Answer:
[tex]W=839.464\ ft*lbf[/tex]
Step-by-step explanation:
The work done is the product of the magnitude of the force applied to the object by the magnitude of the displacement of the object by the cosine of the angle between the force and direction of the displacement. This is:
[tex]W=|F|*|r|cos(\theta)[/tex]
In this case
[tex]\theta=30\°[/tex]
|F|=180 pound force
The magnitude of vector AB is:
[tex]|r|= \sqrt{5^2 + 2^2}\\\\|r|= \sqrt{29}\ fr[/tex]
Finally the work is:
[tex]W=180*\sqrt{29}*cos(30\°)[/tex]
[tex]W=839.464\ ft*lbf[/tex]
Answer:
the answer is option 1, A
Step-by-step explanation:
PLS HELP SHOW ALL YOUR WORKING OUT :D
[tex]AB=\sqrt{(10-1)^2+(3-7)^2}=\sqrt{81+16}=\sqrt{97}\approx9.85[/tex]
The system of equations is solved using the linear combination method. What does 0 = ?12 mean regarding the solution to the system? There are no solutions to the system because the equations represent parallel lines. There are no solutions to the system because the equations represent the same line. There are infinitely many solutions to the system because the equations represent parallel lines. There are infinitely many solutions to the system because the equations represent the same line.
Answer:
There are no solutions to the system because the equations represent parallel lines
Step-by-step explanation:
If you get a solution 0 =12
This is never true, so that means there are no solutions.
The lines are parallel.
If you get 2=2, you will have infinite solutions because they are the same line
In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth, in the box.
Check the picture below.
make sure your calculator is in Degree mode.
Answer:
x=56.7
Step-by-step explanation:
From the given triangle, the opposite side of angle x is 66 mm
79 mm is opposite to the right angle, so hypotenuse = 79 mm
we know the opposite side and the hypotenuse
To find the angle we use sin
[tex]sin(x)= \frac{opposite side}{hypotenuse}[/tex]
opposite side = 66
hypotenuse = 79
[tex]sin(x)= \frac{66}{79}[/tex]
[tex]x=sin^{-1}(\frac{66}{79})[/tex]
x=56.66199855
Round the answer to nearest tenth
x=56.7
The floor of storage unit is 5 meters long and 2 meters wide. Starting at the far left corner, Paula walks down the length, across the width, and then diagonally back to the far left corner. How far does Paula walk? If necessary, round to the nearest tenth.
Answer:
≈ 5.4m
Step-by-step explanation:
a^2 + b^2 = c^2
5^2 + 2^2 = c^2
29 = c^2
c ≈ 5.3852m
Answer:
12.4 meters
Step-by-step explanation:
We do have to use Pythagorean Theorem to get the diagonal part... But we are not done after that. It wants to know how far we have walked after going down the length, the width, and the diagonal. We are going to have to add 3 numbers at the end (3 measurements for the things I just mentioned)
5^2+2^2=c^2
25+4=c^2
29=c^2
c=sqrt(29) approx 5.4
So now we do 5+2+5.4 which is 12.4 meters
Please help ^^ -Rudy has arranged to buy a car for $10,240. He has a $3000 trade-in allowance and will make a $2000 down payment. He will finance the rest with a 3-year auto loan at 3.4% APR.
Monthly Car Loan Payment Per $1000 Borrowed.
(a) How much money will he borrow in an auto loan?
(b) What will his monthly auto payment be?
(c) What is the total amount of interest he will pay?
(d) What is his total payment for the car?
Answer:
(-) $29.26 per thousand for a 3-year 3.4% loan
(a) $5,240
(b) $153.32
(c) $279.52
Step-by-step explanation:
• Payment per thousand
The payment amount can be computed from the formula ...
A = P(r/n)/(1 -(1 +r/n)^(-nt))
where P is the principal amount, r is the annual rate, n is the number of payments per year, and t is the number of years.
For a $1000 3-year loan at 3.4%, this evaluates to ...
A = 1000(0.034/12)/(1 -(1 +0.034/12)^(-12·3)) ≈ $29.26
The monthly car payment per $1000 borrowed is $29.26.
