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2 years ago

7) John is draining his pool at a rate of 6 gallons per minute. His pool starts with

Mathematics

1 answer:

Luba_88 [7]2 years ago

5 0

Answer:

Marie can find the volume of a cube by using the formula V = s³, where s represents the side length of the cube. If Marie’s cube has a side length of 2image centimeters, what is the volume of her cube? Show your work. Write your answer as a fraction.

Step-by-step explanation:

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An investor invested a total of $2,800 in two mutual funds. One fund earned 5% profit while the other earned 3% profit. If the i

Natasha_Volkova [10]

Answer:

The amount invested in the mutual fund that earned 5% was $1,000

The amount invested in the mutual fund that earned 3% was $1,800

Step-by-step explanation:

Let

x ----> the amount invested in the mutual fund that earned 5%

y ----> the amount invested in the mutual fund that earned 3%

we know that

$x+y=2,800$ ----> $y=2,800-x$ ----> equation A

$5\%=5/100=0.05$

$3\%=3/100=0.03$

$0.05x+0.03y=104$ ----> equation B

Solve the system by substitution

substitute equation A in equation B

$0.05x+0.03(2,800-x)=104$

Solve for x

$0.05x+84-0.03x=104$

$0.05x-0.03x=104-84$

$0.02x=20$

$x=\$1,000$

<em>Find the value of y</em>

$y=2,800-x$

$y=2,800-1,000=\$1,800$

therefore

The amount invested in the mutual fund that earned 5% was $1,000 and the amount invested in the mutual fund that earned 3% was $1,800

5 0

3 years ago

I’ll give brainliest

kupik [55]

Answer:

Area= (12^2)pi

Step-by-step explanation:

Area= 150/360 (pi12^2)

= 188.5 total area

5 0

3 years ago

Two triangles have the same heights. One triangle has a base length that is twice the base length of the other triangle. Are the

djyliett [7]

Answer:

Yes

Step-by-step explanation:

The formula for area of a triangle is A = (1/2)bh,

For the first triangle we can leave it in general terms, so it's area is

A = (1/2)bh, depending on what b and h are, but it doesn't matter here...

The second triangle has base that is twice the other triangles base. Bases being multiples of each other is the definition of being proportional so the bases are proportional, an the area of the second triangle is

A = (1/2)(2b)h, which simplifies to

A = bh

Comparing the 2 areas, you can see that one has a multiplier of (1/2), so their areas are proportional

3 0

3 years ago

Evaluate −x+| y | when x=1/3 and y=−7/4. Write your answer as a fraction in simplest form.

Mama L [17]

Answer: = $\frac{17}{12}\quad \left(\mathrm{Decimal:\quad }\:1.41666\dots \right)$

Step-by-step explanation:

$-\frac{1}{3}+\left|-\frac{7}{4}\right|$

$=-\frac{1}{3}+\frac{7}{4}$

$=\frac{17}{12}$

5 0

3 years ago

Find the rate of change of f(x, y, z) = xyz in the direction normal to the surface yx2 + xy2 + yz2 = 3 at (1, 1, 2).

Paladinen [302]

Answer:

Rate of change = 18/√74

Step-by-step explanation:

The rate of change of f at x_o in the direction of the unit vector v is given by: ∇f(x_o) × v

Now, for us to get the direction of the unit vector, since we are told that f(x, y, z) = xyz in the direction normal to the surface yx² + xy² + yz² = 3, we will use; g(x, y, z) = yx² + xy² + yz² = 3 and k =3 to give;

∇g(x,y,z) = (2xy + y², (x² + 2xy + z²), 2yz)

So;

∇g(1, 1, 2) = (2(1 × 1) + 1²) , (1² + 2(1 × 1) + 2²), 2(1 × 2))

This gives;

∇g(1, 1, 2) = (3, 7, 4)

Now,

||∇g(1, 1, 2)|| = √(3² + 7² + 4²)

||∇g(1, 1, 2)|| = √74

Normal vector would be given by the formula;

v = [∇g(1, 1, 2)]/[||∇g(1, 1, 2)||]

Thus;

v = (3, 7, 4)/√74

Let's not forget that our ∇f(1, 1, 2) = (1, 1, 2)

Thus, rate of change is given by;

∇f(1, 1, 2) × v = (1, 1, 2) × (3, 7, 4)/√74

This gives;

Rate of change = [(1 × 3) + (1 × 7) + (2 × 4)]/√74 = 18/√74

7 0

3 years ago