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3 years ago

Simplify using laws of exponents: 5^7 × 5^6 × 52

Mathematics

1 answer:

xxMikexx [17]3 years ago

5 0

$\displaystyle \rm 5 ^{7} \times 5 ^{6} \times 52$

$\displaystyle \rm \: 5 ^{7 + 6} \times 52$

$\displaystyle \rm \: 5 ^{13} \times 52$

$\tt \: 63476562500$

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2470.28277045 To 3 decimal places

jeka57 [31]

To run the these figures to 3 decimal places

you need to count from the digit after the decimal point until you reach the 3rd number which is 2

so now the answer is 2470.283

This is because the decimal point lies between 2 and 7 and since 7 is great than 5 we add 1 to the 2 making it 3

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3 years ago

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Three sixth-grade students competed in the 100-meter dash. The table shows their times.

Sergeeva-Olga [200]

Answer:

It is 12.9, 13.1, 13.2 C.

Step-by-step explanation:

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3 years ago

The circumference of a pizza is 56.52 in. One-fourth of the pizza has been eaten the area of the remaining pizza in sq. Inches r

BabaBlast [244]

Circumference = πD
πD = 56.52
D = 17.99 in

Area of the pizza = π (17.99 ÷ 2)² = 254.19 in²

Area of the pizza eaten = 254.19 ÷ 4 = 63.55 in²

Area of the pizza remain = 254.19 - 63.55 = 190.64 in²

Answer: 190.64 in²

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4 years ago

You go to the store and pick out 3 apples for $0.60 each, 2 bananas for $0.50 each, and 1 quart of yogurt for $4.50. At checkout

Stella [2.4K]

Answer:

$6.21

Step-by-step explanation:

1 apple = $0.60

3 apples = $1.80 (Multiply 0.60 by 3)

2 bananas = $1.00 (Multiply 0.50 by 2)

1 quart of yoghurt = $4.50

Add the prices up first:

1.80 + 1.00 + 4.50 = $7.30

7.30 off 15% = $6.21

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3 years ago

A home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 1584 cubic feet

liq [111]

Answer:

The room dimensions that will minimize the cost of the paint are 12 ft x 12 ft x 11 ft.

Step-by-step explanation:

We can find first the volume equation using the formula of the volume of a box.

$V= xyz$

Thus we get the constraint function

$1584 = xyz$

Then since we are asked to minimize the cost, we can write the cost function which is the area of each one of the walls and ceiling multiplied by the painting cost.

$C=0.11 xy+ 2(0.06)xz+2(0.06yz \\ C =0.11 xy+0.12xz+0.12yz$

Lagrange Multipliers to find minimum cost.

We can continue finding the partial derivatives to build the system of equations required for Lagrange Multipliers method.

$C_x=\lambda V_x \\ C_y = \lambda V_y \\ C_z = \lambda V_z$

And the constraint function

$xyz=1584$

So we get

$0.11y+0.12z=\lambda yz \\ 0.11x+0.12z=\lambda xz \\ 0.12x+0.12y=\lambda xy\\ xyz=1584$

We can multiply each side of each equation by the dimension which is missing to get the full volume on the right side.

$0.11xy+0.12xz=\lambda xyz \\ 0.11xy+0.12yz=\lambda xyz \\ 0.12xz+0.12yz=\lambda xyz$

Then we can set each the equations equal to each other, so from the first one and the second equation we get

$0.11xy+0.12xz= 0.11xy+0.12yz$

We can subtract 0.11xy from both sides.

$0.12xz=0.12yz$

And we can divide both sides by 0.12z to get

$x=y$

We can repeat the process by setting the first and third equation equal to each other.

$0.11xy+0.12xz= 0.12xz+0.12yz$

We can subtract 0.12 xz from both sides

$0.11xy=0.12yz$

And we can solve by z

$z= \cfrac{0.11x}{0.12}\\ z = \cfrac{11x}{12}$

So if we replace that as well y = x on the constraint for the volume euqation we get

$1584=x(x)\left(\cfrac{11}{12}x\right) \\ 1584=\cfrac{11}{12}x^3$

We can then solve for x

$x^3 = \cfrac{1584(12)}{11}$

And taking the cube root

$x = \sqrt[3]{\cfrac{1584(12)}{11}}$

$x = \sqrt[3]{1728}$

$x=12 ft$

So then we can use the equations we have found for y and z in terms of x

$y = x \\ y = 12 ft$

And

$z= \cfrac{11x}{12}\\z= \cfrac{11(12)}{12} \\ z=11ft$

Then the dimensions of the room that will minimize the cost are 12ft x 12 ft x 11 ft. Since you have to enter using commas you can write 12, 12, 11, please check as well if you have to insert the units that are feet for each.

5 0

4 years ago