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3 years ago

14

Samuel has run for 45 minutes. If he has completed 60% of his run, how many minutes will Samuel run in all?

1 answer:

Irina18 [472]3 years ago

6 0

Answer:

27

Step-by-step explanation:

45÷10= 4.5

4.5×6= 27 minutes

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Multiply 3/7 by the reciprocal of -3/14

Alexandra [31]

Multiplying 3/7 by the reciprocal of -3/14,

$\frac{3}{7} \times \frac{14}{ - 3} \\ = \frac{1}{1} \times \frac{2}{ - 1} \\ = \frac{2}{ - 1} \\ = - 2$

Hope it helps!!

7 0

3 years ago

A closed, rectangular-faced box with a square base is to be constructed using only 36 m2 of material. What should the height h a

kkurt [141]

Answer:

$b=h=\sqrt{6}$ m

Step-by-step explanation:

Let

Bas length of box=b

Height of box=h

Material used in constructing of box=36 square m

We have to find the height h and base length b of the box to maximize the volume of box.

Surface area of box= $2b^2+4bh$

$2b^2+4bh=36$

$b^2+2bh=18$

$2bh=18-b^2$

$h=\frac{18-b^2}{2b}$

Volume of box, V= $b^2h$

Substitute the values

$V=b^2\times \frac{18-b^2}{2b}$

$V=\frac{1}{2}(18b-b^3)$

Differentiate w. r.t b

$\frac{dV}{db}=\frac{1}{2}(18-3b^2)$

$\frac{dV}{db}=0$

$\frac{1}{2}(18-3b^2)=0$

$\implies 18-3b^2=0$

$\implies 3b^2=18$

$b^2=6$

$b=\pm \sqrt{6}$

$b=\sqrt{6}$

The negative value of b is not possible because length cannot be negative.

Again differentiate w.r.t b

$\frac{d^2V}{db^2}=-3b$

At $b=\sqrt{6}$

$\frac{d^2V}{db^2}=-3\sqrt{6}$

Hence, the volume of box is maximum at $b=\sqrt{6}$ .

$h=\frac{18-(\sqrt{6})^2}{2\sqrt{6}}$

$h=\frac{18-6}{2\sqrt{6}}$

$h=\frac{12}{2\sqrt{6}}$

$h=\sqrt{6}$

$b=h=\sqrt{6}$ m

7 0

3 years ago

How many solutions can be found for the equation 5x + 3(x − 1) = 10x − 2x − 3?

IRISSAK [1]

One hope you got it right

3 0

3 years ago

Read 2 more answers

Volume of a triangular

Lorico [155]

For volume of a prism, the general rule is multiply the area of the base by the area of the height. For example, for a triangular prism, the volume would be (1/2)b*h*a if you set a = height of the prism and h = height of the triangle from the formula (1/2)bh, which is the area of a triangle.

5 0

4 years ago

Read 2 more answers

What expression gives the distance between the points (4,6) and (7,-3)?

solniwko [45]

Answer:

$\sqrt{(-3^2-6)+(7^2-4^2)}$

Step-by-step explanation:

Use the form: $\sqrt{(x^2-x^1)+(y2-y1)^2$

so: $\sqrt{(-3^2-6)+(7^2-4^2)}$

6 0

3 years ago