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2 years ago

One number is 3 less than 4 times a second number. The difference of the

Mathematics

1 answer:

s344n2d4d5 [400]2 years ago

3 0

Answer:

17 and 5

Step-by-step explanation:

Interesting question!

Turn both sentences to equations:

$a=4b-3\\a-2b=7$

a is the first number, and b is the second number.

A system of equations! A graphing calculator will do the work:

(See picture)

The y in the picture is a, and the x in the picture is b.

So the solution is a=17 and b=5

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If 32% of a number is 64, what is the number?

Verdich [7]

Hey!

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Steps To Solve:

~Turn into decimal

32% = 0.32

~Divide

64 / 0.32 = 200

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Hence, the answer is $\Large\boxed{\mathsf{200}}$

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Hope This Helped! Good Luck!

7 0

3 years ago

Read 2 more answers

What is the volume of a right circular cylinder with a radius of 3in and a height of 10in

WARRIOR [948]

Answer:

282.6 inches cubed

Step-by-step explanation:

The volume of the cylinder with radius 3 in and height 10 in is

$V=\pi (3^2)(10)= \pi (9)(10)= 90\pi = 90(3.14) = 282.6 in^3$

7 0

3 years ago

What is the area of a triangle that has a

almond37 [142]

Answer:

A. 45 in

Step-by-step explanation:

To find area you multiply length and width so you would multiply 9 and 10 but since it is a triangle you would divide by two

Hope this helps!

5 0

3 years ago

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The music for Nadia’s dance routine last for exactly 4 minutes. When Nadia dances her routine, she starts with her music and fin

natima [27]

4 x 60 = 240 seconds

$\frac{12}{60} / \frac{12}{12} = \frac{1}{5}$ of a minute not dancing.

$4 \times 5 = 20 - 1 = 19$ $\frac{19}{20} \times \frac{5}{5} = \frac{95}{100}$

95% of the time dancing

4 0

3 years ago

Read 2 more answers

A box designer has been charged with the task of determining the surface area of various open boxes (no lid) that can be constru

Viktor [21]

Answer:

1) $S = 2\cdot w\cdot l - 8\cdot x^{2}$ , 2) The domain of S is $0 \leq x \leq \frac{\sqrt{w\cdot l}}{2}$ . The range of S is $0 \leq S \leq 2\cdot w \cdot l$ , 3) $S = 176\,in^{2}$ , 4) $x \approx 4.528\,in$ , 5) $S = 164.830\,in^{2}$

Step-by-step explanation:

1) The function of the box is:

$S = 2\cdot (w - 2\cdot x)\cdot x + 2\cdot (l-2\cdot x)\cdot x +(w-2\cdot x)\cdot (l-2\cdot x)$

$S = 2\cdot w\cdot x - 4\cdot x^{2} + 2\cdot l\cdot x - 4\cdot x^{2} + w\cdot l -2\cdot (l + w)\cdot x + l\cdot w$

$S = 2\cdot (w+l)\cdot x - 8\cdpt x^{2} + 2\cdot w \cdot l - 2\cdot (l+w)\cdot x$

$S = 2\cdot w\cdot l - 8\cdot x^{2}$

2) The maximum cutout is:

$2\cdot w \cdot l - 8\cdot x^{2} = 0$

$w\cdot l - 4\cdot x^{2} = 0$

$4\cdot x^{2} = w\cdot l$

$x = \frac{\sqrt{w\cdot l}}{2}$

The domain of S is $0 \leq x \leq \frac{\sqrt{w\cdot l}}{2}$ . The range of S is $0 \leq S \leq 2\cdot w \cdot l$

3) The surface area when a 1'' x 1'' square is cut out is:

$S = 2\cdot (8\,in)\cdot (11.5\,in)-8\cdot (1\,in)^{2}$

$S = 176\,in^{2}$

4) The size is found by solving the following second-order polynomial:

$20\,in^{2} = 2 \cdot (8\,in)\cdot (11.5\,in)-8\cdot x^{2}$

$20\,in^{2} = 184\,in^{2} - 8\cdot x^{2}$

$8\cdot x^{2} - 164\,in^{2} = 0$

$x \approx 4.528\,in$

5) The equation of the box volume is:

$V = (w-2\cdot x)\cdot (l-2\cdot x) \cdot x$

$V = [w\cdot l -2\cdot (w+l)\cdot x + 4\cdot x^{2}]\cdot x$

$V = w\cdot l \cdot x - 2\cdot (w+l)\cdot x^{2} + 4\cdot x^{3}$

$V = (8\,in)\cdot (11.5\,in)\cdot x - 2\cdot (19.5\,in)\cdot x^{2} + 4\cdot x^{3}$

$V = (92\,in^{2})\cdot x - (39\,in)\cdot x^{2} + 4\cdot x^{3}$

The first derivative of the function is:

$V' = 92\,in^{2} - (78\,in)\cdot x + 12\cdot x^{2}$

The critical points are determined by equalizing the derivative to zero:

$12\cdot x^{2}-(78\,in)\cdot x + 92\,in^{2} = 0$

$x_{1} \approx 4.952\,in$

$x_{2}\approx 1.548\,in$

The second derivative is found afterwards:

$V'' = 24\cdot x - 78\,in$

After evaluating each critical point, it follows that $x_{1}$ is an absolute minimum and $x_{2}$ is an absolute maximum. Hence, the value of the cutoff so that volume is maximized is:

$x \approx 1.548\,in$

The surface area of the box is:

$S = 2\cdot (8\,in)\cdot (11.5\,in)-8\cdot (1.548\,in)^{2}$

$S = 164.830\,in^{2}$

4 0

3 years ago