3. Given the following functions f(x)=sinx and g(x)= cosx, find the value of each of the following.
a. (f+g) ( 30)
b. (f*g)(TT/4)

Answer:

24/7 or 6.75 or 6 3/4

Step-by-step explanation:

Answer:

1) 22.4

2) 91

3) 6

explanation:

i converted the fraction to decimals or whole numbers and multiplied

The percentage error for the circumference ≈ -95.53% and the percentage error for the area ≈ -98.23%

Provided:

Exact diameter = 188 cm

Measured diameter = 8.2 cm

To calculate the percentage error in the circumference of a circle, we'll use the formula:

\(\[\text{{Percentage Error in Circumference}} = \left( \frac{{\text{{Measured Circumference}} - \text{{Exact Circumference}}}}{{\text{{Exact Circumference}}}} \right) \times 100\]\)

Exact Circumference = π * Exact Diameter = π * 188 cm

Measured Circumference = π * Measured Diameter = π * 8.2 cm

\(\[\text{Percentage Error in Circumference} = \left(\frac{\pi \cdot 8.2 \, \text{cm} - \pi \cdot 188 \, \text{cm}}{\pi \cdot 188 \, \text{cm}}\right) \times 100\]\)

\(\[=\frac{{8.2 \, \text{cm} - 188 \, \text{cm}}}{{188 \, \text{cm}}} \times 100 \\\\= \frac{{-179.8 \, \text{cm}}}{{188 \, \text{cm}}} \times 100\]\)

≈ -95.53%

Next, to calculate the percentage error in the area of a circle, we'll use the formula:

Percentage Error in Area = \(\(\left(\frac{{\text{{Measured Area}} - \text{{Exact Area}}}}{{\text{{Exact Area}}}}\right) \times 100\)\)

Exact Area = π * (Exact Radius)²

Exact Radius = \(\frac{Exact Diameter}{2}\)

Substituting the values:

Exact Radius = \(\frac{ 188 cm}{2}\)

Measured Radius = \(\frac{8.2 cm}{2}\)

Measured Area = π * (Measured Radius)²

Measured Radius = \(\frac{Measured Diameter}{2}\)

Substituting the values:

Exact Area = π * \((\frac{188 cm}{2} )^2\)

Measured Area = π * \((\frac{8.2 cm}{2} )^2\)

∴ Percentage Error in Area \(=$\left(\frac{\pi \left(\frac{8.2 \text{ cm}}{2}\right)^2 - \pi \left(\frac{188 \text{ cm}}{2}\right)^2}{\pi \left(\frac{188 \text{ cm}}{2}\right)^2}\right) \times 100$\)

\(= \[\frac{{\left(\frac{{8.2 \, \text{cm}}}{2}\right)^2 - \left(\frac{{188 \, \text{cm}}}{2}\right)^2}}{{\left(\frac{{188 \, \text{cm}}}{2}\right)^2}} \times 100\]\)

\(= \[\frac{{(2.05 \, \text{cm})^2 - (47 \, \text{cm})^2}}{{(47 \, \text{cm})^2}} \times 100\]\)

≈ -98.23%

Therefore, the calculated percentage errors are approximately -95.53% for the circumference and -98.23% for the area.

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Answer:

€520=£442.83

=£442.83-£260

=£182.83 into dollars=$251.52

Therefore he receives $251.52

The minimum force that must be applied on the crate to prevent it from sliding down the 35.0-degree incline is 27.21 N.

To calculate the minimum force required, we need to consider the forces acting on the crate. The force of gravity acting on the crate can be decomposed into two components: one parallel to the incline and one perpendicular to the incline.

The perpendicular component of the gravitational force is given by mg * cos(θ), where m is the mass of the crate (3.00 kg) and θ is the angle of the incline (35.0 degrees). Thus, the perpendicular component is 3.00 kg * 9.8 m/s^2 * cos(35.0°) = 24.25 N.

The minimum force required to prevent the crate from sliding down the incline is equal to the maximum static friction force. The maximum static friction force can be calculated using the formula fs = μs * N, where μs is the coefficient of static friction (0.3) and N is the normal force acting on the crate. The normal force is equal to mg * sin(θ), which is 3.00 kg * 9.8 m/s^2 * sin(35.0°) = 16.59 N.

Therefore, the maximum static friction force is 0.3 * 16.59 N = 4.98 N.

To prevent the crate from sliding, the minimum force required must be equal to the maximum static friction force, which is 4.98 N.

To prevent the 3.00 kg crate from sliding down the 35.0-degree incline, a minimum force of 27.21 N must be applied to the crate. This force is necessary to overcome the perpendicular component of the gravitational force and match the maximum static friction force between the crate and the incline.

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Step-by-step explanation:

15+10z=105

10z=105-15

10z=90

z=9

Answer:

Mr. A initially paid approximately N8000 for the land.

Step-by-step explanation:

Step 1: Let's assume Mr. A initially purchased the land for a certain amount, which we'll call "x" in currency units.

Step 2: Mr. A sold the land to Mr. B at a profit of 10%. This means Mr. A sold the land for 110% of the amount he paid (1 + 10/100 = 1.10). Therefore, Mr. A received 1.10x currency units from Mr. B.

Step 3: Mr. B sold the land to Mr. C at a gain of 5%. This means Mr. B sold the land for 105% of the amount he paid (1 + 5/100 = 1.05). Therefore, Mr. B received 1.05 * (1.10x) currency units from Mr. C.

Step 4: According to the given information, Mr. C paid N1240 more for the land than Mr. A paid. This means the difference between what Mr. C paid and what Mr. A paid is N1240. So we have the equation: 1.05 * (1.10x) - x = N1240

Step 5: Simplifying the equation: 1.155x - x = N1240

Step 6: Solving for x: 0.155x = N1240

x = N1240 / 0.155

x ≈ N8000

Therefore, in conclusion, Mr. A initially paid approximately N8000 for the land.

Answer:

\(y=3x+6\)

Step-by-step explanation:

In order to create an equation in slope-intercept form, we need to first find the slope of the line. In order to do this, we use the equation:

\(\frac{y2-y1}{x2-x1} =m\)

Plug your two coordinates into this equation:

\(\frac{(3--3)}{(-1--3)} = \frac{6}{2} = 3\)

Now, you can add the slope to the slope-intercept formula. We still need to find b, though.

\(y=3x+b\)

Choose one coordinate you were given and plug in x and y.

\(3=3(-1)+b\\3=-3+b\\6=b\)

Hence, your equation is:

\(y=3x+6\)

Answer:

y = 3/2x-12

Step-by-step explanation:

The slope-intercept form of a line is

y = mx+b  where m is the slope and b is the y-intercept

The slope is 3/2 and the y-intercept is -12.

y = 3/2x-12

Answer:

\(\sf y = \dfrac{3}{2}x - 12\)

Step-by-step explanation:

The equation of a linear function can be written in the form y = m x + c, where,

m → slope → 3/2

c → y-intercept → -12

we can substitute these values into the equation.

The slope, m, is 3/2, so the equation becomes:

y = (3/2)x + c

The y-intercept, c, is -12, so we can replace c with -12:

\(\sf y = \dfrac{3}{2}x - 12\)

Therefore, the equation of the line is y = (3/2)x - 12

Step-by-step explanation:

0.200 in standard form is 2.00 * 10^(-1).

Assume a businessman has 7 suits and 8 ties. He is planning to take 4 suits and 3 ties with him on his next business trip. Possibilities of selection he have 1960.

A businessman has 7 suits

A businessman has 8 ties.

He is planning to take 4 suits and 3 ties with him on his next business trip.

We have to determining possibilities of selection he have.

