Surface area of [tex]\(r_2(u,v)\)[/tex] is [tex]\(25\)[/tex] times the area of parameter domain[tex]\(D\),[/tex] yielding [tex]\(1600\)[/tex] if [tex]\(D\)[/tex] is [tex]\(8 \times 8\).[/tex]
Let's break it down step by step:
step:-1. **Define the parametric surfaces**: We have two parametric surfaces: [tex]\( r_1(u,v) = f(u,v)i + g(u,v)j + h(u,v)k \)[/tex] and [tex]\( r_2(u,v) = 5r_1(u,v) \).[/tex]
step:-2. **Calculate the partial derivatives**: Compute the partial derivatives of [tex]\( r_1 \)[/tex] with respect to [tex]\( u \)[/tex] and [tex]\( v \)[/tex] denoted by [tex]\( r_{1u} \)[/tex] and [tex]\( r_{1v} \).[/tex]
step:-3. **Multiply by 5**: Since[tex]\( r_2(u,v) = 5r_1(u,v) \),[/tex] the partial derivatives of [tex]\( r_2 \)[/tex] with respect to [tex]\( u \)[/tex] and [tex]\( v \)[/tex] will be 5 times the corresponding partial derivatives of [tex]\( r_1 \)[/tex], denoted by [tex]\( r_{2u} \)[/tex] and [tex]\( r_{2v} \).[/tex]
step:-4. **Calculate the cross product**: Compute the cross product of [tex]\( r_{2u} \)[/tex] and[tex]\( r_{2v} \),[/tex] denoted by [tex]\( \| r_{2u} \times r_{2v} \| \)[/tex]. This will be 25 times the magnitude of the cross product of [tex]\( r_{1u} \)[/tex] and [tex]\( r_{1v} \),[/tex] as the cross product is linear with respect to the vectors involved.
step:-5. **Surface area integral**: Use the formula for the surface area integral: [tex]\( A = \iint_D \| r_u \times r_v \| \, dA \),[/tex] where [tex]\( \| r_{2u} \times r_{2v} \| \)[/tex] replaces [tex]\( \| r_{u} \times r_{v} \| \).[/tex]
step:-6. **Calculate the integral**: Integrate[tex]\( \| r_{2u} \times r_{2v} \| \)[/tex] over the parameter domain [tex]\( D \)[/tex]. Since [tex]\( \| r_{2u} \times r_{2v} \| \)[/tex] is constant and equal to 25 times the magnitude of the cross product of [tex]\( r_{1u} \)[/tex] and [tex]\( r_{1v} \)[/tex], the integral becomes [tex]\( 25 \times \text{Area of } D \).[/tex]
step:-7. **Determine the area of the parameter domain**: If the parameter domain [tex]\( D \)[/tex] is a rectangle with sides of length 8 in both directions, its area is [tex]\( 8 \times 8 = 64 \).[/tex]
step:-8. **Final calculation**: Multiply the area of [tex]\( D \)[/tex] by 25 to get the surface area of[tex]\( r_2(u,v) \)[/tex], which is[tex]\( 25 \times 64 = 1600 \).[/tex]
So, the surface area of the parametric surface given by [tex]\( r_2(u,v) = 5r_1(u,v) \)[/tex] is 1600.
The surface area of the parametric surface [tex]\( \mathf{r}_2(u, v) \)[/tex] is 25.
To find the surface area of the parametric surface given by [tex]\( \mathf{r}_2(u, v) = 5 \mathf{r}_1(u, v) \)[/tex] where [tex]\( -4 \leq u \leq 4 \)[/tex] and [tex]\( -4 \leq v \leq 4 \)[/tex], given that the surface area of [tex]\( \mathf{r}_1(u, v) \)[/tex] over the same parameter range is 1, follow these steps:
Surface Area of [tex]\( \mathf{r}_1(u, v) \)[/tex]
The surface area of [tex]\( \mathf{r}_1(u, v) \)[/tex] is given to be 1.
