sinθ=2/5. cos2θ=1-sin2θ gives cos2θ=1-4/25=21/25 cosθ<0 gives cosθ=-(√21)/5 sin2θ=2sinθcosθ=2×(2/5)×(-(√21)/5)=-4(√21)/25 cos2θ=cos2θ-sin2θ=21/25-4/25=17/25

sinθ=2/5. cos2θ=1-sin2θ gives cos2θ=1-4/25=21/25 cosθ<0 gives cosθ=-(√21)/5 sin2θ=2sinθcosθ=2×(2/5)×(-(√21)/5)=-4(√21)/25 cos2θ=cos2θ-sin2θ=21/25-4/25=17/25

How do you compare fractions? (answer)

or you could divide the numbers and see whether the answer is <=>1, as first number 4 3/8=35/8, second number 34/7 35/8÷34/7=35/8×7/34=245/272 <1 so 34/7 is larger.

2x−y=1 −6x+3y=2 multiply the first equation by -3 to-3 get -6x+3y=-3 the two equations are a set of two parallel lines −6x+3y=2 and -6x+3y=-3 No solution.

15(n+(n+1)+(n+2)+(n+3))=390 15(4n+6)=390 4n+6=26 4n=20 n=5 15(n+3)=120

Algebra Question (answer)

Total cost = $25+$10S Total payment $40 Change $40-($25+$10S)=$(15-10S)

The area of the circle is, as a function of time, A(t)=πr2(t) We are given that dr/dt = 7 cm/min and seek to find dA/dt Differentiating the equation for the area we have dA/dt = 2πr(t)dr/dt which gives that dA/dt=2π×12cm×7cm/min=168π cm2/min

If the bond pays its interest yearly then after one year the owner receives $600×.045=$27 For the final six months the bond will accrue $600×.045×1/2=$13.50 The total interest earned is $40.50

Similar triangles. The right triangle formed by the lamp post and the (24+6) foot side on the ground is similar to the right triangle formed by the person, of height h and his 6 foot shadow. h/25=6/30 h=5

The number pairs you state are in the form of A+B and A-B. Their average is A. For the first that means 23, and for the second that means -b/2.

let x be an irrational number. show that for every k>0 there exist n,m ∈Z such that 0<|nx-m|<k (answer)

Since x is irrational there exists an integer N for which N<x<N+1. Divide the interval [N,N+1] into n2 parts as xj=N+j/n2 for j=0,1,2,...,n2, (xn2=N+1) All of the xj are rational. xj+1-xj=1/n2. No xj is x. There is a j* such that xj*<x<xj*+1 That...

1/(3×22) 1/(3×32) 1/(3×2¹) 1/(3×3¹) 1/(3×20) 1/(3×30) The missing number is 1/(3×20)=1/3

Total distance traveled Time 90×2=180 miles 2 hrs 72×1/2=36 miles ...

1/|×-4|<1/|×+7| multiply both sides by |×-4|×|×+7| to get |×+7|<|×-4| which says that the points you are looking for are those whose distance from -7 is less than their distance from 4. The middle of that interval is the point -3/2. The points we want...

Now find the range of N as N/(-5) + 1 ≤ 7 subtract 1 from each side N/(-5)≤6 now multiply each side by -5 N≥-30 NOTE: multiplying an inequality by a negative number flips the inequality.

equation find m and n (answer)

(m-n)2=m2-2mn+n2=140-2(49)=140-98=42 You only asked for m-n. The question title asks for more.

write the equation of the line in general form whose x-intercept is 3 and y- intercept of -4. (answer)

There is a double intercept form x/3+y/(-4)=1

solve the system (answer)

y=-x+7 y=(x-3)2/2=(x2-6x+9)/2 So -x+7=(x2-6x+9)/2 or -2x+14=x2-6x+9 or 0=x2-4x-5 competing the square we have (x-2)2-9=0 or x-2=±3 or x=5, or x=-1 In which cases y=2 or y= 8 (5,2) and (-1,8) are the solutions

The answer is 19. The explanation is bG = number of boys Gordon plays bJ = number of boys Jayanthi plays gG = number of girls Gordon plays gJ = number of girls Jayanthi plays There are a total of nC2 games...

A circle centered at the origin containing the point (-6,0) has the equation x2+y2=36. Any other question about the circle may be answered using this. Exactly what is your question. What you posted is incomplete.

H = 21 + 979e^−0.1t. For t=60 is 21+979e-6=23.4267 Average over first hour is (1/60)∫060Hdt=21+(979/60)∫060e-.1tdt ∫060e-.1tdt=-10e-.1t|060=10(1-e-6) Average over first hour is 21+(979/6)(1-e-6)=21+162.7622=183.7622 The 21 is simply added because (1/60)∫06021dt...

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