If a and bare unit vectors, and a + b = √3, determine (2ä - 5b). (a + 3b)

Answer:

6. 24

Step-by-step explanation:

A) Use pythogaras theoram

8x8 - 5x5 = axa - bxb = c

64-25= 39

39 square root =6.24

The area of the triangle is 31.54 square units

From the question, we have the following parameters that can be used in our computation:

We have the following values

a = 7 units

c = 11 units

B = 55 degrees

The area of the triangle is calculated using the following area formula

Area = 1/2absin(C)

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 7 * 11 * sin(55 degrees)

Evaluate

Area = 31.54

Hence, the area is 31.54 square units

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Answer:

product means times for e.g

Step-by-step explanation:

what is the product of 5 and 10

this means what

is 5 × 10

which equals to 50

Answer:

Product is the answer to a multiplication problem.

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. 1/3*60:

Multiply 1/3 by 60/1= 60/3= 20

1/3 of a minute = 20 seconds

2. 4/5*60:

multiply 4/5 by 60/1

=240/5= 48

4/5 of a minute= 48 seconds

3.  7/10*1000 = 7000/10 = 700/1 = 700

7/10 of a kilogram is 700 grams

4. 3/5*100 = 300/5 = 60

3/5 of a meter is 60 centimeters

Yusuf's age is 9.

Let's assume William's age as x. Since Yusuf is older, his age can be represented as x + 2, as they are consecutive odd integers.

According to the given information, the sum of the square of Yusuf's age and 5 times William's age is 116. We can express this mathematically as:

\((x + 2)^2 + 5x = 116\)

Expanding the square term, we get:

\(x^2 + 4x + 4 + 5x = 116\)

Combining like terms:

\(x^2 + 9x + 4 = 116\)

Now, let's rearrange the equation to bring all the terms to one side:

\(x^2 + 9x + 4 - 116 = 0\)

Simplifying:

\(x^2 + 9x - 112 = 0\)

To solve this quadratic equation, we can factorize it or use the quadratic formula. In this case, let's factorize:

(x + 16)(x - 7) = 0

Setting each factor to zero:

x + 16 = 0 or x - 7 = 0

If x + 16 = 0, then x = -16

If x - 7 = 0, then x = 7

Since we are considering age, we can discard the negative value. Therefore, William's age, x, is 7.

Yusuf's age, x + 2, is then:

7 + 2 = 9

So, Yusuf's age is 9.

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To determine Yusuf's age, we can solve a quadratic equation derived from the given information.we know Yusuf is older.

Let's assume William's age as x. Since Yusuf is older, his age would be x + 2. The sum of the square of Yusuf's age and 5 times William's age can be expressed as (x + 2)^2 + 5x. According to the given information, this sum is equal to 116. Simplifying the equation, we have x^2 + 4x + 4 + 5x = 116. Combining like terms, we get x^2 + 9x + 4 = 116. Rearranging the equation, we have x^2 + 9x - 112 = 0. Solving this quadratic equation will give us the value of x, which represents William's age. Then, Yusuf's age can be determined by adding 2 to x.

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Answer:

to the right

.............

Answer:The other number is located on the right of -2.5 on the horizontal number line.

Step-by-step explanation: EDMENTUM PLATO

Answer:

  (364.0, 236.4)

Step-by-step explanation:

You want the vector 434∠33° written as an ordered pair.

The "ordered pair" representation of a vector can take different forms. we're not sure the form your curriculum materials are asking for, so we'll show it a couple of ways.

(magnitude; direction) = (434; 33°) or maybe (434, 33)

(x, y) = 434·(cos(33°), sin(33°) ≈ (364.0, 236.4)

__

Additional comment

We like the form used in the problem statement above (434∠33°) for vectors expressed in polar form. For vectors expressed in rectangular form, many calculators work nicely with a complex number representation (364 +236.4i).

The ordered pair using a semicolon (;) separator is written that way to distinguish it from the (x, y) ordered pair. That form is used by some geometry software. A calculator may use [434, 33] or [364, 236.4] (for example), leaving it up to the user to remember what the pair represents.

Some authors use a combination of complex and polar representations like this:

  A(cos(B) +i·sin(B)) = A·cis(B)

In this, the "cis" is a reminder of the "cosine + i·sine" complex number representation. It is also a longer way to write A∠B.

The second attachment shows our preferred calculator using our preferred vector notations. YMMV

→ Be sure your calculator is in "degrees" mode.

The answer is C if you pay attention to the original dotted line and then where the new one goes, which is up two.