Relationship Between [tex]\( \mathf{r}_1 \) and \( \mathf{r}_2 \)[/tex]
[tex]\[ \mathf{r}_2(u, v) = 5 \mathf{r}_1(u, v) \][/tex]
Effect of Scaling on Surface Area
When a surface is scaled by a factor k, the surface area is scaled by a factor of k². This is because surface area is a two-dimensional measure, and scaling each dimension by k multiplies the area by k².
Calculation for [tex]\( \mathf{r}_2(u, v) \)[/tex]
In this problem, the scaling factor k is 5. Therefore, the surface area of [tex]\( \mathf{r}_2(u, v) \)[/tex] will be [tex]\( 5^2 \)[/tex] times the surface area of [tex]\( \mathf{r}_1(u, v) \)[/tex].
[tex]\[\text{Surface area of } \mathf{r}_2(u, v) = 5^2 \times \text{Surface area of } \mathf{r}_1(u, v)\][/tex]
Substitute the Given Surface Area
The surface area of [tex]\( \mathf{r}_1(u, v) \)[/tex] is 1.
[tex]\[\text{Surface area of } \mathf{r}_2(u, v) = 5^2 \times 1 = 25\][/tex]
For a school fundraiser Jeff sold large boxes of candy for three dollars each and small boxes of candy for two dollars each if you sold 37 boxes in all for total of $96 how many more large boxes then small boxes did he sell
A. 7
B. 8
C. 8
D. 12
Answer:
C
Step-by-step explanation:
Answer: The correct option is
(A) 7.
Step-by-step explanation: Given that for a school fundraiser, Jeff sold large boxes of candy for three dollars each and small boxes of candy for two dollars each.
Also, Jeff sold 37 boxes in all for total of $96.
We are to find the number of large boxes more than that of small boxes.
Let x and y represents the number of large boxes and small boxes respectively.
Then, according to the given information, we have
[tex]x+y=37~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x+2y=96~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Multiplying equation (i) by 2 and subtracting from equation (ii), we get
[tex](3x+2y)-(2x+2y)=96-37\times2\\\\\Rightarrow x=96-74\\\\\Rightarrow x=22.[/tex]
From equation (i), we get
[tex]22+y=37\\\\\Rightarrow y=37-22\\\\\Rightarrow y=15.[/tex]
We have,
[tex]x-y=22-15=7.[/tex]
Thus, there are 7 more large boxes than small boxes.
Option (A) is CORRECT.
A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 220 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?
Answer:
* The largest area can be enclosed is 6050 feet²
Step-by-step explanation:
* Lets explain the situation to solve the problem
- There is a rectangular parking
- The parking will surrounded by fencing from three sides only
- The length of fencing is 220 feet
- Lets consider the width of the rectangle is x and the length of it is y
- The side along the street will not fence
* Lets put all of these data in equation
∵ The width of the parking is x
∵ The length of the parking is y
- He will not fence the side along the street
∴ The perimeter of the parking = x + y + x
∴ The perimeter of the parking = 2x + y
- The length of the fencing = the perimeter of the park
∵ The length of the fencing = 220 feet
∵ The perimeter of the parking = 2x + y
∴ 2x + y = 220 ⇒ (1)
- Lets find the area of the parking
∵ The area of any rectangle is length × width
∵ The width of the rectangle is x
∵ The length of the rectangle is y
∴ The area of the parking (A) = x × y
∴ The area of the parking = xy ⇒ (2)
- Lets find the value of y from equation (1) and substitute this value
in equation (2)
∵ 2x + y = 220 ⇒ subtract 2x from both sides
∴ y = 220 - 2x
- Substitute this value in equation (2)
∵ A = xy
∴ A = x(220 - 2x) ⇒ open the bracket
∴ A = 220x - 2x²
- To find the largest area differentiate the area with respect to x
and equate the result by 0 to find x which gives the largest area
∵ A = 220x - 2x²
- Lets remember the differentiation rules
# If y = a x^n, where a is the coefficient of x then dy/dx = (an) x^(n-1)
# If y = ax, then dy/dx = a
# If y = a, where a is constant then dy/dx = 0
∴ dA/dx = 220 - 2(2) x^(2-1)
∴ dA/dx = 220 - 4x
- Put dA/dx = 0 ⇒ for largest area
∵ dA/dx = 0
∴ 220 - 4x = 0 ⇒ add 4x to both sides
∴ 220 = 4x ⇒ divide both sides by 4
∴ 55 = x
* The width of the parking is 55 feet
- Substitute this value of x in the equation of the area to find the
largest area
∵ A = 220x - 2x²
∵ x = 55
∴ A = 220(55) - 2(55)² = 12100 - 6050 = 6050 feet²
* The largest area can be enclosed is 6050 feet²
To find the largest area that can be enclosed by the given amount of fencing, we can use the concept of optimization and solve for a rectangular lot's dimensions that maximize the area. The largest area that can be enclosed is 6050 square feet.
