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goldfiish [28.3K]
3 years ago
7

3.8x = −104.12 what is the answer to the question

Mathematics
1 answer:
Elina [12.6K]3 years ago
7 0

Answer:

-27.4

Step-by-step explanation:

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Assume that the terminal side of thetaθ passes through the point (negative 12 comma 5 )(−12,5) and find the values of trigonomet
zmey [24]

Answer:

\sin \theta = \dfrac{5}{13} and \sec \theta = -\dfrac{13}{12}

Step-by-step explanation:

Assume that the terminal side of thetaθ passes through the point (−12,5).

In ordered pair (-12,5), x-intercept is negative and y-intercept is positive. It means the point lies in 2nd quadrant.

Using Pythagoras theorem:

hypotenuse^2=perpendicular^2+base^2

hypotenuse^2=(5)^2+(12)^2

hypotenuse^2=25+144

hypotenuse^2=169

Taking square root on both sides.

hypotenuse=13

In a right angled triangle

\sin \theta = \dfrac{opposite}{hypotenuse}

\sin \theta = \dfrac{5}{13}

\sec \theta = \dfrac{hypotenuse}{adjacent}

\sec \theta = \dfrac{13}{12}

In second quadrant only sine and cosecant are positive.

\sin \theta = \dfrac{5}{13} and \sec \theta = -\dfrac{13}{12}

6 0
3 years ago
A rectangular flour canister has dimensions of 512 inches by 4 inches by 10 inches. A smaller sugar canister has dimensions of 3
aliina [53]

Answer:

The amount by which the sugar canister is smaller than the flour canister is 136 in³

Step-by-step explanation:

The dimensions of the flour canister = 5 and 1/2 inches by 4 inches by 10 inches

(5 and 1/2 = (5 1/2))

(3 and 1/2 = (3 1/2))

The dimensions of the smaller sugar canister = 3 and 1/2 inches by 3 inches by 8 inches

The volume of the rectangular prism = Length × Width × Height

∴ The volume of the flour canister = (5 1/2) × 4× 10 = 220 in.³

The volume of the sugar canister = (3 1/2) × 3 × 8= 84 in.³

The difference in volume between the flour canister and the sugar canister is given as follows;

220 in.³ - 84 in.³ = 136 in.³

The amount by which the sugar canister is smaller than the flour canister = 136 in.³.

5 0
3 years ago
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