(a) A vector v parallel to the line of intersection L is v = <1, 1, -2>. (b) The cartesian equation of the plane is -7x + 10y - 3z = -1
(a) To find a vector v parallel to the line of intersection L, we need to take the cross product of the normal vectors to the two given planes. The normal vectors are the coefficients of x, y, and z in the equations of the planes.
In this case, the equations of the planes are:
x + y - 2z = 1
4x + y + 3z = 4
The normal vectors to these planes are <1, 1, -2> and <4, 1, 3>, respectively. Since the line of intersection is parallel to both planes, a vector parallel to the line must be perpendicular to both normal vectors.
We can find such a vector by taking the cross product of the two normal vectors, which gives us: <1, 1, -2> × <4, 1, 3> = <-7, 10, -3>
Therefore, a vector v = <1, 1, -2>.
(b) To find the equation of the plane through the point (2, -1, 3) and perpendicular to L, we need to find a normal vector to the plane that is also parallel to L.
We can find such a vector by taking the cross product of the normal vectors to the two given planes. The normal vectors are <1, 1, -2> and <4, 1, 3>, so the cross product is: <1, 1, -2> × <4, 1, 3> = <-7, 10, -3>
This vector is parallel to L, so it can serve as the normal vector to the desired plane. The equation of the plane can be written in point-normal form as: -7(x - 2) + 10(y + 1) - 3(z - 3) = 0
Simplifying, we get:
-7x + 10y - 3z = -1
Therefore, the cartesian equation of the plane is -7x + 10y - 3z = -1, and it passes through the point (2, -1, 3) and is perpendicular to the line of intersection between the given planes.
To know more about cartesian equation, refer here:
https://brainly.com/question/11676110#
#SPJ11
Here is the question...."The magnitude and direction of two forces acting on an object are 80 pound, S58 degree E, and 50 pounds, N76 degree E, repectively. Find the magnitude, to the nearest hundredth of a pound, and the direction angle, to the nearest tenth of a degree, of the resultant force.".....And it has 2 part
The magnitude of the resultant force is approximately 119.89 pounds, and the direction angle is approximately S12.2°W.
To solve the problem, we can use vector addition.
Let F1 be the vector representing the first force, and F2 be the vector representing the second force. Then, we can find the resultant force R by adding the two vectors:
R = F1 + F2
To add two vectors, we need to resolve them into their x and y components. Let's do that first.
For F1:
Magnitude = 80 pounds
Direction = S58°E
To resolve F1 into its x and y components, we can use trigonometry:
Fx1 = 80 cos 58° = 42.57 pounds (east)
Fy1 = 80 sin 58° = 68.13 pounds (south)
For F2:
Magnitude = 50 pounds
Direction = N76°E
To resolve F2 into its x and y components, we can again use trigonometry:
Fx2 = 50 cos (180° - 76°) = -16.92 pounds (east)
Fy2 = 50 sin (180° - 76°) = 48.76 pounds (north)
Note that we used (180° - 76°) for the angle because the direction is N76°E, which means it is 76° east of due north.
Now we can add the x and y components separately:
Rx = Fx1 + Fx2 = 42.57 - 16.92 = 25.65 pounds (east)
Ry = Fy1 + Fy2 = 68.13 + 48.76 = 116.89 pounds (south)
To find the magnitude and direction of the resultant force, we can use trigonometry again:
Magnitude = sqrt(Rx^2 + Ry^2) = sqrt(25.65^2 + 116.89^2) = 119.89 pounds (rounded to the nearest hundredth)
Direction angle = atan(Rx/Ry) = atan(25.65/116.89) = 12.2° (rounded to the nearest tenth)
The direction angle is approximately S12.2°W, and the resultant force has a magnitude of about 119.89 pounds.
Learn more about magnitude at https://brainly.com/question/30676860
#SPJ11
a manufacturing machine has a 80% defect rate. if 109 items are chosen at random, answer the following. a) which is the correct wording for the random variable? select an answer b) pick the correct symbol: ?
The correct words are number of defective items from the sample of 109 items chosen at random and correct symbol is X ~ B(109, 0.8).