Explanation:
To find the largest area that can be enclosed, we can use the concept of optimization. Let's assume the length of the rectangular lot is x feet. The remaining length, which is not fenced, will be 220 - 2x feet. The width of the lot will be y feet. So we have 2x + y = 220. To find the largest area, we need to express the area in terms of a single variable. A = xy, substitute y = 220 - 2x. So A = x(220 - 2x) = 220x - 2x^2. To find the maximum value of A, we can find the vertex of the parabola, which corresponds to the maximum. The x-coordinate of the vertex is -b/2a. In this case, a = -2, b = 220, so x = -220/(-2*2) = 55.Plug this value of x into the equation y = 220 - 2x. y = 220 - 2(55) = 110. So the dimensions of the lot that will enclose the largest area are 55 feet by 110 feet. Substituting these values into the area formula A = xy, we get A = 55 * 110 = 6050 square feet.
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A function in which each y value has more than one corresponding x value is called a
A: nonlinear function
B: many to one function
C one to one function
D linear function
For each Y value to have more than one x value would be a linear function.
It would make a straight line.
The correct answer is B: many-to-one function. This is the type of function where one y value is associated with multiple x values, differing from linear, nonlinear, and one-to-one functions.
A function in which each y value has more than one corresponding x value is known as a many-to-one function. This type of function allows for multiple x values to be paired with a single y value. This should not be confused with nonlinear functions or one-to-one functions. Moreover, while linear function is often associated with straight lines, in algebra, a linear function may actually include more than one term, each having a single multiplicative parameter. For example, y = ax + bx² is linear in this algebraic sense because terms x and x² each have one parameter (a and b). However, a function like y = [tex]x^b[/tex], where b is an exponent rather than a multiplicative parameter, is an example of a nonlinear function as it cannot be accurately described using linear regression.
Eric deposited $9,033.00 into a new savings account that earns interest compounded monthly. After 11 months, the balance in the account was $10,230.00. What was the interest rate on the account?
Round your answer to the nearest tenth of a percent.
Dang that’s tuff I feel bad
A spinner is divided into four equal sections that are numbered 2, 3, 4, and 9. The spinner is spun twice. How many outcomes have a product less than 20 and contain at least one even number?
Answer with Step-by-step explanation:
On spinning the spinner twice,we have 16 different outcomes:.
We write the outcomes with their product:
Product
2 2 4
2 3 6
2 4 8
2 9 18
3 2 6
3 3 9
3 4 12
3 9 27
4 2 8
4 3 12
4 4 16
4 9 36
9 2 18
9 3 27
9 4 36
9 9 81
outcomes have a product less than 20 and contain at least one even number are in bold letters.
Hence, outcomes have a product less than 20 and contain at least one even number are:
10
There are 8 outcomes of spinning the spinner twice that result in a product less than 20 and contain at least one even number.
To determine how many outcomes of spinning a spinner twice result in a product less than 20 and contain at least one even number, we start by listing all possible outcomes.
The spinner is divided into four equal sections: 2, 3, 4, and 9. When spun twice, there are 16 outcomes in total:
(2,2)(2,3)(2,4)(2,9)(3,2)(3,3)(3,4)(3,9)(4,2)(4,3)(4,4)(4,9)(9,2)(9,3)(9,4)(9,9)We now filter these outcomes to find those with a product less than 20 and at least one even number:
(2,2) - Product: 4(2,3) - Product: 6(2,4) - Product: 8(3,2) - Product: 6(3,4) - Product: 12(4,2) - Product: 8(4,3) - Product: 12(4,4) - Product: 16The total number of outcomes that meet the criteria is 8.