Solution given:

left hand limit

f(0)=5×0-9=-9

right hand limit

f(0)=|2-0|=2

functional value

f(0)=|2-0|=2

since left hand limit≠right hand limit.so

d. The limit does not exist

Answer:

el resultado es facil es: 7 1/2 espero que te ayude

Answer:

7 1/2

Step-by-step explanation:

Answer:

11 is your answer.

Step-by-step explanation:

We have the equation: n + 2x^2

We know that n = 3 and x = -2

Substitute the variables for their values.

3 + 2(-2)^2 = ?

Then just solve to get 11.

Answer:11

Step-by-step explanation:

Answer:

Since each question has 3 choices and only one is correct, the probability of answering a single question correctly is 1/3.

To find the probability of answering all 10 questions correctly, we need to multiply the probabilities of each individual question together, since the events are independent.

Therefore, the probability of acing the test is:

(1/3)^10 = 0.000005904

Or approximately 0.0006%, which is a very small probability.

Step-by-step explanation:

Approximately, the LA Dodgers hit 35 home runs.

Approximation is  a mathematical quantity that is close in value to but not the same as a desired quantity

From the question

The total number of home run in the Major League Baseball is 583

The LA Dodgers home run can be gotten by finding 6% of the the total home runs

That is, 6% of 583

= \(\frac{6}{100} *\frac{583}{1}\)

= 34.98 home runs

We can conclude that LA Dodgers hit approximately 35 home runs

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The given function is solved using the power rule. The nth derivative of the given function f(x)=xⁿ is  \(f^{(n)}(x) = n!x^{n-n }= n!\).

The power rule instructs how to differentiate xⁿ. It is used to determine the slope of polynomial functions as well as any other function with a real number exponent.

The given function is considered a power function. This is because the x is raised to the power (n). This n is considered a real number. So the derivative of this function is derived using the power rule.

First, differentiating the given function as follows,

\(\begin{aligned}f'(x)&=nx^{n-1}\\f''(x)&=n(n-1)x^{n-2}\\f'''(x)&=n(n-1)(n-2)x^{n-3}\end{aligned}\)

So observing the pattern, the nth derivative is found as follows, \(f^{(n)}(x) = n!x^{n-n }= n!\)

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The complete question is -

Find the nth derivative of each function by calculating the first few derivatives and observing the pattern that occurs.

f(x)=xⁿ

Answer:

Only student 2

Step-by-step explanation:

Ruben House is approximately 5.32 Km far than the Bank.

From the relation of the triangle we get,

c² = a² + b² - 2ab*cos(C)

where a, b, c are the side lengths opposite to the angles A, B and C respectively.

The diagram of the route of Ruben will be -

In figure A represents the Ruben's house and B represents the Bank and C represents the Store.

So here the distance from the Ruben house to store is (AC) = 37.5 km (given)

The distance of the store to the bank is (BC) = 34.5 Km

The angle ACB will be = 7 degree

We have to find the distance between the Ruben House and the Bank that is the value of AB.  

So,

AB² = AC² + BC² - 2*AC*BC*cos(angle ACB)

AB² = (37.5)² + (34.5)² - 2*37.5*34.5*cos(7)

AB² = 28.29

AB = \(\sqrt{28.29}\approx\) 5.32 (Rounding up to two decimal places)

Hence the distance between Ruben's House and the Bank is approximately 5.32 Km.

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The question in English will be -

"Rubén leaves his house in his car and arrives at the store that is 37.5 km away. But remember that first you have to go to the bank to withdraw money, so turn 7th. If the bank located 34.5 km. Of the store. How far in km is Rubén's house from the bank?"

Answer:

3/2

Step-by-step explanation:

Complementary angles equal 90 degrees.

The other angle would be 90 - 70.2 = 19.8 degrees

Answer: 19.8

Step-by-step explanation: complementary angles add up to 90° :)

The reduced gradient is analogous to the residual for linear models.

In linear regression, the residual represents the difference between the observed values and the predicted values of the dependent variable. Similarly, in optimization, the reduced gradient represents the difference between the current solution and the optimal solution. It is a measure of how far the current solution is from the optimal solution in the direction of the search. By minimizing the reduced gradient, we can move closer to the optimal solution.

The reduced gradient is a widely used optimization technique in non-linear programming that allows for efficient computation of the descent direction at each iteration while accounting for constraints. It involves calculating a partial derivative of the objective function with respect to the variables that are not restricted by the constraints, and then projecting the resulting gradient onto the space defined by the constraints. The resulting vector is called the reduced gradient, and it points in the direction of the steepest descent that is feasible.

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Answer:

x = –1 AND (-1,2)

Step-by-step explanation:

The axis of symmetry is x = –1

and the vertex is (-1,2)

i know this because the graph is on -1, 2

and I also took the quiz hope it helps ;)

The vertex of the function is (-1, 2).