Percent of defective rate in manufacturing machine = 80%
Random number of items chosen = 109
The correct wording for the random variable in this situation is,
The number of defective items in a sample of 109 items chosen at random from the manufacturing machine.
Number of defective items is successes.
A common symbol for the number of successes in a binomial distribution is X.
Use X to represent the random variable in this situation.
The notation for the binomial distribution is usually written as,
X ~ B(n, p)
where X is the random variable,
n is the sample size,
and p is the probability of success on each trial.
X ~ B(109, 0.8).
Therefore, the correcting wording is number of defective items in a sample of 109 items chosen at random and the correct symbol is equal to X ~ B(109, 0.8).
Learn more about defective items here
brainly.com/question/31369855
#SPJ4
Find the component form of u + v given the lengths of u and v and the angles that u and v make with the positive x-axis.
Ilull = 5, Ou = 0°
I|v|I = 2, Ov = 60°
The component form of u + v can be found using the given lengths and angles and it is (6, √3).
To find the component form of u + v given the lengths of u and v and the angles that u and v make with the positive x-axis we will sum the u and v.
Given Ilull = 5 and Ou = 0°, we can represent vector u as (5, 0) in component form. Given |Iv|I = 2 and Ov = 60°, we can represent vector v as (2cos60°, 2sin60°) = (1, √3) in component form.
To find u + v, we add the corresponding components of u and v. This gives us:
u + v = (5, 0) + (1, √3) = (5+1, 0+√3) = (6, √3)
Therefore, the component form of u + v is (6, √3).
For more questions like Vector click the link below:
https://brainly.com/question/29740341
#SPJ11
Complete the sentence.
The focus so far has been on similar triangles, but there are also theorems that deal with similar
The focus so far has been on similar triangles, but there are also theorems that deal with similar polygon
Completing the sentenceTheorems of similar triangles are important properties that hold true for any pair of similar triangles. Some of the most commonly used theorems are:
AA Similarity Theorem: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
SSS Similarity Theorem: If the three sides of one triangle are proportional to the three corresponding sides of another triangle, then the triangles are similar.
SAS Similarity Theorem: If two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are similar.
These theorems are also applicable to similar polygons
Read more about similar triangles at
https://brainly.com/question/14285697
#SPJ1
The focus so far has been on similar triangles, but there are also theorems that deal with similar polygons.
Lulu has 10 feet of ribbon she uses 1 1/3 feet ribbon for a project she uses the rest of the ribbon to make bows she uses 8 inches of ribbon for each bowl how many does lulu make?
The number of bows Lulu can make from the remaining ribbon is 13 bows.
To find the remaining ribbon, first, convert 1 1/3 to an improper fraction (1*3 + 1 = 4, so 1 1/3 = 4/3). Now, subtract 4/3 from 10 feet.
10 - (4/3) = (30/3) - (4/3) = 26/3 feet of ribbon remaining.
She uses 8 inches of ribbon for each bow. Since there are 12 inches in a foot, convert the remaining ribbon to inches:
(26/3) * 12 = 104 inches of ribbon remaining.
Now, divide 104 inches by the 8 inches required for each bow to find the number of bows she can make:
104 / 8 = 13 bows.
Lulu can make 13 bows with the remaining ribbon.
Learn more about improper fraction here: https://brainly.com/question/19318336
#SPJ11
ASAP PLEASE HELP!!
I’ll give brianest
Given that the length of arc DC is 9. 77 inches and the radius of the circle is 8 inches.
to the nearest degree, what is the mZDPC?
The mZDPC is approximately 15 degrees.
How we find the mZDPC?We know that the length of an arc of a circle is given by the formula:
length of arc = (central angle / 360°) × 2πr
where r is the radius of the circle.
In this case, the length of arc DC is 9.77 inches and the radius of the circle is 8 inches. Let's use the above formula to find the central angle mZDPC:
9.77 = (mZDPC / 360°) × 2π(8)
Simplifying this equation, we get:
mZDPC = (9.77 / (2π(8) / 360°))
mZDPC = (9.77 / 0.670206) degrees
mZDPC ≈ 14.58 degrees
Rounding to the nearest degree, we get:
mZDPC ≈ 15 degrees
Learn more about Length of arc
brainly.com/question/16403495
#SPJ11
Here is a sequence of numbers 64,49,36,25,16 find the next number in the sequence
The next number in the sequence is 9.
