Answers
Answer:
Step-by-step explanation:
(a) We can find the position vectors of the points L, M, and N by taking the average of the position vectors of the points they lie between.
The midpoint of AB is given by:
N = (A + B)/2 = (41 + (41 + 21))/2 = (41 + 62)/2 = 51.5i
The midpoint of AD is given by:
L = (A + D)/2 = (41 + 6k)/2 = 23i + 3k
The midpoint of BD is given by:
M = (B + D)/2 = (41 + 21 + 6k)/2 = 31i + 3.5k
Now, we can find the vector MN by subtracting the position vectors of M and N:
MN = M - N = (31i + 3.5k) - (51.5i) = -20.5i + 3.5k
The angle between the directions of MN and OB can be found using the dot product:
cos(θ) = (MN . OB) / (|MN| * |OB|)
where θ is the angle between the two vectors. We can find the dot product and the magnitudes of the vectors as follows:
MN . OB = -20.5i + 3.5k . 41i + 21j = -20.5 * 41 + 3.5 * 21 = -847.5
|MN| = √((-20.5)^2 + (3.5)^2) = 21
|OB| = √(41^2 + 21^2) = √(1764) = 42
Substituting these values into the formula for cos(θ), we get:
cos(θ) = (-847.5) / (21 * 42) = -0.5
The angle θ can be found from the cosine inverse:
θ = cos^-1(-0.5) = 120 degrees
So, the angle between the directions of MN and OB is 120 degrees.
(b) To find the value of p, we can use the intersection of the lines through P and B and the lines through C and L. Let's call the intersection point R.
The line through P and B can be represented as P + t(B - P) = R
where t is a scalar and R is the position vector of the intersection point. Similarly, the line through C and L can be represented as:
C + s(L - C) = R
where s is a scalar. Setting these two expressions equal to each other, we get:
P + t(B - P) = C + s(L - C)
Expanding and simplifying, we get:
P + t(41i + 21j + 6k) = 21i + 6s(23i + 3k)
Comparing the i, j, and k components, we get:
P + 41t = 21 + 6s * 23
t = (21 - P)/41
6s = (P - 21)/23
s = (P - 21)/138
Substituting s back into the equation for C + s(L - C), we get:
C + (P - 21)/138 * (L - C) = R
21i + 6k + (P - 21)/138 * (23i + 3k - 6k) = R
Expanding, we get:
21i + 6k + (23/138) * Pi + (3/138) * k = R
Comparing the i and k components, we get:
21 + (23/138) * P = Ri
6 + (3/138) * P = Rk
Solving for P, we get:
P = 138 * (Ri - 21)/23 = 138 * (Rk - 6)/3
So the value of p for which the line through P and B intersects the line through C and L is given by the above formula.
Related Questions
100 points!!!!
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession
and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute the probability of each of the following events.
Event 4: The sum is greater than 6.
Event B: The sum is not divisible by 3 and not divisible by 6.
Round your answers to two decimal places.
Answers
There are 36 possible outcomes from rolling a die twice (or two dice once) and these result in sums from 2 to 12.
Possible ways to make a sum of 2: 1
Possible ways to make a sum of 3: 2
Possible ways to make a sum of 4: 3
Possible ways to make a sum of 5: 4
Possible ways to make a sum of 6: 5
Possible ways to make a sum of 7: 6
Possible ways to make a sum of 8: 5
Possible ways to make a sum of 9: 4
Possible ways to make a sum of 10: 3
Possible ways to make a sum of 11: 2
Possible ways to make a sum of 12: 1
This means there are 21 ways to make a sum greater than 6.
21/36 ≈ 58.33%
There are 24 ways to make sums that are not divisible by 3 and not divisible by 6. (Note that if a number isn't divisible by 3, it's also not divisible by 6, so that's a weird thing to include.)
24/36 ≈ 66.67%
sum of 2nd term of an infinite geometric series is -1/2 and the third term is 1/4 find the sum of series
Answers
Answer:
2
Step-by-step explanation:
1 plus 1 due to the characterisation of the number 1 increasing by 1 gives you 2
Find the circumference of a circle with a diameter of 8 inches
Answers
Answer:
B
Step-by-step explanation:
c=d*π
c=8*π
c=25.1 inches
Hope this helps! Please give brainliest!
Find the remaining trigonometric functions of 0 if
17
8
CSC 0 =
-
and cos > 0. Answer exactly.
Answers
Answer:
**DUE TOMORROW, NEED ANSWER ASAP**
NASA has asked you to evaluate a number of proposals for telescopes. These proposals include information about where the telescope would be built and what wavelengths it intends to observe at. Based only on these factors, evaluate whether NASA should consider funding each proposal. Justify your recommendations. (Some telescopes may have more than one "correct" answer depending on how you justify it).
a.) An ultraviolet telescope in space
b.) An optical telescope in a remote location in Michigan's upper peninsula
c.) A radio telescope in the Mojave desert in Arizona
d.) An x-ray telescope in the Andes mountains in Chile
e.) An optical telescope in space
Step-by-step explanation:
128 Sa se afle suma dintre produsul numerelor 45 250 şi 98 numer 100 000 şi 89 756.
Answers
45250 • 98 = 4434500
100000 • 89756 = 8975600000
4434500 + 8975600000 = 901994500
Trapezoid WXYZ is rotated about its center and then translated down and to the right to produce trapezoid h j KL the side WZ is 7 cm WX is 5 cm y z is 5 cm and XY is 9 cm how long is side LH
Answers
The length of side LH is given as follows:
LH = 7 cm.
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
This is relevant because the side lengths remain constant.
The equivalent side to side LH is given as follows:
WZ = 7 cm.
Hence the length of side LH is given as follows:
LH = 7 cm.
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The 2 triangles below are similar. Find the missing side. Use your notes to help you. In your answer, type out your proportion and the solution.
PLEASE HURRY !!
Answers
The length of side DF is 5 units.
Similar Triangles :If two figures possess the same shape but not necessarily the same size, they are considered to be similar. We may remark that all circles are similar as an example. Equilateral triangles and squares are similar to one another. Although similar figures need not be congruent, all congruent figures are similar.
Property 1:
Two triangles are similar if their respective sides have the same ratio and their corresponding angles are equal.
Property 2:
The corresponding angles of two similar triangles will have equal values . Equiangular triangles are what they are called.
Now by property 1,
The pairs of corresponding sides of similar traingles are proportional .
Therefore, in the given triangles,
[tex]\frac{BA}{ED} =\frac{AC}{DF}[/tex]
[tex]\frac{6}{3} =\frac{10}{x} \\\\x=5[/tex]
Hence, the value of x = 5 units.
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HelpThe ratio of the perimeters of two similar quadrilaterals is 2:4. What is the ratio of their areas? PLLLLLLLLLLSSSSSSss WILL GIVE 20 POINTS EASY
a.1:2
b. 4.8
c. 2:4
d. 4:16
e. 5:3
Answers
The below area rate can also be further answered as 14, since the supplied border rate can be further answered as 12. Their areas are compared 4/16.
What's meant by rate?
A rate in calculation displays how numerous times one number is contained in another. The rate of oranges to failures, for case, is eight to six if there are eight oranges and six failures in a coliseum of fruit. The proportions of oranges to the overall quantum of fruit are 814 for oranges and 68 for failures, independently. An equation in which two rates are made equal is known as a chance. As an illustration, you could express the rate as 1 3 if there's 1 joe and 3 girls( for every one boy there are 3 girls)Areas If the scale factor of the sides of two analogous polygons is m/ n
also the rate of the areas is (m/n)^2.
Area of analogous Polygons Theorem). Because area is a two- dimensional volume, you square the rate.
It's given that, the rate of peripheries of two analogous quadrilateral is 2 4
now,
to find the rate of area, we can take two quadrilaterals, say square.
Square ABCD of side 2 units and Square PQRS of side 4 units.
now rate of areas,
[tex]=\frac{area \ of\ square\ ABCD }{area \ of\ square\ PQRS }[/tex]
[tex]=\frac{2 \times 2}{4 \times 4}[/tex]
= 4/16
= 1/4
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helpppp ASAP.
1. What is the height of the cone? Explain how you found the height. (4 points)
2. Now that you have the height of the cone, how can you solve for the slant height, s? (3 points)
3. How far does the ant crawl to get from the base of the cone to the top of the hill? Show your work. (3 points)
Answers
1. The height of the cone is, 22.18 mm.
2. The slant height is, 28.14 mm.
3. The ant crawl to get from the base of the cone to the top of the hill is, 28.14 mm.
What is Volume?In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.
The volume of cone V = (1/3)πr²h
Given that,
The volume = 8792 mm³
1. by using the formula to solve for h,
we get h = (3V)/(πr²).
Plugging in the values given,
we have h = (3(8792 mm³))/(π(20 mm)²) ≈ 22.18 mm.
