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madam [21]
3 years ago
7

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. A right rectangular pri

sm has a length of 15 millimeters, width of 3 millimeters, and height of 4 millimeters. What is the surface area of the prism?
Mathematics
1 answer:
Alla [95]3 years ago
6 0

the surface area of the prism is 234mm^2 .

<u>Step-by-step explanation:</u>

Here we have , A right rectangular prism has a length of 15 millimeters, width of 3 millimeters, and height of 4 millimeters.  We need to find  What is the surface area of the prism . Let's find out:

We know that surface area of the prism = 2(lb+bw+wl) . According to question we have following parameters as :

length = 15 mm\\width=3mm\\height=4mm

Putting these values to find area of prism we get:

⇒ Area = 2(lw+wh+hl)

⇒ Area = 2(15(3)+3(4)+4(15))

⇒ Area = 2(45+12+60)

⇒ Area = 2(117)

⇒ Area = 234mm^2

Therefore , the surface area of the prism is 234mm^2 .

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Find the curvature of the parabola y=x^2 at A(1,1)
xxMikexx [17]

Answer:

Step-by-step explanation:

The curvature of the curve y=f(x) is

y=f(x)=x^2\\\\y'=f'(x)=2x\\\\y''=f''(x)=2\\\\K(x)=courbure(in\  French)=\Bigg|\dfrac{y''(x)}{(1+y'(x)^2)^{\dfrac{3}{2} } }\Bigg|\\\\At\ A=(1,1),\\K(1)=\Bigg|\dfrac{2}{(1+2^2)^{\dfrac{3}{2} } }\Bigg|\\\\=\Bigg|\dfrac{2}{(5)^{\dfrac{3}{2} } }\Bigg|\\\\=\Bigg|\dfrac{2}{5*\sqrt{5} }\Bigg|\\\\=\Bigg|\dfrac{2*\sqrt{5}}{25 }\Bigg|\\\\\\\boxed{=\dfrac{2*\sqrt{5}}{25 }}\\\\

6 0
3 years ago
4v^2 + 8v + 5 = 10 What would I add to this equation to create a perfect square?
Dvinal [7]

Answer:

v₁ = 2.5; v₂ = 0.5.

Step-by-step explanation:

4v² + 8v + 5 = 10

4v² + 8v + 5 - 10 = 10 - 10

4v² + 8v - 5 = 0

D = 8² - 4 · 4 · (-5) = 64 + 80 = 144

v_{1} =\dfrac{-8-\sqrt{144} }{2 \cdot 4} =\dfrac{-8-12 }{8} =\dfrac{-20}{8} =-2.5\\\\v_{2} =\dfrac{-8+\sqrt{144} }{2 \cdot 4} =\dfrac{-8+12 }{8} =\dfrac{4}{8} =0.5\\\\

5 0
3 years ago
What is the slope of the line that passes through the points (-10, 8) and
vlada-n [284]

Answer:

slope=3

Step-by-step explanation:

Use the following equation the find the slope:

\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{rise}{run}

Rise over run is the change in the y-axis over the change in the x-axis from one point to the other. This is also known as the "slope". Insert the known values:

(-10_{x1},8_{y1})\\\\(-15_{x2},-7_{y2})\\\\\\\frac{-7-8}{-15-(-10)}\\\\\frac{-7-8}{-15+10}

Solve:

\frac{-7-8}{-15+10}=\frac{-15}{-5}

Simplify. Two negatives make a positive:

\frac{-15}{-5}=\frac{15}{5}

Simplify fraction by dividing top and bottom by 5:

\frac{15}{5}=\frac{3}{1}  =3

The slope is 3.

:Done

8 0
3 years ago
I REALLY NEED HELP!!
Nitella [24]

Based on the calculations on these invertible functions, f⁻¹(f(6.022)) is equal to 6.022 and f⁻¹(-10) + f(-6) is equal to -16.

<h3>What is an invertible function?</h3>

An invertible function refers to a type of function that is obtained by reversing the operation of a given function (f(x)).

In Mathematics, a function and its inverse function has the following property f⁻¹(f(x)) = x. By applying this property, we have:

f⁻¹(f(6.022)) = 6.022.

From the table, we have:

f⁻¹(-10) = -6

f(-6) = -10

Therefore, f⁻¹(-10) + f(-6) is given by:

f⁻¹(-10) + f(-6) = -6 - 10

f⁻¹(-10) + f(-6) = -16.

Read more on invertible function here: brainly.com/question/15635761

#SPJ1

7 0
2 years ago
a wooden dowel has a diameter of 1.20 cm it floats in water with 0.400 cm its diameter above water determine the density of the
yuradex [85]

Answer:

Step-by-step explanation:

7 0
3 years ago
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