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3 years ago

Find x if ƒ(x) = 2x + 7 and ƒ(x) = -1.

Mathematics

2 answers:

Oksi-84 [34.3K]3 years ago

3 0

The answer to this is x= -4

Lelechka [254]3 years ago

3 0

Set them equal to each other

2x + 7 = -1
-7 -7
2x = -8
x = -4

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Zadanie optymalizacyjne z matematyki. Proszę o rozwiązanie i wyjaśnienie

Yakvenalex [24]

Volume of the pyramid:

$V=\dfrac{s^2h}3$

Perimeter of the cross-section:

$40=\sqrt2\,s+2\sqrt{\dfrac{s^2}2+h^2}=\sqrt2\left(s+\sqrt{s^2+2h^2}\right)$

$\implies h=\sqrt{\dfrac{(20\sqrt2-s)^2-s^2}2}=\sqrt{400-20\sqrt2\,s}$

Area of the cross-section:

$P=\dfrac12(\sqrt2\,s)h=\dfrac{sh}{\sqrt2}$

$\implies P=\dfrac{s\sqrt{400-20\sqrt2\,s}}{\sqrt2}=s\sqrt{200-10\sqrt2\,s}$

First derivative test:

$\dfrac{\mathrm dP}{\mathrm ds}=\dfrac{20\sqrt2-3s}{\sqrt{4-\dfrac{\sqrt2}5s}}=0\implies s=\dfrac{20\sqrt2}3$

Then the height of the cross-section/pyramid is

$h=\sqrt{400-20\sqrt2\,s}=\dfrac{20}{\sqrt3}$

The volume of the pyramid that maximizes the cross-sectional area $P$ is

$V=\dfrac{\left(\frac{20\sqrt2}3\right)^2\frac{20}{\sqrt3}}3=\dfrac{16000}{27\sqrt3}$

5 0

3 years ago

Type the correct answer in each box.

Mariulka [41]

Answer:

$(x-5)^2+(y+4)^2=100$

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The distance between the center and any point that lie on the circle is equal to the radius

we have the points

(5,-4) and (-3,2)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

substitute the values

$r=\sqrt{(2+4)^{2}+(-3-5)^{2}}$

$r=\sqrt{(6)^{2}+(-8)^{2}}$

$r=\sqrt{100}\ units$

$r=10\ units$

step 2

Find the equation of the circle

we know that

The equation of a circle in standard form is equal to

$(x-h)^2+(y-k)^2=r^2$

where

(h,k) is the center

r is the radius

we have

$(h,k)=(5,-4)\\r=10\ units$

substitute

$(x-5)^2+(y+4)^2=10^2$

$(x-5)^2+(y+4)^2=100$

6 0

3 years ago

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nlexa [21]

Answer:

15 2/3

Step-by-step explanation:

11 feet + 4 2/3 feet = 15 2/3

11+4= 15 + 2/3 = 15 2/3

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2 years ago

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Answer:

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2 years ago

The product of two 2-digit factors whose product is greater than 200 but less than 600

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3 years ago