The given sequence of numbers are perfect squares of decreasing numbers in descending order. Specifically, the given sequence consists of the squares of the first five counting numbers in descending order, starting from 8², then 7², 6², 5², and 4².
Therefore, the next number in the sequence should be the square of the next counting number in descending order, which is 3. Thus, the next number in the sequence should be 3², which is equal to 9.
To further explain, the sequence can be written as follows:
64 = 8²
49 = 7²
36 = 6²
25 = 5²
16 = 4²
The next number in the sequence is the square of the next counting number in descending order, which is 3. Therefore, the next number in the sequence should be 3², which is equal to 9. Thus, the next number in the sequence is 9.
To know more about perfect squares, refer here:
https://brainly.com/question/13521012#
#SPJ11
Amy graphed a function that gives the height of a car on a roller coaster as a function of time. She said her graph is the graph of a step function. Is this possible? Explain your reasoning
It is not possible for the graph of a height function of a car on a roller coaster to be a step function. Hence Amy is wrong.
A sort of function called a step function is one that only varies at discrete, isolated places in its domain and is constant everywhere else. A step function is one that "steps" down to the next integer at each integer input while remaining constant in between. An example of this is the floor function, which rounds down any input to the nearest integer.
On the other hand, it is doubtful that the height of a roller coaster car as a function of time is a step function because it is anticipated to fluctuate continually as opposed to hopping from one value to another at certain moments. Instead of abrupt increases in height that would be consistent with a step function, roller coasters often entail smooth, continuous curves and elevation changes.
To know more about step function, visit,
https://brainly.com/question/12000188
#SPJ4
the kendall correlation uses rank values to determine the correlation between two variables. the equation for kendall rank shows that if there are more concordant pairs, then the correlation will be positive. using the definition of concordant and disconcordant pairs, explain why this makes sense.
Yes, if there are more concordant pairs in the rank order, it makes sense that the Kendall correlation will be positive, as it suggests a tendency for the two variables to move in the same direction more often.
In Kendall correlation,
Rank values of each observation for the two variables are compared to determine the level of agreement or disagreement between them.
A concordant pair is when the rank order of the two variables is the same both increase or decrease together.
A discordant pair is when the rank order is different one variable increases while the other decreases.
If there are more concordant pairs, it means that the two variables tend to move in the same direction more often.
Which suggests a positive correlation relationship between them.
Conversely, if there are more discordant pairs, it means that the two variables tend to move in opposite directions more often.
Which suggests a negative relationship between them.
Example ,
two variables, X and Y, that are positively correlated.
If we plot the observations of X and Y on a scatter plot.
Expect to see a pattern where as the values of X increase, the values of Y also tend to increase.
Learn more about correlation here
brainly.com/question/19263847
#SPJ4
Please Help!!
Use the credit card information below and the designated method of computing interest to fill in the blanks. (See image)
Adjusted Balance Method-
Interest $______
New Balance $______
Using the Adjusted Balance Method:
Interest: $4.15
New Balance: $569.15
How to solveTo calculate the interest and new balance using the Adjusted Balance Method, we need to first find the adjusted balance.
This method takes the previous balance, adds the purchases made before the payment, and then subtracts the payment.
Here's the calculation:
Calculate the adjusted balance:
Previous balance: $500
Purchases before May 20: $25 (May 12)
Subtotal: $525
Payment: $110
Adjusted balance: $525 - $110 = $415
Calculate the interest:
Interest rate: 1% per month
Interest: $415 * 1% = $4.15
Calculate the new balance:
Adjusted balance: $415
Purchases after May 20: $100 (May 22) + $50 (May 30) = $150
Interest: $4.15
New balance: $415 + $150 + $4.15 = $569.15
So, using the Adjusted Balance Method:
Interest: $4.15
New Balance: $569.15
Read more about adjusted balance here:
https://brainly.com/question/1808408
#SPJ1
Maria claims that any fraction located between 1/5 and 1/7 on a number line must have a denominator of 6.
Enter a fraction to show Maria's claim is incorrect.
To show that Maria's claim is incorrect, we need to find a fraction that is located between 1/5 and 1/7 on a number line but does not have a denominator of 6.
One way to do this is to find the least common multiple (LCM) of 5 and 7, which is 35, and then find a fraction with a denominator of 35 that falls between 1/5 and 1/7.
To do this, we can find the equivalent fractions of 1/5 and 1/7 with a denominator of 35:
1/5 = 7/35
1/7 = 5/35
Now we need to find a fraction between 7/35 and 5/35. One such fraction is:
6/35
This fraction is located between 7/35 and 5/35 on the number line, but its denominator is 35, not 6. Therefore, Maria's claim is incorrect.
Another way to show that Maria's claim is incorrect is to find a counterexample by simply listing all the fractions between 1/5 and 1/7 and showing that not all of them have a denominator of 6. For example:
1/6, 1/7, 1/8, 1/9, 1/10, ..., 1/34, 1/35
As we can see, not all of these fractions have a denominator of 6, so Maria's claim is incorrect.
Answer:
13/70
Step-by-step explanation:
In order to show that Maria's claim is incorrect, we need to find a fraction that is located between 1/5 and 1/7 on a number line, but does not have a denominator of 6.
Let's find the common multiple (CM) of 5 and 7, which is 70, or 35. But this case try 70 and then find a fraction with a denominator of 70 that falls between 1/5 and 1/7.
equivalent fractions of 1/5 and 1/7 with a denominator of 70
1/7 < x < 1/5 , will be equivalent to 1/7 ( 10/10 ) < x < 1/5 ( (14/14)
10/70 < x < 14/70..
x is the fraction between 10/70 and 14 /70. Unknown fraction is:
13/70
This fraction is located between 10/70 and 14/70 on the number line, but its denominator is 70 , not 6. Therefore, Maria's claim is incorrect.
Prove that U(1, 1), Q(4,4), and A(6, 2) are the vertices of a right triangle. Â Use the following as a guide. Find the slopes of sides UQ, QA, and UA. Which segments are perpendicular? How do you know the segments are perpendicular? What are the lengths of each side? Use the Pythagorean Theorem to show that it is a right triangle. â
U(1,1), Q(4,4), and A(6,2) form a right triangle with UQ and QA being the legs and UA being the hypotenuse.
How do we know that UQ and QA are perpendicular?To determine whether U(1,1), Q(4,4), and A(6,2) form a right triangle, we will follow the given guide:
Find the slopes of sides UQ, QA, and UA:
Slope of UQ: (4-1)/(4-1) = 1Slope of QA: (2-4)/(6-4) = -1Slope of UA: (2-1)/(6-1) = 1/5Determine which segments are perpendicular and how we know they are perpendicular:
To determine if two lines are perpendicular, we need to check if their slopes are negative reciprocals of each other.
UQ and QA: Since the slope of UQ is 1 and the slope of QA is -1, we know that UQ and QA are perpendicular.UQ and UA: The slopes of UQ and UA are both positive, so they cannot be perpendicular.QA and UA: The slope of QA is -1, and the slope of UA is 1/5. Their product is -1/5, which is not -1, so QA and UA are not perpendicular.Find the lengths of each side:
Length of UQ: √[(4-1)² + (4-1)²] = √27Length of QA: √[(6-4)² + (2-4)²] = √8Length of UA: √[(6-1)² + (2-1)²] = √26Use the Pythagorean Theorem to show that it is a right triangle:
Since we have determined that UQ and QA are perpendicular, we can use the Pythagorean Theorem to show that it is a right triangle.
(Length of UQ)² + (Length of QA)² = (√27)² + (√8)² = 27 + 8 = 35(Length of UA)² = (√26)² = 26Since (Length of UA)² + (Length of QA)² = (Length of UQ)², we know that the triangle is a right triangle.
