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3 years ago

Find the surface area of the figure. PLEASE HELP!

Mathematics

1 answer:

olya-2409 [2.1K]3 years ago

6 0

Answer:

The total surface area is: 468 in^2 which agrees with answer a)

Step-by-step explanation:

The three lateral faces of the prism are rectangles, and the sums of their areas give:

12 * 10 + 9 * 10 + 15 * 10 = 360 in^2

The area of each triangular base (notice it is a right triangle) is given by:

9 * 12 / 2 = 54 in^2, so we add TWO of these to the three rectangular faces:

Total surface = 360 in^2 + 2 * 54 in^2 = 468 in^2

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3 years ago

Find the cos A and tan B to four decimal places. URGENT

Nikolay [14]

cos A is 0.8511 and tan B is 1.6

Step-by-step explanation:

Find the 3rd length or the hypotenuse.

<u>Pythagoras theorem</u>

$hypotenuse^{2}$ = $adjacent^{2}$ + $opposite^{2}$

$hypotenuse^{2}$ = $8^{2}$ + $5^{2}$

$hypotenuse^{2}$ = 64 + 25

hypotenuse = $\sqrt{89}$

hypotenuse = 9.4

a) Cos A

Adjacent = 8

Hypotenuse = 9.4

<u>Formula:</u>

Cos (Angle) = $\frac{adjacent}{hypotenuse}$

Cos A = $\frac{8}{9.4}$

Cos A = 0.8511

A = $cos^{-1}$ (0.8511)

A = 31.7°

b) Tan B

Opposite = 8

Adjacent = 5

<u>Formula:</u>

Tan (Angle) = $\frac{opposite}{adjacent}$

Tan B = $\frac{8}{5}$

Tan B = 1.6

B = $cos^{-1}$ (1.6)

B = 58°

Therefore, cos A is 0.8511 and tan B is 1.6.

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#LearnwithBrainly

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3 years ago

CAN U GUYS PELASE ANSWER THE SIMULTANEOUS EQUATION QUESTION QUESTIONS ASAP. THIS IS EXTREMELY URGENT. Solve it by using the subs

prisoha [69]

Answer:

a ) y = 1 and x = -1

d) y = 5 and x = -1/2

Step-by-step explanation:

<h2><u>Substitution method</u></h2><h2><u>Question a</u></h2>

y = x+ 2

y = 2x + 3

<em>we can make the first formula in terms of x , so we can place in into the second formula</em>

y = x + 2

x = y - 2

now put y - 2 where x is in the second equation

y = 2x + 3

y = 2(y - 2) + 3

y = 2y - 4 +3

now solve

4 - 3 = 2y -y

y = 1

since y = 1 we can find what x is by putting into the first formula

y = x +2

x = y - 2

x = (1) -2

x = -1

<h3><u>hence y = 1 and x = -1 </u></h3><h3><u /></h3><h2><u>Question d</u></h2>

y = 2x + 6

y = 4 - 2x

<em>we can make the first formula in terms of x , so we can place in into the second formula</em>

y = 2x + 6

y - 6 = 2x

x = (y-6)/ 2

now place (y-6)/2 where x is in the second formula

y = 4 -2x

y = 4 - 2 ( $\frac{y - 6}{2}$ )

now solve

the multiplication by 2 and division by 2 are cancelled out

hence making the simplified equation as:

y = 4 - y + 6

2y = 4 + 6

2y = 10

y = 5

now place this into the first equation

y = 2x + 6

y - 6 = 2x

x = (y-6)/ 2

x = (5-6)/2

x = -1/2

<h3><u>hence y = 5 and x = -1/2</u></h3>

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3 years ago