• ### Emptying the pond calculations?

Pumps A&B empty the pond in 3 hours Pumps B&C empty the pond in 4 hours Pumps C&A empty the pond in 5 hours How long will it take pump A,B and C? Workings too please!! Thank you
Pumps A&B empty the pond in 3 hours Pumps B&C empty the pond in 4 hours Pumps C&A empty the pond in 5 hours How long will it take pump A,B and C? Workings too please!! Thank you
5 answers · Mathematics · 5 years ago
• ### It is estimated that the annual proportionate growth rate R(P) of a particular animal population is....?

It is estimated that the annual proportionate growth rate R(P) of a particular animal population is 1.4 when the population size P is 70, and 1.2 when P is 210. Assuming that the behaviour of the population satisﬁes the logistic model, choose the TWO options that give the approximate proportionate growth rate for low populations, r, and the... show more
It is estimated that the annual proportionate growth rate R(P) of a particular animal population is 1.4 when the population size P is 70, and 1.2 when P is 210. Assuming that the behaviour of the population satisﬁes the logistic model, choose the TWO options that give the approximate proportionate growth rate for low populations, r, and the approximate equilibrium population, E. Options A r = 1.3 B r = 1.5 C r = 2.0 D r = 2.6 E E = 880 F E = 1050 G E = 2100 H E = 2550
1 answer · Zoology · 5 years ago
• ### Write down a definite integral that will give the area under the curve y = x^2 sin(3/4x) between x = 1/3Pi and?

1 answer · Mathematics · 5 years ago
• ### ∫x(4+7x^2)dx in [6 to 8]?

Hi all... please help. I dont know how to write the above but hopefully it makes sense, the 6 would be at the nbottom of the squiggle and the 8 at the top and then the rest of the formula. I need a line by line break down of how to do this please... I have to evaluate the formula Thank you
Hi all... please help. I dont know how to write the above but hopefully it makes sense, the 6 would be at the nbottom of the squiggle and the 8 at the top and then the rest of the formula. I need a line by line break down of how to do this please... I have to evaluate the formula Thank you
7 answers · Mathematics · 5 years ago
• ### Idiots guide required here so i learn what to do and why step by step. Thank you?

(a) Using the exact values of the sine and cosine of 1/6π and 3/4π, and one of the sum and difference formulas, show that the exact value of cos(7/12π) is 1/4(√2 − √6) (b) (i) Using an appropriate double-angle formula, express sin(4θ) in terms of sin(2θ) and cos(2θ). (ii) Using your answer to part(b)(i) and appropriate double-angle formulas,... show more
(a) Using the exact values of the sine and cosine of 1/6π and 3/4π, and one of the sum and difference formulas, show that the exact value of cos(7/12π) is 1/4(√2 − √6) (b) (i) Using an appropriate double-angle formula, express sin(4θ) in terms of sin(2θ) and cos(2θ). (ii) Using your answer to part(b)(i) and appropriate double-angle formulas, derive the formula sin(4θ) = 4 sin θ cos3 θ − 4 sin3 θ cos θ. (c) Given that cosec θ = −2, tan θ = 1/3 √3 and −π < θ < π, find the exact value of the angle θ in radians. Justify your answer. (d) Given that −1/2π < θ < 0 and sin θ = −3/4, use appropriate trigonometric formulas to find the exact values of the following. (i) cos(2θ) (ii) cos θ (iii) sin(2θ)
2 answers · Mathematics · 6 years ago
• ### Let Fn be the Fibonacci sequence.... Idiots guide needed please so I learn what i'm doing and why step by step?

Let Fn be the Fibonacci sequence. (a) (i) Use the Fibonacci recurrence relation to express both Fn+4 and Fn in terms of Fn+1 and Fn+2, for n = 0,1,2, . . .. [5] (ii) Use your answer to part (a)(i) to show that Fn+4 + Fn = 3Fn+2 for n = 0,1,2, . . . . [2] (iii) Would the formula in part (a)(ii) necessarily remain true if the sequence Fn is... show more
Let Fn be the Fibonacci sequence. (a) (i) Use the Fibonacci recurrence relation to express both Fn+4 and Fn in terms of Fn+1 and Fn+2, for n = 0,1,2, . . .. [5] (ii) Use your answer to part (a)(i) to show that Fn+4 + Fn = 3Fn+2 for n = 0,1,2, . . . . [2] (iii) Would the formula in part (a)(ii) necessarily remain true if the sequence Fn is replaced by a sequence with the same recurrence relation as the Fibonacci sequence
1 answer · Mathematics · 6 years ago
• ### Let Un be the sequence Un = 8n + (−3)n (n = 0,1,2, . . .). Show that un satisfies the identity un+1un−1 − u2?

Not sure how to write it all in here but the n should all be little n's like to the power of..... Can I have a complete idiots guide please with line by line explanations please so I learn from the answer to what I am doing and why. Thankyou all so much
Not sure how to write it all in here but the n should all be little n's like to the power of..... Can I have a complete idiots guide please with line by line explanations please so I learn from the answer to what I am doing and why. Thankyou all so much
1 answer · Mathematics · 6 years ago
• ### Find a closed form for the following sequence:u0 = 6, u1=−7, un+2 = −1?

Hi All... sorry I need an idiots guide explaining line by line what to do here and why... thankyou so much
Hi All... sorry I need an idiots guide explaining line by line what to do here and why... thankyou so much
1 answer · Mathematics · 6 years ago
• ### The equation x^2+y^2-6x+10y-16=0 represents a circle. Find it's centre and show that it's radius is 5√2?

Step by Step guide would be brilliant as I am not the cleverest! ! ! Thank you
Step by Step guide would be brilliant as I am not the cleverest! ! ! Thank you
6 answers · Mathematics · 6 years ago
• ### Can anyone help? 2x=2t+7, 10y=-6t-65?

The Question is: Eliminate t in the parametric equation 2x=2t+7, 10y=-6t-65... How? Thank you to anyone who can help and explain the detail for me to learn from too.
The Question is: Eliminate t in the parametric equation 2x=2t+7, 10y=-6t-65... How? Thank you to anyone who can help and explain the detail for me to learn from too.
7 answers · Mathematics · 6 years ago