U(1,1), Q(4,4), and A(6,2) form a right triangle with UQ and QA being the legs and UA being the hypotenuse.
Learn more about UQ and QA
brainly.com/question/27157027
#SPJ11
I NEED HELP WITH THIS ONE AND ANOTHER PLEASE
The missing lengths of BE and IJ using the concept of similar quadrilaterals are:
BE = 32
IJ = 18
How to find the lengths of similar quadrilaterals?Similar quadrilaterals are defined as quadrilaterals that have the same shape, but their sizes may vary. Thus, if two quadrilaterals are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
From the image, we are told that Quadrilateral GHIJ is similar to Quadrilateral BCDE.
Thus:
GJ/BE = IJ/DE = HI/CD
Thus:
12/BE = 6/16
BE = (16 * 12)/6
BE = 32
Similarly:
IJ/48 = 6/16
IJ = (48 * 6)/16
IJ = 18
Read more about Similar Quadrilaterals at: https://brainly.com/question/16261621
#SPJ1
Helppppppppppppppppp
Answer:
it would be at point (6,3)
Step-by-step explanation:
If you were to reflect it over the x-axis you would get (-6,3)
What percent of the customers at the book sale spent less than 20 dollars? Show or explain how you got your answer
Which type of sentence error occurs when a sentence is missing a subject or predicate? No error Fragment Subject -verb agreement Run-on
When the subject or predicate is missing from a sentence, the sentence error is a sentence fragment.
What is a sentence error?Sentence Errors are errors related to grammar and mechanics within sentences in Standard Written English.
An example of a sentence error will be "The children re us"
The phrase "re" is the error word in this sentence.
The three types of sentence errors we have are run-on sentences, sentence fragments and overloaded sentence.
In this problem, the type of sentence error that occurs when a sentence is missing a subject of predicate is a sentence fragment
learn more on sentence error here;
#SPJ1
Ben and his housemates signed a lease for an apartment for 12 months for $563 per month of which ben agreed to pay $215 per month. which of the following statements best gives the reasons that ben’s rent payment is an essential (fixed) expense? a. it cannot be eliminated in a later budget, in order to save money. b. living expenses have a higher priority than any other type of expense. c. the spender controls the amount of the rent by choice of apartment. d. he agreed to pay the same amount every month. please select the best answer from the choices provided a b c d
The statements that gives the best reasons that ben’s rent payment is an essential (fixed) expense is he agreed to pay the same amount every month. The correct answer is D.
In personal finance, an essential expense is a regular expenditure that is necessary for maintaining a basic standard of living. These expenses are typically fixed, meaning that they do not fluctuate from month to month, and are difficult or impossible to eliminate without sacrificing basic needs like food, housing, or healthcare.
Since, this is his rent, the amount of money that he is legally bound to pay every month in order to keep on living in that location.
He has an agreement with his landlord to pay $215 each month and thus he has to do it.
Essential expenses are often considered a top priority in budgeting because they are critical to maintaining health, safety, and overall well-being. In the given scenario, Ben's rent payment is an essential expense because it is a fixed expense that is necessary for maintaining his housing, which is a basic need. The correct answer is D.
Learn more about essential expense at https://brainly.com/question/30804860
#SPJ11
How do I do number 3?
Answer:
V = 1,728 mi³
SA = 864 mi²
Step-by-step explanation:
We can find the volume of the triangular prism by multiplying the area of one of the triangle faces by the prism's depth.
First, we can solve for the area of one of the triangle sides:
A(triangle) = (1/2) · b · h
A(triangle) = (1/2) · 24 · 18
A(triangle) = 12 · 18
A(triangle) = 216 mi²
Next, we can get the volume of the prism by multiplying the area of the triangle face by the prism's depth.
V = A(triangle) · depth
V = 216 · 8
V = 1,728 mi³
__
We can find the surface area by finding the area of each side, then adding all of those areas together.
We already know that the area of each of the triangle sides is 216 mi².
Now, we can solve for the area of the base.
A(base) = length · width
A(base) = 24 · 8
A(base) = 192 cm²
Then, we can find the area of the top side.
A(top) = length · width
A(top) = 30 · 8
A(top) = 240 mi²
Finally, we can solve for the surface area of the prism by adding the areas of each of its sides.
SA = (2 · A(triangle)) + A(base) + A(top)
SA = 2(216) + 192 + 240
SA = 432 + 192 + 240
SA = 624 + 240
SA = 864 mi²
What’s the answer? I need help
The two types of transformations that are produced by the matrix include:
a 90° counter clockwise rotation followed by a reflection in the vertical axis.a 90° clockwise rotation followed by a a reflection in the vertical axis.How to explain the transformationWe can see that a 90° counter-clockwise rotation followed by a dilation produces a transformation that stretches and rotates the figure.
On the other hand, a 90° counter-clockwise rotation followed by a reflection in the vertical axis produces a transformation that reflects and rotates the figure.
Learn more about transformations on
https://brainly.com/question/4289712
#SPJ1
A pyramid 5 meters high has congruent triangular sides and a square base that is 5 meters on each side. Each cross section of the pyramid parallel to the base is a square. What is the volume of the solid in cubic meters?
The volume of the pyramid is approximately 41.67 cubic meters.
How to find the volume?To find the volume of the pyramid, we can use the formula:
V = (1/3) x base area x height
Since the base of the pyramid is a square with side length 5 meters, its area is:
base area = side² = 5² = 25 square meters
The height of the pyramid is also given as 5 meters.
Now, we need to find the area of one of the square cross-sections. Since the pyramid has congruent triangular sides, we know that each of these triangles is similar to the original base square.
Therefore, the side length of each square cross-section is proportional to the height of the pyramid, and we can use the ratio of corresponding side lengths to find the area of one of the squares:
5 / 5 = x / 5
where x is the side length of the square cross-section.
Solving for x, we get:
x = 5
Therefore, each of the square cross-sections has an area of 5 x 5 = 25 square meters.
Now, we can substitute the values we have found into the formula for the volume:
V = (1/3) x base area x height
= (1/3) x 25 x 5
= 41.67 cubic meters
Therefore, the volume of the pyramid is approximately 41.67 cubic meters.
Learn more about Pyramid
brainly.com/question/17615619
#SPJ11
Find the linearization of the function at the given point. f(x, y) = e-¹⁰x-⁸y - 8y at (0, 0) A) L(x, y) = -8x - 10y B) L(x, y) = -8x - 10y + 1 C) L(x, y) = -10x - 8y + 1 D) L(x, y) = -10x - 8y
The linearization of the function f(x, y) = e-¹⁰x-⁸y - 8y at (0, 0) is L(x, y) = -10x - 8y + 1. The correct option is C.
To find the linearization of the given function at the point (0, 0), we need to compute the partial derivatives with respect to x and y and then evaluate them at the given point.
The function is f(x, y) = [tex]e^{(-10x-8y)[/tex] - 8y.
First, find the partial derivative with respect to x:
∂f/∂x = [tex]-10e^{(-10x-8y).[/tex]
Now, evaluate ∂f/∂x at (0, 0):
∂f/∂x(0, 0) = [tex]-10e^{(0)[/tex] = -10.
Next, find the partial derivative with respect to y:
∂f/∂y = [tex]-8e^{(-10x-8y)[/tex] - 8.
Now, evaluate ∂f/∂y at (0, 0):
∂f/∂y(0, 0) = [tex]-8e^{(0)[/tex] - 8 = -8 - 8 = -16.
Now, we can form the linearization:
L(x, y) = f(0, 0) + ∂f/∂x(0, 0)(x - 0) + ∂f/∂y(0, 0)(y - 0).
Evaluate f(0, 0):
f(0, 0) = [tex]e^{(-10(0)-8(0))} - 8(0) = e^{(0)} - 0 = 1.[/tex]
Finally, substitute the values into the linearization formula:
L(x, y) = 1 - 10x - 16y.
Comparing to the given options, the answer is:
C) L(x, y) = -10x - 8y + 1
For more such questions on Linearization.
https://brainly.com/question/31403141#
#SPJ11
HELP - A strip of uniform width is plowed along all four sides of a 12-km by 9-km rectangular cornfield. How wide is the plowed strip of the cornfield is half plowed?
Answer:
Let's start by drawing a diagram of the cornfield with the plowed strip around it:
markdown
Copy code
_____________________________
| |
| |
| |
| |
| _____________________|__
| | |
| | |
| | |
| | |
|_______|_______________________|
The plowed strip has a uniform width, which we'll call w. We want to find w such that half of the cornfield is plowed.
The total area of the cornfield is:
Copy code
12 km x 9 km = 108 km^2
If we plow a strip of width w around the cornfield, the new dimensions of the cornfield will be:
scss
Copy code
(12 + 2w) km x (9 + 2w) km
The area of the plowed strip is the difference between the area of the new cornfield and the area of the original cornfield:
scss
Copy code
(12 + 2w)(9 + 2w) - 12(9) = 108 + 42w + 4w^2
We want half of the cornfield to be plowed, so we set the area of the plowed strip equal to half the area of the original cornfield:
scss
Copy code
108 + 42w + 4w^2 = (1/2)(108)
Simplifying, we get:
Copy code
4w^2 + 42w - 54 = 0
We can solve this quadratic equation using the quadratic formula:
css
Copy code
w = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 4, b = 42, and c = -54. Substituting these values, we get:
scss
Copy code
w = (-42 ± sqrt(42^2 - 4(4)(-54))) / 8
arduino
Copy code
w = (-42 ± sqrt(1936)) / 8
makefile
Copy code
w = (-42 ± 44) / 8
So we have two possible solutions:
makefile
Copy code
w = 1/2 km (discarded since it does not satisfy the given condition)
or
makefile
Copy code
w = 11/2 km
Therefore, the width of the plowed strip is 11/2 km = 5.5 km if half of the cornfield is plowed.
To know more about plowed refer here
https://brainly.com/question/2852405#
#SPJ11
What is the equation of a circle with center (2,3) that passes through the point (5, 3)?
The equation of the circle with center (2, 3) that passes through the point (5, 3) is [tex](x - 2)^2 + (y - 3)^2 = 9.[/tex]
To find the equation of a circle with center (2, 3) that passes through the point (5, 3), we'll need to use the standard equation of a circle and the given information.
The standard equation of a circle is[tex](x - h)^2 + (y - k)^2 = r^2[/tex], where (h, k) is the center and r is the radius.
Step 1: Substitute the center coordinates (h, k) = (2, 3) into the equation:
[tex](x - 2)^2 + (y - 3)^2 = r^2[/tex]
Step 2: Use the point (5, 3) to find the radius. Plug the coordinates of the point into the equation and solve for [tex]r^2[/tex]:
[tex](5 - 2)^2 + (3 - 3)^2 = r^2\\3^2 + 0^2 = r^2\\9 = r^2[/tex]
Step 3: Plug[tex]r^2[/tex] back into the equation:
[tex](x - 2)^2 + (y - 3)^2 = 9[/tex]
So, the equation of the circle with center (2, 3) that passes through the point (5, 3) is [tex](x - 2)^2 + (y - 3)^2 = 9.[/tex]
To know more about circle refer here:
https://brainly.com/question/29142813
#SPJ11
Ken bought a car last year to drive back and forth to work. Last year he spent $1,098 on gas. This year, it was $1,562. What is the inflation rate?
The inflation rate for Ken's gas expenses between the two years is approximately 42.26%.
To calculate the inflation rate for Ken's gas expenses, we can use the following formula: (Current Year Expense - Previous Year Expense) / Previous Year Expense × 100%.
In this case, the previous year's gas expense was $1,098 and the current year's expense is $1,562.
To find the difference in expenses, subtract the previous year's expense from the current year's expense: $1,562 - $1,098 = $464.
Now, divide this difference by the previous year's expense: $464 / $1,098 ≈ 0.4226.
Finally, multiply the result by 100% to get the inflation rate: 0.4226 × 100% ≈ 42.26%.
You can learn more about the inflation rate at: brainly.com/question/31635911
#SPJ11
Rewrite 32 1/2 as a radical form
Therefore, 32 1/2 can be written as a radical form of 32 + √2.
What is fraction?In mathematics, a fraction is a numerical quantity that represents a part of a whole or a ratio between two numbers. Fractions are written in the form of one integer, called the numerator, written above a line, and another integer, called the denominator, written below the line. The denominator represents the total number of equal parts into which a whole is divided, while the numerator represents the number of those parts being considered.
Here,
We can write 32 1/2 as a mixed number, which is equivalent to the fraction 65/2. To express 65/2 as a radical form, we can simplify the fraction by finding a perfect square that divides evenly into both the numerator and the denominator. In this case, 4 is a perfect square that divides into 64 (the nearest perfect square to 65) and 2, so we can write:
65/2 = (64 + 1)/2
= 64/2 + 1/2
= 32 + 1/2
Now, we can express the fraction 1/2 as a radical by taking the square root of the denominator, which gives:
32 1/2 = 32 + √2
To know more about fraction,
https://brainly.com/question/24638688
#SPJ1
A cube has a volume of 200cm3. What is the length of one edge?
Give your answer in cm correct to one decimal place
Answer:
The answer is 5.8cm to 1 d.p
Step-by-step explanation:
volume of cube=L³
200=L³
cube root both sides
³√200=³√L³
L=5.8cm to 1 d.p
Solve for q q : 30 + q = 43 30+q=43
The solution to the equation 30 + q = 43 is q = 13.
What is the value of q?Given the equation in the question:
30 + q = 43
To determine the value of q in the equation 30 + q = 43, isolate q on one side of the equation by performing the same operation on both sides of the equation.
30 + q = 43
q + 30 = 43
Next, we can isolate q by subtracting 30 from both sides of the equation:
q + 30 - 30 = 43 - 30
q = 43 - 30
Subtract 30 from 43
q = 13
Therefore, the value of q is 13.
Learn to solve more equations here: https://brainly.com/question/9236233
#SPJ1
Boris's backyard has cement and grass. Find the area of the part with cement.
(Sides meet at right angles. )
4 m
1 m
2 m
grass
5 m
3 m
cement
5 m
The constant of proportionality between the number of yards Jackson can mow and the number of hours is 3/4.
To find the area of the part with cement, we need to find the area of the entire rectangle and then subtract the area of the part with grass.
The area of the rectangle is: length x width = 5 m x 4 m = 20 m²
The area of the part with grass is: length x width = 3 m x 2 m = 6 m²
So the area of the part with cement is:
20 m² - 6 m² = 14 m²
Therefore, the area of the part with cement is 14 square meters.
To learn more about “area” refer to the https://brainly.com/question/25292087
#SPJ11
Find all solutions of the equation algebraically.
|x2 + 9x| = 6x + 54
The solutions to the equation are x= -9 and x = 6
How to determine the valueFrom the information given, we have that;
|x2 + 9x| = 6x + 54
To solve the quadratic equation, collect the like terms, we have;
x² + 9x - 6x = 54
subtract the terms
x² + 3x = 54
Put in standard form
x² + 3x - 54 = 0
Find the pair factors of -54 that add up to give 3 and substitute the values
x² + 9x - 6x - 54 = 0
group in pairs
(x² + 9x) - (6x - 54) = 0
factorize the expressions
x(x + 9) - 6(x + 9) = 0
Then, we have;
x- 6 = 0
x = 6
x + 9 = 0
x = -9
Learn about quadratic equations at: https://brainly.com/question/1214333
#SPJ1
a student aimed to get a mean mark of 80% in his mathematics test after 9 tests his mean mark is 79%. Calculate the lowest mark he requires in his last test to enable him to achieve his target.
Answer:
89
Step-by-step explanation:
construct the formula to obtain the total of marks in first 9 tests:
79 = x/9
79 * 9 = 711
x = 711
so to get 80% in the next test we construct this formula:
80 = 711 + y / 9 + 1
the value we get for y is 89
to confirm the answer, 711+89/10 gives us 80, which is the correct value we want
