The vector [tex]\( \mathbf{v} = 6\mathbf{i} - 3\mathbf{j} \)[/tex].
Its magnitude is [tex]\( \sqrt{45} \)[/tex] in reduced radical form.
To find vector [tex]\( \mathbf{v} \)[/tex] from point [tex]\( P_1 \)[/tex] to point [tex]\( P_2 \)[/tex], we subtract the coordinates of [tex]\( P_1 \)[/tex] from the coordinates of [tex]\( P_2 \)[/tex]:
[tex]\[\mathbf{v} = \begin{pmatrix} x_2 - x_1 \\ y_2 - y_1 \end{pmatrix}\][/tex]
Given [tex]\( P_1 = (-2, 5) \) and \( P_2 = (4, 2) \), we can calculate \( \mathbf{v} \):[/tex]
[tex]\[\mathbf{v} = \begin{pmatrix} 4 - (-2) \\ 2 - 5 \end{pmatrix} = \begin{pmatrix} 6 \\ -3 \end{pmatrix}\][/tex]
So, [tex]\( \mathbf{v} = 6\mathbf{i} - 3\mathbf{j} \)[/tex].
To find the magnitude of [tex]\( \mathbf{v} \)[/tex], we use the formula:
[tex]\[|\mathbf{v}| = \sqrt{v_x^2 + v_y^2}\][/tex]
Where [tex]\( v_x \)[/tex] and [tex]\( v_y \)[/tex] are the components of [tex]\( \mathbf{v} \)[/tex]
For [tex]\( \mathbf{v} = 6\mathbf{i} - 3\mathbf{j} \), \( v_x = 6 \) and \( v_y = -3 \)[/tex]:
[tex]\[|\mathbf{v}| = \sqrt{(6)^2 + (-3)^2} = \sqrt{36 + 9} = \sqrt{45}\[/tex]
Thus, the magnitude of vector [tex]\( \mathbf{v} \) is \( \sqrt{45} \)[/tex] in reduced radical form.
Correct question is:
Let v be the vector from initial point P1 to terminal point P2.
Write v in terms of i and j, and find the magnitude of vector v.
Leave the magnitude in reduced radical form.
P1 = (-2,5) , P2 = (4,2)
Miguel has an aquarium in the shape of a rectangular prism. The base is 30.25 inches long and 12.5 inches wide. The aquarium is 12.75 inches high. What is the volume of the aquarium to the nearest cubic inches?
The result of 4,816.40625 cubic inches is rounded to 4,816 cubic inches to the nearest cubic inch.
To find the volume of Miguel's aquarium, which is in the shape of a rectangular prism, we use the formula for the volume of a rectangular prism:
Volume = length * width * height
In this case, the length is 30.25 inches, the width is 12.5 inches, and the height is 12.75 inches.
So, the calculation for the volume would be:
Volume = 30.25 inches * 12.5 inches * 12.75 inches
= 4,816.40625 cubic inches.
Rounding to the nearest cubic inch, the volume of the aquarium is 4,816 cubic inches.
For a circle with a diameter of 6 meters, what is the measurement of a central angle (in degrees) subtended by an arc with a length of 7 3 π meters?
Answer : The measurement of a central angle is, [tex]140^o[/tex]
Step-by-step explanation :
Formula used for angle subtended by an arc is:
[tex]s=\frac{\pi r\theta}{180}[/tex]
where,
s = arc length = [tex]\frac{7}{3}\pi m[/tex]
r = radius = [tex]\frac{diameter}{2}=\frac{6m}{2}=3m[/tex]
Now put all the given values in the above formula, we get:
[tex]s=\frac{\pi r\theta}{180}[/tex]
[tex]\frac{7}{3}\pi=\frac{\pi \times (3)\times \theta}{180}[/tex]
[tex]\theta =140^o[/tex]
Thus, the measurement of a central angle is, [tex]140^o[/tex]
round 149,640 to the nearest thousand.
