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3 years ago

What is the following sum 5x(^3sqrt(x^2y)+2(^3sqrtx^5y)

Mathematics

2 answers:

Arturiano [62]3 years ago

8 0

Answer:

7x[∛x^2y]

Step-by-step explanation:

given:

$5x\sqrt[3]{x^2y} +2\sqrt[3]{x^5y} \\5x(x^\frac{2}{3}.y^\frac{1}{3}) + 2.x^\frac{5}{3}.y^\frac{1}{3} \\5x.x^\frac{2}{3}.y^\frac{1}{3} + 2.x^\frac{5}{3}.y^\frac{1}{3} \\5x^\frac{5}{3}.y^\frac{1}{3} + 2.x^\frac{5}{3}.y^\frac{1}{3} \\\\ y^\frac{1}{3} (5x^\frac{5}{3} + 2x^\frac{5}{3} )\\y^\frac{1}{3} (7x^\frac{5}{3}} )\\7\sqrt[3]{x^5y}\\ 7x\sqrt[3]{x^2y}$ !

gulaghasi [49]3 years ago

5 0

Answer:

[/tex]7x\sqrt[3]{x^2y}[/tex]

Step-by-step explanation:

The given equation is:

$5x\sqrt[3]{x^2y} +2\sqrt{3}{x^5y}$

Solving this equation step by step

$5x\sqrt[3]{x^2y} +2\sqrt{3}{x^5y}$

∵ x⁵ = x³ × x²

$5x\sqrt[3]{x^2y} +2\sqrt[3]{(x^3\times x^2)y}$

take the x³ outside the cube root in second term

$5x\sqrt[3]{x^2y} +2x\sqrt[3]{(x^2)y}\\\sqrt[3]{x^2y} (5x+2x)\\7x\sqrt[3]{x^2y}$

Thus, last option is correct.

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Which expression is equivalent to (x Superscript one-fourth Baseline y Superscript 16 Baseline) Superscript one-half?

Phantasy [73]

The expression that is equal to (x Superscript one-fourth Baseline y Superscript 16 Baseline) is x Superscript one-eighth Baseline y Superscript 8.

<h3>What is an Expression?</h3>

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expression that is equal to (x Superscript one-fourth Baseline y Superscript 16 Baseline) can be found by simplifying the given algebraic equation,

$(x^{\frac14}y^{16})^{\frac12}\\\\=x^{(\frac14 \times \frac12)} \times y^{(16 \times \frac12)}\\\\= x^{\frac18}y^{8}$

Hence, the expression that is equal to (x Superscript one-fourth Baseline y Superscript 16 Baseline) is x Superscript one-eighth Baseline y Superscript 8.

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2 years ago

What is the volume of the prism?

mezya [45]

Answer:

40 $\frac{5}{8}$ $cm^{3}$

Step-by-step explanation:

The figure is a rectangular prism, so the formula would be Volume = length x width x height.

length = 6 $\frac{1}{2}$ cm

width = 2 $\frac{1}{2}$ cm

height = 2 $\frac{1}{2}$ cm

If you plug everything you have in the problem into the volume equation, you would get : Volume = 6 $\frac{1}{2}$ cm x 2 $\frac{1}{2}$ cm x 2 $\frac{1}{2}$ cm.

Without a calculator, I would first turn the mixed numbers into improper fractions.

6 $\frac{1}{2}$ = $\frac{13}{2}$

2 $\frac{1}{2}$ = $\frac{5}{2}$

Volume = $\frac{13}{2}$ x $\frac{5}{2}$ x $\frac{5}{2}$

When you multiply everything together you should get $\frac{325}{8}$ .

As a mixed number, that would be 40 $\frac{5}{8}$ $cm^{3}$ .

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2 years ago

What amount would yield an interest of $66 in 2 years at 3% p.a.?

yuradex [85]

It would be 12 because you have to solve for the percent

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3 years ago

A farmer has a basket of peaches. He gives ⅓ of the peaches to one person, ¼ to another, ⅕ to another, ⅛ to another, and then gi

inessss [21]

Answer:

$\frac{1429}{120}$ or $11\frac{109}{120}$

Step-by-step explanation:

Given:

A farmer has a basket of peaches. He gives ⅓ of the peaches to one person, ¼ to another, ⅕ to another, ⅛ to another, and then gives 7 peaches to a 5th person.

Remaining peaches = 4

We need to find the original number of peaches in the basket.

The farmer gives the total number of peaches = $\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{8}+7$

Let x be the former gives the total number of peaches

We multiply and divide by 120 in right side of the above equation because of 120 is divided by all given denominator and then simplify.

$x = \frac{120}{120}(\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{8}+7)$

$x = \frac{1}{120}(\frac{120}{3}+\frac{120}{4}+\frac{120}{5}+\frac{120}{8}+7\times 120)$

$x = \frac{1}{120}(40+30+24+15+840)$

$x = \frac{1}{120}(949)$

$x = \frac{949}{120}$

We add the remaining peaches by given peaches for the original number of peaches in the basket.

Original number of peaches = $\frac{949}{120}+4$

Original number of peaches = $\frac{949+4\times 120}{120}$

Original number of peaches = $\frac{949+480}{120}$

Original number of peaches = $\frac{1429}{120}$

Original number of peaches = $11\frac{109}{120}$

Therefore the original number of peaches in the basket is $\frac{1429}{120}$ or $11\frac{109}{120}$

5 0

3 years ago

A rectangular parking lot has a perimeter of 820 ft. The area of the parking lot measures 42,000 ft2. What is a dimension of the

dalvyx [7]

To solve the problem we must know about quadratic equations.

<h2>Quadratic Equation</h2>

A quadratic equation is an equation that can be written in the form of

ax²+bx+c.

Where a is the leading coefficient, and

c is the constant.

The breadth of the rectangle is 200 ft, while the length is 210 ft.

<h2>Explanation</h2>

Given to us

Area of the parking lot = 42,000 ft²
Perimeter of the parking lot = 820 ft

<h3>Area of the parking lot</h3>

Area of the parking lot = Area of the rectangle

42,000 ft² = Length x Breadth

Solving for L,

$42,000 = L \times B\\\\
L = \dfrac{42,000}{B}$

<h3>Perimeter of the parking lot</h3>

Perimeter of the parking lot = Perimeter of the rectangle

820 ft. = 2(Length + Breadth)

820 ft. = 2(L+ B)

$2(L+ B) = 820\\\\
(L+B) = \dfrac{820}{2}\\\\
(L+B) = 410$

Substituting the value of L,

$(L+B) = 410\\\\
(\dfrac{42,000}{B}) +B = 410\\\\
42000 + B^2 = 410B\\\\
B^2 -410B +42000 = 0$

<h3>Quadratic Expression</h3>

Solving the quadratic Expression,

$B^2 -410B +42000 = 0\\\\
(B-210)(B-200)=0$

Equation the factors against zero,

B-210=0

B = 210

B-200=0

B = 200

Hence, the breadth of the rectangle is 200ft, while the length is 210 ft.

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4 0

2 years ago