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2 years ago

The sum of three consecutive even numbers is-138. What is the smallest of the 3 numbers?

Mathematics

1 answer:

Vlada [557]2 years ago

5 0

Answer:

the smallest of the three consecutive even numbers is 44

Step-by-step explanation:

44+46+48=138

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Miguel bikes 23 km per hour and starts at mile 10. Gabby bikes 28 km per hour and starts at hour 0. Which system of linear equat

Goshia [24]

Answer:

Miguel: d = 23t + 10

Gabby: d = 28t

Step-by-step explanation:

We can write the equation for each case in slope-intercept form, d = mt + b

Where,

d = total distance

t = time

m (rate) = distance/hr

b = initial value

✔️ Miguel:

m = 23 km/hr

b = 10 mile

Equation: subtitle the values into d = mt + b

d = 23t + 10

✔️ Gabby:

m = 28 km/hr

b = 0 mile

Equation: subtitle the values into d = mt + b

d = 28t + 0

d = 28t

4 0

2 years ago

What Force would be needed to extend a spring with a spring constant k=7 N/m that extends<br>0.3m?

vladimir2022 [97]

Answer:

Force = - 2.1 Newton

Step-by-step explanation:

According to question ,

The value of Spring constant , K = 7 N/m Newton per meter

And the spring is extended up to 0.3 meter

The Force experience on the spring is calculated from the Hook's Law

<u>The principal state that , the force applied on spring to extend or compress the spring to some distance is proportion to that distance. </u>

Let the force be F

So, F = - K X

where K is spring constant and X is its displacement

Negative sign shows displacement of spring once it is stretched

And K is spring constant

So ,Force = ( - ) 7 × 0.3

I.e Force = - 2.1 Newton Answer

4 0

3 years ago

A surveyor measures the angle of elevation to a point on a mountain, that is 6 miles away, to be 15 degrees. The vertical change

cricket20 [7]

You can draw a right triangle with the informatio.

The vertical change in elevation (unknown) is the opposed leg to the angle 15°

The distance from the surveyor to the point vertically below the point on the mountain is the adjacent leg = 6 miles.

Then tan(15°) = x / 6 => x = 6tan(15) = 1.61 miles

Answer: 1.61 miles

6 0

2 years ago

Read 2 more answers

Divide (x4 – 11x3 – 49x2 + 899x – 2506) ÷ (x – 8).

pickupchik [31]

Okay first make sure you change negative 8 to a positive 8.
Set the problem up 8 -11 -49 899 -2506
__________________
8 -11 -49 899 -2506
-88 -1096 -1576
____________________
-11 -137 -197 -4082

Your answer will be
-11x^3 - 137x^2 - 197x - 4082

6 0

3 years ago

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this shape must h

mestny [16]

Answer:

Radius =6.518 feet

Height = 26.074 feet

Step-by-step explanation:

The Volume of the Solid formed = Volume of the two Hemisphere + Volume of the Cylinder

Volume of a Hemisphere $=\frac{2}{3}\pi r^3$

Volume of a Cylinder $=\pi r^2 h$

Therefore:

The Volume of the Solid formed

$=2(\frac{2}{3}\pi r^3)+\pi r^2 h\\\frac{4}{3}\pi r^3+\pi r^2 h=4640\\\pi r^2(\frac{4r}{3}+ h)=4640\\\frac{4r}{3}+ h =\frac{4640}{\pi r^2} \\h=\frac{4640}{\pi r^2}-\frac{4r}{3}$

Area of the Hemisphere = $2\pi r^2$

Curved Surface Area of the Cylinder = $2\pi rh$

Total Surface Area=

$2\pi r^2+2\pi r^2+2\pi rh\\=4\pi r^2+2\pi rh$

Cost of the Hemispherical Ends = 2 X Cost of the surface area of the sides.

Therefore total Cost, C

$=2(4\pi r^2)+2\pi rh\\C=8\pi r^2+2\pi rh$

Recall: $h=\frac{4640}{\pi r^2}-\frac{4r}{3}$

Therefore:

$C=8\pi r^2+2\pi r(\frac{4640}{\pi r^2}-\frac{4r}{3})\\C=8\pi r^2+\frac{9280}{r}-\frac{8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{24\pi r^2-8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{16\pi r^2}{3}\\C=\frac{27840+16\pi r^3}{3r}$