Describe the vector as an ordered pair. Round the coordinates to the nearest tenth. The diagram is not drawn to scale.
Answers
ANSWER
[tex]
\angle19.4,50.4 \: > [/tex]
EXPLANATION
The given vector has magnitude 54 units.
The vector is making an angle of 69° with the x-axis.
The horizontal component of the vector is
[tex] = 54 \cos(69) [/tex]
[tex] = 19.35[/tex]
To the nearest tenth, we have,
[tex] = 19.4[/tex]
The vertical component is
[tex] = 54 \sin(69 \degree) [/tex]
[tex] = 50.41[/tex]
[tex] = 50.4[/tex]
to the nearest tenth.
The required vector is
[tex]
\angle19.4,50.4 \: > [/tex]
The components of the vector with magnitude 54 and the angle of 69° from the horizontal can be written as <19.3519, 50.4133>.
What is a vector?A vector is a quantity that has both magnitude and direction. It has two components a vertical component(Sine) and a horizontal component(Cosine). The component of a vector can be written as,
Vertical component, [tex]V_y = \vec V\ Sin(\theta)[/tex]
Horizontal component, [tex]V_x = \vec V\ Cos(\theta)[/tex]
We know that a vector can be divided into two components a horizontal component and a vertical component, therefore, the vector components can be written as,
[tex]V_y = \vec V Sin\theta\\\\V_y = 54\ Sin(69^o)\\\\V_y = 50.4133[/tex]
[tex]V_x = \vec V Cos\theta\\\\V_x = 54\ Cos(69^o)\\\\V_x = 19.3519[/tex]
Hence, the components of the vector with magnitude 54 and the angle of 69° from the horizontal can be written as <19.3519, 50.4133>.
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Related Questions
Patrick ate 2/3 of a fruit bar write an equivalent fraction for the amount of fruit bar Patrick ate
Answers
amy is building a house. the basement floor is at -15 feet. the roof of the house is above the ground 25 feet. write an inequality to compare the heights. explain the meaning of the inequality.
BONUS: what is an inequality.
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For example, this is a problem of heights.
There is a minimum height and a maximum height.
We can use the following inequation to describe the problem:
Let
x = height in feet.
The inequation is:
-15 <= x <= 25
answer:
-15 <= x <= 25
The perimeter of a is 35.54 inches longer than the perimeter of a square of side 6.75 Find the perimeter of the rectangle to the nearest inches. tenth of an inch
Answers
Perimeter of rectangle: 27 + 35.54 = 62.54 inches
Tara is taller than Jeff. Jeff is 47 inches tall. Write an inequality that compares Tara's height in inches, t, to Jeff's height
Answers
Answer:
t > 47
Step-by-step explanation:
Tara is taller than Jeff. Jeff is 47 inches tall.
We need to write an inequality that compares Tara's height to Jeff's height
Let t be the height of Tara
and j be the height of Jeff
Tara is taller than Jeff, we use greater than symbol for taller
So inequality becomes t > j
Given Jeff is 47 inches tall, so replace 'j' with 47
Answer is t > 47
Final answer:
To compare Tara's height to Jeff's, the inequality used is t > 47, indicating Tara is taller than Jeff.
Explanation:
The question asks you to write an inequality that compares Tara's height, represented by t, to Jeff's height, which is 47 inches. To represent that Tara is taller than Jeff using an inequality, you use the 'greater than' symbol (>). Therefore, the correct inequality to show that Tara is taller than Jeff is t > 47. This inequality means that Tara's height in inches is greater than 47 inches.
how to solve -2x+y=7, 3y=6x+4
Answers
To the additional, see the attached graph for this system.
a kittens heartbeat can be as fast as 240 beats per minute . to find the number of times a kittens heart beats in 30 seconds , Aiden says divide 240 ny 30 . do you agree with him why or why not
Answers
In order to get the CORRECT answer, divide 240 by 60 seconds.
This would give you 4 heartbeats per second.
Then, multiply it by 30 seconds, which would give you 120 heartbeats.
CORRECT answer: 120
What is the total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months?
a. $25.47
b. $202.55
c. $611.20
d. $4,861.20
Answers
Answer: Option c. $ 611.20 will be correct.
Explanation:
Since, the total amount of finance charge is [tex]A=P\frac{r(1+r)^n}{(1+r)^n-1}[/tex]
Where P is the principle, r is the rate, n is the times of compound interest (monthly or quarterly etc.) .
