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Naddika [18.5K]

2 years ago

5

Find the surface area of the prism. Enter your answer in the box. A rectangular prism with dimensions 6 meters by 3 meters by 12

meters.

1 answer:

e-lub [12.9K]2 years ago

3 0

Given:

Dimensions of a rectangular prism are 6 meters by 3 meters by 12 meters.

To find:

The surface area of the prism.

Solution:

The surface area of a rectangular prism is:

$A=2(lb+bh+hl)$

Where, l is length, b is breadth and h is height.

Putting $l=6,b=3,h=12$ , we get

$A=2(6\times 3+3\times 12+12\times 6)$

$A=2(18+36+72)$

$A=2(126)$

$A=252$

Therefore, the surface area of the prism is 252 square meters.

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What is the vertex of g(x) = –3x2 + 18x + 2?

blsea [12.9K]

Answer:

$(3,29)$

Step-by-step explanation:

There is a formula that can be used to find the x-value of the vertex of the parabola. This formula is $x=\frac{-b}{2a}$

We have the function $g(x)=-3x^2+18x+2$

From this function, we can find that

$a=-3\\b=18\\c=2$

We can plug in our know values into the formula to get

$x=\frac{-18}{2(-3)\\} \\x=\frac{-18}{-6} \\\\x=3$

Then we can plug in our x-value to find the y-value of the vertex

$g(3)=-3(3)^2+18(3)+2\\\\g(3)=-3(9)+54+2\\\\g(3)=-27+54+2\\\\g(3)=29$

This means that the vertex would be $(3,29)$

6 0

3 years ago

Calculus piecewise function.

Kipish [7]

Part A

The notation $\lim_{x \to 2^{+}}f(x)$ means that we're approaching x = 2 from the right hand side (aka positive side). This is known as a right hand limit.

So we could start at say x = 2.5 and get closer to 2 by getting to x = 2.4 then to x = 2.3 then 2.2, 2.1, 2.01, 2.001, etc

We don't actually arrive at x = 2 itself. We simply move closer and closer.

Since we're on the positive or right hand side of 2, this means we go with the rule involving x > 2

Therefore f(x) = (x/2) + 1

Plug in x = 2 to find that...

f(x) = (x/2) + 1

f(2) = (2/2) + 1

f(2) = 2

This shows $\lim_{x \to 2^{+}}f(x) = 2$

Then for the left hand limit $\lim_{x \to 2^{-}}f(x)$ , we'll involve x < 2 and we go for the first piece. So,

f(x) = 3-x

f(2) = 3-2

f(2) = 1

Therefore, $\lim_{x \to 2^{-}}f(x) = 1$

===============================================================

Part B

Because $\lim_{x \to 2^{+}}f(x) \ne \lim_{x \to 2^{-}}f(x)$ this means that the limit $\lim_{x \to 2}f(x)$ does not exist.

If you are a visual learner, check out the graph below of the piecewise function. Notice the gap or disconnect at x = 2. This can be thought of as two roads that are disconnected. There's no way for a car to go from one road to the other. Because of this disconnect, the limit doesn't exist at x = 2.

===============================================================

Part C

You'll follow the same type of steps shown in part A.

However, keep in mind that x = 4 is above x = 2, so we'll deal with x > 2 only.

So you'd only involve the second piece f(x) = (x/2) + 1

You should find that f(4) = 3, and that both left and right hand limits equal this value. The left and right hand limits approach the same y value. The limit does exist here. There are no gaps to worry about when x = 4.

===============================================================

Part D

As mentioned earlier, since $\lim_{x \to 4^{+}}f(x) = \lim_{x \to 4^{-}}f(x) = 3$ , this means the limit $\lim_{x \to 4}f(x)$ does exist and it's equal to 3.

As x gets closer and closer to 4, the y values are approaching 3. This applies to both directions.

4 0

1 year ago

If mary. Has 1234567891012345678910lambs how many lambs does she have in tons

OLga [1]

On average a lamb weighs about 200 pounds,
so 12345678910 multiplied by 200 =<span>2.469135782e+12
</span>2.469135782e+12 divided by 2000 = <span>1234567891 tons</span>

5 0

3 years ago

Read 2 more answers

Two angles are complementary.The larger angle is 30 degrees more than 4 times the smaller

gregori [183]

Answer:

Step-by-step explanation:

Remark

2 angles are complementary means that 2 angles add up to 90°. That is the guiding princeple behind the problem.

Givens

Let the smallest angle = x

Let the largest angle = 4x + 30

Equation

4x + 30° + x = 90° Combine like terms on the left

Solution

5x + 30 = 90 Subtract 30 from both sides.

5x + 30 - 30 = 90 - 30 Combine

5x = 60 Divide both sides by 5

5x/5 = 60/5

x = 12

Answer

smallest angle = 12
Larger angle = 4*12 + 30 = 78

6 0

1 year ago

Solve The Equation Below

Flura [38]

Answer:

16

Step-by-step explanation:

10 + sqrt(y) = 14

Subtract 10 from each side

10 -10+ sqrt(y) = 14-10

sqrt(y) = 4

Square each side

(sqrt(y)) ^2 = 4^2

y = 16

4 0

2 years ago

Read 2 more answers