A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the 0.025 significance level. H0: μ ≥ 220 H1: μ < 220 Is this a one- or two-tailed test? One-tailed test Two-tailed test What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) What is your decision regarding H0? Reject Do not reject What is the p-value? (Round your answer to 4 decimal places.) rev: 10_28_2017_QC_CS-107404 Next Visit question mapQuestion 2 of 4 Total 2 of 4 Prev
Answer:
15 million
Step-by-step explanation:
This is a one-tailed test with a significance level of 0.025. The test statistic is -1.83, and we reject the null hypothesis. The p-value is approximately 0.0344.
Explanation:This is a one-tailed test because the alternative hypothesis (H1) is specifying a less than condition (<) for the population mean.
The decision rule for a one-tailed test with a significance level of 0.025 is to reject the null hypothesis (H0) if the test statistic is less than the critical value.
The test statistic is calculated by subtracting the hypothesized population mean from the sample mean and dividing by the standard deviation divided by the square root of the sample size. In this case, the test statistic is [(215 - 220) / (15 / sqrt(64))] = -1.83 (rounded to 3 decimal places).
In order to make a decision regarding H0, we compare the test statistic with the critical value. If the test statistic is less than the critical value, we reject H0. Otherwise, if the test statistic is greater than or equal to the critical value, we fail to reject H0. In this case, -1.83 is less than the critical value, so we reject H0.
The p-value is the probability of obtaining a test statistic as extreme as the one observed, assuming that the null hypothesis is true. To find the p-value, we look up the test statistic in the standard normal distribution table. In this case, the p-value is approximately 0.0344 (rounded to 4 decimal places).
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The expression is the result of applying the change of base formula to a logarithmic expression.
Which could be the original expression?
x= 8 is the correct answer
Answer:
x = 8
Step-by-step explanation:
Given equation is,
[tex]log_5(10x-1)=log_5(9x+7)[/tex]
We know that,
[tex]log_a(b)=log_a(c)\implies b = c[/tex]
[tex]\implies 10x -1 = 9x + 7[/tex]
Subtracting 9x on both sides,
[tex]x - 1 = 7[/tex]
Adding 1 on both sides,
[tex]x = 8[/tex]
Hence, the solution would be x = 8
Vance is designing a garden in the shape of an isosceles triangle. The base of the garden is 30 feet long. The function y = 15 tan θ models the height of the triangular garden. What is the height of the triangle when θ = 30 ° ? What is the height of the triangle when θ = 40 ° ? Vance is considering using either θ = 30 ° or θ = 40 ° for his garden. Compare the areas of the two possible gardens. Explain how you found the areas.
Answer:
Part 1) The height of the triangle when θ = 30° is equal to [tex]8.66\ ft[/tex]
Part 2) The height of the triangle when θ = 40° is equal to [tex]12.59\ ft[/tex]
Part 3) The area of triangle with θ = 30° is less than the area of triangle with θ = 40°
Step-by-step explanation:
Part 1) What is the height of the triangle when θ = 30 ° ?
we have
[tex]y=15tan(\theta)[/tex]
substitute the value of theta in the equation and find the height
[tex]y=15tan(30\°)=8.66\ ft[/tex]
Part 2) What is the height of the triangle when θ = 40 ° ?
we have
[tex]y=15tan(\theta)[/tex]
substitute the value of theta in the equation and find the height
[tex]y=15tan(40\°)=12.59\ ft[/tex]
Part 2) Vance is considering using either θ = 30 ° or θ = 40 ° for his garden
Compare the areas of the two possible gardens
step 1
Find the area when θ = 30 °
The height is [tex]8.66\ ft[/tex]
Remember that the area of a triangle is equal to the base multiplied by the height and divided by two
so
[tex]A=(1/2)(30)(8.66)=129.9\ ft^{2}[/tex]
step 2
Find the area when θ = 40°
The height is [tex]12.59\ ft[/tex]
Remember that the area of a triangle is equal to the base multiplied by the height and divided by two
so
[tex]A=(1/2)(30)(12.59)=188.85\ ft^{2}[/tex]
Compare the areas of the two possible gardens
The area of triangle with θ = 30° is less than the area of triangle with θ = 40°
Can someone help me with this math question?
