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3 years ago

Please help!!! Work out the surface area for this solid prism.

Mathematics

1 answer:

zhannawk [14.2K]3 years ago

3 0

Answer:

3060 $cm^{2}$

Step-by-step explanation:

<u>Find the cross-sectional area first of the trapezium</u>

$\frac{1}{2} (a+b)h$

So, $\frac{1}{2}(6+34)15$

which is 40 / 2 x 15 = 20 x 15 = 300 $cm^{2}$

Since there are 2 trapeziums (on the front and back): 300 x 2 = 600 $cm^{2}$

<u>Find the Area of the Rectangles</u>

The first rectangle on the top would be: 6x30 = 180 $cm^{2}$

The slanted rectangle on the right would be: 25x30 = 750 $cm^{2}$

The rectangle on the bottom would be: 30x34 = 1020 $cm^{2}$

The hidden rectangle on the left would be: 17 x 30 = 510 $cm^{2}$

So by combining all these calculations, you will get the total surface area which is:

600 + 180 + 750 + 1020 + 510 = 780 + 1770 + 510 = 2550 + 510 = 3060 $cm^{2}$

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Solve the problem.

krok68 [10]

Answer:

Step-by-step explanation:

Perimeter = 84 feet

Side One = Side Two + 12 feet

Side Two + 17 = Side Three

Side Two + Side Two = Side Four

Perimeter = (Side Two + 12) + (Side Two) + (Side Two + 17) + (Side Two + Side Two) = 5 x (Side Two) + 29 = 84

5x + 29 = 84

5x = 55

x = 11

Side Two = 11 feet

Side One = 11 + 12 = 23 feet

Side Three = 11 + 17 = 28 feet

Side Four = 11 X 2 = 22 feet

7 0

4 years ago

assume x and y are both differentiable functions of t. find dx/dt given x=-1 and dy/dt=8 for the relation: 4x^2+3y^3=28

melomori [17]

Given:

x and y are both differentiable functions of t.

$4x^2+3y^3=28$

$x=-1\text{ and }\dfrac{dy}{dt}=8$

To find:

The value of $\dfrac{dx}{dt}$ .

Solution:

We have,

$4x^2+3y^3=28$ ...(i)

At x=-1,

$4(-1)^2+3y^3=28$

$4+3y^3=28$

$3y^3=28-4$

$3y^3=24$

Divide both sides by 3.

$y^3=8$

Taking cube root on both sides.

$y=2$

So, y=2 at x=-1.

Differentiate (i) with respect to t.

$4(2x\dfrac{dx}{dt})+3(3y^2\dfrac{dy}{dt})=0$

Putting x=-1, y=2 and $\dfrac{dy}{dt}=8$ , we get

$4(2(-1)\dfrac{dx}{dt})+3(3(2)^28)=0$

$-8\dfrac{dx}{dt}+9(4)(8)=0$

$-8(\dfrac{dx}{dt}-9(4))=0$

Divide both sides by -8.

$\dfrac{dx}{dt}-36=0$

$\dfrac{dx}{dt}=36$

Therefore, the value of $4x^2+3y^3=28$ is 36.

6 0

3 years ago

The expression 7^n/7^5 simplifies to 7^p. If n = 18, what is the value of the exponent p? Show your work and explain how you fou

nirvana33 [79]

When you divide two powers of the same base, you subtract the exponents:

$\dfrac{a^b}{a^c} = a^{b-c}$

This means that, in your case,

$\dfrac{7^n}{7^5} = 7^p \iff 7^{n-5} = 7^p \iff n-5 = p$

So, if $n=18$ , the equation becomes

$18-5 = p \iff p = 13$

5 0

3 years ago

Please help me on number 4 or 6 ITS DUE RIGHT NOW

melamori03 [73]

Answer:

#6:

A: $m=-\frac{2}{5}$

Step-by-step explanation:

Points: (3, -5) and (-7, -1)

Slope Formula: $m=\frac{y_{2} - y_{1} }{x_{2} -x_{1} }$

$m = \frac{-5+1}{3-(-7)}$

$m = -\frac{4}{10}$

$m =- \frac{2}{5}$

6 0

3 years ago

Ex. 6. For each of these arguments determine whether the argument is correct or incorrect and explain why. a) Everyone enrolled

mojhsa [17]

Answer:

A) True

B) False

C) False

D) True

Step-by-step explanation:

A) Everyone enrolled in the university has lived in a dormitory. Mia has never lived in a dormitory. Therefore, Mia is not enrolled in the university.

True, because if Mia is enrolled in the university, then she must have lived in a dormitary.

B) A convertible car is fun to drive. Isaac’s car is not a convertible. Therefore, Isaac’s car is not fun to drive.

False, it is known that all convertible cars are fun to drive, but there is no information about inconvertible cars. Some of them may be fun to drive.

C) Quincy likes all action movies. Quincy likes the movie Eight Men Out. Therefore, Eight Men Out is an action movie.

False, Quincy likes all action movies, but also can like another movies. It is not said Quincy likes only action movie, so Eight Men Out can appear to be not action movie.

D) All lobstermen set at least a dozen traps. Hamilton is a lobsterman. Therefore, Hamilton sets at least a dozen traps.

True, Hamilton is a lobsterman and as all lobstermen he set at least a dozen traps.

6 0

3 years ago