Vectors is a quantity that has both magnitude and direction as well. A vector that has 1 magnitude is called unit vector. Unit vector is represented by the symbol '^'.
To find a Unit vector we divide the vector by its magnitude.
First find the slope of the tangent line, slope of a tangent line for a point f(x) is given by f'(x). Hence at point (π/6,1) where x = π/6, the slope of the tangent line is :
[tex]f(x)=2sinx\\f'(x)=2cosx\\f'(\pi /6)=2cos(\pi /6)=2.\frac{\sqrt{3} }{2}=\sqrt{3}[/tex]
The slope of the tangent line at this point is [tex]m=\sqrt{3}[/tex]
Finding a unit vector parallel to the tangent line. since slope is the ratio y and x then we can set an arbitrary vector with slope 4 by letting x=1 and y = √3 or v=[1,√3]. this vector has slope √3 and this is parallel to the tangent line, However this is not unit vector because its magnitude is not equal to 1 so we can divide this vector by its magnitude to find the unit vector.
[tex]u_v=\frac{v}{|v|} =\frac{1 \sqrt{3} }{\sqrt{1^{2}+(\sqrt{3})^2 } } \\=\frac{1}{\sqrt{4} } ,\frac{\sqrt{3} }{\sqrt{4} } =\frac{1}{2}, \frac{\sqrt{3} }{2} =[\frac{1}{2},\frac{\sqrt{3} }{2} ][/tex]
If a line has slope of m then all lines perpendicular of it will have a slope of -1/m
So we are looking for a unit vector of slope of -1/√3
Using the same logic we have unit vector that are perpendicular to the tangent line are [tex][\frac{\sqrt{3} }{2},-\frac{1}{2} ][/tex]
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-15X(-3) please help
Answer:
45x
Hope this helps :)
Step-by-step explanation:
- 15x (- 3) = 45 x
ab+6+ba-8+ab+b/a+2-3ba?
need answar
Answer:
this is the answer assuming the equation was meant to be simplified.
Step-by-step explanation:
A town has accumulated 4 inches of snow and the snow depth is increasing by 3 inches every hour . a nearby town has accumulated 1 inch and the depth is increasing by 5 inches every hour. how many hours will the snowfall of the towns be equal if the snow continues at the given rates?
The time in which the snowfall will be equal in both towns is 1.5 hours.
Time in which the snowfall will be equal in both town
The time in which the snowfall will be equal in both towns is calculated as follows;
let the time in which the snowfall will be equal in both towns = xThe equation becomes;
4 + 3x = 1 + 5x
collect similar terms together
4 - 1 = 5x - 3x
3 = 2x
divide both sides by 2
3/2 = 2x/2
3/2 = x
1.5 hours = x
Thus, the time in which the snowfall will be equal in both towns is 1.5 hours.
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A tree is standing next to a 40 foot high building the tree has a 9 foot shadow of the building has 18 foot shadow how tall is the tree rounded to the nearest foot
The height of the tree is 80 feet
How to determine the height of the tree?The given parameters are:
Building = 40 ftShadow of the building = 9 ftShadow of the tree = 18 ftThe above parameters can be represented as:
Building : Shadow of the building = Tree : Shadow of the tree
This gives
40 : 9 = Tree : 18
Express as fraction
40/9 = Tree/18
Multiply both sides by 18
Tree = 80
Hence, the height of the tree is 80 feet
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by what factor would you need to change the radius of a sphere, such that its volume increased by a factor of 7? give your answer to two digits.
The factor by which radius of the sphere be changed is 1.91, which is calculated hy applying the concepts of surface area and volume on the assigned problem.
What do you mean by volume?
Volume is defined as the 3D measurement that deals with the amount of space required by an object. It is always calculated in cubic units. Its basic unit is cubic metre.
Calculation of the change in radius of sphere when its volume is increased by 7
Let the radius and volume of sphere be r and v respectively
Volume of sphere, v = 3.16 × ( r )3 —- 1
Now, changed radius, R = xr
Where x is the factor, we need to calculate
Changed volume, V = 7v = 3.16 × ( R )3 -— 2
From equations 1 and 2, we get,
7v / v = ( R )3 / ( r )3
7 = ( xr )3 / ( r )3
7 = (x)3 × 1
Taking cube root both sides,
x = 1.913
Hence, the factor by which radius of the sphere be changed is 1.91.
