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yarga [219]
3 years ago
13

Simplify the expression of (7 – c )(–1)

Mathematics
1 answer:
Ivan3 years ago
6 0
Expand out, this literally just wants you to multiply everything by -1.
so 7*-1 = -7
-c*-1 = c 
thus putting them together to get -7+c which is just c-7 
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Which expression is even for all integers a and b?
Irina18 [472]
Do u have a problem that went with this?

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3 years ago
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Construct ∆ABC using the following segment
salantis [7]

Answer:

  Use the angle copy procedure to copy the angles to the ends of c.

Step-by-step explanation:

An angle is copied with a straightedge two settings of a compass.

  1. Set the compass to an arbitrary radius. An appropriate choice is a radius that is half or more of the length of the shortest ray of the angles you want to copy.
  2. Put the point of the compass at the vertex of an angle you want to copy. Using that same radius, draw arcs through both rays of the angle. Do this for all the angles you want to copy.
  3. Put the point of the compass at the place where you want the vertex of the copied angle. Here, that is either (both) end points of segment c. (You might want to label the ends of segment c as "A" and "B" so you know which angle you're copying where.) Using the same radius as before, draw an arc through the segment and through the space where you expect the ray from the copied angle to lie.
  4. For one of the source angles, set the compass radius to the distance between the points where the first arc crosses the angle's rays. Then, put the point of the compass at the place on the segment c where the corresponding arc crosses. Use the compass to mark a point on that arc the same distance as on the source angle. Draw a line from the vertex through the point you just marked. That line will make the same angle with c as the original angle.
  5. Repeat step 4 for the other angle you want to copy, at the other end of segment c. In general, the compass setting will be different (unless all the angles have the same measure).

The place where the rays from the copied angles cross is the third vertex (vertex C) of the triangle you're constructing.

_____

<em>Comments on the attached diagram</em>

In the attached diagram, "step 1" is to place the target vertex. You already have that as one end of segment C. The arcs numbered 2 and 3 in the diagram are the arcs resulting from executing steps 2 and 3 above. (They have arbitrary radius "r", which is the same everywhere.) You will have two sets, because you are copying two angles.

The arcs numbered 4 and 5 in the diagram have radius ST, the distance you set in step 4 above. That distance is used as the radius of arc 5, so the length VW will be the same as the length ST. The straightedge is used to draw a line through B and W, completing the copy of the angle.

6 0
3 years ago
Jenn swam ⅕ mile in ¼ hour. What is her unit rate in miles per hour?
Paladinen [302]

Answer:

1/2 mile/1/5 hour = 5/2 mph = 2 1/2 mph

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
A cylindrical tank has a base of diameter 12 ft and height 5 ft. The tank is full of water (of density 62.4 lb/ft3).(a) Write do
saw5 [17]

Answer:

a.  71884.8 π lb/ft-s²∫₀⁵(9 - y)dy

b.  23961.6 π lb/ft-s²∫₀⁵(5 - y)dy

c. 99840π lb/ft-s²∫₀⁶rdr

Step-by-step explanation:

.(a) Write down an integral for the work needed to pump all of the water to a point 4 feet above the tank.

The work done, W = ∫mgdy where m = mass of cylindrical tank = ρA([5 + 4] - y) where ρ = density of water = 62.4 lb/ft³, A = area of base of tank = πd²/4 where d = diameter of tank = 12 ft.( we add height of the tank + the height of point above the tank and subtract it from the vertical point above the base of the tank, y to get 5 + 4 - y) and g = acceleration due to gravity = 32 ft/s²

So,

W = ∫mgdy

W = ∫ρA([5 + 4] - y)gdy

W = ∫ρA(9 - y)gdy

W = ρgA∫(9 - y)dy

W = ρgπd²/4∫(9 - y)dy

we integrate W from  y from 0 to 5 which is the height of the tank

W = ρgπd²/4∫₀⁵(9 - y)dy

substituting the values of the other variables into the equation, we have

W = 62.4 lb/ft³π(12 ft)² (32 ft/s²)/4∫₀⁵(9 - y)dy

W = 71884.8 π lb/ft-s²∫₀⁵(9 - y)dy

.(b) Write down an integral for the fluid force on the side of the tank

Since force, F = ∫PdA where P = pressure = ρgh where h = (5 - y) since we are moving from h = 0 to h = 5. So, P = ρg(5 - y)

The differential area on the side of the tank is given by

dA = 2πrdy

So.  F = ∫PdA

F = ∫ρg(5 - y)2πrdy

Since we are integrating from y = 0 to y = 5, we have our integral as

F = ∫ρg2πr(5 - y)dy

F = ∫ρgπd(5 - y)dy    since d = 2r

substituting the values of the other variables into the equation, we have

F = ∫₀⁵62.4 lb/ft³π(12 ft) × 32 ft/s²(5 - y)dy

F = 23961.6 π lb/ft-s²∫₀⁵(5 - y)dy

.(c) How would your answer to part (a) change if the tank was on its side

The work done, W = ∫mgdr where m = mass of cylindrical tank = ρAh where ρ = density of water = 62.4 lb/ft³, A = curved surface area of cylindrical tank = 2πrh  where r = radius of tank, d = diameter of tank = 12 ft. and h =  height of the tank = 5 ft and g = acceleration due to gravity = 32 ft/s²

So,

W = ∫mgdr

W = ∫ρAhgdr

W = ∫ρ(2πrh)hgdr

W = ∫2ρπrh²gdr

W = 2ρπh²g∫rdr

we integrate from r = 0 to r = d/2 where d = diameter of cylindrical tank = 12 ft/2 = 6 ft

So,

W = 2ρπh²g∫₀⁶rdr

substituting the values of the other variables into the equation, we have

W = 2 × 62.4 lb/ft³π(5 ft)² × 32 ft/s²∫₀⁶rdr

W = 99840π lb/ft-s²∫₀⁶rdr

7 0
3 years ago
helpppp! The population of a town is 20,000 people in the year 2000. How many people with live in the town in 2016 if the popula
Brut [27]

Answer:

31877 people with live in the town in 2016 if the population increases at a rate of 6% every 2 years

Step-by-step explanation:

The formula used will be

A(t) = P(1+r)^t

A(t) = Future value

P = population

r = rate

t = time

P= 20,000

r =6% or 0.06

t = 16

Since population is increased every 2 years, so t = 16/2 = 8

Putting value:

A(16) = 20,000(1+0.06)^8

A(16)= 20,000(1.06)^8

A(16) = 31876.9 ≈ 31877

So, 31877 people with live in the town in 2016 if the population increases at a rate of 6% every 2 years

5 0
3 years ago
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