The direction cosines of the vector r with direction angles α, β, γ to the x, y and z axis are
cosα = x/r = 3√2/10cosβ = y/r = 4√2/10 and cosγ = z/r = √2/2So, the direction angles are
α = cos⁻¹(x/r) = cos⁻¹(3√2/10) = 64.9°β = cos⁻¹(y/r) = cos⁻¹(4√2/10) = 55.6° and γ = cos⁻¹(z/r) = cos⁻¹(√2/2) = 45°How to find the direction cosines and direction angles of the vector?Given a vector r = xi + yj + zk where
x, y and z are the components of the vector in the x, y and z directions. and r = √(x² + y² + z²)The direction cosines of the vector r with direction angles α, β, γ to the x, y and z axis are
cosα = x/r, cosβ = y/r and cosγ = z/rSo, their direction angles are
α = cos⁻¹(x/r), β = cos⁻¹(y/r) and γ = cos⁻¹(z/r)As an example, let r = 3i + 4j + 5k
So, r = √(x² + y² + z²)
= √(3² + 4² + 5²)
= √(9 + 16 + 25)
= √50
= 5√2
The direction cosines of the vector r with direction angles α, β, γ to the x, y and z axis are
cosα = x/r = 3/5√2 = 3√2/10cosβ = y/r = 4/5√2 = 4√2/10 and cosγ = z/r = 5/5√2 = 1/√2 = √2/2So, the direction angles are
α = cos⁻¹(x/r) = cos⁻¹(3√2/10) = cos⁻¹(0.4243) = 64.9°β = cos⁻¹(y/r) = cos⁻¹(4√2/10) = cos⁻¹(0.5657) = 55.6° and γ = cos⁻¹(z/r) = cos⁻¹(√2/2) = cos⁻¹(0.5657) = 45°Learn more about direction cosine here:
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A law clerk has earned no less than $25,000 since being hired.
Answer:
A. s ≥ 25,000
Hope this helps :)
The law clerk can earn $25,000 or more since being hired.
Solve inequality.
t+8 ≥ 19
To solve the inequality, subtract 8 from both sides. The solution is t ≥ 11 or [11, ∞)
Tips to solve linear inequalities:
Isolate the variable on one side by using subtraction or addition. Subtraction and addition will not change the inequality.Use division or multiplication to find the solution. Multiplication and division by a positive number will not the inequality. However, if we multiply or divide both sides with a negative number, we need to flip the inequality direction.Interval notation is often used for the solution(s). Recall the differences between a bracket [ or ], and a parenthesis ( or ). A bracket means the endpoint is included in the solution while a parenthesis means the endpoint is not included in the solution. Remember, infinity ∞ always use a parenthesis.
Example: x ≥ 2 can be written as [2, ∞), while
x > 0 is written as (2, ∞)
The given problem:
t+8 ≥ 19
Subtract 8 from both sides. Subtracting a number from both sides will not change the inequality. Hence,
t+8 - 8 ≥ 19 - 8
t ≥ 11
Using the interval notation, the solution is [11, ∞)
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The approximate weights of two animals are 4.23 x 103 lbs. and 8.7 x 103 lbs. find the total weight of the two animals. write the final answer in scientific notation with the correct number of significant digits.
The total weight of two animals in scientific notation is 1.3 x 10⁴ lbs.
Scientific Notation:
A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
For example,
650,000,000 can be written in scientific notation as 6.5 ✕ 10⁸.
Given,
The approximate weights of two animals are 4.23 x 10³ lbs. and 8.7 x 10³ lbs.
Here we need to find the total weight of the two animals and we need to write the final answer in scientific notation with the correct number of significant digits.
The total weight of the two animals is calculated as
Total weight = Animal 1 + Animal 2
So,
Total weight = 4.23 x 10³ lbs + 8.7 x 10³ lbs.
Take 10³ lbs as the common term,
Then we get,
Total weight = (4.23 + 8.7) x 10³ lbs.
Total weight = 12.93 x 10³ lbs.
It can we rewritten as,
Total weight = 1.293 x 10⁴ lbs.
When we round off it, then we get,
Total weight = 1.3 x 10⁴ lbs.
Hence, the total weight of the two animals is 1.3 x 10⁴ lbs.
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Andre Marshall is paid 10$per hour for a 40 hour work week
Answer:
$400???