And issue of a magazine contain the following statement dropping less than 2 inches per mile after emerging from the mountains a river drains into the ocean 1 days discharge at its mouth for trillion gallons could supply all of country as household for 5 months based on this statement determine how much water and average household uses each month assume that there are 200 million household in country a country a used approximately how many gallons per household per month
There are 24 different tables to set up for field day.The principal wants the tables set up in equal rows.should she use 3 rows or 5 rows?Explain
A landscape designer has a drawing of a flower bed that measures 6inches by 9 inches. The owner wants the actual flower bed to be 5 feet by 7.5 feet. What is the scale factor the designer must use to install the new flower bed
Let P be the point (1,1,-2). Suppose that the point P0(2, -5, 2) is 1/5 of the way from P to Q. Find the point Q.
what is the volume of a box that can fit exactly 128 1/8 inch cubes with 1/2 inch sides?
A piece of solid, spherical glass has a circumference of 18.84 centimeters. The sphere is cut in half, creating two identical hemispheres. Using 3.14 for π, Tran computes the amount of paint needed to cover the sphere. Which statement about the amount of paint found by Tran is true?
Tran found the minimum amount of paint needed to cover the curved surface of a hemisphere
Tran found the minimum amount of paint needed to cover the entire surface of one of the hemispheres.
Tran found the minimum amount of paint needed to cover both hemispheres.
Tran found the minimum amount of paint needed to cover the bases of both hemispheres.
Final answer:
Tran must calculate the surface area of the hemisphere, including the base, to determine the amount of paint needed, which is the sum of half the surface area of the sphere and the area of the base.
Explanation:
The question is asking what Tran would compute when using π to determine the amount of paint required for a hemisphere. First, Tran needs to calculate the surface area of the sphere to determine the paint needed. Given the circumference C = 18.84 cm, the radius r can be found using C = 2πr, which gives us a radius of r = C / (2π). Once we have the radius, we can find the surface area A of the sphere using A = 4πr², which is necessary to determine the paint needed for the outer surface.
However, when the sphere is cut into two hemispheres, the flat face of each hemisphere (base) also needs paint. The area of the base is a circle with an area of πr². Thus, the total surface area that Tran would need to paint for one hemisphere, including the base, is πr² + 2πr² (half of the sphere's surface area).
Final answer:
Option D.) Tran found the minimum amount of paint needed to cover both hemispheres.
Explanation:
Tran found the minimum amount of paint needed to cover both hemispheres. To calculate the amount of paint needed to cover a hemisphere, we need to find the surface area of the hemisphere. The formula for the surface area of a sphere is 4πr², where r is the radius.
Given that the circumference of the sphere is 18.84 centimeters, we can use the formula C = 2πr to solve for the radius. Plugging in the value for C, we get 18.84 = 2πr.
Simplifying the equation, we find that the radius of the sphere is approximately 3 centimeters.
The surface area of a hemisphere is half the surface area of a sphere, so the surface area of one hemisphere is 2πr²/2 = πr².
Substituting the value of r, we find that the surface area of one hemisphere is approximately 9π square centimeters.
Since Tran cut the sphere in half and created two identical hemispheres, the minimum amount of paint needed to cover both hemispheres would be twice the surface area of one hemisphere, which is approximately 18π square centimeters.
Look at this cube and its net. Cube with one side labeled 8 centimeters. Net of the same cube also shown with one side labeled 8 centimeters. What is the surface area of this cube? cm²
A rectangle is dilated by a scale factor of 4.
a) The original rectangle is 8 cm by 3 cm. What are the dimensions of the new rectangle?
b) Is the new image a reduction or enlargement? Explain.
When p2 – 4p is subtracted from p2 + p – 6, the result is 5p-6 To get p – 9, subtract
Subtract p² - 4p from p² + p - 6 to get 5p - 6. To obtain p - 9, subtract 15 from 5p - 6.
Let's break it down step by step:
1. Subtracting p² - 4p from p² + p - 6:
Start by writing down the expression p² + p - 6.
Now, subtract p² - 4p from it term by term.
(p² + p - 6) - (p² - 4p)
2. Expand and Simplify:
Distribute the subtraction across each term inside the parentheses:
p² + p - 6 - p² + 4p
This simplifies to: (p² - p²) + (p + 4p) - 6
= 0 + 5p - 6
= 5p - 6
3. Now, to get p - 9:
We want to manipulate 5p - 6 to p - 9.
Subtracting 15 from 5p - 6 gives:
5p - 6 - 15
= 5p - 21
Therefore, subtracting 5p - 21 from 5p - 6 results in p - 9.
least common denominator for 1/49 1/21 1/3
Suppose you toss a coin 100 times and get 69 heads and 31 tails. based on these results, what is the probability that the next flip results in a tail?
a 5 inch tall bamboo shoot doubles in height every 3 days. if the equation, y=ab^x where x is the number of doubling periods, represents the height of the bamboo shot, what are the values of a and b?
what is −1.6+(−2.4)?
