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2 years ago

Write the product using exponents. 6.4.6.4.6.4.6.4.b.b.b

Mathematics

1 answer:

maks197457 [2]2 years ago

4 0

Step-by-step explanation:

I count four 6s, four 4s and three b.

so, we have

6⁴×4⁴×b³ or (using the same symbols as above)

6⁴.4⁴.b³

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An old truck has a fuel efficiency rating of 12 mpg. What is the cost

andrew-mc [135]

Answer:

The cost of 5 gallons of fuel would be 5x assuming the cost of 1 gallon to be x.

Step-by-step explanation:

An old truck has a fuel efficiency rating of 12 mpg.

We have to find the cost of gasoline that will be used up after we drive 60 miles.

To drive 60 miles , it uses 5 gallons.

let the cost of 1 gallon of fuel be x.

We have to find the cost of 5 gallons of fuel.

So the cost of 5 gallons of fuel = 5 $\times coat of 1 gallon of fuel$

= 5x

5 0

3 years ago

3. A cone has a heighth and a base with radius r. You want to change the cone so its volume is tripled. What is the new height i

Sphinxa [80]

Answer:

Hence the new height is 3 times the original height .(h1=3h)

Step-by-step explanation:

Given:

A cone with has height and base with radius r .

To Find:

What is new height

Solution:

Consider as cone with height h base radius r, and volume v

Here given that only height changes for the cone i.e. r remains the unchanged or same or constant

The volume for a regular cone is given by ,

$V=pie*r^2*h/3$

Here V is directly proportional to h i.ee pie ,3 and r being constant

$V=K*h$

i.e V/h=constant

V1 and h1 are new dimensions for new cone

V/h=V1/h1

Here V1=3V

So V/h=3V/h1

1/h=3/h1

i.e h1=3h

Hence the height is 3 times the original height .

4 0

2 years ago

40 POINTS is (4,7) a solution of equations? Explain your answer 2x+4y=36 3x-4y=-6

dsp73

2x + 4y = 36
3x - 4y = -6
--------------add
5x = 30
x = 6

2x+4y=36
2(6)+4y=36
12 + 4y = 36
4y = 24
y = 6

answer
(6, 6) is a solution of equations
(4,7) is NOT a solution of equations

6 0

3 years ago

Read 2 more answers

¿Can i get the answer?

NikAS [45]

Answer:

15.7

Step-by-step explanation:

5 x 3.14(pi) = 15.7

3 0

2 years ago

The volume V of an ice cream cone is given by V = 2 3 πR3 + 1 3 πR2h where R is the common radius of the spherical cap and the c

Nuetrik [128]

Answer:

The change in volume is estimated to be 17.20 $\rm{in^3}$

Step-by-step explanation:

The linearization or linear approximation of a function $f(x)$ is given by:

$f(x_0+dx) \approx f(x_0) + df(x)|_{x_0}$ where $df$ is the total differential of the function evaluated in the given point.

For the given function, the linearization is:

$V(R_0+dR, h_0+dh) = V(R_0, h_0) + \frac{\partial V(R_0, h_0)}{\partial R}dR + \frac{\partial V(R_0, h_0)}{\partial h}dh$

Taking $R_0=1.5$ inches and $h=3$ inches and evaluating the partial derivatives we obtain:

$V(R_0+dR, h_0+dh) = V(R_0, h_0) + \frac{\partial V(R_0, h_0)}{\partial R}dR + \frac{\partial V(R_0, h_0)}{\partial h}dh\\V(R, h) = V(R_0, h_0) + (\frac{2 h \pi r}{3} + 2 \pi r^2)dR + (\frac{\pi r^2}{3} )dh$

substituting the values and taking $dx=0.1$ and $dh=0.3$ inches we have:

$V(R_0+dR, h_0+dh) =V(R_0, h_0) + (\frac{2 h \pi r}{3} + 2 \pi r^2)dR + (\frac{\pi r^2}{3} )dh\\V(1.5+0.1, 3+0.3) =V(1.5, 3) + (\frac{2 \cdot 3 \pi \cdot 1.5}{3} + 2 \pi 1.5^2)\cdot 0.1 + (\frac{\pi 1.5^2}{3} )\cdot 0.3\\V(1.5+0.1, 3+0.3) = 17.2002\\\boxed{V(1.5+0.1, 3+0.3) \approx 17.20}$

Therefore the change in volume is estimated to be 17.20 $\rm{in^3}$

4 0

2 years ago