__
• Rudy's trade-in allowance and down payment will reduce the amount he finances to ...
$10,240 -3000 -2000 = $5,240
__
• $5,240 = 5.24 × $1000, so Rudy's payment will be ...
5.24 × $29.26 = $153.32
__
• The amount of interest Rudy pays is the difference between the amount paid back and the amount of the loan.
(36 mo)×($153.32/mo) - 5240 = $279.52
Monthly Car Loan Payment Per $1000 Borrowed is $29.26
(a) money he will borrow for loan = $ 5240
(b) monthly auto payment = $ 153.32
(c) the total amount of interest he will pay is $279.52
(d) Total payment for car= $ 10,519.52
Given Information :
The cost of car is $10,240. He has allowance of $3000 and He will make a $2000 down payment.We find out the monthly car loan payment for every $1000 borrowed.
Lets use monthly payment formula
[tex]A=\frac{P\cdot \frac{r}{n} }{1-(1+\frac{r}{n})^{-nt} }[/tex]
Where P is the loan amount.
r is the rate of interest and t is the number of years
n is the period
P=1000
Given that 3-year auto loan at 3.4% APR.
t=3, r= 3.4%= 0.034, n=12
Substitute all the values and calculate the monthly loan
[tex]A=\frac{P\cdot \frac{r}{n} }{1-(1+\frac{r}{n})^{-nt} }\\A=\frac{1000\cdot \frac{0.034}{12} }{1-(1+\frac{0.034}{12})^{-12\cdot 3} }\\A=\frac{1000\cdot \frac{0.034}{12}}{1-\left(\frac{0.034}{12}+1\right)^{-36}}\\A=\frac{2.83333\dots }{1-1.00283\dots ^{-36}}\\A=29.25782[/tex]
Monthly Car Loan Payment Per $1000 Borrowed is $29.26
The cost of car is $10,240. Allowance = 3000 and down payment = 2000
(a) Auto loan = cost of car - allowance - down payment
[tex]Auto \; loan = 10240 - 3000 -2000=5240[/tex]
(b) Monthly Car Loan Payment Per $1000 Borrowed is $29.26
Monthly car loan payment for $5240 is
[tex]\frac{5240}{1000} * 29.26=153.32[/tex]
(c) first we find out the total loan amount paid in 3 years (36 months)
[tex]36 \cdot 153.3224=5,519.52[/tex]
To find the amount of interest he pay , we subtract the loan amount
[tex]5,519.52-5240=279.52[/tex]
the total amount of interest he will pay is $279.52
(d) Total payment for car = down payment +total loan amount paid
Total payment for car =[tex]5000+5519.52=10,519.52[/tex]
learn more about monthly payment here:
brainly.com/question/9263566
Plz, help! I don't know this ! will give brainlest!
Answer:
its the mean for the data, its showing you the average studying time
What is the answer
Square EFGH stretches vertically by a factor of 2.5 to create rectangle E′F′G′H′. The square stretches with respect to the x-axis. If point H is located at (-2, 0), what are the coordinates of H′ ?
Answer:
The coordinates of H′ are (-2,0).
Step-by-step explanation:
It is given that square EFGH stretches vertically by a factor of 2.5 with respect to the x-axis to create rectangle E′F′G′H′.
If a figure stretches vertically by a factor of 2.5 with respect to the x-axis, then the x-coordinates remains same and the points which lie on the axis are also remains the same after stretch.
It is given that the coordinates of H are (-2,0). This point lie on the x-axis, therefore it will remains the same after stretch.
Therefore the coordinates of H′ are (-2,0).
20 POINTS
Solve x.
sin x= 0.0349
Show work.
Use matrix operations and substitution to determine which of the following numerical values for z can be substituted into the second equation to solve for y?
2x + y - z = -8
2y + 3z = -6
-1/2x + y + z = -4
A. z = -9/8
B. z = 2
C. z = -9/4
D. z = 1
Answer:
B. z = 2
Step-by-step explanation:
Set up the matrix like this. I multiplied the last row by a 2 to get rid of the fractions so that's what you will see:
[tex]\left[\begin{array}{ccc}2&1&-1\\0&2&3\\-1&2&2\end{array}\right][/tex]
I used Cramer's Rule to solve for the value of y. In order to do that you need to find the determinant of the matrix, then you need to find the determinant of the matrix after you sub the solution set into the column representing z.