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An interior designer charges $80 to visit a site, plus $65 to design each room. Identify a function that represents
the total amount he charges for designing a certain number of rooms. What is the value of the function for an
input of 5, and what does it represent?
The function that represents the total amount he charges is y = 80 + 65x and the total amount he charges for designing 5 rooms is $405
Identify a function that represents the total amount he charges for designing a certain number of roomsThe given parameters are
Charge = $80
Rate = $65 per design
The function is then calculated as
y = Charge + Rate * x
Where
y represents the total amount
x represents the number of rooms
So, we have
y = 80 + 65x
What is the value of the function for an input of 5, and what does it represent?Here, we have
x = 5
So, we have
y = 80 + 65 x 5
Evaluate
y = 405
Hence, the total amount he charges for designing 5 rooms is $405
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Math question is shown in the photo. Fairly easy, not sure why I'm having trouble with such a simple problem lol
Answer:
then solve it .....
Step-by-step explanation:
y did u post it if u knew
On Monday Janice worked on Math homework for 1/2 hour, Science homework for 38 minutes, piano for 20 minutes and Spelling homework for 15 minutes. How many minutes did Janice spend on homework?
Answer:
Either 83 or 103
Step-by-step explanation:
If you count piano as homework, the answer is 103. If piano is not homework, the answer is 83.
DeltaMath -
Evaluate the function.
Answer: I hope this helps.
Step-by-step explanation:
Answer:
f(9) = -161
Step-by-step explanation:
Given function:
[tex]\sf -2x^2 + x - 8[/tex]
To find f(9), substitute x = 9 in the function:
[tex]\rightarrow \sf -2(9)^2 + 9 - 8[/tex]
[tex]\rightarrow \sf -2(81) + 9 - 8[/tex]
[tex]\rightarrow \sf -162 + 9 - 8[/tex]
[tex]\rightarrow \sf -161[/tex]
h(x)= 3x+2
find h(x+1)
Step-by-step explanation:
Greetings !
Given expression :-
[tex]h(x) =3 x + 2[/tex]
Goal:-
Find
[tex]h(x + 1)[/tex]
Thus,
plug in x+1 in the first expression as follows;
[tex]h(x + 1) = 3(x + 1) + 2[/tex]
Expand:-
apply distributive law:-
[tex]a(b + c) = ab + ac[/tex]
solve
[tex]3(x + 1) = 3x + 3.1 \\ = 3x + 3 + 2[/tex]
add the numbers:- 3+2 = 5
Finally we get
[tex]h(x + 1) = 3x + 5[/tex]
Hope it helps !!!
Which equation is true if b = 2?
2b + 24 = 30
3b - 2 = 4
B + 4 = 8
2b - 3 = 0
Answer:
2nd equation is correct.
Step-by-step explanation:
1) 2b + 24 = 30
→ 2(2) + 24 = 30
→ 4 + 24 = 30
→ 28 ≠ 30
Hence, it is false.
2) 3b - 2 = 4
→ 3(2) - 2 = 4
→ 6 - 2 = 4
→ 4 = 4
Hence, it is true.
3) B + 4 = 8
→ 2 + 4 = 8
→ 6 ≠ 8
Hence, it is false.
4) 2b - 3 = 0
→ 2(2) - 3 = 0
→ 4 - 3 = 0
→ 1 ≠ 0
Hence, it is false.
Arne and Falk are playing Rock, Paper, Scissors. Arne has won 5/8 of the total number of games, g, they
have played. Falk has won 1/4 of the games which is 6 less than Arne. How many total games did they
play?
Answer:
They have played 14 games
Step-by-step explanation:
5/8 and 2/8 is 7/8 of the time, but if 3/8 is 6 then 1/8 is 2, 2*7 is 14
Which graph shows the solution to the inequality? x − (5 − 3x) ≤ 2x − 1
Answer:
the answer is b
jsjsjsjsjsjsjsjsjsjsjsjsjsjsjs
Answer:
thank me later that's is the answer
ill give 50 points
Xena read 126 books in 9 months. Fill in the blanks on how you would solve this problem?
