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2 years ago

Can anyone please help me with this assignment

Mathematics

1 answer:

sertanlavr [38]2 years ago

3 0

1. The sentences translated to equations looks like:

a) 4x = 32.

b) x + 6y = 43.

c) 3x + 7 = 9x - 4.

d) 76 - 2x = 8x.

2. The equations translated to sentences looks like:

a) The sum of 16 and 9 times x is 50.

b) The sum of the square of x and 6 times y is 4 times w.

c) Three times x is 52.

d) Five-sixth is equal to the product of -10 and x.

Practice Part 1: Translate sentence to equation

a)Four times a number is thirty-two.

Assuming the number to be x, we get the equation, 4x = 32.

b)The sum of and six times is equal to forty-three.

The sentence, when translated to an equation looks like, x + 6y = 43.

c)The sum of 7 and three times equals the difference of 9 times and 4.

The sentence, when translated to an equation looks like, 3x + 7 = 9x - 4.

d)Two times less than 76 is equal to the product of 8 and

The sentence, when translated to an equation looks like, 76 - 2x = 8x.

Practice Part 2: Translate equation into sentence

a) 9x + 16 = 50.

- The sentence for the given equation is, the sum of 16 and 9 times x is 50.

b) x² + 6y = 4w.

- The sentence for the given equation is, the sum of the square of x and 6 times y is 4 times w.

c) 3x = 52.

- The sentence for the given equation is, three times x is 52.

d) 5/6 = -10x.

- The sentence for the given equation is, five-sixth is equal to the product of -10 and x.

Learn more about translating sentences and equations at

brainly.com/question/13155862

#SPJ1

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Answer:

(x - 3)² + (y - 5)² = 16

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r the radius

given (h, k ) = (3, 5 ) we require to find r

r is the distance from the centre to a point on the circle

given x = - 1 is a tangent the r is the distance between the x- coordinates

r = | 3 - (- 1) | = | 3 + 1 | = | 4 | = 4

then equation of circle is

(x - 3)² + (y - 5)² = 4² , that is

(x - 3)² + (y - 5)² = 16

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2 years ago

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Your process is close!

Since 3/10 and 4/15 is the amount you missed you have to subtract that by 1.

1 - 0.3 = 0.70
1 - 0.26 = 0.74

So, you scored higher on the math quiz.

Hope this helps!

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Work out 77 % of 775.66 m Give your answer rounded to 2 DP.

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Step-by-step explanation:

We need to find 77% of 775.66 m.

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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

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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 $b=\sqrt{6}$ .

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

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

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$h=\sqrt{6}$

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

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