Hi I need help differentiating question 1 f please, Thanks

Answer:

f(-3)=-2,5

f(-1)=-1,5

f(3)=¾

Answer:

-5/2

3/2

3/4

Step-by-step explanation:

(a) f(x) =  \(log_2(x)\) is a logarithmic function

(b) g(x) = ∜x is a root function

(c) h(x) = \(2x^3/(1 - x^2)\) is a rational function

(d) u(t) = 1 - 1.1t + \(2.54t^2\) is a polynomial of degree 2

(e) v(t) = \(5^t\)is an exponential function

(f) w(θ) = sin θ \(cos^{2}\theta\) is a trigonometric function.

(a) f(x) = \(log_2(x)\) is a logarithmic function. Logarithmic functions have the logarithm of the independent variable as the output. Here, the logarithm base is 2.

(b) g(x) = ∜x is a root function. Root functions have the square root or higher roots of the independent variable as the output. Here, the root is a cube root.

(c) h(x) = \(2x^3/(1 - x^2)\) is a rational function. Rational functions are functions that are expressed as the quotient of two polynomials. Here, the numerator is a cubic polynomial and the denominator is a quadratic polynomial.

(d) u(t) = 1 - 1.1t + \(2.54t^2\) is a polynomial of degree 2. Polynomials are functions that are expressed as a sum of powers of the independent variable, with coefficients. The degree of a polynomial is the highest power of the independent variable.

(e) v(t) = \(5^t\) is an exponential function. Exponential functions have the independent variable as the exponent. Here, the base is 5.

(f) w(θ) = sin θ \(cos^{2}\theta\) is an algebraic function and a trigonometric function. Algebraic functions are functions that can be expressed using arithmetic operations and algebraic expressions. Trigonometric functions are functions that involve the ratios of the sides of a right triangle. Here, the function is a combination of sine and cosine functions.

Read more about functions:

brainly.com/question/28934802

#SPJ4

The complete question is -

Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.

(a) f(x) =  \(log_2(x)\)    

(b) g(x) = ∜x    

(c) h(x) = \(2x^3/(1 - x^2)\)    

(d) u(t) = 1 - 1.1t + \(2.54t^2\)                    

(e) v(t) = \(5^t\)    

(f) w(θ) = sin θ \(cos^{2}\theta\)

SOLUTION;

Sine it is parallel to the line whose equation is y = - 5x + 5, it means the slope of the new line is also - 5.

Answer:

this list

Step-by-step explanation:

1×12000=12000

2×6000=12000

3×4000=12000

4×3000=12000

5×2400=12000

6×2000=12000

8×1500=12000

10 ×1200=12000

12 ×1000=12000

Answer:

70  cm

Step-by-step explanation:

Answer:

70 cubic feet

Step-by-step explanation:

First step is to multiply the 2 feet deep by th 5 feet wide. which is also written as:

2*5=10

Next multiply 10 by the 7 feet tall. You can write this like:

10*7=70

70 cubic feet is the answer

Step-by-step explanation:

a = k/m    or       ma = k    

using 4 and 9     4* 9 = k = 36

then the equation becomes:

    ma = 36    

  using a = 6

      6 * m = 36     shows m = 6 kg

Regardless of the type of triangle, all triangles have internal angles that sum up to 180°. An isosceles triangle will have two equal-sized angles.

The hypotenuse, or side across from the right angle, has a square whose length is equal to the sum of the squares of the other two sides in a right triangle, according to the Pythagorean theorem. In other words, if the hypotenuse's length is c and the lengths of the other two sides are a and b, then c2 = a2 + b2.

Whatever the type of triangle, all triangles have internal angles which sum to 180°. The two angles of an isosceles triangle will be equal in size. Every angle of an equilateral triangle is 60 degrees. The other two angles in a right-angled triangle will add up to 90° because the triangle has one angle that is 90°.