Find the determinant requires that I "pick up" the first 2 columns and then drop them at the end of the matrix and do the multiplication of the majors minus the minors. The matrix looks like this:
2 1 -1 2 1
0 2 3 0 2
-1 2 2 -1 2
The multiplication of the majors:
[(2×2×2)+(1×3×-1)+(-1×0×2)] = (8-3+0)=5
The multiplication of the minors:
[(-1×2×-1)+(2×3×2)+(2×0×1)] = (2+12+0) = 14
So the determinant of the matrix is I A I = 5 - 14 = -9
Now for the determinant of z, noted as I [tex]A_{z}[/tex] I. Notice that I am replacing the laast column with the solution set this time:
2 1 -8 2 1
0 2 -6 0 2
-1 2 -8 -1 2
The multiplication of the majors:
[(2×2×-8)+(1×-6×-1)+(-8×0×2)] = (-32+6+0) = -26
The multiplication of the minors:
[(-1×2×-8)+(2×-6×2)+(-8×0×1)] = (16 - 24 + 0) = -8
So the determinant of I [tex]A_{z}[/tex] I = -18
Cramer's Rule is to divide I [tex]A_{z}[/tex] I by I A I:
[tex]\frac{-18}{-9}= 2[/tex]
So the value you need for z to solve for y is 2
The value of z is 2.
The correct answer is an option (B) z = 2
What is a matrix?"It is a set of numbers arranged in rows and columns so as to form a rectangular array."
What is inverse of matrix?"An inverse of matrix 'B' is a matrix such that [tex]B\times B'=I[/tex] where [tex]I[/tex] is an identity matrix."
What is system of equations?"It is a set of equations for which we find a common solution."
For given question,
We have been given a system of equations.
2x + y - z = -8
2y + 3z = -6
-1/2x + y + z = -4
We can write the third equation as, -x + 2y + 2z = -8
So, we have system of equations,
2x + y - z = -8
2y + 3z = -6
-x + 2y + 2z = -8
We write above system of equations in matrix form as,
[tex]\Rightarrow \begin{bmatrix}2 & 1 & -1 \\0 & 2 & 3 \\-1 & 2 & 2\end{bmatrix}[/tex] [tex]\begin{bmatrix}x \\y \\z\end{bmatrix}[/tex] [tex]=\begin{bmatrix}-8 \\-6 \\-8\end{bmatrix}[/tex]
⇒ AX = B
We use inverse matrix to find the solution of given system of equations.
Pre-multiply both the sides of above equation by [tex]A^{-1}[/tex]
[tex]\Rightarrow A^{-1} AX = A^{-1}B\\\\\Rightarrow IX=A^{-1}B\\\\\Rightarrow X=A^{-1}B[/tex]
The inverse of matrix A is,
[tex]A^{-1}=\begin{bmatrix}\frac{2}{9} & \frac{4}{9} & \frac{-5}{9} \\\\\frac{1}{3} & \frac{-1}{3} & \frac{2}{3} \\\\\frac{-2}{9} & \frac{5}{9} & \frac{-4}{9}\end{bmatrix}[/tex]
So, the solution of given system of equations would be,
[tex]\Rightarrow \begin{bmatrix}x \\y \\z\end{bmatrix}=\begin{bmatrix}\frac{2}{9} & \frac{4}{9} & \frac{-5}{9} \\\\\frac{1}{3} & \frac{-1}{3} & \frac{2}{3} \\\\\frac{-2}{9} & \frac{5}{9} & \frac{-4}{9}\end{bmatrix} . \begin{bmatrix}-8 \\-6 \\-8\end{bmatrix}[/tex]
[tex]\Rightarrow \begin{bmatrix}x \\y \\z\end{bmatrix}= \begin{bmatrix}0 \\-6 \\2\end{bmatrix}[/tex]
Therefore, the value of z is 2.
