Increase 42 by 16% show working please​

Answer:

a sin(bθ−c)+d

→ Using this, find the amplitude based off of the given formula. Use the expression as a reference to help you identify a.

a = 3

b = 4

c = 0(no defined value)

d = 0(impossible to identify)

→ Find a.

→ Since a is already given, we know that a = 3, therefore, the amplitude is 3

Answer:

V = 81π/4

To find the volume of the solid formed by rotating the region bounded by the graph of y = x^2, x = 3, and y = 0 around the x-axis, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is:

V = ∫[a,b] 2πx * f(x) * dx

In this case, the region is bounded by x = 3, y = 0, and the curve y = x^2. We need to determine the limits of integration (a and b) based on the intersection points of these curves.

Since y = x^2 and y = 0, we can set x^2 = 0 and solve for x to find the intersection point:

x^2 = 0

x = 0

Therefore, the limits of integration are from x = 0 to x = 3.

Now we can set up the integral:

V = ∫[0,3] 2πx * (x^2) * dx

Integrating this expression will give us the volume of the solid. Evaluating the integral:

V = ∫[0,3] 2πx^3 dx

V = π * [(1/4)x^4] [0,3]

V = π * (1/4) * (3^4 - 0^4)

V = π * (1/4) * (81 - 0)

V = π * (1/4) * 81

V = 81π/4

Therefore, the volume of the solid formed by rotating the region bounded by the graph of y = x^2, x = 3, and y = 0 around the x-axis is 81π/4 cubic units.

Explanation:

Refer to the fundamental theorem of algebra. That theorem says the most roots or zeros a polynomial of degree n can have is n roots.

Example: The cubic x^3+5x has at most 3 real roots.

both is 14 hope it helps

first picture is incorrect second one is correct. answer is 14

True , if a and b are matrices corresponding to orthogonal projections, then the matrix is also the matrix corresponding to some orthogonal projection .

Given :

Orthogonal projections of matrices :

A square matrix P is called an orthogonal projector (or projection matrix) if it is both idempotent and symmetric  that is, P^2 = P and P′ = P .

The matrix must obey or to be the both symmetric and idempotent matrices to be an orthogonal projector .

so the matrix is also the matrix corresponding to some orthogonal projection .

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The expected value of y is (D.) 35.5.

The expected value of a discrete random variable is found by multiplying each value of the variable by its corresponding probability and then summing these products. In this case, the probability distribution of y is given in the table.

To find the expected value of y, we need to calculate the sum of the products of each value of y and its corresponding probability.

y * probability = y * P(y)

The expected value of y is E(y) = 100.10 + 200.25 + 300.05 + 400.30 + 500.20 + 600.10

= 2 + 5 + 1.5 + 12 + 10 + 6 = 37.

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Because the z-critical value for a 95% C.I is longer than the z-critical value for a 90% C.I, the 95% c.I is always wider than the 90% CI for any given sample.

We are aware that the width of the C.I. ale o inverses grows with confidence level. As a result, the 95% C.I. is wider than the 90% C.I. since the critical value of the 95% C.I. is higher.

Because the z-critical value for a 95% C.I is longer than the z-critical value for a 90% C.I, the 95% c.I is always wider than the 90% CI for any given sample.

Percentage:

Use the percentage formula to express a number or percentage in terms of 100. % simply indicates one out of one hundred. An expression for a number between 0 and 1 can be made using the percentage formula. It is a number that is represented as a fraction of 100. The sign % is used to denote it and it is mostly used to compare and calculate ratios. The formula for percentage increases is the ratio of the increased value to the original value multiplied by 100. It is described in percentage form. If anything is valued more highly, both its value and proportion will rise.

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These equatiοns represent the fact that the slοpes and y-intercepts οf the lines fοrming the sides οf the triangle are related, and that the lines intersect at the vertices οf the triangle.

An equatiοn is a mathematical statement that asserts that twο expressiοns are equal. It cοnsists οf twο sides, a left-hand side and a right-hand side, cοnnected by an equal sign "=". The expressiοns οn either side οf the equal sign can be numbers, variables, οr cοmbinatiοns οf bοth.

Here,

Part a: If the three sides οf the triangle are denοted by a, b, and c, then we can write the fοllοwing system οf equatiοns:

a + b = c

b - a = 3

These equatiοns represent the fact that the sum οf twο sides οf a triangle is equal tο the third side (a + b = c), and that the difference between twο sides is equal tο a given value (b - a = 3).