Here P=$4250 r=13.25%, and n=24.
So according to the formula So, the finance charge= [tex]4250\frac{13.25(1+13.25)^{24}}{(1+13.25)^{24}-1}[/tex] = $ 611.20
The total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months is c) $611.20.
To calculate the total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months, we can use the following formula:
Total finance charge = Principal * (1 + Monthly interest rate)^Number of months - Principal
Where:
Principal is the amount of the loan ($4,250)
Monthly interest rate is the annual interest rate divided by 12 (13.25% / 12 = 1.1042%)
Number of months is the term of the loan in months (24)
Total finance charge = 4250 * (1 + 0.011042)^24 - 4250
Total finance charge = 611.20
Therefore, the answer is c. $611.20.
Note that this formula is for calculating the total finance charge over the entire term of the loan. If you want to calculate the monthly finance charge, you can simply divide the total finance charge by the number of months in the loan term. For example, the monthly finance charge for this loan would be $611.20 / 24 = $25.47.
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Which is a disadvantage of withdrawing more money than is available in a checking account?
Answers
A disadvantage of withdrawing more than you have in your account is you will be charged an overdraft fee.
What is an Overdraft Fee?An overdraft fee can be described as the fee your bank charges you when you make a withdrawal from your account beyond what you have in it.
An overdraft fee is one of the disadvantages of withdrawing more money than you have in your account..
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A radar gun used to determine the speed of passing cars must be within 7 mph of the actual speed of a selected car. If a highway patrol officer reads a speed of 59 mph for a car, does he have irrefutable evidence that the car was speeding in a 55 mph zone?
Answers
What is 1/4 as a whole number?
Answers
What is the difference of 54.59 and 26.61?
Answers
Do you know the answer???????? Help!!!!!
Answers
The area of a triangle is [tex]A _{t} = \frac{1}{2} (base)(height)[/tex], and we know from our figure that our triangle has base=10 feet and height=5 feet, so:
[tex]A_{t} = \frac{1}{2} (10feet)(5feet)[/tex]
[tex]A_{t} = 25feet^{2} [/tex]
The area of a rectangle is [tex]A_{r} =(length)(width)[/tex]. We have tow rectangles in our figure, so for our first one:
[tex]A _{r1} =(10feet)(1feet)[/tex]
[tex]A_{r1}=10feet^{2} [/tex]
for our second one:
[tex]A_{r2} =(8feet)(2feet)[/tex]
[tex]A_{r2} =16feet^{2} [/tex]
Now that we have the areas of all out figures, lets add them to find the area of the shaded region:
[tex]A _{total} =25feet^{2} +10feet^{2} +16feet^{2} [/tex]
[tex]A _{total} =51feet^{2} [/tex]
We can conclude that the area of the shaded region is 51 square feet.
If f(x)=7+4x and g(x)=1/2x What is the value of (f/g)(5)?
Answers
Answer:
[tex]\bigg(\displaystyle\frac{f}{g}\bigg)(5) = 270[/tex]
Step-by-step explanation:
We are given the following information in the question:
[tex]f(x) = 7 +4x\\\\g(x) = \displaystyle\frac{1}{2x}[/tex]
We have to find the values of [tex]\displaystyle\frac{f}{g}(x)[/tex]
[tex]\bigg(\displaystyle\frac{f}{g}\bigg)(x) = \frac{f(x)}{g(x)} = \frac{7 + 4x}{\frac{1}{2x}} = 2x(7+4x)[/tex]
Putting x = 5, we have:
[tex]\bigg(\displaystyle\frac{f}{g}\bigg)(x) = 2x(7+4x)\\\\\bigg(\displaystyle\frac{f}{g}\bigg)(5) = 2(5)(7+20)=270[/tex]
270 is the required value of [tex]\bigg(\displaystyle\frac{f}{g}\bigg)(5)[/tex].
if the parent function is square root x. describe the translation of of the fuction square root x-1
Answers
f(x)->f(x-h)+k
when the functions has been translated h units to the right, and k units up.
Compare with
sqrt(x)->sqrt(x-1)+0
we see that h=1, k=0.
Thus it is a horizontal translation of 1 unit to the right. (zero unit up).
Final answer:
The function √(x-1) is a horizontal translation of the function √x by 1 unit to the right along the x-axis.
Explanation:
The function √(x-1) represents a horizontal translation of the parent function √x. The translation is 1 unit to the right along the x-axis.