To learn more about triangle refer to:

https://brainly.com/question/1058720

#SPJ1

Answer:

340%

Step-by-step explanation:

119000/35000

Answer:

y'=|x-5|-1

Step-by-step explanation:

Learn more about the question here:

https://brainly.com/question/11939052

Answer:

\(P" = (-1,7)\)

Step-by-step explanation:

Given

\(Point - (-7,5)\)

90 degrees clockwise rotation

6 points left translation

Required

The new point

Apply the first transformation

90 degrees clockwise transformation

When a point P (x,y) is rotated in the clockwise direction by 90 degrees, the new point is: P' (y, -x)

So:

\(P = (-7,5)\) becomes

\(P' = (5,7)\)

Apply the second transformation

6 points left translation

To do this, we simply subtract 6 from the x coordinate

\(P' = (5,7)\) becomes

\(P" = (5-6,7)\)

\(P" = (-1,7)\)

Answer:

7.8 miles

Step-by-step explanation:

5.9 + 1.9 = 7.8miles

Answer:

\(Area = 123.55 m^2\)

Step-by-step explanation:

Given

\(Area = 1330ft^2\)

Required

Convert to \(m^2\)

To convert from square feet to square meter, we simply divide by 3.281^2

So, we have:

\(Area = \frac{1330}{3.281^2}m^2\)

\(Area = \frac{1330}{10.765}m^2\)

\(Area = 123.55 m^2\)

Answer:15 and 25

Step-by-step explanation:

3:4= 7

35/7=5

5x3=15

5x4=20

Answer:

\((-\infty,2)\)

Step-by-step explanation:

Since \(-3x+6\nless 0\), then \(x\ngtr 2\), therefore, the domain of the function is \((-\infty,2)\).

Answer:

B

Step-by-step explanation:

To find the equation, we can use the point-slope form:

\(y-y_1=m(x-x_1)\)

Where m is the slope and (x₁, y₁) is a point.

First, we will need to find the slope. Since we have two points, we can use the slope formula:

\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)

Let (2, -1) be (x₁, y₁) and let (0, 5) be (x₂, y₂). Substitute and evaluate:

\(\displaystyle m=\frac{5-(-1)}{0-2}=6/-2=-3\)

Therefore, the slope m is -3.

Now, we can use the point-slope form. We also need a point. Let’s use (2, -1) for consistency. So, we will substitute -3 for m and (2, -1) for (x₁, y₁). This yields:

\(y-(-1)=-3(x-2)\)

We will now convert this to slope-intercept form. Simplify the left and distribute the right:

\(y+1=-3x+6\)

Subtract 1 from both sides. Therefore, our equation is:

\(y=-3x+5\)

Thus, our answer is B.

The population of the country will be 796 million approximately in the year 2022.

To find when the population of the country will be 796 million, we can set the equation equal to 796 and solve for t:

\(A = 433.4e^{(0.032t)}\\796 = 433.4e^{(0.032t)}\)

Divide both sides by 433.4:

\(e^{(0.032t)} = 1.836\)

Take the natural logarithm of both sides:

\(ln(e^{(0.032t)}) = ln(1.836)\)

0.032t = 0.605

Divide both sides by 0.032:

t = 18.91

Therefore, the population of the country will be 796 million approximately 19 years after 2003. To find the year, we add 19 to 2003:

2003 + 19 = 2022

Therefore, the population of the country will be 796 million approximately in the year 2022.

Learn more about Population of the country  at

brainly.com/question/26835559

#SPJ1

Answer:

6,000

Step-by-step explanation:

1 ton is 2,000 pounds, so 3 tons are 6,000 pounds because 2,000 x 3 = 6,000.

Have a great day!

The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

Option B is the correct answer.

We have,

The null hypothesis states that the population mean for the number of hours spent studying by full-time students at 4-year colleges in the United States is equal to 14 hours per week,

while the alternative hypothesis states that it is different from 14 hours per week.

By using a two-tailed test, we are checking for any significant change in either direction, whether the average number of hours spent studying has increased or decreased from 14 hours per week.

Thus,

The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

Learn more about hypothesis testing here:

https://brainly.com/question/30588452

#SPJ1

There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

For more such questions on vertex

https://brainly.com/question/25651698

#SPJ8

Answer: 1/6 of the total sheet cake

Step-by-step explanation: 1/2 divided by 3 = 1/6

Answer:

The answer to you question is D or the last one.

Step-by-step explanation:

I took the test on Edg

The equation that represent this situation is (3/5) * b = 79.50

An equation is an expression that shows the relationship between two or more numbers and variables.

Let b represent the amount of the total bill. Given that 3.5 of the total bill was for labor cost.

