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nevsk [136]
3 years ago
15

What is the distance from the point (a, −b, −4) to the origin?

Mathematics
1 answer:
laiz [17]3 years ago
6 0

Answer:

  \sqrt{a^2+b^2+16}

Step-by-step explanation:

The distance (d) between two points in 3 dimensions is ...

  d = √((x2 -x1)² +(y2 -y1)² +(z2 -z1)²)

Then the distance between (a, -b, -4) and (0, 0, 0) is ...

  d = √((a -0)² +(-b -0)² +(-4 -0)²)

  = √(a² +b² +16)

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In circle E with m DEF 36 and DE = 3 units find area of
deff fn [24]

Answer:

A ≈ 2.83 units²

Step-by-step explanation:

The area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × \frac{36}{360}

   = π × 3² × \frac{1}{10}

    = \frac{9\pi }{10}

   ≈ 2.83 units² ( to the nearest hundredth )

4 0
3 years ago
Explain your work please
Vlad1618 [11]
30 = 60% of x
x being our variable, we need to figure out what x equals. Use the formula I put in the attachment. Multiply 30 by 60, and then divide the product by 100. That will give you the answer :)

7 0
3 years ago
HELP PLEASE THANKS (;
Zielflug [23.3K]
You have 2 equations that are both equal to y. If they are both equal to y, then by the transitive property of equality, they are equal to each other (if a = b, and b = c, then a = c).
5x - 17 = x + 3 and
4x = 20 and x = 5. Now sub in that x value of 5 to solve for y:
y = 5 + 3 and y = 8. So the ordered pair is (5, 8)
5 0
3 years ago
Plz read and answerrrrrrrrrrr
natulia [17]

Answer:

16.7%.

Step-by-step explanation:

There are initially 24 + 15 + 8 = 47 pencils in the bag.

Take a pencil out of this bag of 47 pencils. 15 out of the 47 pencils blue. Let A represent the event of getting a blue pencil on the first pick. The probability of getting a blue pencil is:

\displaystyle P(A) = \frac{15}{47}.

There are now 47 - 1 = 46 pencils left in the bag. However, given that the first pencil removed from the bag is blue, the number of red pencils in the bag will still be 24. Take another pencil out of this bag of 46 pencils. Let B represent the event of getting a red pencil on the second pick. The possibility that the second pencil is red given that the first pencil is blue will be:

\displaystyle P(B|A) = \frac{24}{46}.

The question is asking for the possibility that the first pencil is blue and the second pencil is red. That is:

\displaystyle P(A\cap B) = P(A) \cdot P(B|A) = \frac{15}{47}\times \frac{24}{46} = 0.166512 \approx 16.7\%.

5 0
4 years ago
Given the following trigonometric ratio, enumerate the meaning ratio ​
Likurg_2 [28]

Answer:

The trigonometric ratios are presented below:

\sin \theta = \frac{AC}{\sqrt{AC^{2} + BC^{2}}}

\cos \theta = \frac{BC}{\sqrt{AC^{2} + BC^{2}}}

\cot \theta = \frac{BC}{AC}

\sec \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{BC}

\csc \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{AC}

Step-by-step explanation:

From Trigonometry we know the following definitions for each trigonometric ratio:

Sine

\sin \theta = \frac{y}{h} (1)

Cosine

\cos \theta = \frac{x}{h} (2)

Tangent

\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{y}{x} (3)

Cotangent

\cot \theta = \frac{\cos \theta}{\sin \theta} = \frac{x}{y} (4)

Secant

\sec \theta = \frac{1}{\cos \theta} = \frac{h}{x} (5)

Cosecant

\csc \theta = \frac{1}{\sin \theta} = \frac{h}{y} (6)

Where:

x - Adjacent leg.

y - Opposite leg.

h - Hypotenuse.

The length of the hypotenuse is determined by the Pythagorean Theorem:

h = \sqrt{x^{2}+y^{2}}

If y = AC and x = BC, then the trigonometric ratios are presented below:

\sin \theta = \frac{AC}{\sqrt{AC^{2} + BC^{2}}}

\cos \theta = \frac{BC}{\sqrt{AC^{2} + BC^{2}}}

\cot \theta = \frac{BC}{AC}

\sec \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{BC}

\csc \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{AC}

6 0
3 years ago
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