In function transformation terms, when a function f(x) is altered to become f(x - a), this translates the graph of the function to the right by 'a' units if 'a' is positive and to the left by 'a' units if 'a' is negative.
To illustrate, the graph of f(x) = √x is translated to become g(x) = √(x-1). Compared with the graph of f(x), every point on the graph of g(x) will be 1 unit to the right.
There are no changes vertically, so there is no translation up or down.
A triangle has side lengths of 8 inches, 12 inches, and 16 inches Determine whether this is a right triangle
Answers
Answer:
No, because 8^2+12^2 doesn't equal 16^2
Step-by-step explanation:
The triangle ABC is not a right angle triangle
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now , the measure of sides of the triangle are
The measure of side AB = 8 inches
The measure of side BC = 12 inches
The measure of side AC = 16 inches
Now , For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Substituting the values in the equation , we get
AC² = AB² + BC²
16² = 8² + 12²
256 ≠ 64 + 144
256 ≠ 208
Therefore , it does not satisfy Pythagoras relation
Hence , the triangle is not a right angle triangle
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which is equivalent to (9y2 – 4x)(9y2 + 4x), and what type of special product is it?
81y4 – 16x2, a perfect square trinomial
81y4 – 16x2, the difference of squares
81y4 – 72xy2 – 16x2, a perfect square trinomial
81y4 – 72xy2 – 16x2, the difference of squares
Answers
81y4 -16x, the difference of squares.
The expression (9y2 – 4x)(9y2 + 4x) is equivalent to 81y4 – 16x2, a difference of squares in mathematical terms.
Explanation:The expression you are asking about is equivalent to
81y4 – 16x2
, which is a special product known as
the difference of squares
. In mathematics, a difference of squares is a term that describes an expression of the form a^2 - b^2. It can be factored into the multiplication of two binomials: (a+b)(a-b). In your example, (9y2)^2 is 81y4 and (-2x)^2 is 16x2, so the final expression is 81y4 – 16x2.
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Which statement best compares -1/2 and -2 1/2
Answers
The Comparison between -1/2 and -2 1/2 is -1/2 is -2 more than -5/2.
What are fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
-1/2 and -2 1/2
So, -1/2 and -5/2.
So, the quantity -1/2 > -5/2
Also, -1/2 is -2 more than -5/2.
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HELP ME PLEASE! How is the graph of mc027-1.jpg related to its parent function, mc027-2.jpg?
Answers
The graph of [tex]y = \sqrt{-2x[/tex] relates to its parent function as a result of (d) horizontal compression by a factor of 2, and a reflection across the y-axis
What is a function transformation?A function transformation involves changing the form or equation of a function to another through reflection, dilation, translation or rotation
How to determine the function transformationThe parent function is given as:
[tex]y = \sqrt x[/tex]
Compress the function horizontally by a factor of 2, using the following rule
[tex](x,y) \to (2x,y)[/tex]
So, we have:
[tex]y = \sqrt {2x[/tex]
Next, reflect the function over the y-axis, using the following rule
[tex](x,y) \to (-x,y)[/tex]
So, we have:
[tex]y = \sqrt {-2x[/tex]
Hence, the function transformation is (d)
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Find the sum of the geometric series with a1 = -1, r = -2 And a10 = 512
Answers
[tex]S_n=a_1+a_2+\cdots+a_{n-1}+a_n[/tex]
[tex]S_n=a_1+ra_1+\cdots+r^{n-2}a_1+r^{n-1}a_1[/tex]
[tex]rS_n=ra_1+r^2a_1+\cdots+r^{n-1}a_1+r^na_1[/tex]
[tex]\implies S_n-rS_n=a_1-r^na_1\iff(1-r)S_n=(1-r^n)a_1\implies S_n=\dfrac{1-r^n}{1-r}a_1[/tex]
You're given that [tex]a_1=-1[/tex] and [tex]r=-2[/tex], so
[tex]S_n=\dfrac{1-(-2)^n}{1-(-2)}(-1)=-\dfrac{1-(-2)^n}3[/tex]
The fact that you're given [tex]a_{10}[/tex] makes me think you're supposed to find [tex]S_{10}[/tex], which is just a matter of setting [tex]n=10[/tex] in the formula above.
[tex]S_{10}=-\dfrac{1-(-2)^{10}}3=-\dfrac{1-1024}3=341[/tex]
Rearrange the formula A = P + Prt for t.