Therefore, the height of the cone is approximately 22.18 mm.
2. it is known that, from the Pythagoras theorem
s² = h² + r²,
where s is the slant height, h is the height, and r is the radius.
Plugging in the values we found in part 1,
we have s² = (22.18 mm)² + (20 mm)² ≈ 791.88 mm².
Taking the square root of both sides, we get s ≈ 28.14 mm.
Therefore, the slant height is approximately 28.14 mm.
3. To find the distance the ant crawls to get from the base of the cone to the top of the hill, we need to find the length of the slant height.
Using the value we found in part 2,
the length of the slant height is approximately 28.14 mm.
Therefore, that is the distance the ant would crawl to get from the base of the cone to the top of the hill.
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Examine the figure below, solve for a, round to the nearest whole number.
Answers
26 is the value of a from the given figure.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
We need to find the value of a from the figure.
∠D is 46 degrees.
AD is 28, AT is 37
CosD=Adjacent side/ Hypotenuse
Cos46=a/37
0.695=a/37
a=0.697×37
a=26
Hence, the value of a is 26
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what is the inequality shown
Answers
The inequality on the graph is written as:
-4 < x ≤ 5
What is the inequality shown on the number line?
Here we have an inequality graphed on a number line.
First, we can see that we have an open circle at x = -4 and then the line goes to the right.
That means that the value of x must be larger than -4, so we can start by writting:
-4 < x
Then we have a closed circle at x = 5.
That means that x can be smaller or equal to 5, then:
x ≤ 5
Then the inequality is:
-4 < x ≤ 5
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NEED HELP!!!!!!!!!!!
Answers
Answer:
[tex]4x^{2} y^{3}[/tex]
Step-by-step explanation:
[tex]\frac{36x^{4}y^{5}}{(3xy)^{2}}[/tex]
In the denominator, all the terms in the brackets or parenthesis will be squared:
= [tex]\frac{36x^{4}y^{5}}{9x^{2} y^{2}}[/tex]
Law of indices is applied:
[tex]\frac{a^{n}}{a^{m}}[/tex]= [tex]a^{n - m}[/tex]
= [tex]4x^{4 - 2} y^{5 - 2}[/tex]
= [tex]4x^{2} y^{3}[/tex]
∴Option B
The polynomial function f(x) = x³ - 4x²-3x + 18 has (x+2) as one of its linear factors. Use long division to find the other linear factors.
Separate multiple factors with a comma. If there are any repeated factors, only write them once.
Answers
The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).
What is a polynomial ?
A polynomial is a mathematical expression involving a sum of powers in one or more variables (indeterminates) multiplied by coefficients.
where n is a non-negative integer (the degree of the polynomial), x is the variable, and (the coefficients of the polynomial). The highest power of x in the expression is n, and this term is called the leading term. The coefficient of the leading term, a_n, is called the leading coefficient.
To find the other linear factors of the polynomial function f(x) = x³ - 4x² - 3x + 18, we can use long division by dividing the polynomial function by (x + 2).
Here's how the long division would look like:
x³ - 4x² - 3x + 18
÷ x + 2
__________________________
x² - 6x - 20
÷ x + 2
__________________________
x - 22
÷ x + 2
__________________________
-20
here -20 is the remainder.
The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).
So, the other linear factors are x - 22.
Therefore, The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).
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7) Given the geometric sequence
9, 3, 1, 1/3, ...
What is the sum of the first 8 terms?
Answers
The sum of the first 8 terms is 13.5
What is the sum of the first 8 terms?From the question, we have the following parameters that can be used in our computation:
9, 3, 1, 1/3, ...
Using the above as a guide, we have the following:
First term, a = 9
Common ratio, r = 1/3
The sum of GP (of n terms) is calculated as
Sum = Sn = a(r^n - 1) / (r - 1)
substitute the known values in the above equation, so, we have the following representation
Sum = 9 * ((1/3)^8 - 1)/((1/3) - 1)
Evaluate
Sum = 13.5
Hence, the sum is 13.5
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(a) The perimeter of a rectangular parking lot is 330 m.
If the length of the parking lot is 92 m, what is its width?
Answers
Answer: Width = 73 m
Step-by-step explanation:
Perimeter = Length(2) + Width(2)
330 - (92 x 2)
330 - 184 = 146
146 = Width of 2 sides
146/2 = 73 m
Help me with this question
Answers
The volume of the cylinder will be 666 cubic centimeters. Then the correct option is D.
What is the volume?Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.
The radius and height of the cone and the cylinder are the same. Then the ratio of the volume of the cylinder to the volume of the cone is 3. Then we have
(Volume of the cylinder) / (Volume of the Cone) = 3
Volume of the cylinder / 222 = 3
Volume of the cylinder = 666 cubic cm
The volume of the cylinder will be 666 cubic centimeters. Then the correct option is D.
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In right triangle ABC, m∠A=90 ∘ , cos B=x+0.26, and sin C=3x+0.14. Solve for x.
Answers
In right triangle ABC, the value of x is equal to 0.06.
What is a right angle?In Mathematics, a right angle can be defined as a type of angle that is formed in a triangle by the intersection of two (2) straight lines at 90 degrees. This ultimately implies that, a right angled triangle has a measure of 90 degrees.
Since the angle formed by side A is a right triangle, we have the following complementary angles;
C + B = 90
sin(C) = cos(B)
x + 0.26 = 3x + 0.14
3x - x = 0.26 - 0.14
2x = 0.12
x = 0.12/2
x = 0.06
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A boat has a top speed of 26 knots and a displacement of approximately 93,000 tons. Express the top speed in miles per hour and the displacement in metric tons
Answers
The boat's displacement is approximately 84,016.8 metric tons.
How to convert from knots to miles?To convert the boat's top speed from knots to miles per hour, we can use the conversion factor of 1.15078 miles per hour per knot:
26 knots × 1.15078 miles per hour per knot = 29.86 miles per hour (rounded to two decimal places)
Therefore, the boat's top speed is approximately 29.86 miles per hour.
To convert the boat's displacement from tons to metric tons, we can use the conversion factor of 0.907185 metric tons per ton:
93,000 tons × 0.907185 metric tons per ton = 84,016.8 metric tons (rounded to one decimal place)
Therefore, the boat's displacement is approximately 84,016.8 metric tons.
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A credit car company charges 7% simple
interest. What is the total interest on a $1,900
loan at the end of the two years?
Answers
Answer: 266
Step-by-step explanation:
I = prt
p= 1900
r=.07
t=2
1900x.07x2=266
A business puchases a computer system for $3,000. The value of the system decreases at a rate of 15% per year. Write an exponentioal function to model this situation. Then determine how much the comoputer will be work after 3 years
Answers
Value of system after 'x' years = [tex]3000*(0.85)^x[/tex]
The value of the computer after 3 years is $1842.375
What is an exponential function?The formula for an exponential function is f(x) =[tex]a^x[/tex], where 'x' is variable and 'a' is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
Given that, computer system values at $3000 decrease at a rate of 15% each year.
If the value decreases by 15%, it means that the new value is 85% of the old value.
new value = old value * (85/100)
new value = old value * 0.85
value in 1st year = $3000
value after 1st year = $3000 * 0.85
value after 2nd year = $3000 * 0.85 * 0.85
value after nth year = $3000 * [tex]0.85^n[/tex]
Value of the system after 3 years = $3000 * [tex]0.85^3[/tex]
= $3000 * 0.614125
= $1842.375
Therefore, The value of the computer system after 3 years is $1842.375
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If x=3. what is y=?
Y=
X: -3 0 3 6
Y: -5 -4 -3 -3
Answers
Answer:
Step-by-step explanation:
y = -3
A bee weighs 2.5 x 10-4 pounds. A
moose weighs 1.25 × 10³ pounds.
How many bees would equal the
weight of a moose? (Give your
answer in standard form.)
Answers
The number of bees that will equal the mass of a single moose is 5 × 10⁶.
How many bees would equal the weight of a moose?Given the data in the question;
Mass of one bee = 2.5 × 10⁻⁴ poundsMass of one moose = 1.25 × 10³ poundsTo determine the number of bees that will equal the mass of a single moose.
Let the number be represented by x.
Hence;
Number of bees × mass of bee = mass of moose
n × ( 2.5 × 10⁻⁴ ) = 1.25 × 10³
Divide both sides by ( 2.5 × 10⁻⁴ ).
n = ( 1.25 × 10³ ) / ( 2.5 × 10⁻⁴ )
n = 1250 / 0.00025
n = 5,000,000
Therefore, the number of bees is 5,000,000.
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a toy manufacturer needs a piece of plastic in the shape of a right triangle with one leg 5 cm longer than the other and the hypotenuse 10 cm longer than the shorter leg. what is the perimeter of the triangle
Answers
The triangle's perimeter is roughly 25.29 cm.
In arithmetic, what is perimeter?The area around a form's edge is known as its perimeter. The perimeter of various forms can be calculated by summing the lengths of their sides.
Let's call the right triangle's shorter leg "x" for short.
The longer leg is then 5 cm longer than x, or x + 5, according to the situation.
The hypotenuse measures x + 10 cm longer than x.
By the Pythagorean theorem, we know that:
x² + (x+5)² = (x+10)²
Expanding and simplifying this equation gives:
2x² + 10x - 75 = 0
Dividing both sides by 2 gives:
x² + 5x - 37.5 = 0
We can find the value of x by using the quadratic formula:
x = (-5 ± sqrt(5² - 4(1)(-37.5))) / 2
x = (-5 ± sqrt(175)) / 2
x ≈ -8.68 or x ≈ 3.43
Since x represents a length, we must choose the positive solution x = 3.43 cm.
Therefore, the shorter leg of the triangle is 3.43 cm, the longer leg is 8.43 cm (3.43 + 5), and the hypotenuse is 13.43 cm (3.43 + 10). The perimeter of the triangle is the sum of the three sides, which is:
3.43 + 8.43 + 13.43 = 25.29 cm
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tyrone runs 1 1/4 miles in 8 1/2 minutes how many miles can he run in 20 minutes
Answers
Answer:
2 [tex]\frac{16}{17}[/tex] miles
Step-by-step explanation:
[tex]\frac{miles}{minutes}[/tex] = [tex]\frac{miles}{minutes}[/tex]
[tex]\frac{1 1/4}{8 1/2}[/tex] = [tex]\frac{x}{20}[/tex]
1 [tex]\frac{1}{4}[/tex] is the same as [tex]\frac{4}{4}[/tex] + [tex]\frac{1}{4}[/tex] (1 = [tex]\frac{4}{4}[/tex] )
8 [tex]\frac{1}{2}[/tex] is the same as [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{17}{2}[/tex] (1 = [tex]\frac{2}{2}[/tex])
[tex]\frac{\frac{5}{4} }{\frac{17}{2} }[/tex] = [tex]\frac{x}{20}[/tex]
[tex]\frac{17}{2}[/tex] x = 20 multiply both sides by [tex]\frac{2}{17}[/tex]
[tex]\frac{2}{17}[/tex] [tex](\frac{17}{2})[/tex]x = [tex]\frac{2}{17}[/tex][tex](\frac{20}{1})[/tex]
x = [tex]\frac{40}{17}[/tex]
[tex]\frac{5}{4}[/tex] [tex](\frac{40}{17})[/tex] = x
[tex]\frac{50}{17}[/tex] or 2 [tex]\frac{16}{17}[/tex]
Can someone please help me with this question please
Answers
Answer:
77.5°
Step-by-step explanation:
You want the measures of the angles formed when ray OX bisects the 155° angle AOB.
BisectorThe angle bisector creates two equal angles, each of which is half the measure of the original angle. The measures of the angles formed are ...
155°/2 = 77.5°
Identify the y- intercept of the graph below
b= -4
b=6
b=4
b= -10
Answers
This is where the line crosses the y axis, or point ( 0, 4 ).
Devaughn is 8 years older than Sydney. The sum of their ages is 94. What is Sydney's age?
Answers
Answer:
Step-by-step explanation:
S+8=D
S+D equals 94.
94/2= 45+2=47
47-8=39
Sydney is 39
Answer:
43
Step-by-step explanation:
94-8= 86
86/2= 43
43+8= 51
a:43
prove it :
51+43= 94
Proper subset is a set that contains elements contained in another set but not equal
to that set.
True or false
Answers
Answer: A proper subset of a set A is a subset of A that is not equal to A
Step-by-step explanation:
(9+w) (2w+3)=0
If there is more than one solution, please seperate with commas
Answers
2w^2+21w+27=0
the table shows the rate at which justin can make widgets. how many widgets can justin make in 36 minutes?
Answers
The number of widgets that Justin can make in 36 minutes is given as follows:
y = 36k.
In which the constant k is the number of widgets that can be made per minute, and is obtained dividing a value of y by it's respective value of x from the table.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
The variables for this problem are given as follows:
Input x: number of minutes.Output y: number of widgets.The constant is obtained as follows:
k = y/x.
For a time of 36 minutes, we have that x = 36, hence the number of widgets is given as follows:
y = 36k.
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