2+0.8^2}} \\[/tex]
[tex]&\Rightarrow E_1=36 \mathrm{~N} / \mathrm{C}[/tex]
[tex]&\theta=\tan ^{-1} \frac{0.8}{0.6} \\[/tex]
[tex]&\Rightarrow \theta=53.13^{\circ} \\[/tex]
[tex]&E_1=36 \cos 53.13^{\circ} \hat{i}+36 \sin 53.13^{\circ} \hat{j} \\[/tex]
[tex]&\Rightarrow E_1=21.6 \hat{i}+28.8 \hat{j}[/tex]
[tex]&E_2=\frac{k q_2}{r_2^2} \\[/tex]
[tex]&\Rightarrow E_2=\frac{9 \times 10^9 \times 6 \times 10^{-9}}{0.6^2} \\[/tex]
[tex]&\Rightarrow E_2=150 \mathrm{~N} / \mathrm{C}[/tex]
The charge [tex]$q_2$[/tex] is on the [tex]$\mathrm{x}$[/tex] axis itself and it is pointing towards the origin (left side) so the sign will be negative
[tex]E_2=-150 \hat{i}[/tex]
Resultant electric field
[tex]&E=E_1+E_2 \\[/tex]
[tex]&\Rightarrow E=21.6 \hat{i}+28.8 \hat{j}+(-150 \hat{i}) \\[/tex]
[tex]&\Rightarrow E=-128.4 \hat{i}+28.8 \hat{j}[/tex]
Magnitude of electric field is given by
[tex]&|E|=\sqrt{(-128.4)^2+28.8^2} \\[/tex]
[tex]&\Rightarrow|E|=121.6 \mathrm{~N} / \mathrm{C}[/tex]
Magnitude of the net electric field is [tex]$121.6 \mathrm{~N} / \mathrm{C}$[/tex]
Direction is given by
[tex]\theta=\tan ^{-1} \frac{128.4}{28.8}=77.36^{\circ}[/tex]
From the -x axis
[tex](90+77.36)^{\circ}=167.36^{\circ}[/tex]
The direction of the net magnetic field is [tex]$167.36^{\circ}$[/tex]
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A student and teacher are racing to finish a book. It takes the teacher 14.4 hours to complete the book. It takes the student 1.75 times as long to finish. Based on this information, which statement is true?
Answer:
I don't know about that and I don't understand
latoya plots the integers -8, -5, and 2 on a number line. which of the following is the distance between one pair of integers that she plotted?
distance between one pair of integers that she plotted: 10 unit, 7 unit, 3 unit.
Number line :
the line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, for example, in plotting a point.
The numbers on the left are smaller than the numbers on the right of the number line. A number line can also be used to carry out addition, subtraction, and multiplication. We always move right to add, move left to subtract, and skip count to multiply.
Distance formula :
D= right side integer of horizontal line - left side integer of the horizontal line
Distance between the points -8 and 2
d = 2-(-8)
d=10 unit
Distance between the points -5 and 2
d= 2-(-5)
d=2+5
d=7 unit
Distance between the points -5 and -8
d= -5-(-8)
d=-5+8
d=3
distance between one pair of integers that she plotted: 10 unit, 7 unit, 3 unit.
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What is the slope of this graph? On a coordinate plane, a line goes through points A (1, 4) and B (3, 2).
Answer:
yes hdhdhzbw Ziad uebs U ue susna
let f(x)=-x+3 Write a function g whose graph is a translation 3 units up from the graph of f.
g(x)=?
The function g whose graph is a translation 3 units up from the graph of F is given as g(x) = -x+6
What is the explanation for the above?Given:
f(x) = -x + 3...............1
Transformation is 3 units up from the graph of F
hence,
g(x) = f(x) + 3...........2
Recall that f(x) = -x+3 Hence
Substituting f(x) in to Equation 2
We have:
g(x) = -x + 3 +3, hence
g(x) = -x + 6
Hence we can conclude that the function g whose graph is a translation 3 units up from the graph of F is given as g(x) = -x+6.
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99×78+33×66=？
How to calculate it without using a calculator?
Answer:
cool hahahahhahahahahaha ano to app nato
Answer:
Do it on Paper.99 x 78 = 7722
+ 33
= 7755
x 66
= 511830Answer = 511830Hope this helpsace that workGood luck ✅
Evaluate the expression 5(7-4)2 ÷ 3 + 11.
