Use the figure below to answer the questions.a. What is the name of the 3D shape?


b. What is the formula for total surface area for this shape?


c. What is the surface area of the figure?

Final answer:

The distance of the run is 13.125 miles. The total time for the slower jogger was found to be 2.625 hours. Thus, both joggers ran the same distance, but at different speeds resulting in different finish times.

Explanation:

The problem deals with the concept of relative speed in mathematics. To find the distance of the run, we first need to figure out the time it took for each jogger to finish the run. We know that the slower jogger finished 45 minutes after the faster one. Since the speed equivalence is expressed in miles per hour (mph), let's convert 45 minutes into hours by dividing 45 by 60, giving us 0.75 hours.

Given that the slower jogger runs at 5 mph, and they took 0.75 hours longer than the faster one, we know they ran for a certain time 't', so we can represent this as t = total time of slower jogger's run.

The faster jogger ran at 7 mph. Since the jogger was 0.75 hours ahead of the slower one, the time would be represented by t - 0.75 hours = total time of faster jogger's run. The distance travelled by each jogger is 'speed x time'.

Following this, we equal these distances because it's the same course: 5t = 7(t - 0.75).

Solving this equation gives us t = 2.625 hours (total time for slower jogger). To find the run's distance, we can now substitute total time into either jogger's speed x time calculation. We'll use the slower jogger here: Distance = 5t = 5*2.625 = 13.125 miles.

Learn more about Relative Speed here:

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Step-by-step explanation:

Answer:

\frac{7}{4}

4

7

Explanation:

______________________

We know the values of

i) cos0° = 1

ii) sin45° = \frac{1}{\sqrt{2}}

2

1

iii) sin30° = \frac{1}{2}

2

1

iv) sin90° = 0

v) cos45° = \frac{1}{\sqrt{2}}

2

1

vi ) cos60° = \frac{1}{2}

2

1

_____________________

Now,

The value of

(cos 0+sin 45+sin 30)(sin 90-cos 45+cos 60)

= \left(1+\frac{1}{\sqrt{2}}+\frac{1}{2}\right)\left(1-\frac{1}{\sqrt{2}}+\frac{1}{2}\right)(1+

2

1

+

2

1

)(1−

2

1

+

2

1

)

= \left(\frac{3}{2}+\frac{1}{\sqrt{2}}\right)\left(\frac{3}{2}-\frac{1}{\sqrt{2}}\right)(

2

3

+

2

1

)(

2

3

−

2

1

)

= \left(\frac{3}{2}\right)^{2}-\left(\frac{1}{\sqrt{2}}\right)^{2}(

2

3

)

2

−(

2

1

)

2

/* By algebraic identity

(a-b)(a+b) = a²-b² */

= \left( \frac{9}{4}-\frac{1}{2}\right)(

4

9

−

2

1

)

= \frac{9-2}{4}

4

9−2

= \frac{7}{4}

4

7

••••

Answer:

Step-by-step explanation:

Answer:

So the triangle ABC is an isosceles triangle

Step-by-step explanation:

By definition the perimeter of a triangle is equal to the sum of the lengths of its sides.

In this case we know that the perimeter is 63

The lengths of its sides depend on x.

So:

Now we solve for the variable x.

Therefore:

The triangle has two sides of equal length. The triangles that have two equal sides are the isosceles triangles.

So the triangle ABC is an isosceles triangle

Answer:

B. -6

Step-by-step explanation:

hope this helps!

Answer:

-6

Step-by-step explanation:

from (-6,-4) to (x,8) there are already 12 spaces in between the y- axis from -4 to 8. So because there are already 12 spaces in between you dont need to add any space between x and -6 so you can conclude that if x is -6 then there will be 12 spaces inbetween because of -4 and 8

Answer:

30

Step-by-step explanation:

Assuming your parallelogram looks like the one in the attached image.

The area of a parallelogram is base x height,  .

The base is 10; the height is 3, so A = 10 x 3 = 30.

Answer:

30

Step-by-step explanation: