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2 years ago

Let sin a = 12 13 with a in qii and sin b = − 15 17 with b in qiii. find sin(a + b), cos(a + b), and tan(a + b)

1 answer:

7 0

Sin(A) = 15/17 15^2 + x^2 = 17^2 17^2 - 15^2 = x^2 289 - 225 = x^2 64 = x^2 8 = x
cos(A) = -8/17
------------
QIII sin(B) = -4/5 (-4)^2 + x^2 = 5^2 5^2 - (-4)^2 = x^2 25 - 16 = x^2 9 = x^2 3 = x
cos(B) = -3/5 ------------------- knowing the identity ; sin(A+B) = sin(A) cos(B) + cos(A) sin(B) sin(A+B) = (15/17) (-3/5) + (-8/17) (-4/5) sin(A+B) = (-9/17) + (32/85) sin(A+B) = (-13/85)

knowing the identity ; cos(A+B)=cos(A) cos(B) - sin(A) sin(B) cos(A+B) = (-8/17) (-3/5) - (15/17) (-4/5) cos(A+B) = (24/85) + (12/17) cos(A+B) = (84/85)

knowing the identity ; tan(A+B) = sin(A + B) / cos(A + B) tan(A+B) = (-13/85) / (84/85) tan(A+B) = (-13/84)

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saveliy_v [14]

Answer: $19,461\ ft^3$

Step-by-step explanation:

The missing figure is attached.

The volume of grain that could completely fill this silo is the sum of the volume of the cylinder and the volume of the hemisphere.

By definition, the volume of a cylinder can be calculated with this formula:

$V_c=\pi r^2h$

Where "r" is the radius and "h" is the height.

In this case you know that:

$r=6\ ft\\\\h=168\ ft$

And the volume of a hemisphere can be found using the following formula:

$V_h=\frac{2}{3} \pi r^3$

Where "r" is the radius.

In this case:

$r=6\ ft$

Therefore, the volume of grain that could completely fill this silo, rounded to the nearest whole number, is:

$V_{grain}=(\frac{22}{7})(6\ ft)^2 (168\ ft)+\frac{2}{3} (\frac{22}{7})(6\ ft)^3\\\\V_{grain}\approx19,461\ ft^3$

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2 years ago

Which statement follows from the given theorem? Theorem: The diagonal of a parallelogram divides it into two congruent triangles

777dan777 [17]

Answer with explanation:

Theorem : The diagonal of a parallelogram divides it into two congruent triangles.

Properties of parallelogram

1. Opposite sides are equal and parallel.

2. Diagonal bisect each other.

3. Opposite Angles are equal.

If you will look at the first three options

A: Diagonals of a parallelogram bisect opposite angles.→→False(Alternate angles are equal)

B: Consecutive sides of a parallelogram are congruent.→→→False(Opposite sides are congruent)

C: Consecutive angles of a parallelogram are congruent.→→→False(Opposite angles are congruent)

D: Consecutive angles of a parallelogram are supplementary.→→→→True

For,any parallelogram, having vertices , A, B and C and D

Opposite sides are parallel, so

1.∠A + ∠B=180°

2.∠C + ∠B=180°

3.∠C+ ∠D=180°

4. ∠A + ∠D=180°

Option D

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2 years ago

Evaluate ∫SF⃗ ⋅dA⃗ , where F⃗ =(bx/a)i⃗ +(ay/b)j⃗ and S is the elliptic cylinder oriented away from the z-axis, and given by x2/

Norma-Jean [14]

Answer:

Therefore surface integral is $\pi(a^2+b^2)c-0-0=\pi(a^2+b^2)c$ .

Step-by-step explanation:

Given function is,

$\vec{F}=\frac{bx}{a}\uvec{i}+\frac{ay}{b}\uvec{j}$

To find,

$\int\int_{S}\vec{F}dS$

where S=A=surfece of elliptic cylinder we have to apply Divergence theorem so that,

$\int\int_{S}\vec{F}dS$

$=\int\int\int_V\nabla.\vec{F}dV$

$=\int\int\int_V(\frac{b}{a}+\frac{a}{b})dV$

$=\frac{a^2+b^2}{ab}\int\int\int_VdV$

$=\frac{a^2+b^2}{ab}\times \textit{Volume of the elliptic cylinder}$

$=\frac{a^2+b^2}{ab}\times \pi ab\times 2c=\pi (a^2+b^2)c$

If unit vector $\cap{n}$ directed in positive (outward) direction then z=c and,

$\int\int_{S_1}\vex{F}.dS_1=\int\int_{S_1} . dA$

$=\int\int_{S_1}.dA=0$

If unit vector $\cap{n}$ directed in negative (inward) direction then z=-c and,

$\int\int_{S_2}\vex{F}.dS_2=\int\int_{S_2}. -dA$

$=\int\int_{S_2}. -dA=0$

Therefore surface integral without unit vector of the surface is,

$\pi(a^2+b^2)c-0-0=\pi(a^2+b^2)c$

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2 years ago

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Andre45 [30]

23 pipe cleaners cause 23 x 6= 138

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2 years ago

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wariber [46]

Answer:

27m

Step-by-step explanation:

It's the Pythagorean Theorem.

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400+324=c^2

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take the square root of both sides

26.9m=c

to the nearest meter = 27

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2 years ago