For a labor of $79.50

(3/5) * b = 79.50

The equation that represent this situation is (3/5) * b = 79.50

Find out more on Equation at: https://brainly.com/question/13763238

Answer:Oop

Step-by-step explanation:

Answer:

Since the Confidence is 0.90 or 90%, the value of \(\alpha=0.1\) and \(\alpha/2 =0.05\), and the critical value would be \(t_{\alpha/2}=1.669\)

And replacing we got

\(17.5-1.669\frac{4.2}{\sqrt{65}}=16.63\)    

\(17.5+1.669\frac{4.2}{\sqrt{65}}=18.37\)    

For the 95% confidence the critical value is \(t_{\alpha/2}=1.998\)

\(17.5-1.998\frac{4.2}{\sqrt{65}}=16.46\)    

\(17.5+1.998\frac{4.2}{\sqrt{65}}=18.54\)    

Step-by-step explanation:

Information given

\(\bar X¿ 17.5\) represent the sample mean

\(\mu\) population mean (variable of interest)

s¿4.2 represent the sample standard deviation

n¿65 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

\(\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}\)   (1)

The degrees of freedom are given by:

\(df=n-1=65-1=64\)

Since the Confidence is 0.90 or 90%, the value of \(\alpha=0.1\) and \(\alpha/2 =0.05\), and the critical value would be \(t_{\alpha/2}=1.669\)

And replacing we got

\(17.5-1.669\frac{4.2}{\sqrt{65}}=16.63\)    

\(17.5+1.669\frac{4.2}{\sqrt{65}}=18.37\)    

For the 95% confidence the critical value is \(t_{\alpha/2}=1.998\)

\(17.5-1.998\frac{4.2}{\sqrt{65}}=16.46\)    

\(17.5+1.998\frac{4.2}{\sqrt{65}}=18.54\)    

263,187.70 rad / hour is the angular velocity of the nail in radians per hour.

The equation relating angular velocity and linear velocity is:

w = v / r

where,

w = angular velocity, v = linear velocity, and r = radius

Since r is in inches, convert v to inches:

v = (54 miles per hour) * (63360 inches / mile)

v = 3,421,440 inches / hour

Solving for w:

w = (3,421,440 inches / hour) / 13 inches

w = 263,187.70 rad / hour

To learn more about angular velocity  refer to:

https://brainly.com/question/1452612

#SPJ1

The domain is:

D: {-4, 5, 6, 8}

The range is:

R: {-4, 3, 5}

And yes, the relation is a function.

For a relation that maps elements x into elements y (in the form (x, y)), we define the domain as the set of the inputs (values of x) and the range as the set of the outputs (values of y).

Here our relation is defined by: {(6,3), (8,5), (-4,-4), (5,5)}

The domain is the set of the first values of each pair, so we have:

D: {-4, 5, 6, 8}

The range is the set of the second values of each pair:

R: {-4, 3, 5}

Now, is this a function?

Yes, it is a function, because each input is mapped into only one output.

If you want to learn more about domain and range:

https://brainly.com/question/10197594

#SPJ1

To be able to determine the bags of fertilizer that the gardener will need, let's first determine the area of the garden.

Since the shape of the garden is a trapezoid, we will be using the following formula:

We get,

Let's determine how many bags of fertilizer will be used.

We get,

Therefore, the gardener will be needing 22 Bags of Fertilizer.

The estimated profits for each company are given as follows:

Jones Corporation:

Davis Company:

The function that defines the profit for Jones Corporation is an exponential function defined as follows:

y = 10(0.99)^t

In which t is the number of years since 2015, while the profit is measured in millions of dollars.

Thus the coefficient a = 10 means that the estimated profit for the year of 2015 is of 10 million dollars.

For the year of 2025, that is, 10 years after 2015, the estimate is calculated as follows:

y = 10(0.99)^10 = 9.084821 = $9,084,821.

For Davis Company, the profit function is given as follows:

y = 8(1.01)^t.

Hence the profits are modeled as follows:

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1

Answer:

-10.575

Step-by-step explanation:

Answer:

1, 120

Step-by-step explanation:

    3.2 x 107 = 342.4

+   7.2 x 108 = 777.6

_____________________

                       1, 120                          

Answer:

(3.2 × 107) + (7.2 × 108) =

342.4 + 777.6 =

1120

Step-by-step explanation: