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3 years ago

Use the Pythagorean Theorem to find the missing length in the right triangle

Mathematics

1 answer:

Gelneren [198K]3 years ago

8 0

Answer:

it depends

Step-by-step explanation:

If 17 is the hypotenuse

$c=17\\\\b=12\\\\a=?\\\\c^{2} =a^2+b^2\\\\17^2=a^2+12^2\\\\17^2-12^2=a^2\\\\(17-12)(17+12)=a^2\\\\5(27)=a^2\\\\a=\sqrt{9*3*5} \\\\a=3\sqrt{15} \\\\a=11.6$

if you are looking for the hypotenuse

$a=17\\\\b=12\\\\c=?\\\\a^2+b^2=c^2\\\\17^2+12^2=c^2\\\\289+144=c^2\\\\433=c^2\\\\c=\sqrt{433} \\\\c=20.8$

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2 years ago

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

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

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

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3 years ago

Solve the quadratic equation. (x + 6)2 = 49

kykrilka [37]

Answer:

Step-by-step explanation:

To solve, use inverse operations:

$(x+6)^2=49\\\sqrt{(x+6)^2} =\sqrt{49} \\x+6=+/-7$

Now we solve for both +/- 7.

x+6=7

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3 years ago

Finding the area of A=1/2bh

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Yes that is correct.

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3 years ago

A store is having a sale in which all items are reduced by 20%. Including tax, Jennifer paid $21 for a pair of shorts. If the sa

Tju [1.3M]

Answer: the original price of the shorts was $25

Step-by-step explanation:

Let x represent the original price of the shorts.

The store is having a sale in which all items are reduced by 20%. This means that the amount of discount on the shorts is

20/100 × x = 0.2x

The price of the shorts would be

x - 0.2x = 0.8x

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3 years ago