Answer:
see attachment
Step-by-step explanation:
It is convenient to use a spreadsheet for this purpose.
The first row of numbers is constant at $45, as there is no daily charge associated with that payment method.
The second row of numbers uses the formula ...
cost = $12 + $4×(number of days)
The third row of numbers uses the formula ...
cost = $6×(number of days)
___
Of course, you can use these formulas to fill in the numbers by hand. For example, for 15 days, the charges are ...
Early Pay: $45 (no calculation necessary)Deposit Plus: $12 + $4×15 = $12 +60 = $72Daily Pay: $6×15 = $90The function f(x) = x2 - 6x + 9 is shifted 5 units to the left to create g(x). What is g(x)?
Answer:
g(x) = x^2 + 4x + 4
Step-by-step explanation:
In translation of functions, adding a constant to the domain values (x) of a function will move the graph to the left, while subtracting from the input of the function will move the graph to the right.
Given the function;
f(x) = x2 - 6x + 9
a shift 5 units to the left implies that we shall be adding the constant 5 to the x values of the function;
g(x) = f(x+5)
g(x) = (x+5)^2 - 6(x+5) + 9
g(x) = x^2 + 10x + 25 - 6x -30 + 9
g(x) = x^2 + 4x + 4
Please help me simplified this
For this case we have that by definition, the perimeter of the quadrilateral shown is given by the sum of its sides:
Let "p" be the perimeter of the quadrilateral, then:
[tex]p = 7 + y + 7 + x\\p = 7 + 7 + x + y\\p = 14 + x + y[/tex]
So, the perimeter of the figure is: [tex]14 + x + y[/tex]
Answer:
[tex]p = 14 + x + y[/tex]
Answer:
perimeter = x + y + 14
Step-by-step explanation:
The perimeter is the sum of the side lengths:
perimeter = x + 7 + y + 7
The constants can be combined to give ...
perimeter = x + y + 14
___
An "equation" will have an equal sign somewhere. Since you want to find the perimeter, it makes sense for the equation to show you how to find the perimeter. (I have used "perimeter" to represent the perimeter. It is often represented using the letter P. Of course, you can choose any variable or other representation you like.)
Last answer choice is 4,2
Help
Use the midpoint formula:
(-7,-4) (-1,8)
(-7 + -1) /2 , (-4 +8) /2
-8/2 , 4/2
Midpoint = (-4,2)
The angle formed by the intersection of a secant and a tangent is equal to the sum of the measures of the intercepted arcs.
True
False
Answer: False
Step-by-step explanation:
The measure of the created angle is equal to the difference of the measure of the arcs.
The angle formed by the intersection of a secant and a tangent is equal to half the measure of the intercepted arc, not the sum of the measures of the intercepted arcs.
Explanation:The statement is False. The angle formed by the intersection of a secant and a tangent is half the measure of the intercepted arc, not equal to the sum of the measures of the intercepted arcs.
For example, let's consider a circle with a secant and a tangent line intersecting at a point. The intercepted arc is represented by the section of the circumference between the two points of intersection. The angle formed by the intersection of the secant and the tangent is equal to half the measure of this intercepted arc.
So, in conclusion, the angle formed by the intersection of a secant and a tangent is equal to half the measure of the intercepted arc.
Which of the following expressions is true
A. 2^4 * 2^3 = 2^12
B. 3^3 * 3^6 >3^8
C. 4^2 * 4^2 >4^4
D. 5^5 * 5^2 =5^10
3³ X 3⁶ > 3⁸ is the correct expression.
What is Equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Here, Let first equation is true,
then, LHS = 2⁴ X 2³
= 2⁴⁺³
= 2⁷
≠ RHS
Option A is false.
Again assume option B is true.
Now check, LHS = 3³ X 3⁶
= 3³⁺⁶
= 3⁹
>3⁸
LHS > RHS
Thus, 3³ X 3⁶ > 3⁸ is the correct expression.
