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3 years ago

I need the answer pleaseeeeeeeee

Mathematics

1 answer:

Vaselesa [24]3 years ago

7 0

I'm thinking you would have to add the probabilities that you choose a boy with you choose someone in the science club minus a boy in the science club. You can't count these people twice. I'm getting 59% (11+10-2)/32

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How is this solved using trig identities (sum/difference)?

GenaCL600 [577]

FIRST PART
We need to find sin α, cos α, and cos β, tan β
α and β is located on third quadrant, sin α, cos α, and sin β, cos β are negative

Determine ratio of ∠α
Use the help of right triangle figure to find the ratio
tan α = 5/12
side in front of the angle/ side adjacent to the angle = 5/12
Draw the figure, see image attached

Using pythagorean theorem, we find the length of the hypotenuse is 13
sin α = side in front of the angle / hypotenuse
sin α = -12/13

cos α = side adjacent to the angle / hypotenuse
cos α = -5/13

Determine ratio of ∠β
sin β = -1/2
sin β = sin 210° (third quadrant)
β = 210°

$cos \beta = -\frac{1}{2} \sqrt{3}$

$tan \beta= \frac{1}{3} \sqrt{3}$

SECOND PART
Solve the questions
Find sin (α + β)
sin (α + β) = sin α cos β + cos α sin β
$sin( \alpha + \beta )=(- \frac{12}{13} )( -\frac{1}{2} \sqrt{3})+( -\frac{5}{13} )( -\frac{1}{2} )$
$sin( \alpha + \beta )=(\frac{12}{26}\sqrt{3})+( \frac{5}{26} )$
$sin( \alpha + \beta )=(\frac{5+12\sqrt{3}}{26})$

Find cos (α - β)
cos (α - β) = cos α cos β + sin α sin β
$cos( \alpha + \beta )=(- \frac{5}{13} )( -\frac{1}{2} \sqrt{3})+( -\frac{12}{13} )( -\frac{1}{2} )$
$cos( \alpha + \beta )=(\frac{5}{26} \sqrt{3})+( \frac{12}{26} )$
$cos( \alpha + \beta )=(\frac{5\sqrt{3}+12}{26} )$

Find tan (α - β)
$tan( \alpha - \beta )= \frac{ tan \alpha-tan \beta }{1+tan \alpha tan \beta }$
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{1+(\frac{5}{12}) ( \frac{1}{2} \sqrt{3})}$

Simplify the denominator
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{1+(\frac{5\sqrt{3}}{24})}$
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }$

Simplify the numerator
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{6}{12} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }$
$tan( \alpha - \beta )= \frac{ \frac{5-6\sqrt{3}}{12} }{ \frac{24+5\sqrt{3}}{24} }$

Simplify the fraction
$tan( \alpha - \beta )= (\frac{5-6\sqrt{3}}{12} })({ \frac{24}{24+5\sqrt{3}})$
$tan( \alpha - \beta )= \frac{10-12\sqrt{3} }{ 24+5\sqrt{3}}$

7 0

3 years ago

Question 1!!! PLEASE HELP

andreev551 [17]

Quickly using a calculator (or long division) reveals that 191/238=0.8025=80.25%, which is close to 80%=4/5
Similarly, 106/160=0.6625=66.25%, which is close to 66.67%=2/3

7 0

4 years ago

Can someone help me and explain on paper , I’m still so confused

Oksanka [162]

Answer:

Your answer is -5

Step-by-step explanation:

On paper;

8 0

3 years ago

A bottle of medicine contains 0.5 kilograms of medicine. One dose of medicine is 20g for kids & 45g for adults. If a medical

vaieri [72.5K]

No (see picture for explanation)

3 0

3 years ago

The area of circle B is 121 times greater than the area of circle A. The radius of circle B is 44. What is the radius of circle

xxMikexx [17]

Formula:
$\bigg( \dfrac{radius_1}{radius_2} \bigg)^2 = \dfrac{area_1}{area_2}$

Plug in the values:
$\bigg( \dfrac{r}{44} \bigg)^2 = \dfrac{1}{121}$

Simplify LHS:
$\dfrac{r^2}{1936} = \dfrac{1}{121}$

Multiply by 1936 on both sides:
$r^2 = \dfrac{1936}{121}
$

Simplify RHS:
$r^2 = 16$

Square root both sides:
$r = 4$

Answer: The radius is 4 units. (Answer B)

5 0

3 years ago