Step-by-step explanation:
If, thats the whole question.
The square of a certain negative number is equal to five more than one-half of that number. What is the number?
-2
-5/2
-1/2
Answer:
-2
Step-by-step explanation:
Cuánto es 22=5(y–8)????????
Answer:12.4
Step-by-step explanation:
22=5(y-8) Use the distribution property
22=5y-40 Add 40 to both sides
62=5y Divide 5 from both sides
12.4 = y
Answer:
y=62/5
Step-by-step explanation:
mueva los términos
22=5y-40
calcule
-5y=-40-22
multiplique ambos lados
-5y=-62
y=62/5
If m< EBC = 3y+10 and m< ABE = 2y-20, find m< EBF.
By applying the supplementary angle theorem, the magnitude of angle EBF (m<EBF) is equal to 60°.
What is a supplementary angle?A supplementary angle can be defined as two (2) angles or arc whose sum is equal to 180 degrees.
Mathematically, a supplementary angle can be calculated by using this formula:
Q + R = 180
Where:
Q and R are measure of the angles subtended.
Substituting the given parameters into the formula, we have;
m<EBC + m<ABE = 180
3y + 10 + 2y - 20 = 180
5y - 20 = 180
5y = 180 + 20
5y = 200
y = 200/5
y = 40
Now, we can determine the magnitude of angle EBF (m<EBF) based on the given diagram:
m<ABE = m<EBF
m<EBF = 2y - 20
m<EBF = 2(40) - 20
m<EBF = 80 - 20
m<EBF = 60°
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3s≤ 19;s=-6
Tell whether the value is a solution of the inequality.
Yes , s = - 6 is the solution of the given inequality 3s ≤ 19 .
When two real numbers or algebraic expressions are related by the symbols '>', '<', '≥', '≤', the relationship is called an inequality. In algebra, an inequality is a mathematical statement that uses the inequality symbol to show the relationship between two expressions. A solution set is a set of values that satisfy a given inequality. This means that all values in the solution set satisfy the inequality and other values do not.If s = - 6 is the solution of given inequality 3s ≤ 19 ...... (1) then , it must satisfy the inequality.
Putting s = - 6 in equation (1) , we get
[tex]3(-6)\leq 19\\-18\leq 19[/tex]
As the above condition is true so , s = - 6 is the solution of given inequality.
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TEMPERATURE The temperature on a thermometer dropped from a reading of 25°to -8°. Find the midpoint of these temperatures.
Answer:
8.5°
Step-by-step explanation:
25 + (-8)
=25 - 8
=17 ÷ 2
= 8.5°
What is 1.3 x 10^4 in standard notation?
Answer: 13000
Step-by-step explanation:
So I believe this may be the answer though I'm not very good at this.
Answer: 13,000
Step-by-step explanation:
First look at the first number given and it's decimal place.
Once you figure the decimal place look for the number it is being multiplied by.
Next look at the number it's to the power to.
In this case the number is 4 so the decimal place of the first number will be moved over to the right 4 times.
Next look at the second number given and calculate what the number is to the power of and after multiply the first given number.
Lastly, once you have multiplied You will receive your final given answ⊕er and that will be the standard form.
One roofer can put a new roof on a house three times faster than another. working together they can roof a house in 5 days. how many days would it take the faster roofer to put a new roof on a house working alone? round the answer to the nearest tenth. (assume the roofs of the houses are similar sizes.)
According to the given statement the quicker roofer can finish a house's roof in around 6.7 days when working alone.
How do you rounding off ?In a given base, a round number is a number that ends including one or more "0s." So, 590 is more round than 592, but less round than 600. A round number is frequently interpreted in both technical and casual language to stand for something like a value or values close to the nominal value represented.
According to the given data:If the faster roofer takes t, the slowest one will take 3t.
Their total daily charges for roofing are
1/t + 1/(3t) = 1/5
4/(3t) = 1/5
multiply by 5t
t = 5(4/3)
= 20/3
= 6.7
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A recipe called for using 5 1/8 cups of flour before baking and another 8 7/9 cups after baking. What is the total amount of flour needed for the recipe?
Answer:
13 65/72 is your answer.
Step-by-step explanation:
Answer:
13 65/72
Step-by-step explanation:
One side of a cube is 3 cm long. Its mass is 110 g. What is the density of the cube?
The density of the cube is 4.1g/cm³
How to calculate the density of the cube ?
The first step is to calculate the volume
Volume= area³
= 3³
= 27
The density can be calculated as follows
= mass/volume
= 110/27
= 4.1
Hence the density of the cube is 4.1gram/cm³
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The end points of AB are A (-7.7)and B (10.5). Find the coordinates of mid point M
The midpoint becomes Midpoint M is 3/2, 6.
According to the statement
We have to find that the midpoint.
So, For this purpose, we know that the
Midpoint is the the point on a line segment or an arc that is equidistant, when measured along the line or the arc, from both endpoints.
From the given information:
The end points of AB are A (-7,7)and B (10,5).
Then
Midpoint M = Midpoint of A, Midpoint of B
Then
Midpoint M = -7+10 /2, 7+5/2
Midpoint M = 3/2, 12/2
Midpoint M = 3/2, 6.
Then the midpoint of the AB becomes the 3/2, 6. which represent the 3/2 is the x coordinates and the y coordinates is a 6.
So, The midpoint becomes Midpoint M is 3/2, 6.
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If it takes 3 seconds to fill up a 16 ounce
jar, how many seconds will it take to fill up a
100 ounce bucket?
Answer:
18,000
Step-by-step explanation:
(PLS HELP I NEED THIS ITS DUE IN 30 MIN) The perimeter of the quadrilateral is 120 feet and BA = x + 30, BC = 2x + 10, and CD = x + 20. Determine the length of the sum of the smallest side and the largest side.
The length of the sum of the smallest value and the largest value is 105 feet.
Given data
BA = x + 30
BC = 2x + 10
CD = x + 20
Perimeter = 120 feet
How to find the length of the sum of the smallest side and the largest side.The perimeter refers to the sum of all the dimensions which is given as 120 feet. We sum the dimensions given to find the value of x.
This is done as follows:
Perimeter = BA + BC +CD
120 = x + 30 + 2x + 10 + x + 20
120 = x + 2x + x + 30 + 10 + 20
120 = 4x + 60
4x = 120 - 60
4x = 60
x = 60 / 4
x = 15
plugging in x = 15 into the dimensions given we have
BA = x + 30
BA = 15 + 30
BA = 45
BC = 2x + 10
BC = 2 * 15 + 10
BC = 30 + 40
BC = 70
CD = x + 20
CD = 15 + 20
CD = 35
Hence we can say that the smallest value is 35 and the largest value is 70.
sum of the values
70 + 35 = 105
The sum of the smallest value and the largest value is 105 feet.
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Can I get help on number 3 please
Select the correct answer. what is the value of the third quartile of the data set represented by this box plot? a box plot with lower quartile, median and upper quartile values as 21, 26, and 29, respectively. the whiskers on both the ends end at 19 (minimum) and 33 (maximum). a. 19 b. 21 c. 26 d. 29
Answer:
D. 29
Step-by-step explanation:
just did the test and got it correct. Edmentum, Plato.
Mariam took a taxi from her house to the airport. The taxi company charged a pick-
up fee of $2.90 plus $1.25 per mile. The total fare was $6.65, not including the tip.
Write and solve an equation which can be used to determine m, the number of miles
in the taxi ride.
The equation illustrates that the number of miles will be 3 miles.
How to compute the value?The taxi company charged a pick- up fee of $2.90 plus $1.25 per mile.
Let the number of miles be m.
Therefore, this will be:
2.90 + (1.25 × m) = 6.65
2.90 + 1.25m = 6.65
Collect like terms
1.25m = 6.65 - 2.90
1.25m = 3.75
m = 3.75/1.25
m = 3
The number of miles is 3 miles.
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whats the answer to 1.17-0.07+ (3.92a)
Answer:
3.92a + 1.1
Step-by-step explanation:
remove the parentheses
1.17 - 0.07 + 3.92a
subtract
1.17 - 0.07 = 1.1
= 3.92a + 1.1
How would I multiply these matrices? (I thought this would be undefined but my teacher said it wasn’t)
When we do Matrix multiplication, we keep these two conditions in mind: 1 The number of columns of the first matrix in the multiplication process must equal the number of rows of the second.
here number of columns of 1st matrix is not equal to number of rows of 2nd matrix.
To multiply two matrices, we must first determine if the first matrix's number of columns and rows equals the second matrix's number of rows. Then sum all of the results after multiplying each element of the first matrix's column by each element of the second matrix's row.
In dealing with many ideas in linear algebra, matrices are crucial. In mathematics, a matrix is a rectangular array or table with rows and columns of integers, symbols, or expressions. Matrix operations include addition, subtraction, multiplication, and other operations.
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What is the answer for 35% of 21?
Answer:
7. 35
Step-by-step explanation:
21/x=100/35
(21/x)*x=(100/35)*x - we multiply both sides of the equation by x
21=2.85714285714*x - we divide both sides of the equation by (2.85714285714) to get x
21/2.85714285714=x
7.35=x answer
x=7.35
now we have:
35% of 21=7.35
How many liters of water should be evaporated from 60 liters of a 28% salt solution so that the remaining solution contains 32% salt?
7.5 liters
8.4 liters
43.2 liters
52.5 liters
Answer:
7.5 liter
Step-by-step explanation:
That is right 7.5 liters
Answer:
7.5 liters
its hard to explain for me because i don't know some other English words.
Please answer ASAP Due in 4 hours
Answer:
+6
Step-by-step explanation:
Number 67.89 is rational or irrational with explanation
Answer:
67.89 is rational
Step-by-step explanation:
67.89 is a terminating decimal, so it is a rational number.
please help it’s about finding the mean
The mean of the data is 16 cm and the absolute mean deviation is 1.4 cm.
Given we have the data set values.
Total number of data set values = 10
to find the mean we need to find the sum of the data set values and then divide it by the total number of data set values.
Therefore, mean = 13₊14₊14₊16₊16₊16₊16₊18₊18₊19 / 10
mean = 160/10
mean = 16 cm
To find the absolute mean deviation we need to find the deviation from the mean, from that the absolute mean deviation.
Data value Deviation from mean Absolute mean deviation
13 13 ₋ 16 = ₋3 I ₋3 I = 3
14 14 ₋ 16 = ₋2 I ₋2 I = 2
14 14 ₋ 16 = ₋2 I ₋2 I = 2
16 16 ₋ 16 = 0 0
16 16 ₋ 16 = 0 0
16 16 ₋ 16 = 0 0
16 16 ₋ 16 = 0 0
18 18 ₋ 16 = 2 2
18 18 ₋ 16 = 2 2
19 19 ₋ 16 = 2 3
Now the total of the absolute mean deviation is 14
divide it by 10
= 14/10
= 1.4 cm
Hence we get the mean and the absolute mean deviation as 16 cm and 1.4 cm.
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20% de los animales en un centro de rescate de animales son gatos. ¿Qué porcentaje son perros?
Answer:
80% son perros,
Step-by-step explanation:
Se considera que el total corresponde al 100%
Por tanto:
100% - 20% = 80%
Find the product of 4.5 x 1012 and 5.12 x 109. write the final answer in scientific notation. 23.04 x 1021 23.04 x 1022 2.304 x 1021 2.304 x 1022
Answer: 4.5 x 1012 = 4554x
Step-by-step explanation:
5.12 x 109 = 558.08
please help!!!!!!! i really need the answer
Answer:
When you will take a money.
How many times per year
What is the approximate value of 8–√ ?
The value of 8-√5 is approximately 5.76 which is calculated by rounding the square root of 5 to 2 decimal places.
A number y whose square (the outcome of multiplying the number by itself, or y × y), is x (y² = x) is said to be the square root of a number x.
For instance, since 4² = (4)² = 16, 4 and -4 are the square roots of 16.Every nonnegative real number x has a singular nonnegative square root, denoted by √n where the symbol √ is known as the radical sign or radix, which is known as the primary square root.For instance, we write to indicate that the primary square root of √9 is 3. The radicand is the phrase (or integer) whose square root is being analyzed. The quantity or phrase that appears beneath the radical sign is known as the radicand.Now the given expression is of the form ( 8 - √5 )
We know that √5 = 2.2360... ≈ 2.24 (rounded to 2 decimal places.)
∴ 8 - √5
= 8 - 2.24
= 5.76
Hence the value of the expression is approximately 5.76 .
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Disclaimer: The complete question is:
What is the approximate value of 8–√5 ?
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