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STatiana [176]
2 years ago
11

Make w the subject of the formula z = w + 3

Mathematics
1 answer:
bogdanovich [222]2 years ago
3 0

Answer:

w = -z(-w) + 3(-w)

Step-by-step explanation:

z = w + 3 | Given

-w + z = 3 | Subtract w from both sides.

-w = -z + 3 | Subtract z from both sides

w = -z(-w) + 3(-w) | Multiply -w on both sides.

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Marcus buys a tent priced at $50 if the sales tax is 5% how much tax will Marcus pay
seraphim [82]

5% = 0.05

50 x 0.05 = $2.50

 Total tax will be $2.50


 Total amount he will pay = 50 + 2.50 = $52.50

3 0
3 years ago
Read 2 more answers
Function g can be thought of as a translated (shifted) version of f(x)=|x|.
klasskru [66]

Answer:

Step-by-step explanation:

g(x) = |x+4| +6 ( to go 4 to the left and 6 up)

7 0
3 years ago
The base of an aquarium with given volume V is made of slate and the sides are made of glass. If slate costs five times as much
Y_Kistochka [10]

Answer:

x = ∛ 2*V/5  

y = ∛ 2*V/5

h  = V/ ∛ 4*V²/25

Step-by-step explanation:

Dimensions of the aquarium base is  x*y

We call c₁ cost per unit area of the sides, then cost per unit area of slate is equal 5c₁.

let call h the height of the aquarium then volume of the aquarium is:

V = x*y*h      where   h =  V / x*y

As the base is a rectangular one there are 2 sides x*h .  and 2 sides  y*h

According to this:

Ct (cost of aquarium )  = cost of the base  + cost of the sides

cₐ  ( cost of the base) = 5*c₁*x*y

c₆ (cost of the sides ) = c₁*2*x*h   +   c₁*2*y*h

C(t)  =  5*c₁*x*y +2* c₁*x* V/x*y  +  2* c₁*y* V/x*y    or

C(t)  =  5*c₁*x*y  + 2*c₁*V/y   *2*c₁* V/x

Taking partial derivatives en x and y we have:

C´(x)  =  5*c₁*y - 2*c₁*V/x²

C´(y)  =  5*c₁*x - 2*c₁*V/y²

C´(x)  = C´(y)        ⇒  5*c₁*y - 2*c₁*V/x²  =   5*c₁*x - 2*c₁*V/y²

or    5*y - 2*V/x²  =   5*x - 2*V/y²

(5*y*x² - 2*V)/x²  = ( 5*y²x - 2*V) /y²

(5*y*x² - 2*V)*y²  = ( 5*y²x - 2*V)*x²

5*y³*x² - 2*V*y²  =  5*y²x³  - 2*V*x²

5*y³*x² - 5*y²x³  =  2*V * ( y² - x²)

by symmetry  x =  y

Then using x = y  and plugging that value on the derivatives

C´(x) =  5*c₁*y - 2*c₁*V/x²

C´(x) =  5*c₁*x - 2*c₁*V/x²

C´(x) = 0          ⇒     5*c₁*x - 2*c₁*V/x²  = 0

5*x  - 2*V/x² = 0      ⇒  5*x³ - 2*V = 0   ⇒   5*x³  = 2*V  ⇒ x³ = 2*V/5

x = ∛ 2*V/5       and   y = ∛ 2*V/5    and   h  =  V/ x*y    h  = V/ ∛ 4*V²/25

7 0
3 years ago
Find the value of x round to the nearest tenth
gayaneshka [121]
Tan inverse 3/5 is 30.96
so the answer is x = 31.0
3 0
3 years ago
What is the sum? StartFraction 3 y Over y squared + 7 y + 10 EndFraction + StartFraction 2 Over y + 2 EndFraction
katovenus [111]

Answer:

\dfrac{5}{y+5}

Step-by-step explanation:

Here, we have to find the sum of 2 fractions:

1st fraction: \dfrac{3y}{y^{2}+7y+10}

2nd fraction: \dfrac{2}{y+2}

Considering the denominator of 1st fraction:

y^{2}+7y+10

Using factorization method:

7y can be written as (2y + 5y).

\Rightarrow y^{2}+2y+5y+10

Taking <em>5 common</em> from 5y+10 and <em>y common</em> from y^{2}+2y: \Rightarrow y(y+2)+5(y+2)

Now taking (y+2) common:

\Rightarrow (y+5)(y+2)

\dfrac{3y}{y^{2}+7y+10} can be written as \dfrac{3y}{(y+5)(y+2)}

Now, calculating the sum:

\dfrac{2y}{(y+5)(y+2)} + \dfrac{2}{y+2}

Taking <em>LCM</em> and solving:

\Rightarrow \dfrac{3y+2(y+5)}{(y+5)(y+2)}\\\Rightarrow \dfrac{5y+10}{(y+5)(y+2)}\\\Rightarrow \dfrac{5(y+2)}{(y+5)(y+2)}\\\Rightarrow \dfrac{5}{(y+5)}

Hence, answer is \dfrac{5}{y+5}.

4 0
3 years ago
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