126 books/months=
books/1month=
Answer:
126 books/month= 14 books a month
books/1months = 14
Step-by-step explanation:
126/9=14
Answer:
14 books per month
Step-by-step explanation:
[tex]\frac{126books}{9 months}[/tex] = [tex]\frac{14books}{1month}[/tex]
Using the chart in problem 1, what is the least place value of 0.24
Answer:
The thousandths place.
Step-by-step explanation:
4 is furthest away from the decimal on the right side and it is in the thousandths place.
Simplify the radical expression ∛81x^7y^9z^5. Show your work! Show the step-by-step process on how you got your answer so I can understand how to do it. Brainliest to the best answer that shows all steps!!
The simplified radical expression for this problem is given by:
[tex]3x^2y^3z\sqrt[3]{3xz^2}[/tex]
How to simplify the given radical expression?To simplify the given radical expression, we divide all the exponents by 3, and the ones that can be simplified are placed outside the root, multiplying.
Looking at each term, we have that:
81 is equivalent to 3^4, hence [tex]\sqrt[3]{81} = \sqrt[3]{3^4} = 3\sqrt[3]{3}[/tex], as 4 divided by 3 has quotient 1 and remainder 1.For x^7, we have that 7 divided by 3 has quotient 2 and remainder 1, hence [tex]\sqrt[3]{x^7} = x^2\sqrt[3]{x}[/tex].For y^9, we have that 9 divided by 3 has quotient 3, hence [tex]\sqrt[3]{y^9} = y^3[/tex]For z^5, we have that 5 divided by 3 has quotient 1 and remainder 2, hence [tex]\sqrt[3]{z^5} = z\sqrt[3]{z^2}[/tex].Thus, the simplified radical is given by:
[tex]3 \times \sqrt[3]{3} \times x^2 \times \sqrt[3]{x} \times y^3 \times z \times \sqrt[3]{z^2}[/tex]
[tex]3x^2y^3z\sqrt[3]{3xz^2}[/tex]
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Helpppp....
The work is due tmr
Answer:
My best guess is 172.05
Step-by-step explanation:
Answer: The answer is from sanakhatri5.
Step-by-step explanation: Area of star is 81.25cm
Eight friends went to the movies. Each ticket cost $6.75. How much did the tickets cost all together?
Answer:
$54
Step-by-step explanation:
6.75*8=54
Answer:54
Step-by-step explanation:8x6.75=54
Volume of Spheres
\
Volume of SpheresVolume of Spheres
Find the sum of -19 + 26 + 14
Please help this is due tonight!
Answer:
21
Step-by-step explanation:
-19+26= 7
7+14= 21
A large grain silo is to be constructed in the shape of a circular cylinder with a hemisphere attached to the top. The diameter of the silo is to be 30 feet, but the height is yet to be determined. Find the height h of the silo that will result in a volume of 11,475(3.14) ft cubed
The height of the silo is 56 feet.
Here, we are given that a large grain silo is to be constructed in the shape of a circular cylinder.
The diameter of the silo = 30 feet
⇒ The radius of the cylinder = 15 feet
and also the radius of the hemisphere = 15 feet
The volume of a hemisphere = 2πr^3/3
Volume = 2 × π × 15 × 15 × 15 × 1/3
Volume of cube = 2250π
Thus, the volume of cylinder = volume of the silo - volume of the hemisphere
= 11,475(3.14) - 2250π
π = 3.14
⇒ 11,475(3.14) - 2250(3.14)
3.14 (11,475 - 2250)
= 3.14 (9225)
= 9225π
Now, the volume of cylinder = πr^2h
Thus, 9225π = π(15) (15) h
9225π/ 225π = h
h = 9225/225
h = 41
Thus, the height of the cylinder = 41
The height of the silo will be the height of hemisphere + height of the cylinder = 15 + 41 = 56 feet.
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A gallon of gasoline costs $2.96. Your car has a 25-gallon gas tank and can travel 28.8 miles on each gallon of gasoline.
a. Find the cost of filling your gas tank if it is already 38 38 full.
b. You take a trip of length 705 miles. How much money do you spend on gasoline?
The cost of filling your gas tank if it is already 38 38 full. $48.88 required to fill the gas tank if it is already 38% full.
Money do you spend on gasoline is $72.46 is spends on that trip.