Which values of x will make the absolute value equation true? |x – 3| = 40
A. {–43, –37}
B. {43, –37}
C. {40, –40}
D. {43, 37}
The values of x that satisfy the absolute value equation |x – 3| = 40 are 43 and -37. These are derived from solving the two possible scenarios for absolute value equations, resulting in a positive and a negative solution.
Explanation:To find which values of x will make the absolute value equation |x – 3| = 40 true, we need to consider both the positive and negative scenarios that can result from the absolute value. The absolute value of a number equals the number itself if it is positive or zero, and it equals the negative of the number if it is negative.
So, we set up two equations:
x - 3 = 40 (when x – 3 is non-negative)x - 3 = -40 (when x – 3 is negative)Solving the first equation for x, we add 3 to both sides:
x = 40 + 3
x = 43
Solving the second equation for x, we add 3 to both sides:
x = -40 + 3
x = -37
Therefore, the values of x that will satisfy the equation are 43 and -37. Option D is the correct answer.
Final answer:
The values of x that make the absolute value equation true are 43 and -37.
Explanation:
To solve the equation |x-3| = 40, we need to consider two cases:
1. x-3 = 40: In this case, we add 3 to both sides to isolate x and get x = 43.
2. -(x-3) = 40: In this case, we distribute the negative sign and add 3 to both sides to isolate x, which gives x = -37.
Therefore, the values of x that make the absolute value equation true are {43, -37}.
silvio earns 10% for each car sale he makes while working at a used car dealership. If he sells a used car for $2,000 what is his commission
If silvio earns 10% for each car sale he makes while working at a used car dealership then he earns $200 as commission for selling car for $2,000.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that silvio earns 10% for each car sale he makes while working at a used car dealership.
silvio sells a used car for $2,000.
We have to find the commission earned by Silvio.
We have to calculate 10% of $2000 to find the commission.
Convert 10% to decimal value by dividing with 100.
commission = 10% of $2000
commission = 0.1 x $2000
commission = $200
Hence, if silvio earns 10% for each car sale he makes while working at a used car dealership then he earns $200 as commission for selling car for $2,000.
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does 6% of a pound weigh more than an ounce
Answer:
6% of a pound does not weigh more than 1 ounce.
Step-by-step explanation:
First, we will calculate 6% (0.06) of 1 pound.
0.06 × 1 lb = 0.06 lb
1 pound is equal to 16 ounces. 0.06 pounds, expressed in ounces is:
0.06 lb × (16 oz/ 1 lb) = 0.96 oz
6% of a pound = 0.96 oz
0.96 oz < 1 oz
Due to the transitive property, we can affirm that 6% of a pound does not weigh more than 1 ounce.
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Anita owns a beauty supply store. Every two weeks she receives a supply of shampoo. Every four weeks she receives a carton of nail polishes. Every eight weeks she receives a box of combs, and every twelve weeks she receives a box of hair dyes. If Anita received a shipment of all these supplies today, when is the next time all four supplies will arrive on the same day?
A person's website specializes in the sale of rare or unusual vegetable seeds. he sells packets of sweet-pepper seeds for $2.32 each and packets of hot-pepper seeds for $4.40 each. he also offers a 16-packet mixed pepper assortment combining packets of both types of seeds at $2.58 per packet. how many packets of each type of seed are in the assortment?
You estimate the distance from your house to your school to be 1.6 miles. The actual distance is 1.9 miles. Find the percent error. Round your answer to the nearest tenth of a percent.
Final answer:
The percent error of the estimated distance from your house to school is 15.8% when rounded to the nearest tenth.
Explanation:
To find the percent error of your estimate, you use the formula:
Error = (|Estimated value - Actual value| / Actual value) × 100
Plugging the values from your question:
Error = (|1.6 miles - 1.9 miles| / 1.9 miles) × 100
Error = (|-0.3 miles| / 1.9 miles) × 100
Error = (0.3 miles / 1.9 miles) × 100
Error = 0.15789473684 × 100
Error = 15.789473684%
When rounded to the nearest tenth of a percent, the percent error is 15.8%.