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Emerson is making a box without a top from a rectangular piece of cardboard, with dimensions 12in by 16in, by cutting out square corners with side length x in.
A) Write an equation for the volume V of the box in terms of x.
B) Use technology to estimate the value of x that gives the greatest volume. Round the value to the nearest tenth.
C) Assume Emerson used the value of d you found in Part (b) to make his box. What were the dimensions of Emerson’s box?
Answer:
Step-by-step explanation:
The volume of a rectangular box is width times length times height:
V = wlh
After the cardboard is folded, the width is 12 - 2x, the length is 16 - 2x, and the height is x.
So the volume is:
V = (12 - 2x) (16 - 2x) x
If we graph this, we get a wave: desmos.com/calculator/rsjosgzuxz
The wave is the highest at around x = 2.3 in.
If we set x = 2.3:
w = 12 - 2x = 7.4
l = 16 - 2x = 11.4
h = x = 2.3
In one town, 4242% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are both Democrats. Round to the nearest thousandth if necessary.
Answer:
hi
Step-by-step explanation:
Mike wants to redesign a box. Currently, it’s length is 20 cm, it’s width is 30 cm and it’s height is 40cm. he wants to keep the volume and the length unchanged and increase the height by 25 percent. What will be the new width of the box?
Answer:
24 cm
Step-by-step explanation:
The product of height and width will remain the same, so the new width (w) will be given by ...
w·(new height) = (old width)·(old height)
w·(1.25·40 cm) = (30 cm)(40 cm)
w = (30 cm)/1.25 = 24 cm . . . . . . . divide by 1.25·40 cm and simplify
_____
This derives from the fact that volume and length are unchanged. The formula for the volume in terms of length, width, and height is ...
V = LWH
Then the product of W and H is the constant ...
V/L = WH . . . . . divide by L
For our purpose, we only need to know that V and L are unchanged, so the product WH is unchanged. We don't need to know their values.
Of course, increasing the height by 25% is equivalent to multiplying it by 1.25:
H + 25/100·H = H·(1 + 0.25) = 1.25H
PLEASE HELP!!! Solve -(6)^x-1+5=(2/3)^2-x by graphing. Round to the nearest tenth.
X = 1.8 <--- ANSWER
Answer:
x= 1.8
Step-by-step explanation:
We have been given the equation;
-(6)^(x-1)+5=(2/3)^(2-x)
We are required to determine the value of via graphing. To do this we can split up the right and the left hand sides of the equation to form the following two separate equations;
y = -(6)^(x-1)+5
y = (2/3)^(2-x)
We then proceed to graph the two equations on the same graph. The solution will be the point where the equations will intersect. Find the attachment below for the graph;
The value of x is 1.785. To the nearest tenth we have x = 1.8
etermine if the following statement is true or false. If there is clearance for 95% of males, there will certainly be clearance for all women in the bottom 5%. A. The statement is true because some women will have sitting knee heights that are outliers. B. The statement is false because the 95th percentile for men is greater than the 5th percentile for women. C. The statement is true because the 95th percentile for men is greater than the 5th percentile for women. D. The statement is false because some women will have sitting knee heights that are outliers.
Answer:
C. The statement is true because the 95th percentile for men is greater than the 5th percentile for women.
Step-by-step explanation:
We suspect relevant data is missing, including exactly what clearance the the statement is referring to. It would be nice to know where the various men's and women's percentiles lie.
We give the above answer on the basis of the assumption that the largest of men are always larger than the smallest of women.
For each x and n, find the multiplicative inverse mod n of x. Your answer should be an integer s in the range 0 through n - 1. Check your solution by verifying that sx mod n = 1.(a) x = 52, n = 77(b) x = 77, n = 52(c) x = 53, n = 71(d) x = 71, n = 53
To find the multiplicative inverse of x modulo n, we need to find an integer s such that (x * s) mod n = 1. We can calculate the multiplicative inverses for the given values: (a) x = 52, n = 77: s = 65. (b) x = 77, n = 52: s = 33. (c) x = 53, n = 71: s = 51. (d) x = 71, n = 53: s = 9.