Answers
A=P+Prt
Solving for t.
Factor out P from the right side of the equation.
A=P(1+rt)
Divide both sides by P.
A/P= 1+rt
Subtract 1 from both sides
A/P-1=rt
Divide both sides by r.
(A/P) / r - 1/r= t
or
t= (A/P) / r - 1/r
t= A/Pr - 1/r
t= (A-P)/r
Answer: t= (A-P)/rP
In matrix T, what is the value of element t13?
Answers
in the matrix T the element t(13) refers to the element in row 1 and column 3
therefore
the answer is 7
Answer:
[tex]t_{13} =7[/tex]
Step-by-step explanation:
[tex]t_{13}[/tex] here 1 represents that it is in 1st row whereas 3 represents that it is in 3rd column so the element placed in 1st row and 3rd column is 7
therefore answer is
[tex]t_{13} =7[/tex]
What is the solution to 2log9(x)=log^9(8)+log9(x-2)
Answers
Log₉x² = log₉8 + log₉(x-2)
Log₉x² = log₉(8×(x-2))
Log₉x² = log₉8x-16
Log₉x² - log₉8x-16 = 0
Log₉(x²/(8x-16)) = 0
x²/(8x-16) = 9°
x² = 1 × 8x-16
x²-8x+16 = 0
x²-4x-4x+16 = 0
x(x-4)-4(x-4) = 0
(x-4)(x-4) =0
Therefore x = 4.....
Answer:
C. x=4
Step-by-step explanation:
The diameter of the base of a cylinder cookies is 8 inches. The volume of the cookie jar is 160 cubic inches. What is the height of the cookie jar?
Answers
To calculate the height of the cookie jar, we must use this formula.
FORMULA FOR HEIGHT:
H = V ÷ 3.14 × r × r
First, let's fine the radius. The radius of a circle is always half of the diameter. This means we must divide the diameter by 2.
r = d ÷ 2
r = 8 ÷ 2
r = 4 inches
The radius is 4 inches. Now, let's use the formula and find that height!
FORMULA:
H = V ÷ 3.14 × r × r
V = 160 cubic inches
Pi = 3.14
r = 4 inches
h = ?
First, square the radius.
160 = (3.14(4 × 4))h
160 = (3.14 (16))h
Now multiply that by pi.
160 = 50.24h
Finally, divide this by the volume:
160 ÷ 50.24 = 3.18 (Repeating Decimal)
Just round the repeating decimal to 3.2
A N S W E R:
The height of the cookie jar is about 3.2 inches.
what is the solution to -9×<63
Answers
I'm assuming that the multiplication sign is x.
When you are multiply something by x, you divide -9 on both sides. When you divide a negative number in an equality, you switch the signs.
x>-7 <== solution
I hope this helps!
~kaikers
Suppose that with a budget of $100, Deborah spends $60 on sushi and $40 on bagels when sushi costs $2 per piece and bagels cost $2 per bagel. But then, the price of bagels falls to $1 per bagel.
Answers
40 divided by 2 =20
and thats all i got xD
40/2=20
with a new price of that bagel drop is 50%
(40/40+60=80
and 20$ is the money that Deborah income reducing
Solve 4y - 8 -2y + 5 = 0
Answers
Solve 2x2 + x − 4 = 0. x2 + x + = 0
Answers
Answer:
1/2 and -2 are the first answers to the question
1/16 and 1/16 are the next answers
1/4 and 33/16 are the last ones
and for the multiple choice answer which is last is A
Step-by-step explanation:
To solve the quadratic equation 2x^2 + x - 4 = 0, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a). Substituting the given values into the formula, we find two solutions: x = (-1 ± √33) / 4.
Explanation:To solve the equation 2x2 + x - 4 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b2 - 4ac)) / (2a)
For our equation, a = 2, b = 1, and c = -4. Substituting these values into the formula, we have:
x = (-1 ± √(1 - 4(2)(-4))) / (2(2))
Simplifying further, we get two solutions: x = (-1 ± √33) / 4.
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Identify the type of correlation shown in the scatter plot
A. Positive Correlation
B. Negative Correlation
C. No correlation.
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what is the square root of 4 multiplied by 16
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the answer is 32.
The sum between two numbers is 170 and their difference is 110, what is the larger of the two numbers
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x - y = 110 Add these two equations.
2x = 280 Divide by 2
x = 280/2
x = 140