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GaryK [48]
3 years ago
10

Question 3 of 10

Mathematics
1 answer:
Georgia [21]3 years ago
4 0

Answer:

The correct answer is A.

Step-by-step explanation:

From the picture you provided, you choose option A, f(x) = x^7 - x^3 - 3x^2 + 3 . Hope that helped :)

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Pat bought running shoes for $60. This was four
serg [7]

Answer:

$22.40

Step-by-step explanation:

Set up the equation like this: 2.5x + 4 = 60

Then solve for x.

7 0
2 years ago
Michael stands 10 feet from a table, and notices a plate resting on the edge of the table. The top of the table is 3 feet high,
Aleks04 [339]

Answer:

17

Step-by-step explanation:

quick mafs

3 0
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

<em>u</em> = <em>y</em> + <em>x</em>

<em>v</em> = <em>y</em> - <em>x</em>

<em />

Solving for <em>x</em> and <em>y</em>, we would have

<em>x</em> = (<em>u</em> - <em>v</em>)/2

<em>y</em> = (<em>u</em> + <em>v</em>)/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 <em>R</em> has two of its edges on the lines <em>x</em> + <em>y</em> = 8 and <em>x</em> + <em>y</em> = 9, so right away, we have 8 ≤ <em>u</em> ≤ 9.

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

-<em>x</em> ≤ <em>v</em> ≤ <em>y</em>

-(<em>u</em> - <em>v</em>)/2 ≤ <em>v</em> ≤ (<em>u</em> + <em>v</em>)/2

-<em>u</em> + <em>v</em> ≤ 2<em>v</em> ≤ <em>u</em> + <em>v</em>

-<em>u</em> ≤ <em>v</em> ≤ <em>u</em>

<em />

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
Speed = distance divided by time taken. car 1 travels 10 miles every 5 minutes. car 2 travels 30 miles every 20 minutes. what is
Setler [38]
Car 1
2 miles............................1 minute
10 miles.........................5 minutes
20 miles.........................10 minutes
40 miles..........................20 minutes
car2
1.5 miles...........................1 minute
15miles.............................10 minutes
30 miles...........................20 minutes
the difference is 0.5 miles per minute

0.5*60=30 miles/hour
5 0
2 years ago
What is the area of a sector with a central angle of 108 degrees and a diameter of 21.2 cm?
Rasek [7]

Answer:

105.84\ cm^2

Step-by-step explanation:

step 1

Find the area of the circle

The area of the circle is

A=\pi r^{2}

we have

r=21.2/2=10.6\ cm ----> the radius is half the diameter

substitute

A=\pi (10.6)^{2}

A=112.36\pi\ cm^2

step 2

Find the area of a sector

Remember that

The area of the circle subtends a central angle of 360 degrees

so

using proportion

Find out the area of a sector with a central angle of 108 degrees

\frac{112.36\pi}{360^o}=\frac{x}{108^o}\\\\x=112.36\pi(108)/360\\\\x=33.708\pi\ cm^2

assume

\pi=3.14

substitute

33.708(3.14)=105.84\ cm^2

7 0
3 years ago
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