Help pleaseeeeeeeeeeeeeeeeee
A thermometer is removed from a room where the temperature is 70° f and is taken outside, where the air temperature is 30° f. after one-half minute the thermometer reads 50° f. what is the reading of the thermometer at t = 1 min? (round your answer to two decimal places.)
Find the domain and range of the relation and determine whether it is a function.
a. domain: all real numbers; range: all real numbers; Yes, it is a function.
b. domain: positive integers; range: positive integers; No, it is not a function.
c. domain: x ≥ 0; range: y > 3; No, it is not a function.
d. domain: x > 3; range: y > 0; Yes, it is a function.
Using function concepts, it is found that the correct option is:
d. domain: x > 3; range: y > 0; Yes, it is a function.
A relation is a function if for each value of the input, there is only one respective value of the output. In a graph, it means that for each value of x, there is only one respective value of y.
In this graph, there is only one value of y for each value of x, hence, it is a function.The domain of a function is the set that contains all possible input values. In a graph, it is the values assumed by x, the horizontal axis.
In this graph, x assumes values greater than 3, hence the domain is x > 3.The range of a function is the set that contains all possible output values. In a graph, it is the values assumed by y, the vertical axis.
In this graph, y assumes values greater than 0, hence the range is y > 0.A similar problem is given at https://brainly.com/question/10891721
One leg of an isosceles right triangle measures 5 inches. Rounded to the nearest tenth, what is the approximate length of the hypotenuse? 2.5 inches 5.0 inches 7.1 inches 9.8 inches
Answer: 7.1 inches
Step-by-step explanation:
Given: One leg of isosceles right triangle = 5 inches
Since in isosceles right triangle , two sides have same side length , therefore the length of the other leg should be 5 inches.
Let H be the hypotenuse of the isosceles right triangle
Now, by Pythagoras Theorem , we have
[tex]H^2=5^2+5^2=25+25=50\\\\\Rightarrow\ H=\sqrt{50}=5\sqrt{2}\\\\\Rightarrow\ H==5\times(1.41421356237)\\\\\Rightarrow\ H==7.07106781187\approx7.1\ inches[/tex]
Hence, the approximate length of the hypotenuse = 7.1 inches
Answer: C
Step-by-step explanation: 7.1 inches
One side of a triangle is increasing at a rate of 9 cm/s and a second side is decreasing at a rate of 2 cm/s. if the area of the triangle remains constant, at what rate does the angle between the sides change when the first side is 21 cm long, the second side is 36 cm, and the angle is π/6? (round your answer to three decimal places.)
The rate at which the angle between the sides of the triangle is changing is 4/9 radians per second.
Explanation:In this problem, we are given that one side of the triangle is increasing at a rate of 9 cm/s and a second side is decreasing at a rate of 2 cm/s. We need to find the rate at which the angle between the sides is changing.
To solve this, we can use the formula:
angle_rate = (-side2_rate/side1)*(cos(angle))/(sin(angle))
Substituting the given values:
angle_rate = (-(-2)/9)*(cos(π/6))/(sin(π/6))
Simplifying, we get:
angle_rate = 4/9
Therefore, the rate at which the angle between the sides is changing is 4/9 radians per second.
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Two numbers add to 336 and the first is 124 bigger than the second. What are the two numbers?
Final answer:
To solve the problem, a system of equations is set up with the second number as 'x' and the first as 'x + 124.' The equations are simplified to find 'x = 106,' which makes the first number '230.' The two numbers are 106 and 230.
Explanation:
To find the two numbers that add to 336 and where the first number is 124 larger than the second, we need to set up a system of equations based on the information given:
Let the second number be x.
Then the first number will be x + 124 since it is 124 bigger than the second.
The sum of the two numbers is 336, so we can write the equation x + (x + 124) = 336.
Simplifying this equation, we get 2x + 124 = 336.
Subtract 124 from both sides to isolate the term with x, yielding 2x = 212.
Divide both sides by 2 to find x, which gives x = 106.
Since the first number is 124 larger, we add 124 to 106, resulting in the first number being 230.
Therefore, the two numbers are 106 and 230.
If w is inversely proportional to the square of v, and w=3 when v=6, fund w when v=3
The measure of DF is 108. What is the measure of DEF, the tangent-chord angle?
Answer:
The measure of DE is 108°. What is the measure of ZDEF, the tangent-chord angle?
54
Step-by-step explanation: