Having a bit of trouble solving this problem

Janice is building a model volcano for the science fair. To find the right ratio, she starts by mixing small amounts of baking s

marishachu [46]

Answer:

6 tablespoons of baking soda

Step-by-step explanation:

There are 8 fluid ounces in 1 cup and shes going to use half a cup so that means shes going to use 4 fluid ounces of vinegar. To find how much baking soda she is going to use, we are going to multiply.

1.5 * 4 = 6

Best of Luck!

8 0

3 years ago

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Find the solution r(t)r(t) of the differential equation with the given initial condition: r′(t)=⟨sin9t,sin6t,9t⟩,r(0)=⟨4,6,3⟩

klemol [59]

$\mathbf r'(t)=\langle\sin9t,\sin6t,9t\rangle$

$\mathbf r(t)=\displaystyle\int\mathbf r'(t)\,\mathrm dt$

$\mathbf r(t)=\left\langle\displaystyle\int\sin9t\,\mathrm dt,\int\sin6t\,\mathrm dt,\int9t\,\mathrm dt\right\rangle$

$\displaystyle\int\sin9t\,\mathrm dt=\frac19\cos9t+C_1$

$\displaystyle\int\sin6t\,\mathrm dt=\frac16\cos6t+C_2$

$\displaystyle\int9t\,\mathrm dt=\frac92t^2+C_3$

With the initial condition $\mathbf r(0)=\langle4,6,3\rangle$ , we find

$\dfrac19\cos0+C_1=4\implies C_1=\dfrac{35}9$

$\dfrac16\cos0+C_2=6\implies C_2=\dfrac{35}6$

$\dfrac92\cdot0^2+C_3=3\implies C_3=3$

So the particular solution to the IVP is

$\mathbf r(t)=\left\langle\dfrac19\cos9t+\dfrac{35}9,\dfrac16\cos6t+\dfrac{35}6,\dfrac92t^2+3\right\rangle$

4 0

3 years ago

Pediatricians prescribe 5mL of cough syrup for every 25lb of a child's weight. How many mililiters of cough syrup will the docto

Marianna [84]

Answer:

9 ml

Step-by-step explanation:

The Pediatrician prescribes 5 milliliters of cough syrup for every 25 lb of child weight.

Now, the weight of Jocelyn is 45 lb.

If the rate of prescribing the cough syrup in ml per weight of patients remains constant,

Then we can use the unitary method to get the amount of cough syrup prescribed by the Pediatrician for Jocelyn, and that will be

$\frac{5*45}{25} =9$ ml. (Answer)

3 0

3 years ago

7/8 & 4/9 is closest to 0,1,2,3

Mrrafil [7]

7/8 is closest to 1 and 4/9 is closest to 0

4 0

3 years ago

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Figure a is dilated by a scale factor of 1/2 to form figure b. What is the length of x?

PIT_PIT [208]

Answer:

The correct option is 3. The value of x is 8 inches.

Step-by-step explanation:

It is given that Figure A is dilated by a scale factor of 1/2 to form Figure B. It means both figure are similar and corresponding sides of similar figures are proportional.

$\text{scale factor}=\frac{\text{Side of image}}{\text{Side of preimage}}$

$\frac{1}{2}=\frac{x}{16}$

Multiply both sides by 16.

$\frac{16}{2}=x$

$8=x$

Since scale factor is 1/2, so we can directly say that the side length of image is half of the corresponding side of preimage.

The length of x is 8 inches. Therefore the correct option is 3.

3 0

3 years ago

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