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3 years ago

What are the means of the following proportion? 3⁄15 = 12⁄60

Mathematics

1 answer:

Advocard [28]3 years ago

8 0

A. 3 and 60." The means of the proportion is 15 and 12.

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Evaluate the integral:

Bogdan [553]

Substitute x = √7 sin(t) and dx = √7 cos(t) dt. Then

∫ √(7 - x²) dx = ∫ √(7 - (√7 sin(t))²) • √7 cos(t) dt

… = √7 ∫ √(7 - 7 sin²(t)) cos(t) dt

… = 7 ∫ √(1 - sin²(t)) cos(t) dt

… = 7 ∫ √(cos²(t)) cos(t) dt

We require that -π/2 ≤ t ≤ π/2 in order for the substitution we made to be reversible. Over this domain, cos(t) ≥ 0, so

√(cos²(t)) = |cos(t)| = cos(t)

and the integral reduces to

… = 7 ∫ cos²(t) dt

Recall the half-angle identity for cosine:

cos²(t) = (1 + cos(2t))/2

Then the integral is

… = 7/2 ∫ (1 + cos(2t)) dt

… = 7/2 (t + 1/2 sin(2t)) + C

… = 7t/2 + 7/4 sin(2t) + C

Get the antiderivative back in terms of x. Recall the double angle identity for sine:

sin(2t) = 2 sin(t) cos(t)

We have t = arcsin(x/√7), which gives

sin(t) = sin(arcsin(x/√7)) = x/√7

cos(t) = cos(arcsin(x/√7)) = √(7 - x²)/√7

Then

∫ √(7 - x²) dx = 7/2 arcsin(x/√7) + 7/4 • 2 sin(arcsin(x/√7)) cos(arcsin(x/√7)) + C

… = 7/2 arcsin(x/√7) + x/2 √(7 - x²) + C

5 0

2 years ago

Helpppppppppppppppppppppppppppp

algol13

Answer:

I would say it is 9

Step-by-step explanation:

5 0

3 years ago

Write an equation in standard form of the line that contains the point (-5,6) amd is perpendicular to 4x-y=3

Anestetic [448]

4x-y=3
-y=-4x+3
y=4x-3

Since it is perpendicular, the slope must be a negative reciprocal.

therefore the slope is -x/4

Substituting the x and the y values (to find the b)

6=5/4+b
6-5/4=b
19/4=b

therefore the equation of the line is
y=-x/4+19/4

8 0

3 years ago

Read 2 more answers

For a triangle with length of its sides of 5, 13, and 14, determine if it is a right triangle.

AlexFokin [52]

Answer:

it's not a right triangle

Step-by-step explanation:

5² + 13² = 14²

=> 25 + 169 = 196

=> 194 ≠ 196

6 0

3 years ago

The penguins currently living on an island are of two types, Chinstrap penguins and Gentoo penguins. The range of the heights of

velikii [3]

Answer:

The answer is "Option A"

Step-by-step explanation:

Using the range difference to calculate the maximum and minimum value.

The range of the chinstrap penguins are:

$R(c) = Max(c) - Min(c) = 13.2$

The range of the Gentoo penguins are:

$R(g) = Max(g) - Min(g) = 15.4$

For point A:

$Max(c) = x\\\\Max(g) = x + 5.8\\\\R(c) = x - Min(c) = 13.2 \to x = 13.2 + Min(c)\\\\R(g) = x + 5.8 - Min(g) = 15.4 \to x = 9.6 + Min(g)$

equate both of them

$13.2 + Min(c) = 9.6 + Min(g)Min(g) - Min(c) = 3.6$

It indicates that Min(c) surpasses Min(g), whereas Max(g) exceeds Max (c).

Therefore, the Max is picked for g for all penguins and the minimum is picked for c.

Range of all penguins $= Max(g) - Min(c) = x + 5.8 - x + 13.2 = 19$

Therefore, it will be determined as the option.

For point B:

In estimating the range the median height cannot help.

For point C:

In order to calculate the variety, the connection between both the mean height cannot be sued.

7 0

3 years ago