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lana [24]
2 years ago
11

Y Varies directly as X and inversely as Z. Y=100 when X=5 and Z=10 Find Y when X=3 and Z=60

Mathematics
1 answer:
Law Incorporation [45]2 years ago
5 0

Answer:

y = 10

Step-by-step explanation:

based on the question if y  varries directly as x

mathematically

y ∝ x

also, y varries inversly as z can be mathematically expressed as

y ∝ 1/z

combining the two expressions

y ∝ x ∝ 1/z

i. e

y = kx/z..... where k is the constant of proportionality

make  k the subject of formulae

yz = kx

Divide both sides by x

k =yz/x

when y=100 , x = 5 z =10

k = 100 × 10/5

k = 200

to find y when x = 3 and z = 60

<h3>from the equation connecting x,y,z</h3>

k =yz/x

200 =60y/3

cross multiply

60y = 200 × 3

60y = 600

divide both sides by 60

y = 10

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All numbers bigger than five, or at most negative one
Kisachek [45]

Answer:

Hi there!

Your answer is:

-1 >=x>5

This can be broken down to:

x <= -1

x>5

Which fits your requirements!

6 0
3 years ago
A triangular prism is 4 millimeters long. It has a triangular face with a base of 13 millimeters. The volume of the prism is 416
muminat

Answer:

16 millimeters

Step-by-step explanation:

  • Length of the Triangular Prism=4 millimeters
  • Base Length of One Triangular Face=13 millimeters.
  • Volume of the Prism =416 cubic millimeters.

Now:

Volume of a Prism=Base Area X Prism Length

Since we have a triangular base:

Volume of the Prism=(0.5 X Base X Height) X Prism Length

Substituting the given values, we obtain:

416=(0.5 X 13 X Height) X 4

416=26 X Height

Divide both sides by 26

Height of its triangular face=16 millimeters

4 0
2 years ago
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What is 2 7/8 plus 2 3/8 ?
enot [183]
2 7/8 + 2 3/8= 4 10/8, which equals 5 2/8, which is also equal to 5 1/4
8 0
2 years ago
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If 32^2c= 8^c+7, what is the value of c
Leona [35]

\bf 32^{2c}=8^{c+7}~~ \begin{cases} 32=2\cdot 2\cdot 2\cdot 2\cdot 2\\ \qquad 2^5\\ 8=2\cdot 2\cdot 2\\ \qquad 2^3 \end{cases}\implies (2^5)^{2c}=(2^3)^{c+7} \\\\\\ 2^{5(2c)}=2^{3(c+7)}\implies \stackrel{\textit{if the bases are the same, then so are the exponents}}{5(2c)=3(c+7)\implies 10c=3c+21} \\\\\\ 7c=21\implies c=\cfrac{21}{7}\implies c=3

3 0
2 years ago
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Ilia_Sergeevich [38]

Answer:

25

Step-by-step explanation:

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