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tamaranim1 [39]
3 years ago
15

A parallelogram has sides of lengths 8 and 6, and one angle is 55°. find the lengths of the diagonals. (round your answers to tw

o decimal places. enter your answers as a comma-separated list.)
Mathematics
1 answer:
Rudiy273 years ago
8 0
Here shall use the cosine rule:
let the length of the first diagonal be d;
thus
d²=8²+6²-2*6*8cos55
d²=64+36-96cos55
d²=44.93666211
d=6.7035

We know that two adjacent angles of parallelogram are supplementary, so since 180-55=125°, the length of the second diagonal d', we shall have:
d'²=8²+6²-2×8×6cos 125
d'²=64+36-96cos125
d'²=155.0633379
d=12.45244
Answers: (6.7035,12.45244)

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A line with a slope of -4 passes through the point (0, 0). What is its equation in
Dahasolnce [82]

Answer: y = -4x

Step-by-step explanation: You would use the formula y = mx + b to solve your problem. When you plug the numbers in, you get y = -4x. There would be no "+ b" because in this case, the y-intercept (b) is equal to zero. Therefore, you would not need to write "y = -4x + 0" because that would not be the equation in its simplest form.

4 0
3 years ago
Look at the triangle below which of the following represents two of the angle measures of the triangle
Gelneren [198K]

Answer:

C. 60° and 80°

Step-by-step explanation:

Sum of triangle = 180°

Therefore,

8x + 4 + 6x - 2 + 10x + 10 = 180

Add like terms

8x + 6x + 10x + 4 - 2 + 10 = 180

24x + 12 = 180

24x = 180 - 12

24x = 168

x = 168/24

x = 7

Find each measure of the angles by substitute x = 7 into each expression

8x + 4 = 8(7) + 4 = 60°

6x - 2 = 6(7) - 2 = 40°

10x + 10 = 10(7) + 10 = 80°

The answer is 60° and 80°

6 0
3 years ago
Joshua is 1.45 meters tall. At 2 p.m., he measures the length of a tree's shadow to be 31.65 meters. He stands 26.2 meters away
Lena [83]

Answer:

The height of the tree=8.42 m

Step-by-step explanation:

We are given that

Height of Joshua, h=1.45 m

Length of tree's shadow, L=31.65 m

Distance between tree and Joshua=26.2 m

We have to find the height of the tree.

BC=26.2 m

BD=31.65m

CD=BD-BC

CD=31.65-26.2=5.45 m

EC=1.45 m

All right triangles are similar .When two triangles are similar then the ratio of their corresponding sides are equal.

\triangle ABD\sim \triangle ECD

\frac{AB}{EC}=\frac{BD}{CD}

Substitute the values

\frac{AB}{1.45}=\frac{31.65}{5.45}

AB=\frac{31.65\times 1.45}{5.45}

AB=8.42m

Hence, the height of the tree=8.42 m

6 0
3 years ago
Use the surface integral in​ Stokes' Theorem to calculate the circulation of the field Bold Upper F equals x squared Bold i plus
Alinara [238K]

Answer:

The circulation of the field f(x) over curve C is Zero

Step-by-step explanation:

The function f(x)=(x^{2},4x,z^{2}) and curve C is ellipse of equation

16x^{2} + 4y^{2} = 3

Theory: Stokes Theorem is given by:

I= \int \int\limits {{Curl f\cdot \hat{N }} \, dx

Where, Curl f(x) = \left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\\frac{∂}{∂x} &\frac{∂}{∂y} &\frac{∂}{∂z} \\F1&F2&F3\end{array}\right]

Also, f(x) = (F1,F2,F3)

\hat{N} = grad(g(x))

Using Stokes Theorem,

Surface is given by g(x) = 16x^{2} + 4y^{2} - 3

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\hat{N} = grad(16x^{2} + 4y^{2} - 3)

\hat{N} = (32x,8y,0)

Now,  f(x)=(x^{2},4x,z^{2})

Curl f(x) = \left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\\frac{∂}{∂x} &\frac{∂}{∂y} &\frac{∂}{∂z} \\F1&F2&F3\end{array}\right]

Curl f(x) = \left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\\frac{∂}{∂x} &\frac{∂}{∂y} &\frac{∂}{∂z} \\x^{2}&4x&z^{2}\end{array}\right]

Curl f(x) = (0,0,4)

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I= \int \int\limits {Curl f\cdot \hat{N} } \, dx

I= \int \int\limits {(0,0,4)\cdot(32x,8y,0)} \, dx

I= \int \int\limits {(0,0,4)\cdot(32x,8y,0)} \, dx

I=0

Thus, The circulation of the field f(x) over curve C is Zero

3 0
3 years ago
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Kitty [74]

Answer:

≈ 520 000

Step-by-step explanation:

2¹⁹=  524 288 ≈ 520 000

6 0
3 years ago
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