The correct answer is an option (B) z = 2
Learn more about the system of equations here:
https://brainly.com/question/22798746
#SPJ2
A high school guidance counselor wants to find the probability that students who study geometry as freshmen will go on to study calculus before graduating. To do this, he has constructed a table, shown below, which shows the number of students who study geometry as freshmen in a given year, and the number of those students who study calculus before graduating.
Year
2000
2001
2002
2003
2004
2005
Geometry Students
680
577
822
743
859
804
Calculus Students
391
336
512
374
465
361
Which year had the highest experimental probability that a freshman studying geometry would take a calculus class before graduation?
a.
2001
b.
2002
c.
2003
d.
2004
Answer:
b. 2002
Step-by-step explanation:
divide the geometry kids by total kids to take calculus.
The experimental probability of a freshman studying geometry taking a calculus class before graduation was greatest in 2002.Option B is correct.
What is the probability?
The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts.
The The experimental probability of a freshman studying geometry taking a calculus class before graduation is obtained by dividing the number of students taking calculus to the number of students of student taking statics.
Referred to the excel table in the attachment for the probability.
The experimental probability of a freshman studying geometry taking a calculus class before graduation in 2002 is found at;
[tex]\rm P_{2002}(\%) = \frac{512}{822} \times 100 \\\\ P_{2002}(\%) =62.29[/tex]
The experimental probability of a freshman studying geometry taking a calculus class before graduation was greatest in 2002.Option B is correct.
Hence,Option B is correct.
To learn more about the probability, refer to the link;
https://brainly.com/question/11234923
#SPJ2
A biologist pollster asks people what their favorite TV show is. This is an example of what kind of statistical study:
1. Experiment
2. Observational Study
3. Survey
Let f(x) = x2 + 6 and g(x) = x + 8x . Find ( g o f)( -7)
Answer: [tex](gof)(-7) =495[/tex]
Step-by-step explanation:
Given the functions f(x) and g(x), to find [tex](gof)(x)[/tex] you need to substitute [tex]x=f(x)=x^2 + 6[/tex] into the function g(x):
[tex](gof)(x) = ( x^2 + 6)+ 8( x^2 + 6)\\\\(gof)(x)=x^2 + 6+ 8x^2 + 48\\\\(gof)(x)=9x^2 + 54[/tex]
Now, to find [tex](gof)(-7)[/tex] you must substitute [tex]x=-7[/tex] into [tex](gof)(x)[/tex], then you get:
[tex](gof)(-7) = 9(-7)^2 + 54\\\\(gof)(-7) =9(49)+54\\\\(gof)(-7) =441+54\\\\(gof)(-7) =495[/tex]
Explain your answer.
Thanks-Aparri
Answer:
2 raisins
Step-by-step explanation:
The mean is calculated in the usual way: the sum divided by the number of numbers.
mean = (5 +9 +5 +5 +7 +11)/6 = 7
The deviations are the differences from the mean:
deviation = {5, 9, 5, 5, 7, 11} -7 = {-2, 2, -2, -2, 0, 4}
and the absolute deviation is the absolute value of these numbers:
absolute deviation = {2, 2, 2, 2, 0, 4}
The mean absolute deviation (MAD) is the average of these values:
(2 +2 +2 +2 +0 +4)/6 = 2
The mean absolute deviation is 2.
_____
It is generally convenient to let technology do the computation. A spreadsheet or graphing calculator can do this easily.
X + 35/17 = 4 The answer is 33/17 but I got it wrong because I multiplied 4 by 17. Why do I minus 35/17 from 4 instead of multiplying 17 to four? Do I always minus a positive fraction instead of multiplying the denominator when solving linear equations?
X=33/17
Here is how it works
By the way what you are working with is called improper factions, which is when the big number is placed over the smaller number.
Now 33/17 is also 1 16/17
35/17 is also 2 1/17
Now we can the proper fractions which are 1 16/17 and 2 1/17
1+2=3 and 16/17 + 1/17 equals 1
3+1=4
I enjoyed solving your problem. please vote my answer brainliest..thanks
PLEASE HELP! I'm on a time limit!!
Identify the reflection of the figure with vertices A(7,8), B(−12,19), and C(14,−21) across the line y=x.
