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fiasKO [112]
3 years ago
5

The value of y varies jointly with the values of x and z When x = 4 and z = 10, the value of y is 360.

Mathematics
1 answer:
Igoryamba3 years ago
3 0

Answer:

A

Step-by-step explanation:

Joint variation is given by:

y=kxz

Where k is some constant.

We are given that y = 360 when x = 4 and z = 10. Therefore:

360=k(4)(10)

Solving for k:

40k=360\Rightarrow k=9

Therefore, our equation is:

y=9xz

Then when x = 5 and z = 12:

y=9(5)(12)=540

The answer is A.

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A rectangle measures 2 1/2 inches by 3/4 inches What is its area?
il63 [147K]

Answer:

1 7/8

Step-by-step explanation:

I think you need to times it like 2 1/2 x 3/4, first you make 2 1/2 into 5/2 then times it like this 5/2 x 3/4. the answer is 1 7/8

8 0
2 years ago
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Show that the sum of two concave functions is concave. Is the product of two concave functions also concave?
spayn [35]

Answer with explanation:

Let us assume that the 2 functions are:

1) f(x)

2) g(x)

Now by definition of concave function we have the first derivative of the function should be strictly decreasing thus for the above 2 function we conclude that

\frac{d}{dx}\cdot f(x)

Now the sum of the 2 functions is shown below

y=f(x)+g(x)

Diffrentiating both sides with respect to 'x' we get

\frac{dy}{dx}=\frac{d}{dx}\cdot f(x)+\frac{d}{dx}\cdot g(x)\\\\

Since each term in the right of the above equation is negative thus we conclude that their sum is also negative thus

\frac{dy}{dx}

Thus the sum of the 2 functions is also a concave function.

Part 2)

The product of the 2 functions is shown below

h=f(x)\cdot g(x)

Diffrentiating both sides with respect to 'x' we get

h'=\frac{d}{dx}\cdot (f(x)\cdot g(x))\\\\h'=g(x)f'(x)+f(x)g'(x)

Now we can see the sign of the terms on the right hand side depend on the signs of the function's themselves hence we remain inconclusive about the sign of the product as a whole. Thus the product can be concave or convex.

8 0
3 years ago
Marcus is trying to make a rectangular picture frame from wood. He nails together two 10-inch pieces of wood and two 8-inch piec
wariber [46]

Answer:

Step-by-step explanation:

You have right triangles, so use the Pythagorean Theorem

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8² + 10² = x²

164 = x²

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3 0
3 years ago
You may use a calculator to complete this test. if 1 egg and 1/3 cup of oil are needed for each bag of brownie mix, how many bag
iren [92.7K]
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If you go from using 1 egg to 3 eggs, you are multiplying the amount you use by 3. If you multiply 1/3 by 3, you get 1 cup of oil. Apply that to your 1 bag of brownie mix, and you get a total of 3 brownie mix bags.

1*3=3
1/3*3=1
4 0
3 years ago
Triangle PQR where P(1,4), Q(-3,-4),R(7,k) is right-angled at Q. find the value of k
NikAS [45]

Answer:

k = -9.

Step-by-step explanation:

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PR^2 = PQ^2 + RQ^2

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k = -9.

8 0
3 years ago
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