Number of possible selections = \(^{7}C_{4}\times ^{8}C_{3}\)

Simplify

Number of possible selections = \(\frac{7!}{4!(7-4)!}\times\frac{8!}{3!(8-3)!}\)

Number of possible selections = \(\frac{7!}{4!3!}\times\frac{8!}{3!5!}\)

Number of possible selections = \(\frac{7\times6\times5\times4!}{4!\times3\times2\times1}\times\frac{8\times7\times6\times5!}{3\times2\times1\times5!}\)

After simplification we get

Number of possible selections = 7 × 5 × 8 × 7

Number of possible selections = 1,960

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Answer:

two-sample t test with Ha: Unew york city (not equal) Uboston

Step-by-step explanation:

khan

Answer:

y-2/3x-4

the answer is (0,3)

3x+4y-12

the answer is (0,3)

The value of the side x is 28. 65

It is important to note the different trigonometric identities, we have;

From the image shown, we have that;

The opposite side = 19

The adjacent side = x

The angle = 38

Using tangent, we have

tan 38 = 19/x

Find the value

x = 19/0.6632

x = 28. 65

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Using it's concept, the domain of the relation is given as follows:

x ≥ 0.

In a graph, the domain and the range are found as follows:

From the graph, we have that the weights of the packages assume all values to the right of 0, hence the domain of the relation is given as follows:

x ≥ 0.

The relation is incomplete, and is given by the graph at the end of the answer.

The question asked is the domain of the relation.

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70 grade must the student earn on the last exam to get an average of an 80 for the marking period.

Division is the process of splitting a number or an amount into equal parts.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

given that,

A student received grades of 84, 87, and 79 on the first three exams.

let, x grade must the student earn on the last exam to get an average of an 80 for the marking period.

i.e. (84+87+79+x)/4=80

solving, we get,

x=70

Hence, 70 grade must the student earn on the last exam to get an average of an 80 for the marking period.

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240-45-6-4-75=188.94$

a) d/dt [√(289 - 8²)] = d/dt [√(255)] = d/dt [√(5²*17)] = 5/2√17 m/s.

b) The required value is the rate of change of x when the top of the ladder is 8 feet from the ground, then y = 15 feet.

a) Determine how fast the bottom of the ladder is sliding away when the top of the ladder is 8 feet from the ground. As the ladder leans against the side of the house, it makes a right angle with the ground. Using Pythagorean Theorem, the length of the ladder is given by.

Ladder length = √(hypotenuse)² - (height)²= √(17² - height²) meters. Taking the derivative of both sides of this equation, we get: dL/dt = [d/dt √(289 - h²)] meters/sec. Let h = 8 feet, dL/dt = -5 feet/sec.

Thus, the rate of change of the bottom of the ladder is d/dt [√(289 - h²)] meters/sec when the top of the ladder is 8 feet from the ground, and the bottom of the ladder is sliding away at a rate of 5 feet/sec.

b) At what rate is the angle o between the ladder and the ground changing then. Let y be the height of the ladder and the angle it makes with the ground be x. From the given values, y = 17 cos x.

Taking the derivative of both sides with respect to time: dy/dt = -17 sin x (dx/dt)In the given problem, dx/dt = -5/17sin x. Then, dy/dt = 5 sin x cos x= (5/2) sin 2x.

Solving this value of sin x by Pythagorean Theorem, sin x = 8/17. Substituting the value in the equation for the derivative, we get: dy/dt = (5/2) * sin 2x= (5/2) * sin 2(arc sin(8/17))= (5/2) * (2*8/17 * 15/17)= (600/289) ft/sec.

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The solution is, the equation of a line parallel to y=3x-3 and passing through point (3,2) is y=3x-7.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

The equation of the given line is,

y=3x-3 ....1

We have to find the equation of a line parallel to y=3x-3 and passing through the point (x1, y1)=(3,2).

The general equation of a line is,

y = mx+c ....2

Here, m is the slope of the line.

Comparing equations (1) and (2), we find that the slope of the line

y=3x-3 is m=3.

The slope of two parallel lines are always equal.

Hence, the slope of a line parallel to the line y=3x-3 is also m=3.

Now, the formula for the point slope form of the equation of a line can be written as,

y - y1 = m (x - x1)

Substitute m=3, x1=3 and y1=2 in the above equation to find the equation of a line parallel to y=3x-3 and passing through point (3,2) is,

y-2 = 3(x - 3)

Therefore, the equation of a line parallel to y=3x-3 and passing through point (3,2) is y=3x-7.