A (8, 7), B (19, −12), C (−21, 14)
A (8, 7), B (12, −19), C (14, −21)
A (8, 7), B (−19, 12), C (14, −21)
A (7, 8), B (19, −12), C (21, −14)
Answer:
A. (8, 7), B (19, −12), C (−21, 14)
Step-by-step explanation:
You swap the X and Y coordinate for reflections over y=x
Answer:
Its the first choice.
Step-by-step explanation:
You flip the coordinates so the point (a, b) shifts to (b, a). So point A (7, 8) shifts to (8.7).
Given: STU with Prove: Complete the steps of the proof. ?: angle STU is congruent to angle XYUtriangle STU is congruent to triangle XYUtriangle STU is similar to triangle XYU ?: substitution propertysubtraction propertytransitive property
Answer: 5 triangle STU is similar to triangle SYU
11 sub traction property.
Step-by-step explanation:
i got it right on edgnuity if its the question with the triangle and the proof chart with 11 statements
Answer:
5: triangle STU is similar to triangle XYU
11: subtraction property
Step-by-step explanation:
points A(-2,4) B(1,3) C(-4,1) and D form a parallelogram. what are the coordinates of D
Answer:
D(-7, 2)
Step-by-step explanation:
The midpoint of diagonal AC is the same as the midpoint of diagonal BD, so ...
(A+C)/2 = (B+D)/2
We can solve for D by multiplying by 2 and subtracting B:
D = A + C - B
D = (-2, 4) +(-4, 1) -(1, 3) = (-2-4-1, 4+1-3)
D = (-7, 2)
How would you describe the difference between the graphs of f(x)=x^2 + 4 and g(y)=y^2+4?
what is the simplified expression of the following polynomial: xy4 + 5y7 - (6xy + 7y7) - x8y2 + (-3xy4) Step by Step
Answer:
-x^8y^2 -2y^7 -2xy^4 -6xy
Step-by-step explanation:
Eliminate parentheses.
xy^4 + 5y^7 - 6xy - 7y^7 - x^8y^2 -3xy^4
Arrange in descending degree order, group like terms.
-x^8y^2 +(5y^7 -7y^7) +(xy^4 -3xy^4) -6xy
Combine like terms.
-x^8y^2 -2y^7 -2xy^4 -6xy
NEED HELP ASAP!! Will give brainliest!
What is the equation of the line that is parallel to y-3x=2 and that passes through (6,1)?
y=3x-17
y=3x+19
y=-3x+19
y=-3x-17
ANSWER
[tex]y = 3x - 17[/tex]
EXPLANATION
The given line has equation;
[tex]y - 3x = 2[/tex]
We solve for y to get;
[tex]y = 3x + 2[/tex]
The slope of this line is 3.
Since tyheline is parallel to this line, it also has slope 3.
The line passes through (6,1), we can use the slope intercept form,
[tex]y-y_1=m(x-x_1)[/tex]
We substitute the point and the slope to get;
[tex]y - 1 = 3(x - 6)[/tex]
[tex]y = 3x - 18 + 1[/tex]
[tex]y = 3x - 17[/tex]
Answer: First Option
[tex]y = 3x - 17[/tex]
Step-by-step explanation:
For a linear equation of the form
[tex]y = mx + b[/tex] the slope of the line is the constant m.
In this case we have the line
[tex]y-3x=2\\y=3x +2[/tex]
Then the slope is [tex]m=3[/tex]
If the equation of the line sought is parallel to the line [tex]y=3x +2[/tex] then by definition both lines have the same slope m = 3
Therefore the equation of the line sought is:
[tex]y = 3x + b[/tex]
Where b is a constant that represents the intersection of the line with the y axis.
[tex]b = y_0 -3(x_0)[/tex]
Where [tex](x_0, y_0)[/tex] is a point belonging to the line sought.
In this case the point is (6, 1)
So
[tex]b =1 -3(6)[/tex]
[tex]b =-17[/tex]
Finally the equation is:
[tex]y = 3x - 17[/tex]
20 points if you help
(08.02 MC)
A pair of equations is shown below:
y = 6x − 4
y = 5x − 3
Part A: In your own words, explain how you can solve the pair of equations graphically. Write the slope and y-intercept for each equation that you will plot on the graph to solve the equations. (6 points)
Part B: What is the solution to the pair of equations? (4 points)
A
The first equation has slope 6 and y intercept -4. I'd plot y intercept (0,-4) and (1,2), and connect the dots and extend for the first line.