Explanation:To find the multiplicative inverse modulo n of x, we need to find an integer s such that (x * s) mod n = 1. Let's calculate the multiplicative inverses for the given values:
a) For x = 52 and n = 77:
x * s ≡ 1 (mod n)
52 * s ≡ 1 (mod 77)
s ≡ 65 (mod 77)
So, the multiplicative inverse of 52 modulo 77 is 65.
b) For x = 77 and n = 52:
77 * s ≡ 1 (mod 52)
s ≡ 33 (mod 52)
The multiplicative inverse of 77 modulo 52 is 33.
c) For x = 53 and n = 71:
53 * s ≡ 1 (mod 71)
s ≡ 51 (mod 71)
The multiplicative inverse of 53 modulo 71 is 51.
d) For x = 71 and n = 53:
71 * s ≡ 1 (mod 53)
s ≡ 9 (mod 53)
The multiplicative inverse of 71 modulo 53 is 9.
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A number is increased by 54. The sumos then divided by 9. The result is 21. Write an equation to represent the discription, use n for the number
Answer:
(n+54)/9 = 21
Step-by-step explanation:
A number: n
Is increased by 54: n+54
The sum is divided by 9: (n +54)/9
and the result is 21:
(n +54)/9 = 21
Solve for x. x2 - 2x - 24 = 0 A. -4, -6 B. -4, 6 C. 2, -6 D. 4, 6 Reset Next
Answer:
B. -4, 6
Step-by-step explanation:
Given the quadratic equation;
x^2 - 2x - 24 = 0
we can determine the solution by first factoring the expression on the left hand side. We determine two numbers whose product is -24 and sum -2. By trial and error the two numbers are found to be;
-6 and 4
We replace the middle term, -2x, with these two values;
x^2 + 4x -6x -24 = 0
x(x+4) -6(x+4) = 0
(x-6)(x+4) = 0
x-6 = 0 or
x + 4 = 0
x = 6 or x = -4
Answer: the answer is B
Step-by-step explanation: -4 & 6 are both zeros of the function .
f(x)=4x2+8x-9 find and simplify f(2+x)
a. 23+x
b. 4x^2+8x-11
c. 4x^2+2x+23
d. 4x^2+24x+23
Answer:
d. 4x^2 +24x +23
Step-by-step explanation:
Evaluating polynomials is sometimes easier when they are written in Horner form:
f(x) = (4x +8)x -9
Substituting (x+2) for x, we have ...
f(x+2) = (4(x+2)+8)(x+2) -9
= (4x +16)(x +2) -9
= 4x^2 +24x +32 -9
= 4x^2 +24x +23 . . . . . matches choice D
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Alternative method
You can observe that the answer choices differ in the coefficient of the x-term. So, to make the correct selection, you only need to find the coefficient of the x-term. That will be the sum of coefficients of the x-terms in 4(x+2)^2 and 8(x+2). Those x-terms are 4·4x and 8x, so have a sum of (16+8)x = 24x. This matches choice D.
Willie has 4 baseball caps. Two of the caps are blue. One of the caps is red and one is green. What fraction of the caps is blue?
Answer:
2/4
when simplified = 1/2
Your answer is 1/2
Step-by-step explanation:
Amt. of Baseball caps = 4
Blue caps = 2
which can be written as 2/4
when simplified 2/4 ÷ 2/2 = 1/2
Willie has 4 baseball caps, of which 2 are blue. To find the fraction of caps that are blue, divide the number of blue caps (2) by the total number of caps (4), resulting in a fraction of 1/2.
Explanation:Willie has 4 baseball caps in total, and 2 of those caps are blue. To determine what fraction of the caps is blue, you divide the number of blue caps by the total number of caps.
So, the calculation would be:
Number of blue caps = 2Total number of caps = 4Fraction of caps that are blue = Number of blue caps ÷ Total number of caps = 2 ÷ 4 = 1/2Therefore, the fraction of Willie's caps that are blue is 1/2, which means half of the caps are blue.
In order to qualify for a role in a play, an actor must be taller than 64 inches but shorter than 68 inches. The inequality 64 < x < 68, where x represents height, can be used to represent the height range. Which is another way of writing the inequality? x > 64 and x < 68 x > 64 or x < 68 x < 64 and x < 68 x < 64 or x < 68
Answer:
Option A is correct.