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Based on typical expectations for the relationship between trunk circumference and tree height, the slope is most likely to be closer to 1.

The slope of the regression model represents the change in the dependent variable (height of the pine tree) for every one-unit increase in the independent variable (circumference of the trunk).

In this scenario, the slope is most likely to be closer to 1. This is because we expect a reasonably linear relationship between the circumference of the trunk and the height of the pine tree. Generally, as the trunk's circumference increases, we anticipate a proportional increase in the height of the tree.

If the slope were closer to 0, it would suggest little to no relationship between the circumference of the trunk and the height of the tree. However, in reality, there is usually a positive correlation between these variables.

If the slope were closer to 0.1 or 100, it would indicate a more extreme relationship where a small change in trunk circumference results in a significantly larger or smaller change in tree height. While this is possible in some cases, it is less likely to be the norm.

Therefore, based on typical expectations for the relationship between trunk circumference and tree height, the slope is most likely to be closer to 1.

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Answer:

y=_

x=_

Step-by-step explanation

horizontal for y=_

vertical for x=_

U(7, 7)

U'(-3,7)

Explanation:

reflecting upon the value of x=2 that means we reflect over y- axis.

*for reflections the distance from the line of reflection to the object is equal to the distance to the image point.

d = 2 + 2 = 4 units.

7 - 4 = 3(since reflection is done towards the negative side)

x' = -3.

Based on the information provided, we have two given values for x: 14 and 15. The range of values for x can be expressed as [14, 15].

However, you also mentioned the value "1620". If this is intended to be part of the range for x, please provide additional clarification or context.

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Both options a. A = 129.9° and b. A = 53.1° are correct.

To find the possible values for angle A in triangle ABC, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

Using the Law of Sines, we have sin(A)/a = sin(B)/b. Plugging in the given values, we get sin(A)/36 = sin(51°)/35.

To find the two possible values for angle A, we can solve the equation sin(A)/36 = sin(51°)/35. Taking the arcsine of both sides, we have A = arcsin((sin(51°)/35)*36).

Calculating this expression, we find two possible values for angle A:

A ≈ 53.1° (rounded to the nearest tenth)

A ≈ 129.9° (rounded to the nearest tenth)

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The function that is positive for the entire interval [–3, –2] is the graph of the function (b)

See attachment for the proper representation of the available options

For a function to be positive on the interval [-3,-2];

It means that the y values must be in the positive quadrant from x = -3 to x =-2

From the list of options, we have:

The y values from x = -3 to x =-2 is at the positive quadrant for the second graph i.e. option B

Hence, the function that is positive for the entire interval [–3, –2] is the graph of the function (b)

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Answer:

Step-by-step explanation:

C

The area of the circular shaped pizza is A = 254.5 cm²

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the pizza be r = 9 cm

The area A of a circle with radius r is given by the formula:

A = πr²

Substituting the given radius of 9 cm, we get:

A = π(9 cm)²

A = π(81 cm²)

A ≈ 254.47 cm²

Rounding to one decimal place, we get:

A ≈ 254.5 cm²

Hence , the area of the circular pizza with a radius of 9 cm is approximately 254.5 cm²

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By taking advantage of the definition of exponential and logarithmic function and their inherent relationship we conclude that the solution is x = 4 · ㏒ 3/(㏒ 7 - ㏒ 3).

Exponential and logarithmic functions are trascendental functions, these are, functions that cannot be described algebraically. In addition, logarithmic functions are the inverse form of exponential functions. In this question we take advantage of this fact to solve a given expression:

By taking advantage of the definition of exponential and logarithmic function and their inherent relationship we conclude that the solution is x = 4 · ㏒ 3/(㏒ 7 - ㏒ 3).

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The true statement that explains the correlation coefficient is: C. As the baby gains weight, the prices of smartphone tend to increase.

The value of the correlation coefficient shows a relationship between two variables. A positive value suggests a positive relationship, meaning as one variable increases, the other also increases.

A correlation coefficient of  0.87 suggests a positive relationship between baby's weight and the price of smartphone, therefore, the true statement is:

C. As the baby gains weight, the prices of smartphone tend to increase.

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