The axis of symmetry of the function is -1.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = (x + 1)² + 2

f(x) = x² + 2x + 1 + 2

f(x) = x² + 2x + 3

Now it is in the form of ax² + bx + c

a = 1

b = 2

c = 3

The coordinate of the Vertex of the function is (-b/2a, f(x)) = (x, y)

-b/2a = -2/2 = -1

f(x) = (-1)² + 2 x (-1) + 3 = 1 - 2 + 3 = 4 - 2 = 2

Vertex = (-1, 2)

The axis of symmetry is the x-coordinate of the vertex.

= -1.

Thus,

Vertex is (-1, 2).

The axis of symmetry is -1.

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True, to calculate the average of numeric values in the list, the first step is to get the total of values in the list.

Steps to calculate the Average:

Let’s assume there are 4 numbers having values of 2,8,22,48 respectively.

To find the average we first have to take the total of all values.

2+8+22+48=80.

Our next step will be to divide this total by the number we have in our question i.e., 4.

so, our average will be 80/4= 20.

So, 20 will be our average.

So yes, it is true that to calculate the average of numeric values in the list, the first step is to get the total of all values in the list.

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The limit of the given function as x approaches 2 is 2.

To find the limit of lim x→2x2 − 4 /x2 − 2x, we can simplify the expression by factoring the numerator and denominator:

lim x→2(x+2)(x-2) / x(x-2)

Canceling out the common factor of (x-2), we get:

lim x→2(x+2) / x

Plugging in x=2, we get:

lim x→2(x+2) / x = lim x→2(2+2) / 2 = 4/2 = 2

Therefore, the limit of the given function as x approaches 2 is 2.

Since we were able to simplify the expression without using l'Hospital's Rule, we can say that it was not appropriate to use it in this case. The more elementary method of factoring and simplifying was sufficient.

To find the limit of the given function as x approaches 2, let's first see if we can use an elementary method before considering l'Hospital's Rule.

Given function: (x^2 - 4) / (x^2 - 2x)

Factor the numerator and the denominator:
Numerator: x^2 - 4 = (x - 2)(x + 2)
Denominator: x^2 - 2x = x(x - 2)

Now, simplify the function:
(x - 2)(x + 2) / x(x - 2)

Since (x - 2) is a common factor in both the numerator and the denominator, we can cancel it out:
(x + 2) / x

Now that the function is simplified, we can find the limit as x approaches 2:

lim (x → 2) (x + 2) / x

Plug in 2 for x:
(2 + 2) / 2 = 4 / 2

The limit is 2. In this case, we didn't need to use l'Hospital's Rule as an elementary method was more appropriate.

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By examining the dotplot, you can see the frequency and distribution of the miles run by Roger. For example, there are 4 instances where Roger ran 0.5 miles, 3 instances where he ran 4 miles, and so on.

The dotplot that displays the data correctly is the one titled "Roger's Training" with a number line labeled "Miles Run" that goes from 0.5 to 5 in increments of 0.5. The dotplot should have the following data points:
0.5, 4
1, 1
1.5, 2
2, 2
2.5, 3
3, 2
3.5, 0
4, 3
4.5, 2
5, 1
This dotplot accurately represents the number of miles Roger ran each day over a 20-day period. Each dot represents a data point from the given list of miles run. The number line indicates the range of miles run, starting from 0.5 and ending at 5, with increments of 0.5.
By examining the dotplot, you can see the frequency and distribution of the miles run by Roger. For example, there are 4 instances where Roger ran 0.5 miles, 3 instances where he ran 4 miles, and so on. This visual representation allows you to easily interpret the data and observe any patterns or trends in Roger's training.

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Answer:

y = 8/7x+3/7

Step-by-step explanation:

We can find the slope using the slope formula

m = ( y2-y1)/(x2-x1)

    = ( 5 - -3)/( 4 - -3)

    = ( 5+3)/ ( 4+3)

    =8/7

The slope intercept form of the equation is y = mx+b

y = 8/7x+b

Substitute a point into the equation

5 = 8/7 *4 +b

5 = 32/7 +b

35/7 = 32/7 +b

Subtract 32/7 from each side

35/7 - 32/7 =b

3/7 =b

y = 8/7x+3/7

Answer:

y = 8/7x+3/7

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The slopes and the y-intercept of a linear function that is represented by the table is: D. the slope is 2/5 and the y-intercept is -1/3.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-2/15 + 1/30)/(-1/2 + 3/4)

Slope (m) = -0.1/0.25

Slope (m) = -0.4 or 2/5.

At data point (-3/4, -1/30) and a slope of 2/5, a linear function in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-1/30) = 2/5(x + 3/4)

y = 2x/5 - 1/3

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