Answer:
26
Step-by-step explanation:
I will assume you meant this: 5 ( 7-4)² ÷ 3 + 11
Using PEDMAS
Parentheses first
5 ( -3)² ÷ 3 + 11
then exponents
5 ( 9) ÷ 3 + 11
then division
5 * 3 + 11
and multiplication
15 + 11 then addition and or subtraction = 26
Answer:
Step-by-step explanation:
Javid makes a large container of fruit juice by mixing orange juice and mango juice in the ratio 3:7 Orange juice costs £6 per 4 litres. Mango juice costs £5 per 10 litres.Javid sells his fruit juice in 2-litre bottles for £2 per bottle. Calculate how much profit he makes for each bottle he sells.
Javid will make a profit of £ 0.40 for each bottle sold.
How much profit does Javid makes for each bottle he sells?
The orange juice capacity to mango juice capacity ratio, the unit cost for each juice and the end product price. First, determine the amount of orange juice and mango juice to produce a 2-litre bottle:
Orange juice capacity
x = (3 / 10) × 2 L
x = 0.6 L
Mango juice
y = (7 / 10) × 2 L
y = 1.4 L
Second, calculate the cost of each juice by simple rule of three:
Orange juice
x' = (0.6 L / 4 L) × 6 GBP
x' = 0.90 GBP
Mango juice
y' = (1.4 L / 10 L) × 5 GBP
y' = 0.70 GBP
Third, add the two results found in the previous step and find the production cost for a 2-litre bottle:
z = x' + y'
z = 0.90 GBP + 0.70 GBP
z = 1.60 GBP
Fourth, calculate the profit by subtracting the result found in the previous step to the end product price:
z' = 2 GBP - 1.60 GBP
z' = 0.40 GBP
Javid will make a profit of £ 0.40 for each bottle sold.
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What is the equation of the line that is perpendicular to the line y =1/2x+5 and passes through the point (-2, 3)?
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{ m}{\downarrow }}{\cfrac{1}{2}}x+5\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{1}\implies -2}}[/tex]
so, we're really looking for the equation of a line with a slope of -2 and that passes through (-2 , 3)
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{3})\hspace{10em} \stackrel{slope}{m} ~=~ - 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{- 2}(x-\stackrel{x_1}{(-2)})\implies y-3=-2(x+2) \\\\\\ y-3=-2x-4\implies y=-2x-1[/tex]
An ordinary deck of 52 cards is shuffled. what is the probability that the top four cards have (a) different denominations? (b) different suits?
The different denomination is 0.6761
The different suits are 0.1055
What are deck of cards consist of?A standard deck of cards has four suites: hearts, clubs, spades, diamonds. Each suite has thirteen cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen and king. Thus the entire deck has 52 cards total.
Given:
Deck of cards= 52
Now,
There are 4 denomination in each cards
and there are 4 suits in deck of cards
a) different denominations
=52*48*44*40/(52*51*50*49)
= 0.6761
b) different suits
=52*39*26*13/ /(52*51*50*49)
= 0.1055
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what is divide 3/2 and 9/4
Answer:
Step-by-step explanation:
1.5 and 2.25
HELP PLS will mark brainliest
[tex](1-\frac{9x^2+4}{12x} )/(\frac{1}{3x}-\frac{1}{2} )+1[/tex]
Answer:
[tex] \frac{3x}{2} [/tex]
Un ciclista tarda 3horas y 25 minutos en recorrer 150km ¿cuantos minutos tardará en recorrer 238km si lleva una velocidad constante?
Answer :
The time it will take to travel a distance of 225km is t = 9 h
What is MRU?
MRU are the acronyms that define the uniform rectilinear movement which is the movement that maintains a variation of the distance with respect to time always constant since the acceleration is null.
We will calculate the speed you have in cyclist with the initial data of traveling a distance of 125km in a time of 5 hours:
Speed = distance / time
Speed = 125km/5h
Speed = 25 km/h
We now determine a time for a 225km course
25 km/h = 225km/t
t = 225km / 25km/h
t = 9 h
is y=10^2 linear or no linear
Answer: it is linear
Step-by-step explanation:
y = 10^2
y = 100
horizontal line going through y = 100
A jet left the airport flying north one hour
before an Air Force plane. The Air Force
plane flew in the opposite direction going
55 mph slower than the jet for ten hours
after which time the planes were 9845 mi.
apart. What was the jet's speed?
Answer:I think the answer would be 179 mi.
Step-by-step explanation:9845 divided by 55 is equal to 179
Find the value of
(8/125) -2/-3
The value of the exponent equation [tex]\frac{8}{125} ^{-2/3}[/tex] is 25/4 or 6.25.
According to the question the exponent equation that we have been given is :
[tex]\frac{8}{125} ^{-2/3}[/tex]
First, we will change the negative sign of the exponent and to change the negative sign of the exponent we will reciprocal the fraction that is
= [tex]\frac{125}{8} ^{2/3}[/tex]
Which is also equal to
= [tex]{125} ^{-2/3}/8^{2/3}[/tex]
Now we know that 5³ =125 and 2³ = 8. Thus replacing the numerator and denominator by it we get,
= [tex](5^{3}) ^{2/3}/(2^{3}) ^{2/3}[/tex]
= 5²/2²
= 25/4
= 6.25
Hence the value of the exponent equation is 25/4 or 6.25
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calculate these values
a= _____
b= _____
The values of a and b of the given matrix multiplication is gotten as; a = 2 and b = 3
How to multiply Matrices?
To multiply matrix, we follow patterns depending on the type of matrix. Thus, from the given matrix, we can say that;
(1 * -1) + (0 * -1) + (1 * 3) = a
-1 + 0 + 3 = a
a = 2
Similarly;
(1 * -1) + (0 * 2) + (1 * 4) = b
-1 + 0 + 4 = b
b = 3
Thus, the values of a and b of the given matrix multiplication is gotten as; a = 2 and b = 3
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[tex]x-2\ \textgreater \ 3 \\[/tex]
The solution set of the inequality is the set of all real numbers larger than 5, written in interval form as (5, ∞)
How to solve the inequality for x?Here we have a simple inequality:
x - 2 > 3
To solve this we need to isolate x in one side of the inequality.
Now, remember that we can do the same operation in both sides of the inequality. So, if we add in both sides the same number, then the truth value of the inequality does not change.
Then if we add 2 in both sides of the inequality we get:
x - 2 + 2 > 3 + 2
x > 5
Then the solution set of the inequality is the set of all real numbers larger than 5, written in interval form as (5, ∞).
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Graph: y < 1/3x + 1/2
Answer: See attached.
Step-by-step explanation:
Since this inequality uses < and not ≤, we will be using a dashed line.
Next, we will shade "below" the line since this inequality uses the < aka less than.
Lastly, our y-intercept is [tex]\frac{1}{2}[/tex].
Identify the property that justifies the statement. ∠LMN ≅ ∠LMN
Please Hurry!!
The property which justifies the statement, ∠LMN ≅ ∠LMN is: C. reflexive property of ≅.
Corresponding parts of two congruent figures.In Mathematics, two geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.
What is the reflexive property of congruence?The reflexive property of congruence states that a line segment, an angle, or geometric shape (geometric figure) is always congruent to itself.
This ultimately implies that, for all angles M , ∠M ≅ ∠M. In this context, we can reasonably infer and logically deduce that the property which justifies the statement, ∠LMN ≅ ∠LMN is reflexive property of ≅.
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Express in simplest radical form.
Square root of 160
Answer:
4 [tex]\sqrt{10}[/tex]
Step-by-step explanation:
Simplify
[tex]\sqrt{160}[/tex]
We can rewrite this as
[tex]\sqrt{16 * 10}[/tex]
Breaking this up
[tex]\sqrt{16} \sqrt{10}[/tex]
We know the square root of 16 is 4
4 [tex]\sqrt{10}[/tex]
sqrt(10) cannot be simplified so
Answer:
[tex]4\sqrt{10}[/tex]
Step-by-step explanation:
160 = 16 * 10
[tex]\sqrt{160} = \sqrt{16 \cdot 10} = \sqrt{16} \cdot \sqrt{10} = 4\sqrt{10}[/tex]
we cannot simplify further as 10 is 2*5, there are no more squares to simplify.
if X over 3 equals to 4 over 6. What is X?
