5. A local flower shop sells a dozen roses for

If 180° < α < 270°, cos⁡ α = −817, 270° < β < 360°, and sin⁡ β = −45, what is cos⁡ (α + β)?

eduard

Answer:

$cos(\alpha+\beta)=-\frac{84}{85}$

Step-by-step explanation:

we know that

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

Remember the identity

$cos^{2} (x)+sin^2(x)=1$

step 1

Find the value of $sin(\alpha)$

we have that

The angle alpha lie on the III Quadrant

so

The values of sine and cosine are negative

$cos(\alpha)=-\frac{8}{17}$

Find the value of sine

$cos^{2} (\alpha)+sin^2(\alpha)=1$

substitute

$(-\frac{8}{17})^{2}+sin^2(\alpha)=1$

$sin^2(\alpha)=1-\frac{64}{289}$

$sin^2(\alpha)=\frac{225}{289}$

$sin(\alpha)=-\frac{15}{17}$

step 2

Find the value of $cos(\beta)$

we have that

The angle beta lie on the IV Quadrant

so

The value of the cosine is positive and the value of the sine is negative

$sin(\beta)=-\frac{4}{5}$

Find the value of cosine

$cos^{2} (\beta)+sin^2(\beta)=1$

substitute

$(-\frac{4}{5})^{2}+cos^2(\beta)=1$

$cos^2(\beta)=1-\frac{16}{25}$

$cos^2(\beta)=\frac{9}{25}$

$cos(\beta)=\frac{3}{5}$

step 3

Find cos⁡ (α + β)

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

we have

$cos(\alpha)=-\frac{8}{17}$

$sin(\alpha)=-\frac{15}{17}$

$sin(\beta)=-\frac{4}{5}$

$cos(\beta)=\frac{3}{5}$

substitute

$cos(\alpha+\beta)=-\frac{8}{17}*\frac{3}{5}-(-\frac{15}{17})*(-\frac{4}{5})$

$cos(\alpha+\beta)=-\frac{24}{85}-\frac{60}{85}$

$cos(\alpha+\beta)=-\frac{84}{85}$

4 0

3 years ago

Dinner for a family of 3 at the local Italian Eatery came to $47.83 before tax. If the family wanted to tip their server 20%, ho

EastWind [94]

Answer:

$9.57

Step-by-step explanation:

47.83 x 20% = 9.57

5 0

2 years ago

lighting if a 25-foot-tall house cast a 75-foot shadow at the same time that a streetlight casts a 60-foot shadow how tall is th

jolli1 [7]

Answer:

The street light is 20 feet tall.

Step-by-step explanation:

This question depends on a proportion. Keep your height of the object in one ratio and the length of the shadow in the other.

25/x = 75/60 Notice the height of the structure is on the left. The length of the shadow is on the right. Cross multiply

75x = 60 * 25 Combine the right

75x = 1500 Divide by 75

x = 1500/75

x = 20

The street light is 20 feet tall.

3 0

2 years ago

Dividing fractions 1/8 / 1/3

agasfer [191]

1/8×3/1=3/8
:)___________

8 0

3 years ago

Read 2 more answers

It takes 10 road workers 5 days to complete a road repair when working 2 hours a day. Working at the same pace, how many days wi

Levart [38]

Answer:

10 days

Step-by-step explanation:

10 workers work 2 hrs a day for 5 days, so the work content is 10*5*2=100 manhours.

2 people work 5 hrs a day, so they deliver 10 manhours a day. To finish a work of 100 manhours,they’ll need 100/10=10 days.

The answer is 10 days.

6 0

2 years ago