Part b: If the cοοrdinates οf the vertices οf the triangle are given by (x₁, y₁), (x₂, y₂), and (x₃, y₃), then we can write three equatiοns representing the three sides οf the triangle. Fοr example, the equatiοn οf the line passing thrοugh (x₁, y₁) and (x₂, y₂) is given by:

(y₂ - y₁)/(x₂ - x1) = (y - y₁)/(x - x₁)

where (x, y) are the cοοrdinates οf any pοint οn the line. Similarly, we can write equatiοns fοr the οther twο sides οf the triangle, and οbtain a system οf three linear equatiοns.

Part c: If the equatiοns οf the three sides οf the triangle are given by Ax + By + C = 0, Dx + Ey + F = 0, and Gx + Hy + I = 0, then we can write the fοllοwing system οf equatiοns:

A/Bx + C/B = -(A/By + C/B) (frοm the first equatiοn)

D/Ex + F/E = -(D/Ey + F/E) (frοm the secοnd equatiοn)

G/Hx + I/H = -(G/Hy + I/H) (frοm the third equatiοn)

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Complete question:

The lines that form the three sides of the triangle can be grouped into three different systems of two linear equations. Create 3 equations using different methods.

Given: Radius of the wheel = 30 inches, Revolutions per minute = 401 rpmThe linear speed of the car in miles per hour can be calculated as follows:

Step 1: Convert the radius from inches to miles by multiplying it by 1/63360 (1 mile = 63360 inches).30 inches × 1/63360 miles/inch = 0.0004734848 milesStep 2: Calculate the distance traveled in one minute by the wheel using the circumference formula.Circumference = 2πr = 2 × π × 30 inches = 188.496 inchesDistance traveled in one minute = 188.496 inches/rev × 401 rev/min = 75507.696 inches/minStep 3: Convert the distance traveled in one minute from inches to miles by multiplying by 1/63360.75507.696 inches/min × 1/63360 miles/inch = 1.18786732 miles/minStep

4: Convert the distance traveled in one minute to miles per hour by multiplying by 60 (there are 60 minutes in one hour).1.18786732 miles/min × 60 min/hour = 71.2720392 miles/hour Therefore, the linear speed of the car is 71.3 miles per hour (rounded to the nearest tenth).Answer: 71.3

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The radius of the wheel on a car is 30 inches. If the wheel is revolving at 401 revolutions per minute, The linear speed of the car is approximately 19.2 miles per hour.

To find the linear speed of the car in miles per hour, we need to calculate the distance traveled in one minute and then convert it to miles per hour. Here's how we can do it step by step:

Calculate the circumference of the wheel:

The circumference of a circle is given by the formula

C = 2πr

where r is the radius of the wheel.

In this case, the radius is 30 inches, so the circumference is

C = 2π(30)

   = 60π inches.

Calculate the distance traveled in one revolution:

Since the circumference represents the distance traveled in one revolution, the distance traveled in inches per revolution is 60π inches.

Calculate the distance traveled in one minute:

Multiply the distance traveled in one revolution by the number of revolutions per minute.

In this case, it is 60π inches/rev * 401 rev/min = 24060π inches/min.

Convert the distance to miles per hour:

There are 12 inches in a foot, 5280 feet in a mile, and 60 minutes in an hour.

Divide the distance traveled in inches per minute by (12 * 5280) to convert it to miles per hour.

The final calculation is (24060π inches/min) / (12 * 5280) = (401π/66) miles/hour.

Approximating π to 3.14, the linear speed of the car is approximately (401 * 3.14 / 66) miles per hour, which is approximately 19.2 miles per hour.

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The area of the composite figure if ab ≅ bc ≅ cd ≅ da ≅ dn is (2π + 40) mm².

The area of a semicircle is the space contained by the circle. The area is the number of square units enclosed by the sides of the shape.

The area of the composite figure if ab ≅ bc ≅ cd ≅ da ≅ dn is given by adding an  area of MKCD , area of ABCD, area of a semi-circle with AB as diameter.

Area of the composite figure = area of MKCD + area of ABCD + area of a semi-circle with AB as diameter.

The area of the composite figure is;

Area A = (DC + MK)/2 × DN + AB² + (1/2)×π×2²

Area A = (4 + 8)/2 × 4 + 4² + (1/2)×π×4

Area A = 24 + 16 + 2π = (2π + 40) mm²

Hence, the area of the composite figure if ab ≅ bc ≅ cd ≅ da ≅ dn is (2π + 40) mm².

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Answer:

246 math and 82 history textbooks

Step-by-step explanation:

this one is a fun one

328 / 4 gives us a value of m and h which is 82

so 328 = 3x + y

328 = 3m(82) + 1h(82)

328 = 246m + 82h

328=328

Answer:

Step-by-step explanation:

Just divide 17.25 by 1.83 and you will get the answer. You'd get 9.4 but you can't have .4 of something so it is just 9.

