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3 years ago

Verify the identity. sin (x+pi/2)=cos x

1 answer:

4 0

Given data
sin (x+pi/2)=cos x
now using sin law
sin(a+b)=sin(a)cos(b)+cos(a)sin(b)
now using above values
sin(pi/2+x)=sin(pi/2)cos(x)+cos(pi/2)sin(x)
as we know that
sin(pi/2)=1
cos(pi/2)=0
now putting these values
sin(pi/2+x)=1*cosx+0*1
sin(pi/2+x)=cosx
hence proved that

sin (x+pi/2)=cos x

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1+2000000000000000000000000000000000000

Pavel [41]

Answer: 2000000000000000000000000000000000001

Step-by-step explanation: simple addition <3

7 0

2 years ago

26. A book costs sh. (x - 300) and a pen costs sh (x + 100). If Ndagire pad sh. 3300 for 3 books and 2 pens, how much did she pa

saul85 [17]

Answer:

500 and 900

Step-by-step explanation:

3(x - 300) + 2(x + 100) = 3300 ← distribute parenthesis

3x - 900 + 2x + 200 = 3300

5x - 700 = 3300 ( add 700 to both sides )

5x = 4000 ( divide both sides by 5 )

x = 800

Then

cost of book = x - 300 = 800 - 300 = 500

cost of pen = x + 100 = 800 + 100 = 900

7 0

1 year ago

A rectangular box is to have a square base and a volume of 12 ft3. If the material for the base costs $0.17/ft2, the material fo

katen-ka-za [31]

Answer:

(a)Length =2 feet

(b)Width =2 feet

(c)Height=3 feet

Step-by-step explanation:

Let the dimensions of the box be x, y and z

The rectangular box has a square base.

Therefore, Volume of the box $V=x^2z$

Volume of the box $=12 ft^3\\$

$Therefore, x^2z=12\\z=\frac{12}{x^2}$

The material for the base costs $\$0.17/ft^2$ , the material for the sides costs $\$0.10/ft^2$ , and the material for the top costs $\$0.13/ft^2$ .

Area of the base $=x^2$

Cost of the Base $=\$0.17x^2$

Area of the sides $=4xz$

Cost of the sides= $=\$0.10(4xz)$

Area of the Top $=x^2$

Cost of the Base $=\$0.13x^2$

Total Cost, $C(x,z) =0.17x^2+0.13x^2+0.10(4xz)$

Substituting $z=\frac{12}{x^2}$

$C(x) =0.17x^2+0.13x^2+0.10(4x)(\frac{12}{x^2})\\C(x)=0.3x^2+\frac{4.8}{x} \\C(x)=\dfrac{0.3x^3+4.8}{x}$

To minimize C(x), we solve for the derivative and obtain its critical point

$C'(x)=\dfrac{0.6x^3-4.8}{x^2}\\Setting \:C'(x)=0\\0.6x^3-4.8=0\\0.6x^3=4.8\\x^3=4.8\div 0.6\\x^3=8\\x=\sqrt[3]{8}=2$

Recall: $z=\frac{12}{x^2}=\frac{12}{2^2}=3\\$

Therefore, the dimensions that minimizes the cost of the box are:

(a)Length =2 feet

(b)Width =2 feet

(c)Height=3 feet

7 0

3 years ago

Which matrix translates the vector 〈4,-3〉 to 〈6,-8〉?

Mars2501 [29]

Answer:

2, -5

Step-by-step explanation:

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3 years ago

A circuit board manufacturer can produce 2,000 boards per hour. How many days will it take to produce 16,500 if the company has

mrs_skeptik [129]

Hi Mrsdiaz1jd1977owwfvt!
OK so 2,000 boards per hour in 10 hours is 2,000*10=20,000 boards in 10 hours. So it can produce 16,500 boards in less than a day.
I may be wrong but I hope this helps!

5 0

3 years ago

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