Answer:
£191.36
Step-by-step explanation:
Sum the parts of the ratio, 1 + 4 = 5 parts
Divide 320 by 5 to find the value of one part of the ratio.
320 ÷ 5 = 64 ← value of 1 part of the ratio , thus
4 parts = 4 × 64 = 256
Thus he bought 64 first class and 256 second class.
Cost = (64 × £0.67) + (256 × £0.58)
= £42.88 + 148.48
= £191.36
<span>a) Differentiate both sides of lnq − 3lnp + 0.003p=7 with respect to p, keeping in mind that q is a function of p and so using the Chain Rule to differentiate any functions of q:
(1/q)(dq/dp) − 3/p + 0.003 = 0
dq/dp = (3/p − 0.003)q.
So E(p) = dq/dp (p/q) = (3/p − 0.003)(q)(p/q) = (3/p − 0.003)p = 3 − 0.003p.
b) The revenue is pq.
Note that (d/dp) of pq = q + p dq/dp = q[1 + dq/dp (p/q)] = q(1 + E(p)), which is zero when E(p) = −1. Therefore, to maximize revenue, set E(p) = −1:
3 − 0.003p = −1
0.003p = 4
p = 4/0.003 = 4000/3 = 1333.33</span>
Join the centre O to the chord (let it be MN) & let OH be the perpendicular to the chord
OH bisects MN into 2 equal parts (each one is x/2)
OMH is a right triangle with one side =8, the second leg =x/2 & the hypotenuse = 12 (Radius)
Apply Pythagoras:
12² = 8² +(x/2)² ==>144=64 + x²/4 ==> x²=4(144-64) =320
x²=320==> x=√320 =17.88 ≈17.9
Answer:
2 cups of blueberry
Step-by-step explanation:
8/4=2
Answer:
12.75w + 25 = 114.25
w = 7
Step-by-step explanation:
since sarah is receiving 12.75 each week for a number of weeks, w (we don't know its value yet) we know that first part of the equation: that 12.75 is the coefficient next to w. Then we have the extra 25, so we know that adding 12.75w and 25 would give us sarah's total amount, which is 114.25.
to find out what w represents, we have to solve for it. solving for w means isolating it on one side. so, what we can do first is subtract 25 from both sides. that would then make the equation:
12.75w = 89.25
now, we have only one step left to isolating w, and that's to get 12.75 on the other side somehow. since we're multiplying 12.75 with w, and we're applying additive inverse properties, meaning the opposite of what is happening to cancel it out on the side it's in, we would divide 12.75 on both sides. in the left, 12.75 would cancel out, and in the right, we would divide 89.25 by 12.75. the quotient is 7.
now there's nothing left to take out to isolate w, so we have:
w = 7
sarah saved up for 7 weeks.
