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Lelechka [254]
2 years ago
9

13.3 mm 16 mm 20.5 mm please find the volume of this triangular prism 20.5 and 16 are the base while 13.3 is the height.​

Mathematics
1 answer:
Sonbull [250]2 years ago
7 0

Answer:

2.2 × 10³ mm³

Step-by-step explanation:

We have a triangular prism with the following dimensions:

Altitude: 20.5 millimeters

Base: 16 millimeters

Height: 13.3 millimeters

We can calculate the volume of a triangular prism using the following expression.

V = (1/2 × Altitude × Base) × Height

where,

(1/2 × Altitude × Base) is the area of the base

V = (1/2 × Altitude × Base) × Height

V = (1/2 × 20.5 mm × 16 mm) × 13.3 mm = 2.2 × 10³ mm³

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Answer:

The sequence of functions \{x^{n}\}_{n\in \mathbb{N}} converges to the function

f(x)=\begin{cases}0&0\leq x.

Step-by-step explanation:

The limit \lim_{n\to \infty }c^{n} exists and converges to zero whenever \lvert c \rvert. But, if c=1 the sequence \{c^{n}\} is constant and all its terms are equal to 1, then converges to 1. Using this result, consider the sequence of functions \{f_{n}\} defined on the interval [0,1] by f_{n}(x)=x^{n}. Then, for all 0\leq x we have that \lim_{n\to \infty}x^{n}=0. Now, if x=1, then \lim_{n\to \infty }x^{n}=1. Therefore, the limit function of the sequence of functions is

f(x)=\begin{cases}0&0\leq x.

To show that the convergence is not uniform consider 0. For any n>1 choose x\in (0,1)  such that \varepsilon^{1/n}. Then

\varepsilon

This implies that the convergence is not uniform.

8 0
3 years ago
I need help I try Photomath I didn’t help me .
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Answer:

8. 8.80

9. 90

Step-by-step explanation:

Question 8: Use the Pythagorean formula

DE² = DF²+EF²

EF² = DE² - DF²

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Question 9: Use the Cosine Rule

GI² = GH² +HI² - 2·GH·HI·Cos ∠GHI

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4 0
3 years ago
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Write the equation of each graph after the indicated transformations. The graph of y = √x is reflected in the x-axis, stretched
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Answer:

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7 0
2 years ago
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Answer:

I got 6.012 times 10^3

Step-by-step explanation:

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6 0
3 years ago
What property does the statement show? (4x8)x3=(8x4)x3
Mariana [72]
1. commutative property states that : a + b = b + a 

<span>2. 3x - 5 = 5x - 17 -- add 5 to both sides </span>
<span>3x = 5x - 17 + 5 -- subtract 5x from both sides </span>
<span>3x - 5x = -17 + 5 -- combine like terms </span>
<span>-2x = -12 -- divide both sides by -2 </span>
<span>x = 6 </span>

<span>3. slope formula : slope = (y2 - y1) / (x2 - x1) </span>
<span>(3,-1) x1 = 3 and y1 = -1 </span>
<span>(-2,-5) x2 = -2 and y2 = -5 </span>
<span>now we sub </span>
<span>slope = ((-5 - (-1)) / (-2 -3) </span>
<span>slope = (-5 + 1) / -5 </span>
<span>slope = -4/-5 </span>
<span>slope = 4/5 </span>

<span>4. x = first integer </span>
<span>x + 2 = 2nd integer </span>
<span>x + x + 2 = 80 -- combine like terms </span>
<span>2x + 2 = 80 -- subtract 2 from both sides </span>
<span>2x = 80 - 2 </span>
<span>2x = 78 -- divide both sides by 2 </span>
<span>x = 39 <== this is the smallest number </span>
<span>x + 2 = 41 </span>

<span>5. p = 1/2g - 3 </span>

<span>6. The union of two sets is all the numbers in both sets, no need to copy the same number more then once. Answer is : (1,2,3,4,5,6,8,10) </span>

<span>7. 2x + 3y <= 6 -- put in y = mx + b form </span>
<span>3y <= -2x + 6 </span>
<span>y <= -2/3x + 2 </span>
<span>In y = mx + b form, the y intercept is in the b position. So the y intercept is (0,2) </span>
<span>To find the x intercept, sub in 0 for y (change inequality sign to equal sign) </span>
<span>2x + 3y = 6 </span>
<span>2x + 3(0) = 6 </span>
<span>2x = 6 </span>
<span>x = 3 </span>
<span>x intercept is (3,0) </span>
<span>So plot your points (3,0) and (0,2) </span>
<span>Connect the points with a solid line because there is an equal sign in there. </span>
<span>Shade below the line because it is less then. </span>

<span>8. 3x + 6y = 8 </span>
<span>6y = -3x + 8 </span>
<span>y = -1/2x + 4/3 </span>

<span>y = 2x - 8 </span>

<span>Perpendicular lines have negative reciprocal slope. All that means is " flip " the slope and change the sign. The slope in these equations are -1/2 and 2. These are negative reciprocals of each other. </span>

<span>9. 7x + 3y - 2 + 6x + 1 + y^2 </span>
<span>y^2 + 3y + 13x - 1 </span>

<span>10. (0,6) x1 = 0 and y1 = 6 </span>
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<span>slope(m) = (y2 - y1) / (x2 - x1) </span>
<span>slope(m) = (0 - 6) / (3 - 0) </span>
<span>slope(m) = -6/3 </span>
<span>slope(m) = -2 </span>

<span>y = mx + b </span>
<span>(0,6) x = 0 and y = 6 </span>
<span>6 = 0(-2) + b </span>
<span>6 = b </span>

<span>your equation is : y = -2x + 6 (slope intercept form) </span>
<span>2x + y = 6 (standard form) </span>

<span>11. x + y = 5 -- put this in y = mx + b form, and the m position is your slope </span>
<span>y = -x + 5 (-x is the same as -1x) so your slope is -1 </span>

<span>12. 4y = 8x - 3 -- put in y = mx + b form, and the b stands for the y intercept </span>
<span>y = 8/4x - 3/4 </span>
<span>y = 2x - 3/4 (the y intercept is -3/4 </span>

<span>13. |a| + b --- (a = -1.4 and b = -2.7) </span>
<span>absolute values, whether they have a negative or not, they are always positive </span>
<span>|a| + b </span>
<span>|-1.4 | + (-2.7) </span>
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<span>14. I cannot see the problem </span>

<span>15. -4 < 2t <= 2 --- divide everything by 2 </span>
<span>-2 < t <= 1 </span>
<span>open circle on -2, closed circle on 1, shading in between </span>

<span>16. x + 2y = -9 ---> x = -2y - 9 </span>
<span>now sub -2y - 9 in for x in the other equation </span>
<span>4x - 2y = 14 </span>
<span>4(-2y - 9) - 2y = 14 -- distribute through the parenthesis </span>
<span>-8y - 36 - 2y = 14 -- add 36 to both sides </span>
<span>-8y - 2y = 14 + 36 combine like terms </span>
<span>-10y = 50 -- divide by -10 </span>
<span>y = -5 </span>
<span>now sub -5 in for y in either of the original equations </span>
<span>x + 2y = -9 </span>
<span>x + 2(-5) = -9 </span>
<span>x - 10 = -9 </span>
<span>x = -9 + 10 </span>
<span>x = 1 </span>
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<span>I was really bored so I thought I would just help out :)</span>
3 0
3 years ago
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