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2 years ago

True or false: equilateral triangles can be classified as acute right or obtuse

1 answer:

8 0

False, since all sides are equal all angles must be equal and when you have an obtuse or right triangle only on angle is obtuse or right. since one is different it cannot be equal on all sides making this statement false

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Evaluate the integral by making an appropriate change of variables.

VARVARA [1.3K]

By inspecting the integrand, the "obvious" choice for substitution would be

u = y + x

v = y - x

Solving for x and y, we would have

x = (u - v)/2

y = (u + v)/2

in which case the Jacobian and its determinant are

$J=\begin{bmatrix}x_u&x_v\\y_u&y_v\end{bmatrix}=\dfrac12\begin{bmatrix}1&-1\\1&1\end{bmatrix}\implies|\det J|=\left|\dfrac12\right|=\dfrac12$

The trapezoid R has two of its edges on the lines x + y = 8 and x + y = 9, so right away, we have 8 ≤ u ≤ 9.

Then for v, we observe that when x = 0 (the lowest edge of R), v = y ; similarly, when y = 0 (the leftmost edge of R), v = -x. So

-x ≤ v ≤ y

-(u - v)/2 ≤ v ≤ (u + v)/2

-u + v ≤ 2v ≤ u + v

-u ≤ v ≤ u

So, the integral becomes

$\displaystyle\iint_R5\cos\left(7\frac{y-x}{y+x}\right)\,\mathrm dA=\int_8^9\int_{-u}^u\frac52\cos\left(\frac{7v}u\right)\,\mathrm dv\,\mathrm du$

$=\displaystyle\frac52\int_8^9\frac u7(\sin7-\sin(-7))\,\mathrm du$

$=\displaystyle\frac57\sin7\int_8^9u\,\mathrm du$

$=\displaystyle\frac5{14}\sin7(9^2-8^2)=\boxed{\frac{85}{14}\sin7}$

4 0

2 years ago

Can someone please help me

ludmilkaskok [199]

Answer:

y - 4 = 3(x-3)

Step-by-step explanation:

7 0

2 years ago

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The sum of three numbers is 10. The first number minus the second number plus the third is 6. The first minus the third is 2 mor

GenaCL600 [577]

So the answer is 6,0,4.

3 0

3 years ago

Kenny wrote the equation for a linear relationship shown below

Ilia_Sergeevich [38]

Y would equal -17! Good luck!

4 0

2 years ago

Read 2 more answers

The equation that models the relationship between the wavelength and frequency of yellow light is:

natima [27]

Answer:

xy= 302,400

Step-by-step explanation:

6 0

3 years ago

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