Answer:

1550 miles

Step-by-step explanation:

rate * time = distance

620 m/hr  *  2.5 hr = 1550 miles

(Note that   2 hr and 30 min is 2 and 1/2 hours = 2.5 hours)

By answering the presented question, we may conclude that As a result, the slope of  y3= -4(x - 5) is -4.

Here, we have,

The slope of a line indicates how steep it is. The term "gradient overflow" refers to a mathematical equation for the gradient (the change in y divided by the change in x).

The slope is defined as the ratio of the vertical change (rise) between two places to the horizontal change (run). The slope-intercept form of an equation is used to express a straight line's equation, which is written as y = mx + b.

The y-intercept is found where the slope of the line is m, b is b, and (0, b). For example, the slope and y-intercept of the equation y = 3x - 7 (0, 7). The slope of the line is m. b is b at the y-intercept, and (0, b).

The above equation is in point-slope form: y -y1 = m(x -x1 ), where (x1,y1 ) is a point on the line and m is the slope.

We can see by comparing the provided equation to the point-slope form that (x1,y1) = (5, 3) and m = -4.

As a result, the slope of y3 = -4(x - 5) is -4.

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complete question;

Linear Functions

Quiz Active

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What is the slope of the equation y-3 = -4(x - 5)?

The standard form is 4x- y= 3.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

y-1=4(x-1)

Now, writing the above equation in standard form

y- 1 = 4x -4

y = 4x - 4 +1

y= 4x - 3

4x - y = 3

Hence, the standard form is 4x- y= 3.

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Answer:

Step-by-step explanation:

1). \((4t-\frac{8}{5})-(3-\frac{4}{3}t)=(4t+\frac{4}{3}t)+(-\frac{8}{5}-3)\)

                                  \(=(\frac{12}{3}t+\frac{4}{3}t)-(\frac{8}{5}+\frac{15}{5})\)

                                  \(=\frac{16}{3}t-\frac{23}{5}\)

2). 7t - 22

3). 5(2t + 1) + (-7t + 28) = 10t + 5 - 7t + 28

                                    = (10t - 7t) + 33

                                    = 3t + 33

4). \(\frac{16}{3}t-\frac{23}{5}\)

5). \((-\frac{9}{2}t+3)+(\frac{7}{4}t+33)=(-\frac{9}{2}t+\frac{7}{4}t)+(3+33)\)

                                       \(=(-\frac{18}{4}t+\frac{7}{4}t)+36\)

                                       \(=(\frac{-18+7}{4})t+36\)

                                       \(=-\frac{11}{4}t+36\)

6). \(-\frac{11}{4}t+36\)

7). 3(3t - 4) - (2t + 10) = 9t - 12 - 2t - 10

                                 = (9t - 2t) - ( 12 + 10)

                                 = 7t - 22

8). 3t + 33

Therefore, equivalent expressions are,

a). \((4t-\frac{8}{5})-(3-\frac{4}{3}t)=\frac{16}{3}t-\frac{23}{5}\)

b). 7t - 22 = 3(3t - 4) - (2t + 10)

c). \((-\frac{9}{2}t+3)+(\frac{7}{4}t+33)=-\frac{11}{4}t+36\)

d). 5(2t + 1) + (-7t + 28) = 3t + 33

I think it's D because the y-intercept is (0, -2), and in D the filled in circle is on (0, -2) and it goes up one and right one, which is the slope. Although C does this it ends with only one filled in circle, but D still has the two circles and line in between them.

Miguel takes 1.6 hours to cover the distance of 84.8 miles with the given speed of 53 miles per hour.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

here,
In the question, we are given a speed = 53 miles per hour and the distance traveled with the given speed is 84.8 miles, we have to determine the time for the same distance.
We know that,
Speed = distance/time
Speed = 84.8 / 53
Speed = 1.6 hours

Thus, the required time evaluated is 1.6 hours.

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Answer:

sorry i dont no

Step-by-step explanation:

Option a, adjacency matrix. An adjacency matrix is a two-dimensional array that represents a graph's edges, where the rows and columns correspond to the vertices of the graph. If there is an edge between two vertices, the corresponding element in the matrix is set to 1, otherwise it is set to 0. This implementation is useful for dense graphs, where the number of edges is close to the maximum possible number of edges.