Given that
A gallon of gasoline costs $2.96.Gas tank capacity of the given car = 25 gallonThat car can travelled 28.8 miles on each gallon of gasoline.To find
The cost of filling your gas tank if it is already 38 % full.How much money spend on gasoline on the trip of 705 miles.So according the question
We have
1 gallon of gasoline = $2.96.Gas tank capacity = 25 gallon.28.8 miles travelled on each gallon of gasoline.Now, for finding
a.) The cost of filling your gas tank if it is already 38 % full.
38 % of 25 gallon = 9.5 gallon
the unfilled part of the tank = 25-9.5 = 15.5 gallon
So the tank can filled 15.5 gallon of gasoline more now.
The cost of 15.5 gallon of gasoline
= 15.5 × cost of 1 gallon of gasoline
= 15.5 × 2.96
= $45.88
$48.88 required to fill the gas tank if it is already 38% full.b.) How much money spend on gasoline on the trip of 705 miles.
∵ Car can travelled in 1 gallon of gasoline = 28.8 miles.
∴ Gasoline required to travel 705 miles = [tex]\frac{705}{28.8}[/tex]
= 24.48 gallon.
The cost of 24.48 gallon of gasoline
= 24.48 × cost of 1 gallon of gasoline
= 24.48 × 2.96
= $72.46
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In a restaurant there are 7 starter dishes, 14 main dishes and 9 desserts. phil is going to choose one of the combinations for his meal. a starter dish and a main dish, a main dish and dessert, a starter dish, main dish and dessert dish. how many different ways are there for him to choose the meal.
There are 1106 different ways for him to choose the meal.
For given question,
In a restaurant there are 7 starter dishes, 14 main dishes and 9 desserts.
The possibilities of selecting a starter = 7
The possibilities of selecting a main dish = 14
The possibilities of selecting a dessert = 9
The meal combinations are: a starter dish and a main dish; a main dish and dessert; a starter dish, main dish and dessert dish.
The possibility of selecting each meal combinations would be,
1) a starter dish and a main dish = 7 × 14
= 98
2) a main dish and dessert = 14 × 9
= 126
3) a starter dish, main dish and dessert dish
= 7 × 9 × 14
= 882
We need to find the total number of different ways to choose the meal.
= 98 + 126 + 882
= 1106
Therefore, there are 1106 different ways for him to choose the meal.
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Make sense of problems. Determine the number , and explain how you came up with he solution
Answer:
5
Step-by-step explanation:
because 5x3=15
15 + 5 = 20
Answer:
5
Step-by-step explanation:
work backwards. Start with 20. minus 5 equals 15. Divide by 3 is 5.
double-check by going the other way.
5x3=15
15+5=20
Loudres plans to jog at least 1.5 miles. write and solve an inequality to find x, the number of hours lopudres bwill have to jog.
The number of hours lopudres will have to jog is .4 hours.
Lord wants to run at least 1.5 miles, and her pace is shown in the picture as 3.75 miles per hour, and the question asks us to construct an inequality expressing x for the amount of hours she would have to run. To meet this inequality, we'll need to apply how quickly or how many miles she wants to cover with how fast she's going to run, so we'll divide 1.5 miles by her rate of 3.75 miles per hour, and when you divide you'll get a number of hours, which comes out to 0.4 hours.
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Find a parametrization of the tangent line at the point indicated. r(t) = cos(6t), sin(3t) , t = 4
The given statement states that the parametrization of both the tangent line there at designated position is 7x - 4y = 3.
What is parametrization?Finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, specified by an implicit equation, is the process of parametrization (or parameterization; see parameterization, parametrization). Implicitization is the term for the opposite process. The parametrization consists of one function of multiple real variables for each coordinate since the state of the system is typically controlled by a finite set of coordinates. The system's degree of freedom is equal to the number of parameters.
According to the given data:r(t) = cos(6t), sin(3t) , t = 4
= -6sin6t, 3cosjt , 1
The parameter of Tangent live is
L(t) = γ(t₀) + tr'(t₀)
therefore
γ(t₀) = γ(ππ₄)
= (0 , 1/√2 , π/4)γ (+0) = γ(π/4)
= ( 6, -3/√2 , 1)
putting in the formula we get:
L(t) = γ(t₀) + tr'(t₀)
L(t) = (0 , 1/√2 , π/4) + t( 6, -3/√2 , 1)
= [tex]\left(6 t-\frac{1}{\sqrt{2}}-\frac{3}{\sqrt{2}} t, \frac{\pi}{4}+t\right)$$[/tex]
= 2.
