Tan20+tan40+tan60.......+tan180=?

How would the fraction 1/3+square root of 2 be rewritten if its denominator is rationalized using difference of squares? A. 3-sq

Vera_Pavlovna [14]

C

given 1 /( 3 + √2 )

then rationalise the denominator by multiplying the numerator/ denominator by the conjugate of the denominator

the conjugate of 3 + √2 is 3 - √2

1 / (3 + √2 ) × (3 - √2 ) / (3 - √2 )

= (3 - √2 ) /( 9 - 2 ) = (3 - √2 ) / 7

4 0

1 year ago

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The quantities xxx and yyy are proportional. xxx yyy 888 222 161616 444 323232 888 Find the constant of proportionality (r)(r)le

Tcecarenko [31]

Answer:

Step-by-step explanation:

1/4

4 0

1 year ago

2. The seniors at our high school decided to play a prank on the principal by completely filling his office with

melisa1 [442]

Answer:

idk

Step-by-step explanation:

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1 year ago

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Eli invested $ 330 $330 in an account in the year 1999, and the value has been growing exponentially at a constant rate. The val

Cloud [144]

Answer:

The value of the account in the year 2009 will be $682.

Step-by-step explanation:

The acount's balance, in t years after 1999, can be modeled by the following equation.

$A(t) = Pe^{rt}$

In which A(t) is the amount after t years, P is the initial money deposited, and r is the rate of interest.

$330 in an account in the year 1999

This means that $P = 330$

$590 in the year 2007

2007 is 8 years after 1999, so P(8) = 590.

We use this to find r.

$A(t) = Pe^{rt}$

$590 = 330e^{8r}$

$e^{8r} = \frac{590}{330}$

$e^{8r} = 1.79$

Applying ln to both sides:

$\ln{e^{8r}} = \ln{1.79}$

$8r = \ln{1.79}$

$r = \frac{\ln{1.79}}{8}$

$r = 0.0726$

Determine the value of the account, to the nearest dollar, in the year 2009.

2009 is 10 years after 1999, so this is A(10).

$A(t) = 330e^{0.0726t}$

$A(10) = 330e^{0.0726*10} = 682$

The value of the account in the year 2009 will be $682.

4 0

2 years ago

You have a budget of $48. You want to buy fruit and granola bars. Fruit costs $4 per pound, and the granola bars are $1 each. Yo

zzz [600]

1)Define the variables you will use in your model.

Let

x------->total pounds of the fruit

y-------> the total number of granola bars

TC----> total cost

Tf------> total cost of the fruit

Tg----> total cost of the granola bars

2) Write an inequality representing the total cost of your purchase. (3 points)

a. Each pound of fruit costs $4. Write an expression that shows the total cost of the fruit. Use the variable you identified in question 1

Tf=4*x

b. Each granola bar costs $1. Write an expression that shows the total cost of the granola bars. Use the variable you identified in question 1.

Tg=1*y--------> Tg=y

c. Combine the expressions from parts a and b to write an expression for the total cost. Then use this expression to write an inequality that compares the total cost with the amount you have to spend.

TC=Tf+Tg

TC=4*x+y

inequality-------> $4x+y \leq 48$

3. Write the inequality that models the number of granola bars you need to buy.

You need at least 10 granola bars

so

$y\geq 10$

4. Describe in words what each of your inequalities means

inequality 1

$4x+y \leq 48$

the total cost of fruits plus the total cost of granola bars must be less than or equal to 48 dollars

inequality 2

$y\geq 10$

5. Graph your system of inequalities.

using a graph tool

see the attached figure

6. Identify one point on the graph that represents a viable solution to the problem, and then identify one point that does not represent a viable solution.

Let

A-------> one point on the graph that represents a viable solution

B-------> one point on the graph that does not represent a viable solution

A(4,20)

x=4-------> total pounds of the fruit

y=20------> the total number of granola bars

check point A

substitute the values of x and y in the inequality 1

$4x+y \leq 48$

$4*4+20\leq 48\\ 36\leq 48$ -------> is ok

substitute the values of x and y in the inequality 2

$y\geq 10$

$20\geq 10$ --------> is ok

the point A represents a viable solution, because satisfies both inequalities

B(10,30)

x=10-------> total pounds of the fruit

y=30------> the total number of granola bars

check point B

substitute the values of x and y in the inequality 1

$4x+y \leq 48$

$4*10+30\leq 48\\ 70\leq 48$ -------> is not a viable solution

substitute the values of x and y in the inequality 2

$y\geq 10$

$30\geq 10$ --------> is ok

the point B is not a viable solution because does not satisfy the inequality 1

3 0

1 year ago