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3 years ago

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The length of a page in a yearbook is 7 inches. The top margin is 1/2 inch, and the bottom margin in 3/4 inch. What is the lengt

h of the page inside the margins?

1 answer:

Andrei [34K]3 years ago

7 0

Can you be more specific?

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Given cosα = −3/5, 180 < α < 270, and sinβ = 12/13, 90 < β < 180

torisob [31]

I got

$- \frac{6 3}{65}$

What we know

cos a=-3/5.

sin b=12/13

Angle A interval are between 180 and 270 or third quadrant

Angle B quadrant is between 90 and 180 or second quadrant.

What we need to find

Cos(b)

Cos(a)

What we are going to apply

Sum and Difference Formulas

Basics Sine and Cosines Identies.

1. Let write out the cos(a-b) formula.

$\cos(a - b) = \cos(a) \cos(b) + \sin(a) \sin(b)$

2. Use the interval it gave us.

According to the given, Angle B must between in second quadrant.

Since sin is opposite/hypotenuse and we are given a sin b=12/13. We. are going to set up an equation using the pythagorean theorem.

.

${12}^{2} + {y}^{2} = {13}^{2}$

$144 + {y}^{2} = 169$

$25 = {y}^{2}$

$y = 5$

so our adjacent side is 5.

Cosine is adjacent/hypotenuse so our cos b=5/13.

Using the interval it gave us, Angle a must be in the third quadrant. Since cos is adjacent/hypotenuse and we are given cos a=-3/5. We are going to set up an equation using pythagorean theorem,

.

$( - 3) {}^{2} + {x}^{2} = {5}^{2}$

$9 + {x}^{2} = 25$

${x}^{2} = 16$

$x = 4$

so our opposite side is 4. sin =Opposite/Hypotenuse so our sin a =4/5.Sin is negative in the third quadrant so

sin a =-4/5.

Now use cosine difference formula

$- \frac{3}{5} \times \frac{5}{13} + - \frac {4}{5} \times \frac{12}{13}$

$- \frac{15}{65} + ( - \frac{48}{65} )$

$- \frac{63}{65}$

Hope this helps

6 0

3 years ago

Will report anybody who gives a link!<br><br> 3,947 ÷ 45 = (?) R (?)

Free_Kalibri [48]

Answer:

87.7(1)

=

87 Remainder 32

8 0

3 years ago

Which is a better buy? 9.30 for 10 sharpies or 6.55 for 7?

ser-zykov [4K]

The 10 sharpies because you get more for less because if you by 7 you get less for more with that amount.

8 0

3 years ago

Read 2 more answers

A hungry college student just finished eating a large cheese and pepperoni pizza from Doug's Pizza Palace and felt there wasn'

Zepler [3.9K]

Answer: 83

Step-by-step explanation:

The confidence interval for population mean is given by :-

$\overline{x}\pm E$

Given : The student obtained the following 95% confidence interval (in grams) for the population mean, (862,1028).

Here,

Lower limit of the confidence interval : $\overline{x}-E=862$ (1)

Upper limit of the confidence interval : $\overline{x}+E=1028$ (2)

Subtracting (1) from (2) , we get

$2E=166\\\\\Rightarrow\ E=\dfrac{166}{2}=83$

Hence, the margin of error = 83

4 0

3 years ago

The volume of the Atlantic Ocean is about 3.1⋅10173.1 \cdot 10^{17}3.1⋅10173, point, 1, dot, 10, start superscript, 17, end supe

Serga [27]

Answer: The annual flow of the Mississippi river would fit in the Atlantic ocean $4.92\times10^5$ times.

Step-by-step explanation:

Given: Volume of Atlantic Ocean= $3.1\times10^{17}$ cubic meters

Annual flow of Mississippi river = $6.3\times10^{11}$ cubic meters.

then, the number of times the annual flow of the Mississippi river would fit in the Atlantic ocean = $\dfrac{\text{ Volume of Atlantic Ocean}}{\text{Annual flow of Mississippi river}}$

$=\dfrac{3.1\times10^{17}}{6.3\times10^{11}}\ \ \=0.492063492063\times10^{17-11}\ \ [\dfrac{a^m}{a^n}=a^{m-n}]\\\\=0.492063492063\times10^6\approx4.92\times10^5$

Hence, the annual flow of the Mississippi river would fit in the Atlantic ocean $4.92\times10^5$ times.

3 0

3 years ago