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2 years ago

What is the value of h?

Mathematics

2 answers:

4vir4ik [10]2 years ago

4 0

Answer:

h=9

Step-by-step explanation:

(3h+18)° + (15h)° =180 because they form straight agle together

Solve for h:

3h+18 + 15h =180

18h=180-18

h= 162/18

h=9

Andreyy892 years ago

3 0

Answer:

3h+18°+15h= 180°(straight angle)

=>18h+18= 180°

=>18h= 180-18° = 162°

=>h= 162°/18= 9

option B

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A cylinder shaped can needs to be constructed to hold 500 cubic centimeters of soup. The material for the sides of the can costs

iogann1982 [59]

Answer:

r=3.628cm

h=12.093cm

Step-by-step explanation:

For this problem we are going to use principles, concepts and calculations from multivariable calculus; mainly we are going to use the Lagrange multipliers method. This method is thought to help us to find a extreme value of a multivariable function 'F' given a restriction 'G'. F represents the function that we want to optimize and G is just a relation between the variables of which F depends. The Lagrange method for just one restriction is:

$\nabla F=\lambda \nabla G$

First, let's build the function that we want to optimize, that is the cost. The cost is a function that must sum the cost of the sides material and the cost of the top and bottom material. The cost of the sides material is the unitary cost (0.03) multiplied by the sides area, which is $A_s=2\pi rh$ for a cylinder; while the cost of the top and bottom material is the unitary cost (0.05) multiplied by the area of this faces, which is $A_{TyB}=2\pi r^2$ for a cylinder.

So, the cost function 'C' is:

$C=2\pi rh*0.03+2\pi r^2*0.05\\C=0.06\pi rh+0.1\pi r^2$

The restriction is the volume, which has to be of 500 cubic centimeters:

$V=500=\pi r^2h\\500=\pi hr^2$

So, let's apply the Lagrange multiplier method:

$\nabla C=\lambda \nabla V\\\frac{\partial C}{\partial r}=0.06\pi h+0.2\pi r\\\frac{\partial C}{\partial h}=0.06\pi r\\\frac{\partial V}{\partial r}=2\pi rh\\\frac{\partial V}{\partial h}=\pi r^2\\(0.06\pi h+0.2\pi r,0.06\pi r)=\lambda (2\pi rh,\pi r^2)$

At this point we have a three variable (h,r, λ)-three equation system, which solution will be the optimum point for the cost (the minimum). Let's write the system:

$0.06\pi h+0.2\pi r=2\lambda \pi rh\\0.06\pi r=\lambda \pi r^2\\500=\pi hr^2$

(In this kind of problems always the additional equation is the restricion, in this case, V=500).

Let's divide the first and second equations by π:

$0.06h+0.2r=2\lambda rh\\0.06r=\lambda r^2\\500=\pi hr^2$

Isolate λ from the second equation:

$\lambda =\frac{0.06}{r}$

Isolate h from the third equation:

$h=\frac{500}{\pi r^2}$

And then, replace λ and h in the first equation:

$0.06*\frac{500}{\pi r^2} +0.2r=2*(\frac{0.06}{r})r\frac{500}{\pi r^2} \\\frac{30}{\pi r^2}+0.2r= \frac{60}{\pi r^2}$

Multiply all the resultant equation by $\pi r^{2}$ :

$30+0.2\pi r^3=60\\0.2\pi r^3=30\\r^3=\frac{30}{0.2\pi } =\frac{150}{\pi}\\r=\sqrt[3]{\frac{150}{\pi}}\approx 3.628cm$

Then, find h by the equation $h=\frac{500}{\pi r^2}$ founded above:

$h=\frac{500}{\pi r^2}\\h=\frac{500}{\pi (3.628)^2}=12.093cm$

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3 years ago

Which graph shows the solution to the system of linear inequalities?

V125BC [204]

<h2><u>Answer:</u></h2>

Which ordered pairs are in the solution set of the system of linear inequalities?

y > Negative one-halfx

y < One-halfx + 1

On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 0) and (4, negative 2). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 2, 0) and (2, 2). Everything below the line is shaded.

(5, –2), (3, 1), (–4, 2)

(5, –2), (3, –1), (4, –3)

(5, –2), (–3, 1), (4, 2)

Step-by-step explanation:

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3 years ago

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Which is the most likely first step needed to solve this equation?

Vanyuwa [196]

Answer:

C. Add 15 to both sides

Step-by-step explanation:

Given equation:

99x – 15 = 45

To solve:

<u>Step 1</u>: Add 15 to both sides:

⇒ 99x – 15 + 15 = 45 + 15

⇒ 99x = 60

<u>Step 2</u>: Divide both sides by 99:

⇒ 99x ÷ 99 = 60 ÷ 99

⇒ x = 60/99

⇒ x = 20/33

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2 years ago

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The price of 41gram apple is 10.25 rupees.then how many rupees for 1 kg apple

Gekata [30.6K]

Answer:

Rs. 250

Step-by-step explanation:

The price of 41 g. apple is Rs 10.25

The price of 1 g. apple is Rs 10.25/41, = Rs 0.25

The price of 1 Kg (1000 g.) is 0.25 x 1000 = Rs 250

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3 years ago

A and B are two cities.

Yuri [45]

<h2><u>Answer: </u></h2>

The bearing of B from A is 28 degrees, approximately

The bearing of A from B is 180+28=208 degrees, approximately.

Step-by-step explanation:

The bearing of B from A is 28 degrees, approximately

The bearing of A from B is 180+28=208 degrees, approximately.

The reason for approximation is from distortion of image.

See attached image to understand ohw the measurement has been obtained.

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2 years ago