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solniwko [45]
3 years ago
5

The total number of cupcakes Carmen can bake depends on the amount of time she spends baking. Carmen can bake 84 cupcakes in 1.6

h. How many can she bake in 2 h?
Mathematics
1 answer:
Vitek1552 [10]3 years ago
8 0
We know that the number of cakes is dependent on the time spent in baking.

We are given that Carmen can bake 84 cakes in 1.6 hours, therefore, to know the number of cakes that she can bake in 2 hours, all you have to do is cross multiplication as follows:
number of cakes = (2*84) / 1.6 = 105 cakes
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4cm 2cm 5cm 5cm.......
babunello [35]

Answer:

33 / the second one

Step-by-step explanation:

5 x 5 = 25

4 x 2 = 8

25 + 8 = 33

7 0
3 years ago
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Find the particular solution of the differential equation that satisfies the initial condition(s). f ''(x) = x−3/2, f '(4) = 1,
sweet [91]

Answer:

Hence, the particular solution of the differential equation is y = \frac{1}{6} \cdot x^{3} - \frac{3}{4}\cdot x^{2} - x.

Step-by-step explanation:

This differential equation has separable variable and can be solved by integration. First derivative is now obtained:

f'' = x - \frac{3}{2}

f' = \int {\left(x-\frac{3}{2}\right) } \, dx

f' = \int {x} \, dx -\frac{3}{2}\int \, dx

f' = \frac{1}{2}\cdot x^{2} - \frac{3}{2}\cdot x + C, where C is the integration constant.

The integration constant can be found by using the initial condition for the first derivative (f'(4) = 1):

1 = \frac{1}{2}\cdot 4^{2} - \frac{3}{2}\cdot (4) + C

C = 1 - \frac{1}{2}\cdot 4^{2} + \frac{3}{2}\cdot (4)

C = -1

The first derivative is y' = \frac{1}{2}\cdot x^{2}- \frac{3}{2}\cdot x - 1, and the particular solution is found by integrating one more time and using the initial condition (f(0) = 0):

y = \int {\left(\frac{1}{2}\cdot x^{2}-\frac{3}{2}\cdot x -1  \right)} \, dx

y = \frac{1}{2}\int {x^{2}} \, dx - \frac{3}{2}\int {x} \, dx - \int \, dx

y = \frac{1}{6} \cdot x^{3} - \frac{3}{4}\cdot x^{2} - x + C

C = 0 - \frac{1}{6}\cdot 0^{3} + \frac{3}{4}\cdot 0^{2} + 0

C = 0

Hence, the particular solution of the differential equation is y = \frac{1}{6} \cdot x^{3} - \frac{3}{4}\cdot x^{2} - x.

5 0
4 years ago
What is the solution to the system of linear equations?
Dmitry_Shevchenko [17]

Answer:

x = 5, y = -1/2

Step-by-step explanation:

3.5x - 5y = 20

3x + 4y = 13 multiply by 1.25 so the y's match up (you could match x's too)

3.75x + 5y = 16.25

–––––––––––––––––––––––

3.5x - 5y = 20

3.75x +5y = 16.25

7.25x + 0y = 36.25 you can add or subtract here (on this equation you add)

7.25x=36.25

x=5 So now we have x=5 and to find y we can just plug in x into one of the equations

–––––––––––––––––––

3(5) + 4y = 13

15 + 4y = 13

4y = -2

y = -1/2

x = 5, y = -1/2

Then you can plug in both to check your answers.

4 0
3 years ago
A line passes through the points
masha68 [24]

Answer:

y=-2x+7

enter the point into point slope form to find the slope and then use one of the points in point slope form  and rearrange it to have y by itself

4 0
3 years ago
If f(x) = x ² +1 and g(x) =3x+ 1,find [f(4)] ²
guajiro [1.7K]

Answer:

289

Step-by-step explanation:

We don't need g at all for this.

We will need to know f(4) before continuing...

f(4) can be found by replacing x in f(x)=x^2+1 with 4:

f(4)=4^2+1

f(4)=16+1

f(4)=17

-------------------

Now let's find [f(4)]^2:

[f(4)]^2

[17]^2

17(17)

289

3 0
3 years ago
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