Answer:2 beacuse if u divide 4 by 2 and 6 by 2 u get 2/3
Step-by-step explanation:
h(x) = 18 - 9x + x4, evaluate h(2)
The value of h(2) for the function h(x) = 18 - 9x + x^4 is 16.
According to the given question.
We have a function h(x) = 18 - 9x + x^4
Here, we have to find the value of h(2). For this we will substiute x = 2 in the function h(x) = 18 - 9x + x^4.
Therefore, the value of h(2) for the function h(x) = 18 - 9x + x^4 is given by
h(x) = 18 - 9x + x^4
h(2) = 18 - 9(2) + 2^4
h(2) = 18 - 18 + 16
h(2) = 16
Hence, the value of h(2) for the function h(x) = 18 - 9x + x^4 is 16.
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Question 2(Multiple Choice Worth 1 points)
(01.01 LC)
Evaluate the expression 5(7-4)2 = 3 + 11.
03
14
026
33
26 is the right answer .
Given expression 5(7 - 4)² ÷ 3 + 11.
BODMAS rule is an acronym that is used to remember the order of operations to be followed while solving expressions in mathematics. It stands for B - Brackets, O - Order of powers or roots, D - Division, M - Multiplication, A - Addition, and S - Subtraction. It means that expressions having multiple operators need to be simplified from left to right in this order only. First, we solve brackets, then powers or roots, then division or multiplication (whichever comes first from the left side of the expression), and then finally, subtraction or addition, whichever comes on the left side.
Using the BODMAS rule, we solve bracket first,
5(3)² ÷ 3 + 11
45 ÷ 3 + 11
= 15 + 11
= 26
after evaluate the expression we get 26 as answer.
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round 1344 to two decimal places
At the beginning of the day, the temperature is -15oF. As the sun comes out, it warms to a high of 8oF. What is the difference in temperature throughout the day?
PLEASE ANSWER FAST IM TIMEDDDD!!!!
Answer:23
Step-by-step explanation: take -15 and negate it which will set you at 15 then add 8 will put you at 23degrees
Given f(-3) = -30 for some polynomial, what factor can f(x) be divided by that will result in a remainder of -30?
Answer:If you can spot a factor of
f(x)
then you can use synthetic division to divide by that factor to give a simpler polynomial to factor.
Step-by-step explanation:
Given x = 1, y = 1, w = 1, and z = 1 and this expression: what is the evaluation of the logical expression?
The evaluation of the expression is 2, if the expression is x - y + z(x + w).
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
Given that x = 1, y = 1, w = 1, and z = 1
We have been given expression
⇒ x - y + z(x + w)
Substitute the values of x = 1, y = 1, w = 1, and z = 1 in the above expression,
⇒ 1 - 1 + 1(1 + 1)
⇒ 0 + 1(2)
⇒ 2
Hence, the evaluation of the expression is 2.
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Your question is incomplete, probably the missing part is:
Given x = 1, y = 1, w = 1, and z = 1 and this expression x - y + z(x + w): what is the evaluation of the logical expression?
6-6x=7x-9x-18 the value of x
Answer:
X = 6
Step-by-step explanation:
6-6X = 7X -9X -18 Combine 7x -9x
6 - 6x = -2x -18 Add 6x to both sides of the equation
6 = 4x - 18 Add 18 to both sides of the equation
24 = 4x Divide both sides by 4
6 = x
Check:
6-6X = 7X -9X -18
6 - 6(6) = 7(6) -9(6) -18
6 - 36 = 42 - 54 -18
-30 = 1-12-18
-30 =-30
I need help w this asap
Answer: 6.8*10⁻⁴=0.00068
Step-by-step explanation:
[tex]6.8*10^{-4}=0.00068[/tex]
19.6 is 24.5% of what number?
- For 11 points
Answer:
80
Step-by-step explanation:
[tex]\frac{24.5}{100} *x = 19.6\\x = 19.6 *\frac{100}{24.5} \\x = 80[/tex]
19.6 is 24.5% of 80
Answer:
24.5% of 80= 19.6
Step-by-step explanation:
24.5% of what number is equal to 19.6
24.5
____ x = 19.6
100 100
x = 19.6 x ____
24.5
= x =80
HOPE IT HELPS
