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Aliun [14]
3 years ago
5

Sin78 ×cos42+cos78×sin42 evaluate without the use of a calculator

Mathematics
1 answer:
Novay_Z [31]3 years ago
4 0
Sin a * cos b + cos a * sin b=sin (a+b)

sin 78 * cos 42 + cos 78* sin 42=sin (78+42)=sin 120=sin(180-120)=
sin 60=√3 / 2

Answer: sin 78 * cos 42 + cos 78* sin 42=<span>√3 / 2</span>
You might be interested in
What is the surface area of the rectangular prism below?
Andrew [12]

Answer:

B ( 432 units^2)

Step-by-step explanation:

Total surface area= 2*(6*6)+ 4*(15*6)

There are 2 squares at each end of the same size so total area will be 2*(6*6)

If we look at the rectangles( bottom, top and the sides), we can see that all are of same dimensions and there are 4 of them so it's 4*(15*6)

In short, total surface area= 2*(6*6)+ 4*(15*6) = 432 units^2

5 0
3 years ago
Are the ratios 1:2 and 3:16 equivalent?<br> yes<br> no
mamaluj [8]

Answer:

the answer to your question is false.

Step-by-step explanation:

These ratios are not equivalent

5 0
2 years ago
Read 2 more answers
Which shows two expressions that are equivalent to (-7)(-15)(-5)?
shusha [124]
B is the correct answer

C and D would be incorrect as 7 and 15 multiplies to 105 not 115
A is incorrect as -5 and -15 make a positive 75 not a negative 75
8 0
3 years ago
The swimming pool at Spring Valley High School is a rectangle with a width of 70 meters and a length of 25 meters. Around the pe
erik [133]
<h3>Answer:   4w^2+190w</h3>

================================================

Explanation:

Check out the attached image below. Specifically, take a look at figure 1. We start with a rectangle which is 70 meters by 25 meters. Then we extend this rectangle out by adding two copies of w to each dimension having the larger rectangle be (70+2w) meters by (25+2w) meters.

The original smaller rectangle has area of 70*25 = 1750 square meters.

The new larger rectangle area is a bit more tricky to figure out, though its not too bad once you get the hang of it. You could use the FOIL rule to get

(70+2w)(25+2w) = 70*25+70*2w+2w*25+2w*2w

(70+2w)(25+2w) = 1750+140w+50w+4w^2

(70+2w)(25+2w) = 1750+190w+4w^2

(70+2w)(25+2w) = 4w^2+190w+1750

Or you could use the box method shown in figure 2.

The idea is to write the terms of (70+2w) and (25+2w) along the edges of the box. Then filling out the 4 inner boxes involves multiplying the outer terms. Example: row1,column2 has 50w inside it because we multiply the outer terms 25 and 2w to get 25*2w = 50w. The other boxes are filled out in a similar fashion.

Although the FOIL rule is handy and taught in a lot of math books/classes, I prefer the box method because the box method can be extended to other cases (not just multiplying two binomials).

Whichever method you use, the larger rectangle has area 4w^2+190w+1750 square meters.

-------------------------------

So,

A = area of larger rectangle = 4w^2+190w+1750

B = area of smaller rectangle = 1750

C = difference in areas of A and B

C = A - B

C = ( A ) - ( B )

C = ( 4w^2+190w+1750 ) - ( 1750 )

C = 4w^2+190w+1750-1750

C = 4w^2+190w

This represents the area of just the tile border alone. We started with the larger rectangle and took out the smaller rectangle inside to only have the border left over.

-------------------------------

If you want, you can factor out a 'w' to get

4w^2+190w = w(4w+190)

Though this may be optional.

8 0
3 years ago
Michael has a life insurance premium of $400 a year on a term life insurance policy for a 40-year term with $150,000 of coverage
iVinArrow [24]
The cost of the premium - $16,000 (40 x $400)
The cost of coverage - $150,000

The cost of the coverage is more
6 0
3 years ago
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