Step-by-step explanation:
64 < x < 68
This inequality represent that the height x should be greater than 64 and less than 68.i.e.
x>64 and x<68
So, Option A is correct.
Answer:
x>64 and x<68
Step-by-step explanation:
Anyone who could help with this it would be amazingly appreciated.
The sum of angles in ΔABD is ...
2a + b + d = 180
The sum of angles in ΔAHG is ...
a + h + 90 = 180
Solving this second equation for a, we have ...
a = 180 -90 -h = 90 -h
Substituting this into the first equation, we have ...
2(90 -h) +b +d = 180
180 -2h +b +d = 180 . . . . . eliminate parentheses
b + d = 2h . . . . . . . . . . . . . add 2h-180
h = (1/2)(b+d) . . . . . . . . . . divide by 2
Mike correctly found the slope and y intercept of the line passing through the points(-5,-2)and (3,14)as follows.
Answer:
y= 2x+8
Step-by-step explanation:
The standard form of an equation of line in slope-intercept form is:
y= mx+b
Where m is the slope of the line and b is the y-intercept of the line.
To obtain the equation from the given information we need to put the values of m and b into the standard form of equation.
We are given
m = 2
and
b = 8
So putting the values of m and b
y = (2)x +8
y= 2x+8 ..
THE ANSWER IS :y=2x +8
just know its right.
Describe the piece wise function below by evaluating the function for given values of the domain.
Answer:
y = -3 (x ≤ -2)y = 2x - 3 (-2 < x ≤ 2)y = 5 (2 < x)Step-by-step explanation:
The leftmost piece of the function is constant at -3.
The middle piece is a line with a slope of 2 that intersects the y-axis at -3, so has equation y = 2x-3. (The slope-intercept form of the equation of a line is y = slope·x + y-intercept. The slope is found by counting the number of vertical grid squares that correspond to each horizontal grid square.)
The rightmost piece is constant at +5.
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We don't know what your choices are, so we can't tell you which to select.
The piecewise function is a horizontal line restricted between x = 0 and x = 20. To evaluate the function, substitute the given values into the function.
Explanation:The given piecewise function is:
f(x) =
a horizontal line for 0 ≤ x ≤ 20restricted to the portion between x = 0 and x = 20To evaluate the function for given values of the domain, you can substitute the given values of x into the function and calculate the corresponding y-values. For example, to find f(5), substitute x = 5 into the function and evaluate.
It is important to note that the question does not provide the equation or specific values of the function, so the evaluation of the function cannot be performed without additional information.
In rhombus JKLM, if m<KLJ = 38°, find m<JIVIL.
Answer:
∠JML = 104°
Step-by-step explanation:
JL bisects angle KLM, so ...
∠KLM = 2·∠KLJ = 2·38° = 76°
Adjacent angles in any parallelogram are supplementary, so ...
∠JML = 180° -∠KLM = 180° -76°
∠JML = 104°
Use the order of operations to simplify the expression: 2^3 + 5 × 10 ÷ 2 – 3^3 + (11 – 8) Question 5 options: A)9 B)10 C)41 D)55 my answer when I worked it ended up being 3. Clearly, that’s not a choice
For this case we have that according to the order of PEMDAS algebraic operations, it is established that:
P: Any calculation is made inside the parentheses, making the most internal ones first.
E: Any exponential expressions are simplified.
MD: All the multiplications and divisions are made, from left to right, as they appear.
AS: All sums and subtractions are made, from left to right, as they appear.
So:
[tex]2 ^ 3[/tex] + 5 * 10 ÷ 2-[tex]3 ^ 3[/tex] + (11-8) =
[tex]2 ^ 3[/tex]+ 5 * 10 ÷ 2-[tex]3 ^ 3[/tex] + 3 =
8 + 5 * 10 ÷ 2-27 + 3 =
8 + 50 ÷ 2-27 + 3 =
8 + 25-27 + 3 =
33-27 + 3
6 + 3 =
9
Answer:
9