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2 years ago

In a class, every student knows French or German (or both). 15 students know French, and 17 students know German.

Mathematics

2 answers:

Nikolay [14]2 years ago

5 0

You would do 15 + 17. Which equals 32, and that is the least, then choose a number that is larger than 32.

yanalaym [24]2 years ago

3 0

The answer is thirty two

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Hello , how to do 6(iii)?

Doss [256]

Answer:

$\displaystyle \frac{dS}{dt}=\frac{3}{50r}$

Step-by-step explanation:

Water is being pumped into an inflated rubber sphere at a constant rate of 0.03 cubic meters per second.

So, dV/dt = 0.03.

We want to show that dS/dt is directly proportional to 1/r.

In other words, we want to establish the relationship that dS/dt = k(1/r), where k is some constant.

First, the volume of a sphere V is given by:

$\displaystyle V=\frac{4}{3}\pi r^3$

Therefore:

$\displaystyle \frac{dV}{dt}=4\pi r^2\frac{dr}{dt}$

Next, the surface area of a sphere S is given by:

$\displaystyle S=4\pi r^2$

Therefore:

$\displaystyle \frac{dS}{dt}=8\pi r\frac{dr}{dt}$

We can divide both sides by 2:

$\displaystyle \frac{1}{2}\frac{dS}{dt}=4\pi r\frac{dr}{dt}$

We can substitute this into dV/dt. Rewriting:

$\displaystyle \frac{dV}{dt}=r\Big(4\pi r\frac{dr}{dt}\Big)$

So:

$\displaystyle \frac{dV}{dt}=\frac{1}{2}r\frac{dS}{dt}$

Since dV/dt = 0.03 or 3/100:

$\displaystyle \frac{3}{100}=\frac{1}{2}r\frac{dS}{dt}$

Therefore:

$\displaystyle \frac{dS}{dt}=\frac{3}{50r}=\frac{3}{50}\Big(\frac{1}{r}\Big)$

Where k = 3/50.

And we have shown that dS/dt is directly proportional to 1/r.

4 0

2 years ago

Please help me it will be very much appreciated

AveGali [126]

Answer:

ΔABC ≅ ΔFED

Explanation:

Look at the alignment and position of the letters.

A = F

B = E

C = D

Properly align the letters in order to their corresponding position.

ΔA ≅ ΔF

ΔAB ≅ ΔFE

ΔABC ≅ ΔFED

8 0

2 years ago

1.Find the area of the trapezoid. Leave your answer in simplest radical form. The figure is not drawn to scale.

sleet_krkn [62]

I´m sure that the answer is 96cm^2, because the area of the triangles is 18 and 6 and the area of the rectangle is 72.

5 0

2 years ago

See attached file. show all work.

andrew11 [14]

The point-slope form of the equation for a line can be written as

... y = m(x -h) +k . . . . . . . for a line with slope m through point (h, k)

Your function gives

... f'(h) = m

... f(h) = k

a) The tangent line is then

... y = 5(x -2) +3

b) The normal line will have a slope that is the negative reciprocal of that of the tangent line.

... y = (-1/5)(x -2) +3

_____

You asked for "an equation." That's what is provided above. Each can be rearranged to whatever form you like.

In standard form, the tangent line's equation is 5x -y = 7. The normal line's equation is x +5y = 17.

3 0

2 years ago

a chef is going to use a mixture of two brands of Italian dressing. The first brand contains 5% vinegar and the second Brian con

tankabanditka [31]

Answer:

273 mL of 5%
117 mL of 15%

Step-by-step explanation:

Let q represent the quantity of 15% dressing used. Then the amount of 5% dressing is (390 -q). The amount of vinegar in the mix is ...

0.15q + 0.05(390 -q) = 0.08(390)

0.10q = 31.2 -19.5 = 11.7 . . . . . . subtract 0.05(390) and simplify

q = 117 . . . . . . . . . . . . . . . . . . multiply by 10

390-q = 273

The chef should use 273 mL of the first brand (5% vinegar) and 117 mL of the second brand (15% vinegar).

<em>Additional comment</em>

You may have noticed that the value of q is (0.08 -0.05)/(0.10 -0.05)×390. The fraction of the mix that is the highest contributor is the ratio of the difference between the mix value and least contributor, divided by the difference between the contributors: (8-5)/(15-5) = 3/10, the fraction that is 15% vinegar. This is the generic solution to mixture problems.

7 0

2 years ago