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Anettt [7]
2 years ago
10

bob is having a party and want to order some cake. there will be 57 guest and he wants to make sure that everyone gets a slice o

f cake. he wants to pay as little as possible for the cakes and for them to be the same size. First cake 20cm, serve 12 people and cost £13.50, second cake 25cm, serve 20 people and cost £18.75
Mathematics
1 answer:
Leviafan [203]2 years ago
4 0
<span>Bob should by the 25cm cake for 18.75 each. He will need to buy 3 of these cakes in order to feed 57 guests. The total cost would be 56.25. If he were to buy the 20cm cake, he would need to purchase 5 cakes for a total of 67.50.</span>
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Which of the following are descriptive images? Select all that apply.
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"A lock of straw-colored hair wedged between the mottled page of a Victor Hugo novel."

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answer A radio station located 120 miles due east of Collinsville has a listening radius of 100 miles. A straight road joins Col
melamori03 [73]

Answer:

168.7602 miles

Step-by-step explanation:

One way to solve this problem is by using an equation that describes the listening radius of the station, and another for the road, then the points where this two-equation intersect each other will represent when the driver starts and stops listening to the station, and the distance between the points is the miles that the driver will receive the signal.

The equation for the listening radius (the radio station is at (0,0)):

x^2+y^2=100^2

The equation for the road that past through the points (-120,0) and (80,100) (Collinsville and Harmony respectively):

m=\frac{y_2-y_1}{x_2-x_1} =\frac{100-0}{80-(-120)}=\frac{100}{200}=\frac{1}{2}

y-y_1=m(x-x_1)\\y-0=\frac{1}{2}(x-(-120))\\ y=\frac{1}{2}x+60

Substitutes the value of y in the equation of the circle:

x^2+(\frac{1}{2}x+60)^2=100^2\\x^2+\frac{1}{4} x^2+60x+3600=10000\\\frac{5}{4} x^2+60x+3600=10000\\\frac{5}{4} x^2+60x+3600-10000=0\\\frac{5}{4} x^2+60x-6400=0\\5 x^2+240x-25600=0\\x^2+48x-5120=0\\

The formula to solve second-degree equations:

x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac} }{2a} \\x_{1,2}=\frac{-48\pm\sqrt{48^2-4(1)(-5120)} }{2(1)}\\x_{1,2}=\frac{-48\pm\sqrt{2304+20480} }{2}\\x_{1,2}=\frac{-48\pm\sqrt{22784} }{2}\\x_{1,2}=\frac{-48\pm16\sqrt{89} }{2}\\x_{1,2}=-24\pm8\sqrt{89} \\x_1=-24+8\sqrt{89}\approx51.4718\\x_2=-24-8\sqrt{89}\approx-99.4718\\

Using the values in x to find the values in y:

y_1=\frac{1}{2}x_1+60\\y_1=\frac{1}{2}(-24+8\sqrt{89} )+60\\y_1=-12+4\sqrt{89}+60\\ y_1=48+4\sqrt{89}\approx85.7359

y_2=\frac{1}{2}x_2+60\\y_2=\frac{1}{2}(-24-8\sqrt{89} )+60\\y_1=-12-4\sqrt{89}+60\\ y_1=48-4\sqrt{89}\approx10.2641

The distance between the points (51.4718,85.7359) and (-99.4718,10.2641) :

d=\sqrt{(x_1 -x_2 )^2+(y_1 -y_2)^2} \\d=\sqrt{(-24+8\sqrt{89} -(-24-8\sqrt{89}) )^2+(48+4\sqrt{89} -(48-4\sqrt{89}) )^2}\\d=\sqrt{(-24+8\sqrt{89} +24+8\sqrt{89} )^2+(48+4\sqrt{89} -48+4\sqrt{89} )^2}\\d=\sqrt{(16\sqrt{89} )^2+(8\sqrt{89} )^2}\\d=\sqrt{22784+5696}\\d=\sqrt{28480}\\d=8\sqrt{445}\approx168.7602miles

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A dairy milker's gross pay per week is $546. If she works 30 hours per week, how much does she earn per hour?
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$18.20

Explanation:
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Your answer is the first point

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