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3 years ago

If x varies jointly as y and z , and x =8 when y = 4 and z=9, find z when x =16 and y =6

2 answers:

7 0

X = 8 when y = 4 and z = 9, then k = x/(yz) = 8/(4*9) = 2/9. The equation is x = (2/9)yz. when x = 16 and y = 6, (2/9)*6*z = 16, solve the equation we get z = 12

GenaCL600 [577]3 years ago

5 0

Answer: Hello mate!

Joint variation means that x varies with the product of z and y, then we can write this as:

x = k *(yz) where k is a real number.

we know that x is 8 when y = 4 and = 9, and with this information, we could obtain the value of k.

8 = k*(4*9) = k*(36)

then k = 8/36 = 2/9

now, if x = 16 and y = 6, we need to find the value of z, we replace the values of x and y in our equation and isolate z:

16 = (2/9)*(6z)

16 = (12/9)z

16*(9/12) = z = 12

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3 years ago

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3 years ago

Find the exponential function that passes through the points (2,80) and (5,5120)

juin [17]

Answer:

y = 5·4^x

Step-by-step explanation:

If you have two points, (x1, y1) and (x2, y2), whose relationship can be described by the exponential function ...

y = a·b^x

you can find the values of 'a' and 'b' as follows.

Substitute the given points:

y1 = a·b^(x1)

y2 = a·b^(x1)

Divide the second equation by the first:

y2/y1 = ((ab^(x2))/(ab^(x1)) = b^(x2 -x1)

Take the inverse power (root):

(y2/y1)^(1/(x2 -x1) = b

Use this value of 'b' to find 'a'. Here, we have solved the first equation for 'a'.

a = y1/(b^(x1))

In summary:

b = (y2/y1)^(1/(x2 -x1))
a = y1·b^(-x1)

For the problem at hand, (x1, y1) = (2, 80) and (x2, y2) = (5, 5120).

b = (5120/80)^(1/(5-2)) = ∛64 = 4

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3 years ago

What is the volume of the following triangular prism? 60 cm3 12 cm3 3.75 cm3 6 cm3

DochEvi [55]

By definition, the prism volume is given by:
$V = Ab * L
$ Where,
Ab: base area
L: long
Substituting values we have:
$V = ((1/2) * (12) * (2.5)) * (4)
 
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Answer:
The volume of the triangular prism is:
$V = 60 cm ^ 3$

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3 years ago

FREE BRAINLIEST!: (n+2) to the power of 2 - 5a + 1 when n=6 and a=2

BlackZzzverrR [31]

Answer:

Step-by-step explanation:

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3 years ago