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3 years ago

Evaluate 7 + (-3x^2) for x = 0.

Mathematics

1 answer:

slava [35]3 years ago

5 0

For x=0:
7+ (-3x^2)
= 7+ (-3*0^2)
= 7+ (-3*0)
= 7+ 0
= 7

The final answer is 7~

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A poster of area 24,000 cm2 has blank margins of width 10 cm on the top and bottom and 6 cm on the sides. find the dimensions th

bogdanovich [222]

The total poster area is:

A = (l + 20) (w + 12)

where l and w is the length and width of the printed area

24000 = (l + 20) (w + 12)

l = [24000/(w + 12)] – 20

The printed area is simply:

a = l w

substituting l:

a = ([24000/(w + 12)] – 20) w

a = (24000w)(w + 12)^-1 – 20 w

Taking the first derivative da/dw:

da/dw = (24000)(w + 12)^-1 - (24000w)(w + 12)^-2 – 20

Set da/dw = 0:

(24000)/(w + 12) - (24000w)/(w + 12)^2 – 20 = 0

Multiply everything by (w + 12)^2:

24000 (w + 12) – 24000w - 20(w + 12)^2 = 0

24000w + 288000 – 24000w – 20 (w^2 + 24w + 144) = 0

-20 w^2 – 480 w + 285120 = 0

w^2 + 24 w = 14256

Completing the square:

(w + 12)^2 = 14256 + 12^2

w + 12 = ±120

w = 108 cm

l = [24000/(w + 12)] – 20

l = [24000/(108 + 12)] – 20

l = 180 cm

Therefore the dimensions of the whole poster are:

w + 12 = 120 cm

l + 20 = 200 cm

The poster should be 200 cm x 120 cm

6 0

3 years ago

Alberto is snowboarding down a mountain with a constant slope. the slope he is on has an overall length of 1560 feet. the top of

Olenka [21]

The slope of the equation is calculated as:

$\frac{h_2-h_1}{t_2-t_1}=m$

Where $h_2$ is the height of the upper part of the slope and $h_1$ is the height of the low er part.

$m=\frac{4000-4600}{24-0}$

$m=-25$

So, the equation of the line is:

$h-4600=-25(t-0)$

$h=-25t+4600$

With this equation we can find the height of Alberto after having passed 10 sec.

$h(10)=-25 (10)+4600\\h(10)=-250+4600\\h(10)=4350$

After 10 seconds Alberto is 350 feet from the bottom of the slope.

Alberto's speed is:

$v=\frac{1560ft}{24s}=65ft/s$

The speed in miles per hour is:

$v=65ft /s*\frac{1 mile}{5280 ft}*\frac{3600s}{1 hour}\\v=44.32 miles/h$

4 0

3 years ago

Answer this question for me please

Evgesh-ka [11]

Answer:

9-2 = 7

8-3 = 5

$\sqrt{5^{2} +7^{2} \\$

= 8.602325267

Step-by-step explanation:

4 0

3 years ago

. The length of a rectangle is 32 inches. The width of the rectangle is 17 inches. Which is the perimeter of the rectangle? *

Illusion [34]

Answer:

98 inches

Step-by-step explanation:

7 0

4 years ago

Read 2 more answers

Find mZ1 and mZ2 .<br><br> I cant figure it out

Ede4ka [16]

Answer:

∠ 1 = 110°, ∠ 2 = 70°

Step-by-step explanation:

∠ 1 and 110° are vertical angles and are congruent, thus

∠ 1 = 110°

∠ 1 and ∠ 2 are same- side interior angles and supplementary, sum to 180°

∠ 1 + ∠ 2 = 180°

110° + ∠ 2 = 180° ( subtract 110° from both sides )

∠ 2 = 70°

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3 years ago