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Y_Kistochka [10]
1 year ago
8

Solve for x. Figures are not necessarily drawn to scale.

Mathematics
1 answer:
kumpel [21]1 year ago
5 0

Answer:

13.2 units

Step-by-step explanation:

12 is to 7.2 as   (12+10) is to x

12/7.2   =  (12+10)/x

x = 22 * 7.2/12 = 13.2 units

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Calculus 3 chapter 16​
o-na [289]

Evaluate \vec F at \vec r :

\vec F(x,y,z) = x\,\vec\imath + y\,\vec\jmath + xy\,\vec k \\\\ \implies \vec F(\vec r(t)) = \vec F(\cos(t), \sin(t), t) = \cos(t)\,\vec\imath + \sin(t)\,\vec\jmath + \sin(t)\cos(t)\,\vec k

Compute the line element d\vec r :

d\vec r = \dfrac{d\vec r}{dt} dt = \left(-\sin(t)\,\vec\imath+\cos(t)\,\vec\jmath+\vec k\bigg) \, dt

Simplifying the integrand, we have

\vec F\cdot d\vec r = \bigg(-\cos(t)\sin(t) + \sin(t)\cos(t) + \sin(t)\cos(t)\bigg) \, dt \\ ~~~~~~~~= \sin(t)\cos(t) \, dt \\\\ ~~~~~~~~= \dfrac12 \sin(2t) \, dt

Then the line integral evaluates to

\displaystyle \int_C \vec F\cdot d\vec r = \int_0^\pi \frac12\sin(2t)\,dt \\\\ ~~~~~~~~ = -\frac14\cos(2t) \bigg|_{t=0}^{t=\pi} \\\\ ~~~~~~~~ = -\frac14(\cos(2\pi)-\cos(0)) = \boxed{0}

3 0
1 year ago
Apple juice has 216 grams of sugar for every 8 servings. The soda has 234 grams of sugar for every 9 servings
pav-90 [236]

Answer:

Apple juice contains 1728 g sugar whereas soda contains 1404 g sugar

Step-by-step explanation:

3 0
2 years ago
Which statement is true? Question 2 options: All parallelograms are rectangles. All rectangles are squares. All quadrilaterals a
alekssr [168]

For this case, we have that:

  • By definition, a rectangle is a parallelogram. So, we discard the first option.
  • On the other hand, we have that all rectangles can not be squares, since a square has all its sides equal, while the rectangle, poir definition, no.So, we discard the second option.
  • All quadrilaterals are not rectangles because there are other figures with four sides that are not necessarily rectangular. We discard the third option.
  • Finally, we have that all squares are rectangles. This statement is true since squares can be rectangles with pairs of equal sides.

Answer:

Option D

5 0
3 years ago
A basket of the fruit contains 12 apples, 8 bananas, and 6 oranges. What is the ratio of bananas to apples? (Please simplify)
mrs_skeptik [129]

Answer:

2 : 3

Step-by-step explanation:

bananas to apples = 8 : 12

simplify by dividing both values by highest common factor of 4:

8 ÷ 4 : 12 ÷ 4 = 2 : 3

6 0
2 years ago
What Value Does Point P Represent On The Number Line Shown Here?
Bezzdna [24]
The value is -3.2. Hope it helps!
7 0
3 years ago
Read 2 more answers
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