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2 years ago

Solve the equation for x.

Mathematics

2 answers:

anzhelika [568]2 years ago

8 0

32x+64 = 160
32x = 96
x = 3

Afina-wow [57]2 years ago

6 0

The Answer for the given equation is 3

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A carpenter is building a rectangular bookcase with diagonal braces across the back, as shown. The carpenter knows that angle AD

Valentin [98]

Refer to the diagram shown below.

Let x = m∠ADB.

Because m∠BDC is 32° greater than m∠ADB, therefore
m∠BDC = x + 32°

Each angle of a rectangle is 90°, therefore
x + (x+32) = 90
2x + 32 = 90
2x = 58
x = 29°
x+32 = 61°

Answer:
m∠BDC = 61°
m∠ADB = 29°

8 0

2 years ago

The harmonic motion of a particle is given by f(t) = 2 cos(3t) + 3 sin(2t), 0 ≤ t ≤ 8. (a) When is the position function decreas

iren [92.7K]

For the last part, you have to find where $f'(t)$ attains its maximum over $0\le t\le8$ . We have

$f'(t)=-6\sin3t+6\cos2t$

so that

$f''(t)=-18\cos3t-12\sin2t$

with critical points at $t$ such that

$-18\cos3t-12\sin2t=0$

$3\cos3t+2\sin2t=0$

$3(\cos^3t-3\cos t\sin^2t)+4\sin t\cos t=0$

$\cos t(3\cos^2t-9\sin^2t+4\sin t)=0$

$\cos t(12\sin^2t-4\sin t-3)=0$

So either

$\cos t=0\implies t=\dfrac{(2n+1)\pi}2$

$12\sin^2t-4\sin t-3=0\implies\sin t=\dfrac{1\pm\sqrt{10}}6\implies t=\sin^{-1}\dfrac{1\pm\sqrt{10}}6+2n\pi$

where $n$ is any integer. We get 8 solutions over the given interval with $n=0,1,2$ from the first set of solutions, $n=0,1$ from the set of solutions where $\sin t=\dfrac{1+\sqrt{10}}6$ , and $n=1$ from the set of solutions where $\sin t=\dfrac{1-\sqrt{10}}6$ . They are approximately

$\dfrac\pi2\approx2$

$\dfrac{3\pi}2\approx5$

$\dfrac{5\pi}2\approx8$

$\sin^{-1}\dfrac{1+\sqrt{10}}6\approx1$

$2\pi+\sin^{-1}\dfrac{1+\sqrt{10}}6\approx7$

$2\pi+\sin^{-1}\dfrac{1-\sqrt{10}}6\approx6$

4 0

2 years ago

Triangle KLM represents a section of a park set aside for picnic tables. The picnic area will take up approximately 400 square y

svetoff [14.1K]

Given triangle KLM with two sides given as 45 yd and 20 yd and a 25 degree angle opposite the 20 yd side.

We find the angle made at the opposite of the 45 yd side using the sine rule as follows.
$\frac{\sin{A}}{a} = \frac{\sin{B}}{b} \\ \frac{\sin{25^o}}{20} = \frac{\sin{B}}{45} \\ \sin{B}= \frac{45\sin{25^o}}{20} = \frac{19.0178}{20} =0.9509 \\ B=\arcsin{(0.9509)}=71.97^o$

Thus, the third angle is given by 180 - 25 - 71.97 = 83.03 degrees.

We also use the sine rule to find the third side of the triangle as follows.
$\frac{\sin{A}}{a} = \frac{\sin{C}}{c} \\ \frac{\sin{25^o}}{20} = \frac{\sin{83.03^o}}{c} \\ c= \frac{20\sin{83.03^o}}{\sin{25^o}} = \frac{19.8522}{\sin{25^o}} =46.97 yds$

Therefore, amount of fencing needed to surround the perimeter of the picnic area = 45 + 20 + 46.97 = 111.97 ≈ 120 yds

6 0

2 years ago

Read 2 more answers

the members of the gardening group plan to build a walkway through the garden as formed by the IHOP potenuse of each of the four

aliya0001 [1]

Answer:

50.24 yards

Step-by-step explanation:

We will use the pythagorean theorem to find hypotenuse of each of the 4 triangles.

Pythagorean Theorem is $Hypotenuse^2=OneLeg^2+AnotherLeg^2$

For Spinach area, two of the legs are 8 and 6. Solving for hypotenuse:

$hyp^2=6^2+8^2\\hyp^2=100\\hyp=10$

For watermelon area, two of the legs are 12 and 8. Solving for hypotenuse:

$hyp^2=12^2+8^2\\hyp^2=208\\hyp=\sqrt{208}$

in red peppers area, the hypotenuse is already given as 15. But we need to find one leg since that will be the leg of the triangle in tomatoes area. Hypotenuse is 15 and one leg is 12, so the other leg is:

$15^2=12^2+eg^2\\15^2-12^2=leg^2\\leg=9$