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3 years ago

A chocolatier makes chocolate covered cherries in the form of spheres. Amelia

Mathematics

1 answer:

Annette [7]3 years ago

8 0

The volume of the chocolate is the amount of choclate used in the cherries

The amount of chocolate used is 17.24 cubic centimeters

<h3>How to determine the amoumt of chocolate?</h3>

Start by calculating the volume of the cherries using:

V = 4/3 π(D/2)^3

The diameter of the cherry is 2.8 cm.

So, we have:

V = 4/3π(2.8/2)^3

Evaluate

V = 11.49

Next, calculate the volume of the cherry and the chocolate.

V = 4/3π(0.5+2.8/2)^3

V = 28.73

Calculate the difference (d) between both volumes

d = 28.73 - 11.49

d = 17.24

Hence, the amount of chocolate used is 17.24 cubic centimeters

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4 years ago

Five cupcakes and two cookies cost $19.75. Two cupcakes and four cookies cost $ 17.50.

alina1380 [7]

Answer:

Step-by-step explanation:

Let x and y represent the cost of a cupcake and cookie respectively.

Given that;

Five cupcakes and two cookies cost $19.75.

$5x+2y=19.75 ---------- 1$

Two cupcakes and four cookies cost $17.50.

$2x+4y=17.50 --------------2$

Let's solve the simultaneous equation by elimination;

Multiply equation 1 by 2;

$10x+4y=39.50-------3\\$

Subtract equation 2 from equation 3;

$10x-2x+4y-4y=39.50-8x=22$

$8x=22$

divide both sides by 8

$\frac{8x}{8} =\frac{22}{8} \\x=2.75$

Since we have the value of x, let substitute into equation 1 to get y;

$5x+2y=19.75\\5(2.75)+2y=19.75\\13.75+2y=19.75\\2y=19.75-13.75\\2y=6\\y=\frac{6}{2} \\y=3.00$

therefore , the cost of cupcakes and cookies are;

$cupcakes= 2.75\\cookies= 3.00$

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3 years ago

How do you solve this triangle by using the law of sine where

mars1129 [50]

Actually, when you know 2 sides and an included angle, you use the Law of Cosines. (and we don't know if theta is an included angle).
Solving for side c
c^2 = a^2 + b^2 -2ab * cos(C)
c^2 = 36 + 16 - 2*6*4 * cos(60)
c^2 = 52 -48*.5
c^2 = 28
c = 5.2915

Using the Law of Sines
side c / sin(C) = side b / sin (B)
5.2915 / sin(60) = 4 / sin (B)
sin(B) = sin(60) * 4 / 5.2915
sin(B) = 0.86603 * 4 / 5.2915
sin(B) = 3.46412 / 5.2915
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Angle B = 40.894 Degrees

sin (A) / side a = sin (B) / side b
sin (A) = 6 * sin (40.894) / 4
sin (A) = 6 * 0.65466 / 4
sin (A) = .98199
angle A = 79.109 Degrees

angle C = 60 Degrees

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4 years ago