The second equation has slope 5 and y intercept -3. I'd plot y intercept (0,-3) and (1,2), and connect the dots and extend for the second line.
We stumbled on the solution, both lines contain (1,2)
B
I don't like the graphing. This is algebra, not connect the dots.
We have two equations for y, we equate them to find the x where they meet.
6x - 4 = 5x - 3
6x - 5x = -3 + 4
x = 1
y = 6(1) - 4 = 2
Check: y = 5(1) - 3 = 2, good
Answer: (1, 2)
The volume of a cube with side length x inches is x^3 cubic inches. If a cube has volume 1000 cubic inches, what is its side length (in inches)?
Answer:
10"
Step-by-step explanation:
The volume for a cube is V = l × w × h
But since this is a cube, all the sides aree the same length, so we could rewrite this in terms of x as:
V = [tex]x^3[/tex]
If we know the volume to be 1000, we sub it in for V:
[tex]1000=x^3[/tex]
We "undo" a cube by taking the cubed root of both sides. The cubd root of x cubed is just x, and the cubed root of 1000 is 10. Therefore, x = 10
What values of x and y satisfy the system of equations {x = −2y + 1 | 13x + 8y = 11?}
Final answer:
To solve the given system of linear equations, we use substitution to find y = 1/9 and then find x = 7/9 as the values that satisfy both equations.
Explanation:
The student is attempting to solve a system of linear equations. To find the values of x and y that satisfy this system, we need to use a method such as substitution or elimination. Given the system:
x = −2y + 1
13x + 8y = 11
We can substitute the expression for x from the first equation into the second equation:
13(−2y + 1) + 8y = 11
−26y + 13 + 8y = 11
−18y + 13 = 11
−18y = −2
y = −2/−18
y = 1/9
Now we can substitute this value of y back into the first equation to find x:
x = −2(1/9) + 1
x = −2/9 + 1
x = −2/9 + 9/9
x = 7/9
Therefore, the solution to the system is x = 7/9 and y = 1/9.
The perimeter of the rectangle is 146 units. What is the length of the longer side? 1 side = 2x, 2nd side = 3x+3
Answer:
45 units
Step-by-step explanation:
The perimeter is equal to 2(width+length)
Let the longer side be the length of the rectangle
2(2x+3x+3)=146
Divide both sides by 2
2x+3x+3=73
5x+3=73
5x=70
x=14
The longer side = 3x+3
substitdude x into the equation
3(14)+3
= 45 units
Brett has consumed 1,400 calories so far today. He has also burned off 400 calories at the gym. He would like to keep his daily calorie total to 2,000 calories per day. How many calories does he have left to consume for the day? Is 1,200 a viable solution to this problem?
Yes; 1,200 is less than 1,400.
Yes; 1,200 is less than 2,000.
No; 1,200 is more than the 400 he burned off at the gym.
No; 1,200 will cause him to exceed 2,000.
Answer:
Easy its D
Step-by-step explanation:
remember he does not want to pass 2,000
1,400 - 400 = 1,000
1,000 + 1,200 = 2,200
Answer:
No; 1,200 will cause him to exceed 2,000.
Step-by-step explanation:
Given that Brett wants to stay within his daily calorie limit of 2,000 calories, and he has already consumed 1,400 calories and burned 400 calories at the gym, the maximum additional calories he can consume without exceeding his limit is:
2,000 (daily limit) - 1,400 (already consumed) - 400 (burned at the gym) = 1,000 calories
So, Brett can consume a maximum of 1000 more calories to stay within his daily limit of 2,000 calories. Therefore, 1,200 calories is not a viable solution because it exceeds his limit by 200 calories.
The correct answer is:
No; 1,200 will cause him to exceed 2,000 calories.
Hope this helps :))
Please Help!!!