Given
f(x, y ) = in(7x² - 4y²)
at the point(1, 1)
Δ f (m, y) = (fn , f4)
= [tex]\frac{14 x}{7 n^2-4 y^2}, \frac{-8 y}{7 x^2-4 y^2}\\\\[/tex]
Δ f (1, 1)
= [tex]\left\langle\frac{14}{3}, \frac{-8}{3}\right\rangle[/tex]
= (a ,b)
The equation of the tangent plane is
a(x - x₀) + 6dy - y₀ = 0
(14/3)(x - 1)- (8/3)(y -1 ) = 0
14x - 14 - 8y + 8 = 0
14x - 8y = 6
7x - 4y = 3
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Use the formula for arc length to find the value of the unknown quantity.
s=rθ
The unknown quantity which is the radius has a length of 49752/π yards.
How to find arc length?The formula for the length of arc is;
S = rθ
where;
r is radius
θ is the central angle in radians
Now, we are given;
θ = 3π/4
S = 4146 * 9 yards
Thus, making r the subject and solving gives;
r = S/θ
r = (4146 * 9)/(3π/4)
r = 49752/π
Thus, the unknown quantity which is the radius has a length of 49752/π yards.
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Jarome is making pizza. He uses 2 1/2 cups of cheese for
every 2 3/4 pizzas. He has 6 1/4 cups of cheese left in the
bag. How many pizza pies can he make with the leftover
cheese?
6 pizzas
By using fundamental concepts of fractions we can conclude that Jarome can make 6 [tex]\frac{7}{8}[/tex] pizzas with the leftover cheese.
Define fractions.Fractions are one of the most important aspects of arithmetic that we use in our daily lives. Fractions are denoted by the symbol / (also known as the fractional line) and represent a numerical value that is a portion of the total value, for example, a/b. Formulas for fractions aid in the development of rules for performing the four basic arithmetic operations of addition, subtraction, multiplication, and division.
Given data:
Cheese used for making 2 [tex]\frac{3}{4}[/tex] pizza = 2 [tex]\frac{1}{2}[/tex]
Cheese used for making 1 pizza = 2 [tex]\frac{1}{2}[/tex] ÷ 2 [tex]\frac{3}{4}[/tex]
Cheese used for making 1 pizza = 10/11
Number of pizza pies that can be made from 6 [tex]\frac{1}{4}[/tex] cheese = 6 [tex]\frac{1}{4}[/tex] ÷ 10/11
Number of pizza pies that can be made from 6 [tex]\frac{1}{4}[/tex] cheese = 55/8
Number of pizza pies that can be made from 6 [tex]\frac{1}{4}[/tex] cheese = 6 [tex]\frac{7}{8}[/tex].
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PLEASE HELPP
What must be true for lines a and b to be parallel lines select two options.
There is two statement will be needed for lines A&B to be parallel linesin Angle .
m∠2 = 58°m∠1 = (4x-10)°Given that
A figure that, showing 4 lines a,b,c and d.Angle between line b and c is (4x-10)°Angle between line b and c is 58°.To find
True statements that prove the lines a and b are parallel.So according the question
We have
Angle between line a and c = m∠1Angle between line a and d = m∠1Angle between line b and c = (4x-10)°Angle between line b and d = 58°Angle between line c and d = (3x-1)There are two angles from the c and d lines with the lines a and b being equal that can be used to determine whether the lines a and b are parallel.
That's mean
Angle between line a and c = Angle between line b and cm∠1 = (4x-10)°
Angle between line a and d = Angle between line b and dm∠2 = (58)°
m∠2 = 58°
Answer: There is two statements are true,
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since there is an infinity of possible vulnerabilities, but a finite number of threat types, the following can be stated
Threat-asset matrices can be constructed, but not vulnerability-asset matrices.
What is vulnerability information security?
A security system weakness, fault, or error that could be used by a threat agent to compromise a secure network is known as a security vulnerability.
What do you think is the primary threat for service providers?
Inadvertent acts, potential human mistake or failure, potential variations in service quality by service providers, and power anomalies are among the main dangers to physical security.
The different types of vulnerability
In the table below four different types of vulnerability have been identified, Human-social, Physical, Economic and Environmental and their associated direct and indirect losses.
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