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bagirrra123 [75]

2 years ago

9

Use a calculator to find the values of the inverse trigonometric functions. Round to the nearest degree. sin–1 = __° tan–1(4) =_

_ ° cos–1(0.1) =__

2 answers:

elena-s [515]2 years ago

6 0

Solution:

As 360°= 2 π Radian

1 Radian = $\frac{180 degree}{\pi }$

1. Sin(-1)= Sin ( $\frac{-180 degree}{\pi }$ )

= Sin (-57°16'22")=-0.84147

2. $Tan^{-1}4=Tan(\frac{720}{\pi }})$

= $Tan^{-1}$ (229°54'32")

=75.963757 Degrees

3. $Cos^{-1}(0.1)=Cos^{-1}(\frac{18}{\pi})=Cos^{-1}(\frac{63}{11})=$

= $Cos^{-1}$ (5°43'38")

= 84.26083 Degrees

Mice21 [21]2 years ago

3 0

Well, as you mentioned in the question,

you only need to replace the arguments of those functions in your calculator.

For instance, tan-1(4) = 76 <span>°

and

cos-1(0.1) = 84</span><span>°</span>

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A drawing of a surfboard in a catalog shows its length as 8 4/9 inches. Find the actual length of the surfboard if 1/2 inch leng

jonny [76]

3/8 of a foot = 3/8 x 12/1 or 4 1/2 inches

So our 1/2 inch grows by a factor of 9 because 4 1/2 ÷ 1/2 = 9 Think how many 1/2 dollars are in 4 1/2 dollars. (Answer is 9)

So our 8 4/9 in the catalog has to grow the same

8 4/9 x 9 = 8 4/9 x 9/1 = 76/9 x 9/1 or 76 inches which is 6 ft 4 inches.
(76 ÷12 = 6 r4)

6 0

2 years ago

A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

3 0

2 years ago

The championship record in baseball in a certain year was 52 games won, and 14 lost. What percent of the games were won?

slamgirl [31]

Number of games won/Number of total games played x 100%

52/66 x 100% = 78.79%

Hope u understood! :)

5 0

2 years ago

Brandon bought 21 chicken wings for $39.90. How much would it cost for 15 wings?

Pachacha [2.7K]

Answer:

$28.50

Step-by-step explanation:

21 chicken wings= $39.90

1 chicken wing= 39.90÷21= $1.90

15 chicken wings= 15×1.90= $28.50

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2 years ago

In a particularly sunny month, Solaire's solar panels generated 110 percent as much power as expected.What fraction of the expec

vfiekz [6]

we are given

In a particularly sunny month, Solaire's solar panels generated 110 percent as much power as expected.

so, we need to change percent into fraction to get our value

we can write

110%= $\frac{110}{100}$

now, we can simplify it

and we get

110%= $\frac{11}{10}$

so,

Solaire's solar panels generate $\frac{11}{10}$ of the expected amount of power.............Answer

8 0

2 years ago

Read 2 more answers