In order to unload clay easily, the body of a dump truck must be elevated to at least 50°. The body of a dump truck that is 15 feet long has been raised to 9 feet. Will the clay pour out easily? Show your work and draw a diagram to support your answer.
Please include the following:
• A diagram
• The trig equation you are solving and the steps you take to solve it.
• An answer in the context of the problem.
_________ (Yes or No), The clay ___________ (will or will not) pour out easily when the body of the dump truck is raised to 9 feet. I know this because ______________________________________.
Answer:
No, the clay will not pour out easily. I know this because the angle of the truck bed is less than 50°, which is the minimum angle for easy pouring.
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that ...
Sin = Opposite/Hypotenuse
If α represents the angle of the truck bed, this means ...
sin(α) = 9/15
We can find α using the inverse sine function:
α = arcsin(9/15) ≈ 36.87°
We note this angle is less than 50° so we expect the clay will not pour out easily.
Using the tangent function of trigonometry, we find that the angle of the raised dump truck is approximately 30.96°. Since this is less than the necessary 50°, the clay will not pour out easily when the dump truck is raised to 9 feet.
Explanation:In order to solve this problem, we need to use trigonometry, specifically the tangent function. We form a right triangle, using the truck's bed length (15 feet) as the hypotenuse, the height it's been lifted (9 feet) as the opposite, and we want to find the angle this makes with the ground.
We use the relationship in trigonometry: Tan(angle) = Opposite/Hypotenuse. Converting the values to this equation, Tan(angle) = 9/15. Solving this gives us the angle as the inverse tan of 9/15.
Using a calculator to find the Inverse tan (also known as arctan or tan^-1) of 9/15 gives us an angle, which is approximately 30.96°.
No, The clay will not pour out easily when the body of the dump truck is raised to 9 feet. I know this because the body angle of the dump truck (approximately 30.96°) is less than the necessary 50° for the clay to pour out easily.
Learn more about Trigonometry here:https://brainly.com/question/31896723
#SPJ11
One number is five more than another, and their sum is three less than three times the smaller. Find the numbers. If x represents the smaller number, which equation could be used to solve for x? X 2 + 5 = 3x - 3 2x + 5 = 3x - 3 2x + 5 = 3(x - 3)
Answer:
2x+5=3x-3
Step-by-step explanation:
The larger number is represented by X=5, and that number plus x would be 2x+5. The sum of those is 3 less than 3 times x, which is shown by 3x-3. So, 2x+5=3x-3
Answer:
The numbers are 8 and 13. Hopefully that can help with the equation.
Step-by-step explanation:
Which describes an isometric transformation? dilation/ rotation/ side length change/ angle change
Answer:
rotation
Step-by-step explanation:
"Isometric" means all measures stay the same.
dilation changes all lengthsrotation changes no measures -- an isometric transformationside length change obviously changes the length of a sideangle change obviously changes the measure of an angleRotations that describe the isometric transformation.
Isometric transformationAn isometric transformation (or isometry) exists as a shape-preserving transformation (movement) in the plane or space. The isometric transformations are reflection, rotation, and translation, and varieties of them such as the glide, which exists as the mixture of a translation and a reflection. Therefore, the correct answer is rotation.
To learn more about isometric transformation
https://brainly.com/question/110297
#SPJ2
Divide 1/3 yd by 9/13 ? please show work
Answer:
13/27
Step-by-step explanation:
1/3 ÷ 9/13
Copy dot flip
1/3 * 13/9
13/27
(x + 2)²
Given: (x + y)² = x² + 2xy + y²
Answer:
x² +4x +4
Step-by-step explanation:
Matching the expressions, you see you have y=2. Put 2 where y is and simplify.
(x +2)² = x² +2x(2) +(2)² = x² +4x +4
ANSWER
[tex] {x}^{2} + 4x + 4[/tex]
EXPLANATION
We want to expand:
[tex](x { + 2)}^{2} [/tex]
Using the identity:
[tex] {( x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} [/tex]
We put y=2 into the identity to obtain;
[tex] {( x + 2)}^{2} = {x}^{2} + 2x(2) + {2}^{2} [/tex]
This simplifies to:
[tex]{( x + 2)}^{2} = {x}^{2} +4x + 4[/tex]