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1 year ago

Identify the variation as direct, inverse, joint or combined. y = 7x

Mathematics

2 answers:

densk [106]1 year ago

7 0

Answer:

y =7x , follows the direct variation.

Step-by-step explanation:

Direct variation states that a relationship between two variables in which one is a constant multiple of the other. In other words, when one variable changes the other changes in proportion to the first.

If y is directly proportional to x i.e, $y \propto x$ or

y = kx .....[1] where k is the constant variation

Given : y = 7x

On comparing this with equation [1] we get;

k(constant of variation) = 7

therefore,

it follows the direct variation as $y \propto x$ or

y = 7x where k =7 is the constant of variation.

Therefore, y =7x follows the direct variation.

damaskus [11]1 year ago

6 0

Possibly direct variation

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Javier has four cylindrical models. The heights, radii, and diagonals of the vertical cross-sections of the models are shown in

Sever21 [200]

Given the heights, radii, and diagonals of the vertical cross-sections of the models, the model in which the lateral surface meet the base at a right angle is the model in which the height, the diameter and the diagonal of the vertical cross-section forms a right triangle.

i.e. the sum of the squares of the height (h) and the diameter (d) gives the square of the diagonal vertical cross-section (l).

For model 1:

radius: 14 cm, thus diameter = 2(14) = 28 cm
height: 48 cm
diagonal: 50 cm

 $d^2+h^2=28^2+48^2 \\ \\ =784+2,304=3,090\neq50^2=l^2$

Thus, the lateral surface of model 1 does not meets the base at right angle.

For model 2:

radius: 6 cm, thus diameter = 2(6) = 12 cm
height: 35 cm
diagonal: 37 cm

[tex]d^2+h^2=12^2+35^2 \\ \\ =144+1,225=1,369=37^2=l^2[/tex]

Thus, the lateral surface of model 2 meets the base at right angle.

For model 3:

radius: 20 cm, thus, diameter = 2(20) = 40 cm
height: 40 cm
diagonal: 60 cm

 $d^2+h^2=40^2+40^2 \\ \\ =1,600+1,600=3,200\neq60^2=l^2$

Thus, the lateral surface of model 3 does not meets the base at right angle.

For model 4:

radius: 24 cm, thus, diameter = 2(24) = 48 cm
height: 9 cm
diagonal: 30 cm

 $d^2+h^2=48^2+9^2 \\ \\ =2,304+81=2,385\neq30^2=l^2$

Thus, the lateral surface of model 3 does not meets the base at right angle.

Therefore, the model in which the lateral surface meets the base at a right angle is model 2 (option b)

8 0

2 years ago

Read 2 more answers

If mBC = (9x-53) and mCD = (2x + 45) find mBAD

Rom4ik [11]

Answer:

$m\angle BAD=73^o$

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the value of x

Let

O ----> the center of the circle

we know that

Triangle BOC≅Triangle COD

$m\angle BOC=arc\ BC$ ----> by central angle

$m\angle COD=arc\ CD$ ----> by central angle

$m\angle BOC=m\angle COD$

therefore

$arc\ BC=arc\ CD$

substitute the given values

$(9x-53)^o=(2x+45)^o$

solve for x

$9x-2x=45+53\\7x=98\\x=14$

step 2

Find the measure of angle BAD

we know that

The inscribed angle is half that of the arc it comprises.

$m\angle BAD=\frac{1}{2} [arc\ BC+arc\ CD]$

$arc\ BC=9(14)-53=73^o$

$arc\ CD=2(14)+45=73^o$

substitute

$m\angle BAD=\frac{1}{2} [73^o+73^o]=73^o$

7 0

1 year ago

Which expression is equivalent to x Superscript negative five-thirds? StartFraction 1 Over RootIndex 5 StartRoot x cubed EndRoot

Anastasy [175]

Option B : $\frac{1}{\sqrt[3]{x^{5} } }$ is the expression equivalent to $x^{-\frac{5}{3}$

Explanation:

The given expression is $x^{-\frac{5}{3}$

Rewriting the expression $x^{-\frac{5}{3}$ using the exponent rule, $a^{-b}=\frac{1}{a^{b}}$

Hence, we get,

$\frac{1}{x^{\frac{5}{3} } }$

Simplifying, we get,

$\frac{1}{\left(x^{5}\right)^{\frac{1}{3}}}$

Applying the rule, $a^{\frac{1}{n}}=\sqrt[n]{a}$

Thus, we have,

$\frac{1}{\sqrt[3]{x^{5} } }$

Now, we shall determine from the options that which expression is equivalent to $x^{-\frac{5}{3}$

Option A: $\frac{1}{\sqrt[5]{x^{3} } }$

The expression $\frac{1}{\sqrt[5]{x^{3} } }$ is not equivalent to simplified expression $\frac{1}{\sqrt[3]{x^{5} } }$

Thus, the expression $\frac{1}{\sqrt[5]{x^{3} } }$ is not equivalent to $x^{-\frac{5}{3}$

Hence, Option A is not the correct answer.

Option B: $\frac{1}{\sqrt[3]{x^{5} } }$

The expression $\frac{1}{\sqrt[3]{x^{5} } }$ is equivalent to the simplified expression $\frac{1}{\sqrt[3]{x^{5} } }$

Thus, the expression $\frac{1}{\sqrt[3]{x^{5} } }$ is equivalent to $x^{-\frac{5}{3}$

Hence, Option B is the correct answer.

Option C: $-\sqrt[3]{x^5}$

The expression $-\sqrt[3]{x^5}$ is not equivalent to the simplified expression $\frac{1}{\sqrt[3]{x^{5} } }$

Thus, the expression $-\sqrt[3]{x^5}$ is not equivalent to $x^{-\frac{5}{3}$

Hence, Option C is not the correct answer.

Option D: $-\sqrt[5]{x^3}$

The expression $-\sqrt[5]{x^3}$ is not equivalent to the simplified expression $\frac{1}{\sqrt[3]{x^{5} } }$

Thus, the expression $-\sqrt[5]{x^3}$ is not equivalent to $x^{-\frac{5}{3}$

Hence, Option D is not the correct answer.

4 0

1 year ago

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The manager of an industrial plant is planning to buy a new machine. For each day’s operation, the number of repairs X, that the

horsena [70]

Answer: Expected value of the daily cost of operating the machine is 235.264.

Step-by-step explanation:

Since we have given that

E[x]= 0.96 repairs per day

And Var[x] = 0.96 repairs per day.

$C=160+40x^2$

$E[c]=160+40E[x^2]\\\\E[c]=160+40(Var[x]+(E[x])^2)\\\\E[c]=160+40(0.96+0.96^2)\\\\E[c]=235.264$

Hence, Expected value of the daily cost of operating the machine is 235.264.

5 0

2 years ago

Can y’all answer the question for me

raketka [301]

Answer:

The answer is A

Step-by-step explanation:

87,688 - 86,789 = 899

4 0

2 years ago

Read 2 more answers