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julia-pushkina [17]
3 years ago
13

Find the volume of the composite solid.

Mathematics
1 answer:
OLEGan [10]3 years ago
4 0

Here's the solution,

the volume of the given figure is :

=》

volume \:  \: of \:  \: (pyramid \:  + rectangular \:  \: prism)

volume of pyramid :

=》

\dfrac{l \times b \times h}{3}

=》

\dfrac{4 \times 5 \times 6}{3}

=》

\dfrac{120}{3}

=》

40

volume of pyramid = 40 cm³

now, volume of rectangular prism :

=》

l \times b \times h

=》

4 \times 5 \times 2

=》

40

volume of rectangular prism = 40 cm³

volume of composite figure = 40 + 40

=》80 cm³

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50
ozzi

Answer:

90 km, N 46° E

Step-by-step explanation:

<em>A jet flies due North for a distance of 50 km and then on a bearing of N 70° E for a further 60 km. Find the distance and bearing of the jet from its starting point.</em>

Look at the diagram I drew of this scenario. You can see the jet flies North for 50 km, and then turns at a 70° angle to fly another 60 km. We want to find the distance from the starting point, SP, to angle C (labeled).

This will be the jet's distance from its starting point.

In order to find the bearing of the jet from its starting point, we will need to find the angle formed between distances b and c, labeled angle A.

The <u>Law of Cosines</u> will allow us to use two known sides and one known angle to solve for the sides opposite of the known angle.

In this case, the known angle is 110° (angle B) so we will use the <u>Law of Cosines</u> respective to B.

  • b² = a² + c² - 2ac cosB

Substitute the known values into the equation and solve for b, the distance from the starting point (A) to the endpoint (C).

  • b² = (60)² + (50)² - 2(60)(50) cos(110°)
  • b² = 6100 -(-2052.12086)
  • b² = 8152.12086
  • b = 90.28909602
  • b ≈ 90 km

The distance of the jet from its starting point is 90 km. Now we can use this b value in order to calculate angle A, the bearing of the jet.

The <u>Law of Cosines</u> with respect to A:

  • a² = b² + c² - 2bc cosA

Substitute the known values into the equation and solve for A, the bearing from the starting point (clockwise of North).

  • (60)² = (90.28909602)² + (50)² - 2(90.28909602)(50) cosA
  • 3600 = 8152.12086 - 6528.909602 cosA
  • -4552.12086 = -6528.909602 cosA
  • 0.6972252853 = cosA
  • A = cos⁻¹(0.6972252853)
  • A = 45.79519
  • A ≈ 46°

The bearing of the jet from its starting point is N 46° E. This means that it is facing northeast at an angle of 46° clockwise from the North.

7 0
3 years ago
What does the line 5x + 4y = -6 look like
RoseWind [281]

Answer:

See attached photo for graph

Step-by-step explanation:

Solve the equation for y...  (that means get y by itself)

4y = -5x - 6         (subtract 5x from both sides)

y = -(5/4)x - 6/4  (divide both sides by 4)

y = -(5/4)x - 3/2      (simplify)

Now you can graph using slope-intercept method.   The y-intercept is -3/2, and the slope is -5/4    

5 0
3 years ago
at a basketball game, a vendor sold a combined total of 218 sodas and hotdogs. The number of hotdogs sold was 50 less than the n
velikii [3]

9514 1404 393

Answer:

  • 134 soda
  • 84 hot dogs

Step-by-step explanation:

Let s represent the number of sodas sold. Then the number of hot dogs sold is (s-50) and the total is ...

  s +(s -50) = 218

  2s = 268 . . . . . . . . . add 50

  s = 134 . . . . . . . divide by 2

134 sodas were sold; 84 hot dogs were sold.

5 0
3 years ago
Can you ask 5 people to name as much states in 60 seconds please?
Lyrx [107]

Answer:

Alabama, Alaska, American Samoa, Arizona, Arkansas.

California, Colorado, Connecticut.

Delaware, District of Columbia.

Florida.

Georgia, Guam.

Hawaii.

Idaho, Illinois, Indiana, Iowa.

Kansas, Kentucky.

4 0
3 years ago
A graphic artist has a picture that is 5 inches by 10 inches. The picture
tangare [24]

Answer:

15 inches

Step-by-step explanation:

7 0
3 years ago
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