An adjacency matrix is a simple and efficient way to represent graphs that have a large number of vertices and edges. It allows for fast lookups of the existence of an edge and is useful for various algorithms that require graph representation. However, it is not suitable for sparse graphs, where the number of edges is much smaller than the maximum possible number of edges. In such cases, an adjacency list would be more appropriate.

The common implementation of a graph that uses a two-dimensional array to represent the graph's edges is called an adjacency matrix.

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Answer:

x=16

Step-by-step explanation:

3*4=12

4*4=16

Answer:

100.00-20=80

320.00-20=300

Step-by-step explanation:

Answer:

102

Step-by-step explanation:

12 x 9 x 51 = 5508

5508 / 54 = 102

Hope this helps!

Answer:

102.00

Step-by-step explanation:

12 feet high *  9 feet wide * 51 feet long / 54 = the answer

The solution to the initial value problem is \(y(t) = (e^{3t}cos(4t) + e^{3t}sin{4t})/4 + u(t).\)

To solve the given initial value problem using the method of Laplace transforms, we can follow these steps:

Apply the Laplace transform to both sides of the differential equation, utilizing the linearity property of Laplace transforms. We also apply the initial value conditions:

\(s^2Y(s) - sy(0) - y'(0) - 6(sY(s) - y(0)) + 25Y(s) = 20/s,\)

where Y(s) represents the Laplace transform of y(t).

Simplify the equation by substituting the initial values: y(0) = 1 and y'(0) = 5. This yields:

\(s^2Y(s) - s - 5 - 6sY(s) + 6 + 25Y(s) = 20/s.\)

Rearrange the equation and solve for Y(s):

(s^2 - 6s + 25)Y(s) = 20/s + s + 1,

\((s^2 - 6s + 25)Y(s) = (s^2 + s + 20)/s + 1,\)

\(Y(s) = (s^2 + s + 20)/[(s^2 - 6s + 25)s] + 1/(s^2 - 6s + 25).\)

Use partial fraction decomposition to express Y(s) as a sum of simpler fractions. This requires factoring the denominator of the first term in the numerator:

\(Y(s) = [(s^2 + s + 20)/[(s - 3)^2 + 16]]/[(s - 3)^2 + 16] + 1/(s^2 - 6s + 25).\)

Apply the inverse Laplace transform to each term using the table of Laplace transforms and the properties of Laplace transforms.

The inverse Laplace transform of the first term involves the exponential function and trigonometric functions.

The inverse Laplace transform of the second term is simply the unit step function u(t).

After applying the inverse Laplace transform, we obtain:

\(y(t) = (e^{3t}cos(4t) + e^{3t}sin(4t))/4 + u(t).\)

Therefore, the solution to the initial value problem is \(y(t) = (e^{3t}cos(4t) + e^{3t}sin(4t))/4 + u(t).\)

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Answer:

45 degrees

Step-by-step explanation:

To estimate the volume of the chord of wood, since the wood exists cut into equal lengths and stacked evenly in a rack then we can use a cylinder as a model.

In mathematics, a cylinder exists as a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases exist normally circular (like a circle) and the center of the two bases exists joined by a line segment, which exists named the axis.

A cylinder exists as a closed solid that contains two parallel circular bases joined by a curved surface.

To calculate the volume of the chord of wood, since the wood exists cut into equal lengths and stacked evenly in a rack then we can use a cylinder as a model.

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Answer:

\( \: \)

Step-by-step explanation:

Let us assume A, B, C and D are the four angles of the parallelogram. Where, ∠A = 20° and we have to find the measure of ∠B, ∠C and ∠D

So, If ∠A = 20°, then So, also ∠C = 20°.

Therefore,

⠀

And, ∠A and ∠B are adjacent angles. We know,

So,

⇒ ∠A + ∠B = 180°

⇒ 20° + ∠B = 180°

⇒ ∠B = 180° – 20°

⇒ ∠B = 160°

So,

⠀

So, If ∠B = 160°, then So, also ∠D = 160°.

Therefore,

We can conclude after answering the presented question that Use the equation data to discover potential for process changes that might result in a reduction in the time necessary to perform the activity.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or readings of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the calculation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

The procedures that a manufacturing organisation might take to undertake a time study analysis are as follows:

List the tasks performed by the workers and describe what constitutes a complete unit of labour.

Choose a representative sample of employees to observe. The sample size should be high enough to be statistically significant, but not so large that observing all workers becomes unfeasible.

Use the data to discover potential for process changes that might result in a reduction in the time necessary to perform the activity.

By doing a time study analysis, the manufacturing organisation may acquire useful insights into their workers' productivity and find chances for process changes that will help them fulfil the rising demand for their products.

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Answer:

answers are a and b

picture shown